200810445_Fiber_teory

Robust OpticalTransmission Systems Modulation and Equalization Dirk van den Borne Robust Optical Transmission Systems Modulation and Equalization PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op woensdag 19 maart 2008 om 16.00 uur door Dirk van den Borne geboren te Bladel en Netersel Dit proefschrift is goedgekeurd door de promotoren: prof.ir. G.D. Khoe en prof.ir. A.M.J. Koonen Copromotor: dr.ir. H. de Waardt CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN Borne, Dirk van den Robust optical transmission systems : modulation and equalization / by Dirk van den Borne. - Eindhoven : Technische Universiteit Eindhoven, 2008. Proefschrift. - ISBN 978-90-386-1794-7 NUR 959 Trefw.: optische telecommunicatie / modulatie / signaalverwerking / optische polarisatie. Subject headings: optical fibre communication / electro-optical modulation / signal processing / optical fibre polarisation. Copyright c _2008 by Dirk van den Borne All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without the prior written consent of the author. Typeset using L A T E X, printed in The Netherlands ”The only constant in technology is change.” Samenstelling van de promotiecommissie: prof.dr.ir. A.C.P.M Backx, Technische Universiteit Eindhoven, voorzitter prof.ir. G.D. Khoe, Technische Universiteit Eindhoven, eerste promotor prof.ir. A.M.J. Koonen, Technische Universiteit Eindhoven, tweede promotor dr.ir. H. de Waardt, Technische Universiteit Eindhoven, copromotor prof.dr.tech. P. Jeppesen, Danmarks Tekniske Universitet prof.dr.-ing. P.M. Krummrich, Technische Universit¨ at Dortmund dr. R.I. Killey, University College London dr. J.J.G.M. van der Tol, Technische Universiteit Eindhoven The work leading to this thesis was part of a cooperation between Nokia Siemens Networks (previously Siemens Communications) in Munich, Germany and the Electro-Optical Communi- cations group, department of Electrical Engineering of the Eindhoven University of Technology, The Netherlands. The studies presented in this thesis were performed within the long-haul optical transmission R&D department of Nokia Siemens Networks. iv Summary Robust optical transmission systems Modulation and Equalization Since the introduction of the first optical transmission systems, capacities have steadily increased and the cost per transmitted bit has gradually decreased. The core of the global telecommuni- cation network consists today of wavelength division multiplexed (WDM) optical transmission systems. WDM is for these systems the technology of choice as it allows for a high spectral ef- ficiency, i.e. the transmitted capacity per unit bandwidth. Commercial WDM systems generally use up to 80 wavelength channels with a 50-GHz channel spacing and a bit rate of 10-Gb/s or sometimes 40-Gb/s per wavelength channel. This translates into a spectral efficiency between 0.2 and 0.8-b/s/Hz. However, to cope with the forecasted increase in data traffic it will be necessary to develop next-generation transmission systems with even higher capacities. These transmis- sion systems are expected to have a 40-Gb/s or 100-Gb/s bit rate per wavelength channel, with a spectral efficiency of between 0.8 and 2.0-b/s/Hz. At the same time, such systems should be robust, i.e. provide a tolerance towards transmission impairments similar to currently deployed systems. Traditionally, optical transmission systems have used amplitude modulation. However, for the next generation of transmission systems this is not a suitable choice. They normally require a too large channel spacing, have a high optical-signal-to-noise ratio (OSNR) requirement and generate significant nonlinear impairments. Current state-of-the-art transmission systems therefore often use differential phase shift keying (DPSK). Compared to amplitude modulation, DPSK generates less nonlinear impairments and has a lower OSNR requirement. However, due to the high symbol rate (e.g. 40-Gbaud) the robustness against the most significant linear transmission impairments, i.e. chromatic dispersion and polarization-mode dispersion (PMD) is still small. Tunable optical dispersion compensators can be used to improve the chromatic dispersion tolerance and PMD impairments are generally avoided through fiber selection. But optical compensation and fiber selection are generally not suitable for cost-sensitive applications. The first part of this thesis focuses on modulation formats that can further increase the capac- ity and robustness of long-haul WDM transmission links. In particular 40-Gb/s differential v quadrature phase shift keying (DQPSK) modulation is discussed extensively in this thesis. As a quaternary modulation format, it modulates 2 bits per symbol and therefore requires only a 20-Gbaud symbol rate. The lower symbol rate improves the tolerance towards both chromatic dispersion and PMD. As well, the narrow optical spectrum allows for a high spectral efficiency. On the other hand, DQPSK also requires a more complex transmitter and receiver structure, has a higher OSNR requirement and reduces the nonlinear tolerance. We further verify the feasibil- ity of long-haul 40-Gb/s DQPSK transmission and show that a transmission reach of 2,800-km is viable with a 0.8-b/s/Hz spectral efficiency. In order to realize ultra long-haul transmission we combine DQPSK modulation with optical phase conjugation, which improves the nonlinear tolerance and enables a 4,500-km transmission distance. In addition, we discuss the combination of 40-Gb/s DQPSK modulation with different chromatic dispersion compensation technologies, such as lumped dispersion compensation and fiber-Bragg gratings. The second part of this thesis discusses polarization-multiplexed (POLMUX) signaling. This is an attractive transmission format as it modulates independent data onto each of the two orthogo- nal polarizations of an optical fiber. This can double the spectral efficiency and halve the symbol rate in comparison to single-polarization modulation. To further increase the spectral efficiency, POLMUX signaling and DQPSK modulation can be combined to realize optical modulation with 4 bits per symbol. We discuss a transmission experiment with 80-Gb/s POLMUX-RZ-DQPSK and verify the feasibility of long-haul transmission (1,700 km) with a 1.6-b/s/Hz spectral effi- ciency. However, the interaction between PMD and other transmission impairments makes it challenging to realize transmission systems employing POLMUX signaling without the com- pensation of PMD-related impairments. In the third part of this thesis we review electronic equalization techniques. This can be used to mitigate some of the drawbacks of DQPSK modulation and POLMUX signaling. For direct detection receivers, we show that multi-symbol phase estimation (MSPE) can be used to improve the OSNR requirement and nonlinear tolerance of D(Q)PSK modulation. In addition, Maximum likelihood sequence estimation (MLSE) can be used to increase the chromatic dispersion and PMD tolerance. Electronic equalization is particulary attractive when combined with coherent detection. In a coherent receiver, not only the amplitude of the optical signal, but the full base- band optical field is transferred to the electronic domain (amplitude, phase and state of polariza- tion). This enables the equalization of nearly arbitrarily high amounts of chromatic dispersion and PMD, as well as electronic polarization de-multiplexing in the case of POLMUX signaling. We discuss the required system architecture for a digital coherent receiver and demonstrate its feasibility through a 100-Gb/s POLMUX-DQPSK transmission experiment over 2,375 km and with a 2.0-b/s/Hz spectral efficiency. The work discussed in this thesis shows that multi-level modulation formats enable long-haul transmission systems with a bit rate of 40-Gb/s or 100-Gb/s per WDM channel and a 50-GHz channel spacing. Electronic equalization improves the transmission tolerances, simplifies system design and allows these formats to be used on the existing infrastructure of systems optimized for 10-Gb/s transmission. vi Contents 1 Introduction 1 1.1 The global telecommunication hierarchy . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Framework & objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 The fiber-optic transmission channel 11 2.1 Fiber attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Chromatic dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Polarization of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Nonlinear transmission impairments . . . . . . . . . . . . . . . . . . . . . . . . 22 3 Long-haul optical transmission systems 35 3.1 Transmitter & receiver structure . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2 Fiber loss compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.3 Chromatic dispersion compensation . . . . . . . . . . . . . . . . . . . . . . . . 48 3.4 PMD compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.5 Narrowband-optical filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.6 Optical phase conjugation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 vii Contents 4 Binary modulation formats 67 4.1 On-off-keying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2 Duobinary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3 Differential phase shift keying . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.4 Partial DPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5 Differential quadrature phase shift keying 87 5.1 Transmitter & receiver structure . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.2 Back-to-back OSNR requirement . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.3 Transmitter & receiver properties . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.4 Nonlinear tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.5 Pseudo random quaternary sequences . . . . . . . . . . . . . . . . . . . . . . . 101 5.6 Summary & conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6 Long-haul DQPSK transmission 105 6.1 21.4-Gb/s RZ-DQPSK transmission . . . . . . . . . . . . . . . . . . . . . . . . 106 6.2 42.8-Gb/s RZ-DQPSK transmission . . . . . . . . . . . . . . . . . . . . . . . . 108 6.3 Lumped dispersion compensation . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.4 Chirped-FBGs based dispersion compensation . . . . . . . . . . . . . . . . . . . 113 6.5 OPC-supported long-haul transmission . . . . . . . . . . . . . . . . . . . . . . . 121 6.6 Comparison of DQPSK transmission experiments . . . . . . . . . . . . . . . . . 126 6.7 Summary & conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7 Polarization-multiplexing 131 7.1 Principle of polarization-multiplexing . . . . . . . . . . . . . . . . . . . . . . . 132 7.2 Transmitter & receiver structure . . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.3 Transmitter & receiver properties . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.4 Nonlinear tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 viii Contents 7.5 Summary & conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 8 Polarization-multiplexed DQPSK 157 8.1 Transmitter & receiver structure . . . . . . . . . . . . . . . . . . . . . . . . . . 158 8.2 Long-haul transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 8.3 Transmission with a high spectral efficiency . . . . . . . . . . . . . . . . . . . . 169 8.4 Summary & conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 9 Digital direct detection receivers 173 9.1 Multi-symbol phase estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 9.2 Maximum likelihood sequence estimation . . . . . . . . . . . . . . . . . . . . . 184 9.3 Summary & conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 10 Digital coherent receivers 203 10.1 Analog coherent receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 10.2 Digital coherent receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 10.3 Digital equalization algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 10.4 Distortion compensation at 43-Gb/s . . . . . . . . . . . . . . . . . . . . . . . . 218 10.5 Distortion compensation at 111-Gb/s . . . . . . . . . . . . . . . . . . . . . . . . 224 10.6 Long-haul transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 10.7 Distortion compensation using baud-rate equalizers . . . . . . . . . . . . . . . . 234 10.8 Summary & conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 11 Outlook & recommendations 239 11.1 Robust optical modulation formats . . . . . . . . . . . . . . . . . . . . . . . . . 239 11.2 Robust electronic equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 A List of symbols & abbreviations 243 A.1 List of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 ix Contents A.2 List of abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 B Definition of the Q-factor and eye opening penalty 249 B.1 Q-factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 B.2 Eye opening penalty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 C Asymmetric 3 x 3 coupler for coherent detection 253 References 257 List of publications 281 Samenvatting 287 Acknowledgement 289 Curriculum Vitae 291 Index 293 x 1 Introduction 1.1 The global telecommunication hierarchy Today’s society has been shaped in all its aspects by the progress in telecommunication technol- ogy. Ever since the first developments that led to today’s Internet and, later on, to the invention of the World Wide Web, data traffic has been increasing exponentially. This exponential band- width growth has spurred the development of new technologies, which in turn made it possible to offer services that relied on even higher bandwidth requirements. Today, Internet services such as Skype [1], YouTube [2] or Google earth [3] depend on a backbone of high-speed ‘data pipes’ so that they can be accessed by people around the world, anywhere, anytime. Although many people are not aware of it, fiber-optic transmission plays a key role in global transport of telecommunications services. This is best described through the telecommunication network hierarchy. Figure 1.1 shows a simplified model of this network hierarchy, dividing it up into a long-haul core network, regional networks and ’last-mile’ access networks. In addition, Table 1.1 depicts the typical distances covered by transmission links in such networks. The core of the global telecommunication network is used for transnational, transcontinental and transoceanic communication. A transmission link in this (ultra) long-haul core network therefore transports the largest amount of data over the longest distances (>1000 km). In the core network, transport technologies are required that enable a long regenerator-free transmission distance at the lowest cost. Fiber-optic transmission is ideally suited for this purpose as it allows for both high throughput and long transmission distance. Such systems are engineered to transmit a large capacity over a long-haul transmission distances, and the physical limits of optical fiber as a transmission medium has a significant impact on their design. 1 Chapter 1. Introduction Long-haul core network Regional / Metropolitan networks ‘last-mile’ access networks Internet enterprise storage residential mobile Figure 1.1: Optical network hierarchy; Long-haul core network, regional/metropolitan and ’last-mile’ access network. To exemplify the capacity increase in long-haul data transport we look more closely at the Trans- Atlantic Internet protocol (IP) traffic. This connection is one of the better documented transmis- sion links in the core network, and serves therefore well as an example. Between 2004 and 2006 traffic has grown over 200%, from 0.5 Tb/s to 1.6 Tb/s [4]. This increase in required capacity is largely fueled by new internet video-on-demand services. When we extrapolate the current annual growth in data traffic over a 10 year period with a conservative 30% per year, we arrive at a figure of 22 Tb/s for the Trans-Atlantic IP traffic in 2016. When we take into consideration that the aggregated traffic is carried over multiple transmission links, each consisting of a number of fibers, the required capacity per fiber will still be in the range of 2 to 3 Tb/s. Considering the vast distances that have to be spanned for a Trans-oceanic link, this presents a significant engineering challenge. Moving down in the telecommunication hierarchy, and interlinked to the core network, are smaller regional and metropolitan networks. Such networks provide data transport within a smaller geographical region, for example a metropolitan area (<300 km) or a small country (<1000 km). The amount of traffic carried on a typical metropolitan network is much smaller than on a link in the core network. However, the number of exchange points, i.e. the points where data originates from or is destined to, is much larger. Consequently, the challenge for such systems is predominantly the cost-effective realization of a complex network switching architec- ture. A metropolitan network connects again a number of access or ’last-mile’ networks together. Such networks facilitate the connection of the end-user to the global telecommunication hierar- 2 1.2. Motivation chy. Many different kinds of end-user applications are possible, spanning from residential inter- net access to business and storage area networks. As a result, a large variety in access network technologies exists, each with their own requirements and specific end-users. Legacy last-mile networks are still largely based on copper networks, either co-axial or twisted pair. The preferred transmission format to increase bit rates over this infrastructure is digital subscriber line (DSL) technology. However, even with DSL technology the bandwidth of copper networks is limited, especially when the distance between the local exchange point and the end-user is longer than a few kilometers. Optical fibers has a significant advantage over copper networks due to its much higher bandwidth-distance product, which enables high-speed connections over longer distances. Fiber-optic solutions are therefore also gaining momentum in ’last-mile’ networks, and ’fiber-to- the-home’ or ’fiber-to-the-curb’ technology is already deployed on a significant scale. As the infrastructure of an access network is generally not shared by a large number of customers, such networks are predominantly engineered to provide a lowest-cost solution [5]. An overview of fiber-based technologies for ’last-mile’ access can be found in [6]. Table 1.1: CLASSIFICATION OF OPTICAL TRANSMISSION SYSTEMS, AFTER [7]. System Distance (km) Access <100 Metro <300 Regional 300 - 1,000 Long-haul 1,000 - 3,000 Ultra long-haul >3,000 1.2 Motivation The backbone of the global telecommunication hierarchy consists of long-haul wavelength- division-multiplexed (WDM) transmission links. A WDM transmission link transports large amount of data traffic by multiplexing a number of lower capacity wavelength channels onto a single fiber. The use of WDM therefore allows for a manifold increase in the capacity of long- haul optical transmission systems. Or, maybe even more importantly, it allows for a tremendous decrease in the cost of the transmitted bandwidth, i.e. the cost per transmitted bit. To cope with the expected bandwidth demand in the near future, new technologies have to be researched, developed and subsequently deployed in long-haul transmission systems. The optical transmission links in the backbone of the telecommunication network can be classi- fied, depending on their regenerator-free transmission distance, as shown in Table 1.1. We focus here in particular on terrestrial long-haul transmission systems. Figure 1.2 shows the typical lay- out of a long-haul optical transmission system and Figure 1.3 depicts an example of an optical spectrum for a high-capacity WDM system. In an optical transmitter (Tx), a data sequence is modulated onto an optical carrier, generated by a laser. The separate wavelength channels are then multiplexed together using a wavelength multiplexer, for example an arrayed waveguide 3 Chapter 1. Introduction grating (AWG), which typically has a 100-GHz channel spacing. The density of the WDM chan- nels can be further increased through channel interleaving with an optical interleaver (INT). This results in WDM systems with a 50-GHz channel spacing and a total number of 80 WDM chan- nels that are multiplexed on a single optical fiber. Deployed transmission systems with 80 WDM channels are currently state-of-the-art, but in long-haul transmission experiments up to 200 chan- nels are sometimes multiplexed onto a single fiber. Such transmission links rely nowadays on bit rates of 10-Gb/s and sometimes 40-Gb/s per wavelength channel to realize a 1 to 3-Tb/s aggregate capacity 1 . The bit rate and wavelength spacing of a transmission system is often ex- pressed in terms of the spectral efficiency, which is the transmitted capacity per unit bandwidth. For currently deployed systems the spectral efficiency is between 0.2 and 0.8-b/s/Hz. Next- generation transmission links will use bit rates of 40-Gb/s or 100-Gb/s per wavelength channel, which results in a spectral efficiency between 0.8 and 2.0-b/s/Hz. The aggregate capacity of such systems would then increase to 3 to 8-Tb/s over a single fiber. At the receiver side of the trans- mission link, the WDM channels are de-multiplexed using a combination of de-interleaver and de-multiplexers. Each of the de-multiplexed channels is then fed into an optical receiver (Rx), which converts the signal back to the electrical domain. As most optical transmission systems are bi-directional (on separate fibers) the optical transmitter and receiver are usually combined in a single module, which is referred to as a transponder. The transmission link itself consists of cascaded fiber spans with optical amplifiers in-between. The optical amplifiers amplify the weak input signal from the previous span and launch it again into the next span. This allows long-haul transmission while maintaining a sufficiently high op- tical signal-to-noise ratio (OSNR) at the output of the fiber link. At bit rates of 10-Gb/s, and in particular 40-Gb/s or 100-Gb/s, transmission impairments such as chromatic dispersion and polarization-mode dispersion (PMD) have to be precisely dealt with. And as such impairments accumulate in a long-haul optical transmission link, this can severely limit the feasible transmis- sion distance. Some transmission impairments are deterministic and therefore straightforward to compensate with proper link design. For example, the accumulated chromatic dispersion is normally compensated using a dispersion compensation module (DCM) placed in-between two fiber spans. Other signal impairments are more difficult to compensate as they fluctuate over time, such as PMD. As not all transmission impairments can be compensated along the transmis- sion link, the receiver should be able to recover the transmitted data sequence in their presence. The tolerance of a transmission system against isolated transmission impairments, such as chro- matic dispersion or DGD, is often expressed in terms of the required OSNR margin 2 . An important aspect of the optical transmission systems that we consider in this thesis is their robustness. When an optical transmission system is upgraded, e.g. from a 10-Gb/s to a 40-Gb/s 1 The actual transmitted bit rate includes an overhead for forward error correction (FEC), which is typically 7%. The bit rate used in this thesis is therefore 10.7-Gb/s for 10-Gb/s transmission and 42.8-Gb/s for 40-Gb/s transmission. For 100-Gb/s transmission an additional 4% overhead is normally taken into account for 64B/66B coding, as required for Ethernet transport, which increases the bit rate to 111-Gb/s. 2 The OSNR margin is dependent on the required bit-error-ratio (BER). In this thesis we used a BER of 10 −5 to quantify the required OSNR in the analytical simulation as this matches a transmission system that operates with a 3-dB margin with respect to the FEC limit. However, in the transmission experiments or simulations that use a Monte-Carlo approach, a BER of 10 −3 or 10 −4 is used to improve the accuracy of the estimation. This is discussed in more detail in Appendix B. 4 1.2. Motivation bit rate per wavelength channel, ideally, no modifications are made in the transmission link. This would require a 40-Gb/s transponder that has a similar tolerance to transmission impairments as the deployed 10-Gb/s transponders. However, this is not straightforward as the tolerance against most transmission impairments scales linearly or even quadratically with the symbol rate. To counter the lower transmission tolerances at a higher bit rate, either sophisticated modulation formats, optical compensation or electronic equalization can be used. In this thesis we define a 40-Gb/s or 100-Gb/s transmission format to be robust when its transmission tolerances are sufficiently high to allow deployment on links optimized for transmission with 10-Gb/s bit rate. I N T A W G I N T A W G A W G A W G Up to 80 channels RX RX RX RX TX TX TX laser TX DCM DCM Optical Add/Drop Optical amplifier Photo diode Fiber Figure 1.2: Typical layout of a WDM optical transmission link. 1530 1535 1540 1545 1550 1555 1560 1565 -30 -20 -10 0 Wavelength (nm) P S D ( d B ) Figure 1.3: Measured WDM spectrum with 89 channels and a 85.6-Gb/s bit rate per channel. A second important consideration for optical transmission systems, is that they are rapidly evolv- ing frompoint-to-point links to meshed optical networks. This requires the flexibility to pass mul- tiple optical add-drop multiplexer (OADM) nodes along the transmission link. At such OADM nodes traffic is routed to other links, thereby creating a meshed network. Today, most deployed long-haul transmission systems have a 50-GHz spacing between the WDM channels. At such a channel spacing, the width of the optical spectrum is not a significant concern for 10-Gb/s sys- tems and WDM channels can be switched transparently through an optical network. However, when the symbol rate of the optical signal is doubled or quadrupled, the spectral width scales accordingly. Hence, when transmission systems that are designed for a 10-Gb/s bit rate are up- graded to a 40-Gb/s or 100-Gb/s bit rate per WDM channel, the spectral width of the optical signal can become a key concern [8, 9]. This requires optical modulation formats that are toler- ant to the narrowband optical filtering that occurs when multiple OADMs are cascaded along a transmission link. In this thesis we focus predominantly on two technologies that can enable more robust optical transmission. First of all, we discuss the use of robust multi-level optical modulation formats. Such modulation formats often have favorable transmission properties that can be used to either 5 Chapter 1. Introduction increase the capacity of an optical transmission link or increase its robustness against transmis- sion impairments. Secondly, we focus on electronic equalization that can be combined with robust modulation formats to further improve the performance of the transmission link. 1.2.1 Robust optical modulation formats The modulation format defines the characteristics of the optical signal that is transmitted over the transmission link. Until recently, the optical modulation format of choice for nearly all op- tical transmission systems has been non-return-to-zero on-off keying (NRZ-OOK). NRZ-OOK combines a cost-effective transmitter and receiver structure with a transmission performance suf- ficient to realize long-haul 10-Gb/s transmission systems. This has largely prevented the use of more complex modulation formats and NRZ-OOK is still used nearly exclusively in deployed 10-Gb/s terrestrial long-haul transmission systems. Only recently the growing interest in more robust optical transmission technologies has opened up the possibility for commercial deploy- ment of different modulation formats. This is particulary true for 40-Gb/s or 100-Gb/s bit rates, where the transmission tolerances of NRZ-OOK modulation are too small to realize robust long- haul transmission systems with a 50-GHz channel spacing. In addition, for 40-Gb/s or 100-Gb/s bit rates the spectral efficiency is an important consideration. Binary modulation restricts the achievable spectral efficiency to 1-b/s/Hz [10]. And in practical systems, the realizable spectral efficiency is significantly lower than 1-b/s/Hz because WDM is considered to be transparent, i.e. crosstalk from neighboring channels is assumed to be unknown and hence treated as a noise source. And other system design aspects that further reduce the spectral efficiency have to be taken into account, such as the 7% overhead usually required for forward error correction (FEC), wavelength drift in the transmitter laser and (de-)multiplexing filters as well as the limited filter order of optical filters and interleavers. Combined, the required margins restrict the feasible spectral efficiency to approximately <0.7-b/s/Hz when using NRZ- OOK modulation. Currently deployed 40-Gb/s transmission systems use modulation formats that are more robust against transmission impairments than NRZ-OOK. This includes duobinary, which can be used to improve the tolerance against chromatic dispersion and narrowband optical filtering. But in particular phase modulation, using differential phase shift keying (DPSK), is currently the most widely used state-of-the-art modulation format. Modulation formats such as duobinary or DPSK are more tolerant to narrowband optical filtering and allow a spectral efficiency of up to 0.8-b/s/Hz. Multi-level modulation with 2 bits per symbol, such as return-to-zero differential quadrature phase shift keying (RZ-DQPSK) modulation, can increase this to ∼1.6-b/s/Hz. In addition it is more tolerant to many linear transmission impairments as well as narrowband optical filtering. Another potential candidate to reduce the symbol rate is polarization multiplexing (POLMUX). This doubles the number of bits per symbol by transmitting independent information in each of the two orthogonal polarizations of an optical fiber. Combined with DQPSK modulation, POLMUX signaling enables modulation with 4 bits per symbol. 6 1.2. Motivation Multi-level modulation is particulary beneficial for 100-Gb/s transmission. Although 100-Gb/s NRZ-OOK has been demonstrated using ultra-high frequency electronics [11, 12] the use of such a modulation format would pose considerable challenges in deployed transmission systems due its high OSNR requirement and low chromatic dispersion and PMD tolerance. DQPSK is therefore a more likely candidate for long-haul 100-Gb/s transmission and a number of long-haul transmission experiments have demonstrated its feasibility [13, 14, 15]. For 100-Gb/s modulation the main advantage of DQPSK is that it reduces the bandwidth requirement of the electrical components in the transponder as it operates at a 50-Gbaud symbol rate. Taking this approach a step further, POLMUX-RZ-DQPSK modulation enables 100-Gb/s transmission with only a ∼25-Gbaud symbol rate. This increases the tolerance to chromatic dispersion and PMD and will enable next-generation optical transmission systems with a spectral efficiency of 2.0-b/s/Hz. This thesis focuses on multi-level modulation formats that can enable robust 40-Gb/s and 100- Gb/s modulation per wavelength channel. In particular, we look more closely at the potential impact of DQPSK modulation and POLMUX signaling in long-haul transmission systems. 1.2.2 Robust electronic equalization Digital signal processing speeds have increased exponentially over the years [16] and have now started to catch up with bit rates common in optical transmission systems. In particular, high- speed analog-to-digital converters (ADC) have become available to convert the analog signal in an optical receiver to the digital domain for subsequent digital signal processing. Current state-of-the-art ADCs in commercial products have a sample rate of ∼25-Gbaud [17, 18] and sample rates up to ∼50-Gbaud have shown to be feasible in research and development as well as measurement equipment. The conversion of the optical signal to the digital domains enables the use of powerful digital signal processing algorithms. Digital signal processing increases the robustness of the transpon- der and can help to simplify transmission link design. It reduces the need for precise optical compensation of chromatic dispersion and it negates the need for fiber selection to reduce the PMD on an optical transmission link [19, 20]. Digital signal processing can further be used to lower the required OSNR through the use of improved decision variables as well as an increase in nonlinear tolerance. The combination of multi-level modulation formats and digital signal processing is a particularly interesting approach to realize high spectrally efficient transmission. For efficient digital signal processing, the signal has to be sampled at twice the symbol rate. This implies that for binary modulation formats a sample rate of 80-Gbaud and 200-Gbaud is required for 40-Gb/s and 100-Gb/s transponders, respectively. These figures are well beyond the sample rates that seem to be feasible in the foreseeable future. However, combined with multi-level mod- ulation such as POLMUX-DQPSK, the sample rate requirements for a 100-Gb/s transponder are lowered to ∼50-Gbaud. A figure that seems to be feasible in the foreseeable future. The electronic equalization schemes that have attracted the most significant interest in recent years include feed-forward and decision-feedback equalizers, maximum likelihood sequence es- timation (MLSE), pre-distortion, multi-symbol phase estimation (MSPE) or related approaches 7 Chapter 1. Introduction and digital coherent receivers. In particular the combination of coherent receivers with digital signal processing has proven to be useful together with multi-level modulation formats. In ad- dition, it can potentially recover polarization multiplexed data and correct for linear distortions, such as chromatic dispersion and PMD, in the electrical domain. Hence, the combination of dig- ital coherent detection and multi-level modulation formats such as POLMUX-DQPSK seems to be one of the most suitable choices for the next generation of high-capacity optical transmission systems. 1.3 Framework & objectives Long-haul WDM optical transmission systems with a 10-Gb/s bit rate per wavelength channel have been deployed on a significant scale over the last decade. But after the telecom bust in 2001, the optical systems industry has become more cost-oriented and moved away from performance- oriented system design that was common during the telecom boom. The first generation of trans- mission systems with a 40-Gb/s bit rate per wavelength channel could therefore not compete on a cost basis with deployed systems that operated with 10-Gb/s bit rates. This has prevented commercial deployment of such systems and limited their use to transmission experiments and field-trails. However, the use of sophisticated optical modulation formats and electronic equal- ization can enable more robust 40-Gb/s and 100-Gb/s optical transmission systems. This has spurred a significant research and development effort by the optical systems industry into devel- oping these technologies for their next-generation products. The research discussed in this thesis focuses on a number of next-generation transmission tech- nologies that might significantly impact the design of long-haul transmission systems in the foreseeable future. Ideally, these technologies will allow for 40-Gb/s and 100-Gb/s transmis- sion systems that can be cost-effective in comparison to existing 10-Gb/s systems. This thesis describes in particular the most promising modulation and equalization technologies and demon- strates their feasibility using long-haul optical transmission experiments. The work described in this thesis has been carried out at Nokia-Siemens networks (previously Siemens Communications) in Munich, Germany, in cooperation with the Electro-Optical Com- munications group, department of Electrical Engineering of the Eindhoven University of Tech- nology, The Netherlands. This work has been part of the ’MultiTeraNet’ and ’Eibone’ projects from the German Bundesministerium f¨ ur Bildung und Forschung (BMBF). In addition, it has been carried out in close cooperation with the work of Jansen [21], which focuses on optical phase conjugation in long-haul transmission systems. 1.4 Outline of this thesis In this section we give a general overview of the thesis structure. The first part of the thesis con- sists of the Chapters 2 and 3, which discuss the fiber-optic transmission channel and long-haul 8 1.4. Outline of this thesis transmission systems, respectively. The aim of these two chapters is to provide a physical frame- work of the optical fiber as the transmission medium in long-haul telecommunication systems. In addition, we discuss in detail the relevant technologies for amplification and distortion compen- sation in a state-of-the-art transmission systems. These technologies are used in the transmission experiments described in the remainder of this thesis. The second part of the thesis consists of the Chapters 4 to 8, which deal with the relevant op- tical modulation formats for long-haul transmission systems. Chapter 4 discusses in detail the binary modulation formats which are currently deployed in state-of-the-art 40-Gb/s transmission systems. Next, Chapters 5 and 6 focus on the most significant multi-level modulation format described in this thesis, DQPSK modulation. Chapter 5 introduces the properties of DQPSK modulation, whereas Chapter 6 discusses in detail a number of long-haul transmission exper- iments that make use of DQPSK modulation. Subsequently, Chapter 7 discusses POLMUX signaling, in particular the specific transmission impairments that occur when two orthogonal polarizations are used to transmit information. Polarization multiplexing is then combined with DQPSK modulation in Chapter 8 to realize high spectrally efficient long-haul transmission. Finally, the third part of the thesis focuses on electronic equalization and digital signal process- ing. In Chapter 9, digital signal processing combined with direct detection receivers is discussed in more detail. And in Chapter 10 the use of digital coherent receivers is treated. In addition, long-haul transmission experiments are described that use digital coherent detection together with multi-level modulation formats to realize robust long-haul transmission with a 2.0-b/s/Hz spectral efficiency. 9 Chapter 1. Introduction 10 2 The fiber-optic transmission channel Single-mode optical fibers are circular dielectric waveguides that weakly guide a single trans- verse mode in two orthogonal polarizations. Made from silica glass, single-mode fibers have very advantageous properties for the transmission of guided waves over long-distances. The use of glass fiber for communication at optical frequencies was first proposed by Kao and Hock- ham in 1966 [22]. Since then, progress in material technology and fiber manufacturing [23] has resulted in the widespread availability of optical fiber with near optimal properties. coating cladding core (a) 0 core radius n n silica ǻn § 0.5 % core cladding (b) Figure 2.1: (a) Cross-section of an optical fiber and (b) refractive index profile of standard single-mode fiber. Figure 2.1a shows a cross-section of an optical fiber. In the center of the fiber is the core, which is surrounded by the fiber cladding. For silica fibers the refractive index of the core is n ≈ 1.48 (at 1550 nm) and is higher by ∼0.5% than the refractive index of the cladding [24]. This can be achieved either by doping the core with Germanium-Oxide (GeO 2 ), which raises the refractive index, or doping the cladding with fluoride (F), which lowers the refractive index. The fiber cladding confines the light to the fiber core through total internal reflection and the low refractive index difference of the core-cladding boundary reduces the scattering loss. Note that the majority, 11 Chapter 2. The fiber-optic transmission channel but not all of the optical wave propagates through the core. The core size is upper-bounded by the need for single-mode propagation in the wavelength range of interest. A too large core diameter with respect to the signal wavelength can result in multi-mode propagation. This is characterized by the cut-off wavelength, which is the lowest wavelength that allows for single-mode operation. Finally, a coating of the optical fiber is necessary for protection of the fiber. The most widely used fiber type in optical transmission systems is standard single-mode fiber (SSMF), which is sometimes referred to as G.652 fiber [25]. SSMF has a step refractive index profile, as depicted in Figure 2.1b. The fiber core has a typical diameter of 9 µm and the cut- off wavelength is < 1260 nm so that it provides single-mode operation in the entire low-loss wavelength range of the optical fiber. It was the first single-mode fiber type to be developed, but it is still widely used in optical transmission systems. The core of a SSMF is normally doped with GeO 2 . As doping with GeO 2 slightly raises the fiber attenuation, it is preferable to dope the cladding with fluoride for low-attenuation fibers [26]. Such fibers are referred to as pure-silica core fibers and are used in Trans-oceanic optical transmission systems. Most optical fibers are fabricated (drawn) from a preform in a fiber drawing tower. A preform is a glass rod which has a diameter of a few centimeters and is roughly a meter in length. When heated close to the melting point in a furnace, the preform is pulled into a thin fiber [23]. The preformcontains a part with an increased refractive index along its axis, which after fiber drawing becomes the fiber core. The remainder of the preform becomes the cladding of the optical fiber. This chapter discusses the physical properties of an optical fiber that are the most relevant to long-haul fiber-optic transmission systems. This includes fiber attenuation (Section 2.1), chro- matic dispersion (Section 2.2), polarization properties (Section 2.3) and fiber nonlinearities (Sec- tion 2.4). 2.1 Fiber attenuation As any physical medium besides vacuum, optical fiber has an intrinsic power loss when a signal propagates along it. The signal power P(z) in [W] decreases exponentially with the fiber length, which is referred to a fiber attenuation. After a transmission distance z in [km], the signal power can be denoted by, P(z) = P 0 exp(−αz), (2.1) where P 0 is the power coupled into the optical fiber in [W] and α is the attenuation coefficient in Neper per kilometer [Np/km]. The Neper is a logarithmic unit that uses base e, but it is more convenient to define the fiber attenuation in decibel per kilometer (base 10 logarithmic), following Equation 2.2, α dB = 10log 10 (exp(α Np )) = 10log 10 (e) α Np = 4.343 α Np . (2.2) In the remainder of the thesis, the fiber attenuation coefficient in [dB/km] will be used unless noted otherwise. 12 2.1. Fiber attenuation The fiber loss as a function of wavelength and frequency is depicted in Figure 2.2. The wave- length (λ) and the optical frequency ( f ) of a spectral component are related according to λ =c/ f , where c is the speed of light in vacuumwhich is equal to c =2, 9979 10 8 m/s. The minimumfiber loss occurs between 1.5 µm and 1.6 µm and can be as low as 0.148 dB/km [27]. In comparison, the attenuation of conventional (window) glass is approximately 1000 dB/km. This extremely small attenuation in single-mode silica fiber, allowing for un-repeated transmission links up to 500 km [28]. For long-haul transmission links, ∼100 km spans with re-amplification after each span is widely used. 0.1 0.2 0.3 0.4 0.5 0.6 A t t e n u a t i o n ( d B / k m ) O E S C L U 1200 1260 1360 1460 1530 1565 1625 1675 1715 Wavelength (nm) 250 240 230 220 210 200 190 180 Frequency (THz) S i O 2 a b s o r p t i o n Bending losses R a y le ig h s c a tte rin g OH - -absorption Figure 2.2: Fiber loss as a function of wavelength and frequency. The remaining contributions to the fiber attenuation in low-loss optical fibers comes from several sources of which the most dominant are: Rayleigh scattering, OH − absorption, bending losses and SiO 2 absorption [29]. Rayleigh scattering results from microscopic fluctuations in the mate- rial density much smaller than the wavelength of the light. It is proportional to the inverse fourth power of wavelength, and therefore attenuates shorter wavelength more than longer wavelength [30]. For longer wavelength (> 1600 nm) the dominant sources of fiber attenuation are bending losses and SiO 2 absorption. Bending losses are more dominant for longer wavelength because the bending radius relative to the wavelength becomes too small, which increases the scattering losses. For even longer wavelength (> 1700 nm), SiO 2 absorption becomes the dominant loss mechanism. This results from the harmonic vibrations in the bonds of the silica molecules that make up the glass. Apart from the higher fiber attenuation at lower and higher wavelengths, there is often an OH − absorption peak around 1.4 µm [31]. However, this absorption peak can be nearly eliminated by reducing the concentration of hydroxyl (OH − ) ions in the core of the op- tical fiber [32, 26]. Optical fibers with a negligible OH − absorption peak are commonly referred to as water-free or G.652C/D fibers [25]. Such fibers have a ∼60-THz low-loss bandwidth with an attenuation below 0.4 dB/km. In principle, this entire wavelength band can be used for optical communication purposes. The wavelength bands of interest for optical fiber communication are defined by the Interna- tional Telecommunication Union Standardization (ITU-T) in [33], which span from 1260 nm to 1625 nm. The wavelength range is lower bounded by the fiber cut-off wavelength and upper- bounded by bending and SiO 2 absorption losses. This wavelength range is divided into 6 wave- 13 Chapter 2. The fiber-optic transmission channel length bands: O, E, S, C, L and U, as depicted in Figure 2.2. For long-haul optical transmission systems the C-band is generally used, which spans the wavelength range between 1528.77 nm and 1568.36 nm. In addition, to increase the transmission capacity the L-band is sometimes used in commercial long-haul systems, which spans the wavelength range between 1568.77 nm and 1610.49 nm. Combined, both bands allow a total of approximately 160 wavelength chan- nels on a 50-GHz WDM grid [34]. The O-band is used extensively for optical communication in metropolitan networks, as cost-effective vertical cavity emitting lasers are available for this wavelength band. [5, 6, 35]. The other wavelength bands are only sporadically used in dense- WDM optical transmission systems due to the higher fiber loss and lack of optical amplifiers with a high efficiency. All wavelength bands combined are also used in metropolitan networks to enable WDM transmission with a large 20 nm channel spacing. Such a channel spacing allows the use of uncooled lasers, and is known as coarse-WDM (CWDM) [36, 37]. 2.2 Chromatic dispersion Chromatic dispersion in a single-mode fiber refers to the pulse broadening induced through the wavelength dependence of the fiber’s refractive index, and it results for optical transmission systems in inter-symbol interference (ISI). This restricts the dispersion limited reach, i.e. the feasible transmission distance without the need for regeneration or dispersion compensation. In this section the background of chromatic dispersion and the impact on optical transmission links is explained. The speed at which the phase of any one frequency component of a wave travels along an optical fiber is equal to, v p (ω) = c n+n(ω) , (2.3) where v p is the phase velocity of a spectral component, n is the refractive index of the guiding material and ω is the angular frequency in [rad/s]. As the refractive index n is larger than 1, the speed of light in an optical fiber is lower than in vacuum. In single-mode optical fibers, the main dispersion effects are material and waveguide dispersion. Waveguide dispersion is related to the optical field being not totally confined to the core of the fiber. A part of the optical field propagates therefore in the cladding, which has a different refractive index. This mismatch in refractive index causes waveguide dispersion. The dependency of the refractive index on the angular frequency is known as material dispersion. The impact of material dispersion on a modulated signal can be described by the mode-propagation constant β β(ω) = ω v p (ω) = [n+n(ω)] ω c , (2.4) The wavelength dependency of β(ω) can be approximated with a polynomial using a Taylor series expansion. This results in Equation 2.5. β(ω) = [n+n(ω)] ω c ≈β 0 +β 1 (ω −ω 0 ) + 1 2 β 2 (ω −ω 0 ) 2 + 1 6 β 3 (ω −ω 0 ) 3 +... (2.5) 14 2.2. Chromatic dispersion where β n is defined as the n th derivative of β with respect to the angular frequency, β n = ∂ n β ∂ω n [ ω=ω 0 . (2.6) In the context of pulse propagation inside an optical fiber, the term β 0 in [1/km] represents a constant phase shift and β 1 in [ps/km] corresponds to the speed at which the envelope of the pulse propagates. The group-velocity of the pulse is then defined by β 1 = 1/v g . The second order term β 2 defines the acceleration of the spectral components in the pulse, which is known as the group velocity dispersion (GVD) in [ps 2 /km]. The third order derivative correspond to β 3 in [ps 3 /km] and is known as the GVD slope. In fiber-optic communication it is common to use the dispersion (D) and dispersion slope (S), which defines the change in GVD and GVD slope with respect to a reference wavelength λ, respectively. They are related to β 2 and β 3 as D = ∂β 1 ∂λ =− 2πc λ 2 β 2 S = ∂D ∂λ = 4πc λ 3 (β 2 + πc λ β 3 ), (2.7) Where D is expressed in [ps/nm/km] and S is expressed in [ps 2 /nm/km]. The wavelength for which Dequals zero is referred to as the zero-dispersion wavelength (λ 0 ), it is also the wavelength where waveguide and material dispersion have the same magnitude (but opposite signs). The term chromatic dispersion is commonly used to refer to the fiber dispersion. This is in principle not correct as chromatic dispersion implies that different spectral components travel at different velocities. But the fiber dispersion is related to the group-velocity dispersion and not to the group- velocity of the spectral components. However, as it is common terminology in the literature to refer the fiber dispersion as chromatic dispersion, this nomenclature is also adopted in this thesis. 1300 1350 1400 1450 1500 1550 1600 1650 -10 -5 0 5 10 15 20 25 1250 Wavelength (nm) D i s p e r s i o n ( p s / n m / k m ) Standard Single Mode Fiber (SSMF) G.652 Dispersion Shifted Fiber (DSF) G.653 C- band L- band Non-zero Dispersion Shifted Fibers (NZDSF) G.655 O- band Figure 2.3: Dispersion as a function of wavelength for the most common fiber types in optical communi- cation. Figure 2.3 shows the dispersion as a function of wavelength for the most common optical fiber types in optical fiber communication. The zero-dispersion wavelength of SSMF is near 1310 nm [38]. This is widely exploited in access and metropolitan networks, as it significantly increases 15 Chapter 2. The fiber-optic transmission channel the dispersion limited reach [35]. In the C-band, the chromatic dispersion of SSMF is typically between D = 15.5 ps/nm/km around 1528 nm and D = 17.8 ps/nm/km around 1568 nm. The dispersion slope for SSMF is approximately S = 0.057 ps 2 /nm/km. By changing the core-cladding refractive index profile of the fiber, both the material and wave- guide dispersion can be modified. For example, by increasing the waveguide dispersion the zero-dispersion wavelength shifts to higher wavelengths. It is also possible to lower the disper- sion slope and create a fiber with a nearly flat dispersion profile [39]. Dispersion-shifted fibers (DSF) have a zero-dispersion wavelength in the C-band around 1550 nm and are also known as G.653 fibers [40]. DSF have been developed to extend the dispersion limited reach of optical transmission systems employing the C-band. A low chromatic dispersion coefficient however in- creases inter-channel nonlinear impairments (see Section 2.4) which makes such fiber unsuitable for WDM transmission systems. A third class of optical fibers that are frequently used in long- haul fiber-optic transmission systems are non-zero dispersion-shifted fibers (NZDSF) or G.655 fiber [41]. There is no common definition for NZDSF, but different manufactures have their own proprietary solutions, e.g. Alcatel TeraLight, Corning LEAF and Lucent TrueWave. The zero- dispersion wavelength of NZDSF fiber is around ∼ 1460 nm and the chromatic dispersion in the C-band between 3-8 ps/nm/km, depending on the exact fiber type. The ISI induced through chromatic dispersion in a fiber-optic transmission link can be quantized by using a normalized dispersion length L D , as defined in Equation 2.8 [42]. L D = T 2 0 [β 2 [ (2.8) The normalized dispersion length defines the propagation distance over which the pulse broadens with approximately a factor √ 2. The pulsewidth T 0 is the width of a chirp-free transform limited pulse. As T 0 is inverse proportional to the symbol rate, the chromatic dispersion tolerance scales quadratically with the symbol rate. By modifying the refractive index profile it is also possible to create fibers that have a both a negative chromatic dispersion and dispersion slope. Such fibers can compensate for the chromatic dispersion of transmission fibers and are therefore referred to as dispersion compensating fiber (DCF), which is discussed in Section 3.3. 2.3 Polarization of light The polarization of light is the property of electromagnetic waves that describes the direction of the transverse electric field. All electromagnetic waves propagating in vacuum or in a waveguide have electric and magnetic fields that are orthogonal to each other in a transverse plane. The transverse plane is again orthogonal to the direction of propagation z. In the transverse plane, the electric field vector can be divided into two orthogonal components x and y. Note that we do not define a frame of reference for the x and y component, and their orientation is therefore arbitrary. The magnetic field vector is normally ignored as it is orthogonal to the electric field vector. The state of polarization (SOP) is then defined as the pattern traced out by the electric field in the 16 2.3. Polarization of light transverse plane as a function of time. In [43], the mathematical background of the polarization of light is discussed in detail. x y (a) x y (b) x y (c) Figure 2.4: Example of different SOP of an electro-magnetic wave; (a) 45 o linear, (b) right circular and (c) left elliptical. In an optical fiber, the two orthogonal components in the transverse plane can be interpret as the fiber supporting two orthogonal polarizations. The SOP is then defined by relative amplitude and phase of the orthogonal polarization components x and y, as shown in Figure 2.4. When there is no phase difference between the x and y components, the light is linear polarized. The angle of the linear polarized light depends on the amplitude in the x component with respect to the amplitude in the y component. For horizontally polarized light the pulse travel completely in the x component, whereas for vertically polarized light the pulse travels in the y component. When there is a phase difference between the x and y component the light is elliptically polarized (Figure 2.4c). In the special case both components contain an equal amplitude and have a +90 o phase difference, the light is right-circular polarized or left-circular polarized for a −90 o phase difference (Figure 2.4b). Note that not all light is polarized, for example sunlight is un-polarized light. However, it is still possible to model un-polarized light as polarized light by assuming a random change in SOP for each fraction of time. The polarization of an optical signal can be described in a vector notation by separately describ- ing the electric field vector of the x and y component, _ E x E y _ = _ √ P x exp( j[ω 0 t +ϕ x (t)]) _ P y exp( j[ω 0 t +ϕ y (t)]) _ . (2.9) The SOP of an optical signal can be described using the vector notation of the complex envelope, which is also known as the Jones vector, _ √ P x exp( jϕ x ) _ P y exp( jϕ y ) _ = _ P x +P y exp( jφ x ) _ cosψ exp( j[φ x −φ y [)sinψ _ , (2.10) where ψ is defined such that tanψ = √ P x / _ P y . The normalized Jones vector with unity ampli- tude is widely used to characterize the SOP of an optical signal. An alternative representation to describe the SOP of an optical signal are the Stokes parameters, which can also describe partially or unpolarized light [43]. An additional advantage of using Stokes parameters, is that they express the SOP in term of optical powers instead of the elec- tric field, which is more straightforward to measure. The Stokes vector consists of four stokes 17 Chapter 2. The fiber-optic transmission channel S 1 S 2 S 3 Horizontally polarized Vertically polarized +90 o circular polarized -90 o circular polarized -45 o linear polarized +45 o linear polarized Figure 2.5: The Poincar´ e sphere. parameters, S = [S 0 S 1 S 2 S 3 ] T , which can be defined in terms of the electrical field vectors using, ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ S 0 = E x E ∗ x +E y E ∗ y = E 2 x +E 2 y S 1 = E x E ∗ x −E y E ∗ y = E 2 x −E 2 y S 2 = E x E ∗ y +E y E ∗ x = 2E x E y cos([ϕ x −ϕ y [) S 3 = iE x E ∗ y −iE y E ∗ x = 2E x E y sin([ϕ x −ϕ y [) (2.11) The Stokes parameters are often normalized with respect to the total optical power S 0 . The Poincar´ e sphere is a graphical representation of the SOP which uses the normalized Stokes pa- rameters as the axis of a 3-dimensional coordinate system, as shown in Figure 2.5. Fully polar- ized light can be described by a point on the Poincar´ e sphere, whereas partially or unpolarized light is described by a point within the sphere. The degree of polarization (DOP) defines the distance from S to the center of the Poincar´ e sphere and it is therefore an important parameter to quantify depolarization. Expressed in term of the Stokes parameters the DOP is equal to, DOP = _ S 2 1 +S 2 2 +S 2 3 S 0 . (2.12) 2.3.1 First-order polarization mode dispersion In an ideal optical fiber with no imperfections and circular symmetry, both orthogonal polar- izations have an identical group delay. Hence, the signal will not couple into the orthogonal 18 2.3. Polarization of light polarization and the received SOP is identical to the SOP launched into the fiber. However, the core of the optical fiber is in practice not completely symmetric and the material has imperfec- tions, which results in fiber birefringence ∆n and a difference in the group delay ∆β 1 between the two orthogonal polarizations. ∆β 1 =[β 1,x −β 1,y [ = ω c [n x −n y [, (2.13) DGD Transmission link fast axis slow axis Figure 2.6: Differential group delay in an optical fiber; the signal coupled into the slow axis travels slower than the signal coupled into the fast axis. In a fiber with constant birefringence, both orthogonal polarizations periodically exchange power with a periodicity equal to the beat length 2π/∆β 1 in [km] when the signal is coupled into the fiber in between both orthogonal polarizations. An example of a fiber type with constant bire- fringence are polarization-maintaining fibers, which are fabricated by artificially enhancing the stress induced birefringence in the fiber core [44]. On the Poincar´ e sphere the constant birefrin- gence results in a periodic rotation of the output SOP around two orthogonal polarization axes, the principle states of polarization (PSP). When the signal is coupled into one of the PSP, the SOP is constant along the fiber. The PSP with the lower refractive index is referred to as the fast axis, because a signal traveling along this axis has a higher group velocity. Following a similar argument the orthogonal PSP, which is on the opposite side of the Poincar´ e sphere, is then called the slow axis. After an optical signal propagated over a distance L, the differential group delay (DGD) is equal to ∆τ =∆β 1 L. Figure 2.6 illustrates DGD in an optical transmission link. Figure 2.7: Possible causes of random birefringence in non-ideal optical fibers. From left to right, an oval core shape, outside pressure due to mechanical stress, wind or temperature, fiber bending and fiber twisting. In the fibers used for optical transmission links, birefringence is random, and changes both along the optical fiber and over time. Rashleigh and Ulrich were in 1978 the first to note that this random coupling between both orthogonal polarizations could result in signal impairments [45]. The random coupling can be the result of both imperfections introduced in the manufacturing process or external influences as depicted in Figure 2.7. Consequently, the birefringence results 19 Chapter 2. The fiber-optic transmission channel in a random change of the SOP that is analog to the random walk theorem [46]. The random birefringence in a fiber also implies that the DGD is a statistic distribution. This is known as polarization mode dispersion (PMD) in [ps], which is defined as the statistical average of the DGD. PMD =<∆τ > (2.14) where <∆τ > is the mean DGD and ¸) denotes an ensemble average. The DGD variance var(< ∆τ >) can be denoted through a square relation with the average DGD [47]. var(<∆τ >) = 3 π/8 <∆τ > 2 (2.15) We assume now that the fiber consists of an infinitely large number of infinitely small fiber sec- tion, which all rotate the SOP according to the random walk theorem. Then the central limit theorem states that the distribution of the sum of a large number of independent but identically distributed variables is approximately Gaussian distributed, independent of the specific distri- bution of the variables [48]. For optical fiber with random birefringence this implies that the normalized stokes parameters S 1..3 are Gaussian distributed. The PMD properties of an optical fiber can be characterized through the PMD vector τ [49]. τ is a vector in normalized Stokes space, pointing in the direction of the slow PSP, and with a magnitude equal to the DGD. When the normalized stokes parameters S 1..3 are Gaussian distributed, the probability density function of the magnitude of the PMD vector is Maxwellian distributed [50]. Pr¦∆τ¦ = 32∆τ 2 π 2 <∆τ > 3 exp(− 4∆τ 2 π <∆τ > 2 ) (2.16) The Maxwellian distribution of Pr¦∆τ¦ is only correct when the differential group delay is equally distributed over all (infinitely small) fiber sections. When there are points along the fiber with a high local birefringence, the distribution will begin to resemble the square root of a non-central Chi-square distribution with three degrees of freedom [51]. This is also known as the Hinge model [52, 53]. A high local birefringence can result from tight bends in the fiber or points of alleviated mechanical vibrations such a roads or railroad tracks. For random coupling, the mean DGD (< ∆τ >) does not increase linearly with propagation distance, but with its root-mean-square [29]. The PMD coefficient is the PMD (mean DGD) divided by the square root of the propagation length ( √ L) in [ps/ √ km]. The unit [ps/ √ km] shows that the maximum allowable PMD decreases with approximately a factor of two when the symbol rate is doubled. Note, however, that the PMD limited transmission distance scales quadratically with the symbol rate. Due to the statistical nature of PMD there is a finite probability that an arbitrarily high DGD will occur. Usually, one therefore defines a system outage probability, which implies that the DGD can not exceed a certain value during more than a specific fraction of the time. A widely accepted value for the system outage probability is 30 minutes per year or a probability of 5.7 10 −5 . This is equal to an average PMD of between 10% and 15% percent of the symbol rate. For older installed optical fibers the typical PMD coefficient can be as high as 1 ps/ √ km. But modern optical fibers can have a much lower PMD value, in the order of 0.05 ps/ √ km [54]. The lower 20 2.3. Polarization of light PMD results mainly from improvements in the manufacturing process, such as fiber spinning during the drawing stage of fiber manufacturing [55]. Due to the improvements in fiber PMD, the PMD-related penalties in state-of-the-art transmission systems are often dominated by PMD in the dispersion compensation and fiber amplifiers. The probability distribution of PMD can, for example, be determined by measuring the change in DGD over either time or frequency and an overview of PMD measurement techniques can be found in [56]. 2.3.2 Second-order polarization mode dispersion The change in SOP under the influence of fiber birefringence is wavelength dependent. Using the PMD vector the frequency derivative of the Stokes vector S is defined as, S ω = ∂S ∂ω =τ S. (2.17) This describes how S rotates over the Poincar´ e sphere when the frequency is changed. Using S ω it can be shown that with a change in frequency the output PMD vector rotates around the PSP’s, where the magnitude of the DGD determines the rate of rotation. When the PMD vector is aligned with the PSP’s there is no rotation on the Poincar´ e sphere, and the PMD consists only of the DGD. On the other hand, when S is launched in between the PSP’s the rotation angle is maximized because τ S has its largest value. The magnitude and the orientation of the PMD vector change with wavelength and Equation 2.17 applies only for a narrow wavelength range. The change in the PMD vector with wavelength re- sults in higher-order PMD, which refers to all orders of PMD excluding first-order PMD (DGD). We limit here the description of higher-order PMD to second-order PMD (SOPMD), which is the most important contribution to higher-order PMD for WDM transmission systems. The change of the PMD vector with wavelength can be described by a Taylor expansion of the PMD vector around a carrier frequency ω 0 [49]. The first frequency derivative describes SOPMD, which is then denoted by, τ ω = dτ dω =∆τ ω ˆ p+∆τ ˆ p ω , (2.18) where the subscript ω denotes differentiation with respect to frequency. The first term of the SOPMD expression denotes the change of the DGD with wavelength (∆τ ω ), which is known as polarization chromatic dispersion (PCD). The second term denotes the change of the PSP with frequency ( ˆ p ω ) and describes the depolarization of the signal. When visualized on the Poincar´ e sphere the PSP’s would trace out a random path with frequency, due to depolarization. Similar to the DGD variance, the average PCD in [ps 2 ] is related to the square of the average PMD, <∆τ ω >≈0.5831 <∆τ > 2 . (2.19) The average SOPMD depolarization component is equal to zero which follows directly from the definition of a vector in normalized stokes space. The variance of the statistical distribution of both PCD and the depolarization component of the SOPMD in [ps 4 ] can be described by [47], var(<∆τ ω >) = 3π 2 64 <∆τ > 4 , var(< p ω >) = π 2 192 <∆τ > 4 . (2.20) 21 Chapter 2. The fiber-optic transmission channel This shows that the SOPMD variance is related to the fourth power of the average DGD. SOPMD can be particulary important for higher symbol rates (e.g. 40 Gbaud), because of the broader spectral width of the signal. Compared with the impact of DGD, the influence of SOPMD is normally small for lower symbol rates (e.g. 10 Gbaud). However, the influence of SOPMD can increase considerably for high average PMD, due to the fourth power dependence between SOPMD variance and average DGD. This can be of particular importance for optical transmis- sion systems that use PMD compensation. 2.3.3 Polarization dependent loss Polarization dependent loss (PDL) refers to the polarization dependence of the insertion loss. It mainly occurs in in-line optical components, such as isolators and couplers. It results in a change of the optical power in the transmission link, which depends on the random evolution of the SOP over time, frequency and along the fiber. The PDL at the end of the transmission link is therefore statistically distritbuted, and the worst-case cumulative PDL is normally much lower than the added PDL of all components in the link. In the remainder of the thesis we assume 3-dB of PDL as a realistic figure for a long-haul transmission link. The polarization dependent change in optical power causes depolarization, as both PSP’s are no longer orthogonal to each other, and can result in fluctuations in the OSNR. The OSNR consists of both ASE polarized parallel to the signal and ASE polarized orthogonally to the signal. The influence of ASE orthogonal to the signal is minimal as it does not coherently interfere with the optical signal. However, in the presence of severe PDL, the noise emitted in the orthogonal polarization can become polarized parallel to the signal, which causes an OSNR penalty [57]. The amount of average PDL that results in a penalty of 1 dB (with probability of 99.9%) due to PDL-induced OSNR fluctuations is approximately 3 dB [58, 59]. PDL further impacts the probability distribution of DGD and SOPMD, which can cause an increase in DGD and SOPMD related impairments. But as reported by Shtaif and Rosenberg in [59], it requires unrealistically high values of PDL before a noticeable penalty occurs. The impact of PDL is more significant for modulation formats which use the SOP to transmit information, or which periodically change the SOP to enhance the nonlinear tolerance. This is discussed in more detail in Section 7.3.4. 2.4 Nonlinear transmission impairments Optical fibers are essentially a nonlinear guiding medium for electromagnetic waves at deep in- frared wavelengths. Although silica is only a weakly nonlinear medium, the nonlinear properties of optical fiber are important to consider. This results from the high confinement of the propagat- ing electromagnetic waves to the core of a single-mode optical fiber. For SSMF, the effective area of the fiber core is typical 85 µm 2 and it is even smaller for fiber types such as DCF or NZDSF. 22 2.4. Nonlinear transmission impairments For optical powers in the mW range, the light intensities within the fiber’s core are then in the MW/m 2 range. For such intensities, the nonlinear properties of optical fiber become important. This is especially the case for long-haul optical transmission links, where nonlinear impairments add up over long propagation distances. There are three types of nonlinear processes that are important for optical transmission systems. The first type are the nonlinear processes where there is no energy transfer between the optical field and the dielectric medium. Such nonlinear processes are called non-resonant and can be described as an intensity dependent variation in the refractive index of the silica fiber. This change in the refractive index of a fiber is known as the Kerr effect, discovered in 1875 by John Kerr. The most important Kerr nonlinear processes are self-phase modulation (SPM) which is discussed in Section 2.4.2, cross phase modulation (XPM, Section 2.4.3), cross-polarization modulation (XPolM, Section 2.4.4), four-wave mixing (FWM, Section 2.4.5) and intra-channel XPM and FWM (Section 2.4.6). The second type of nonlinear processes describes the nonlinear interaction between signal and noise, also known as nonlinear phase noise. The impact of nonlinear phase noise on optical transmission systems is discussed in Section 2.4.7. The third type of nonlinear processes are known as the resonant processes or non-elastic scattering processes. In non-elastic processes the optical field transfers a part of its energy to the dielectric medium. The most important non- elastic scatting processes, stimulated raman scattering (SRS) and stimulated Brillouin scattering (SBS) are discussed in Section 2.4.8. 2.4.1 Pulse propagation The Schr¨ odinger equation, proposed by Erwin Schr¨ odinger in 1926 describes the space- and time-dependence of a quantum mechanical system and plays therefore a central role in quantum mechanics. The nonlinear Schr¨ odinger equation (NLSE) is related to the Schr¨ odinger equation used in quantum mechanics and models the evolution of a (single polarization) optical field E(z, t) in an optical fiber [42]. It can be written as: ∂E ∂z = − α 2 E .¸¸. attenuation − j β 2 2 ∂ 2 E ∂T 2 . ¸¸ . dispersion + β 3 6 ∂ 3 E ∂T 3 . ¸¸ . dispersion slope + jγ[E[ 2 E . ¸¸ . Kerr nonlinearities (2.21) Where E is the complex envelope of the optical field, z the propagation distance in [km], T = t −β 1 z is the time measured in a retarded frame and α is denoted in [Np/km]. The term jγ[E[ 2 E represents the nonlinear contribution to the NLSE, which is proportional to the power of the optical field times the nonlinear coefficient γ. The nonlinear coefficient can be derived from the wave equation, which describes the propagation of light through an optical fiber and is denoted by, ∇∇E(z, t) =− 1 c 2 ∂ 2 E(z, t) ∂t 2 −µ 0 ∂ 2 P(z, t) ∂t 2 , (2.22) 23 Chapter 2. The fiber-optic transmission channel where ∇ is the vector differential operator, E(z, t) the electrical field vector and P(z, t) the dielec- tric polarization vector. When the optical frequency of the signal is far away from the resonance frequency of the medium (in this case silica) the dielectric polarization vector P(z, t) can be described as a power series of the electrical field vector E(z, t). P(z, t) = ε 0 (χ (1) E(z, t) +χ (2) : E 2 (z, t) +χ (3) . . .E 3 (z, t) +...), (2.23) where ε 0 is the vacuum permittivity and χ (n) is the n th order susceptibility, a tensor of order n+1. The first order susceptibility χ (1) determines the linear behavior of an optical fiber. The second order susceptibility χ (2) vanishes for optical fibers because SiO 2 is a symmetric medium. How- ever other materials can have a strong second order susceptibility. For example, the nonlinear processes that enables optical phase conjugation as discussed in Section 3.6, are related to χ (2) . The nonlinear effects that play a role in optical transmission links are included through the third order susceptibility χ (3) . Higher order susceptibility are small and can be neglected. When an intense pulse travels through an optical fiber, it changes the refractive index of the fiber. The dependence of the refractive index on the power of the optical field is denoted by, ¯ n(ω, [E[ 2 ) = n 0 (ω) +n 2 [E[ 2 /A e f f , (2.24) where [E[ 2 in [W] is the power of the optical field in the fiber, A e f f in [m 2 ] the effective mode area, n 0 the linear refractive index and n 2 in [m 2 /W] the nonlinear contribution to the refractive index. The linear refractive index is related to the first order susceptibility χ (1) by: n 0 = _ 1+Re¦χ (1) ¦. (2.25) The nonlinear contribution to the refractive index depends on the third order susceptibility χ (3) and the linear refractive index, n 2 = 3 8n 0 Re¦χ (3) xxxx ¦. (2.26) The nonlinear refractive index is a material parameter which is related to the chemical composi- tion of the optical fiber. For silica fiber it is approximately n 2 = 2.3 10 −20 m 2 /W, but this value is slightly higher for fiber doped with GeO 2 [42]. As a smaller core area results in stronger con- finement of the light, the nonlinear interaction in an optical fiber depends also on the effective core area A e f f in [µm 2 ]. The nonlinearity coefficient γ in [km −1 W −1 ] combines the nonlinear refractive index and the effective core area of the fiber in a single coefficient. γ = 2π n 2 λ A e f f . (2.27) The nonlinearity coefficient for SSMF and a wavelength around 1.5 µm is γ = 1.3 km −1 W −1 . In highly nonlinear fibers for nonlinear signal processing the nonlinearity can be as high as γ = 21 km −1 W −1 [60] while for a photonic crystal fibers this value can reach γ = 640 km −1 W −1 [61]. Due to fiber attenuation, the influence of fiber nonlinearities is not evenly divided over the fiber length but the majority of the nonlinear interaction takes place in first part of the fiber. This can 24 2.4. Nonlinear transmission impairments be denoted by the effective length of the fiber, which has an asymptotic behavior for increasing fiber length. L e f f = 1−exp(−αL) α , (2.28) where α is defined in [Np/km]. For long fibers this van be approximated with L e f f ≈ 1/α. For example, for a fiber attenuation of 0.2 dB/km and a fiber span of 100 km the effective length is equal to 21.5 km. The signal power as a function of the transmission distance is also referred to as the power map. Because nonlinear impairments results from the combined impact of fiber nonlinearities and chromatic dispersion, the asymmetric power map in a fiber has a strong impact on the dispersion map, i.e. where along the fiber the chromatic dispersion is compensated. This is discussed in more detail in Section 3.3.1. 2.4.2 Self-phase modulation The nonlinear change in the refractive index causes an intensity dependent nonlinear phase shift, which is referred to as self-phase modulation (SPM). The impact of SPM can be analytically studied using the NLSE in the absence of chromatic dispersion. In this case Equation 2.21 reduces to ∂E ∂z = − α 2 E .¸¸. attenuation + jγ[E[ 2 E . ¸¸ . Kerr nonlinearities . (2.29) This equation can be solved analytically, which results in, E(z, T) = E(0, T) exp(− αz 2 ) exp( jφ SPM (z, T)) (2.30) where E(0, T) is the complex field amplitude at z =0 and the SPM induced nonlinear phase shift is defined as φ SPM (z, T) = γ[E(0, T)[ 2 1−exp(−αz) α . (2.31) The maximum nonlinear phase shift is obtained after propagation over length L and for a peak power P 0 at the center of the pulse (T = 0), Equation 2.31 then reduces to, φ SPM,max = γP 0 L e f f . (2.32) Equation 2.31 shows that the nonlinear phase shift changes across the pulse because different parts of the pulse have a different intensity, this results in a SPM-induced chirp, which causes pulse broadening. The combined effect of SPM-induced nonlinear chirp and chromatic dispersion results in am- plitude distortions. The SPM-induced nonlinear chirp shift the leading edge of a pulse to lower frequencies (red-shift) and the trailing edge of pulse to higher frequencies (blue-shift). In the presence of chromatic dispersion, the red-shifted and blue-shifted parts of the pulse travel at a different speed. When two pulse components with different frequency are overlapping they 25 Chapter 2. The fiber-optic transmission channel interfere, which causes amplitude distortions. Unlike chromatic dispersion, the nonlinear SPM- induced chirp cannot be compensated as this would require a material with a negative Kerr effect. As these amplitude distortions are dependent on the signal power, they are commonly referred to as nonlinear impairments. The combined effect SPM-induced nonlinear chirp and chromatic dispersion can be used to re- duce the impact of nonlinear impairments. For a positive chromatic dispersion coefficient (D>0) the nonlinear and dispersion-induced chirp have opposite signs, and therefore (partially) cancel each other out. This can be used to reduce the impact of SPM by appropriately choosing the residual chromatic dispersion at the receiver, which is known as post-compensation [62]. Figure 2.8: Eye diagrams showing the impact of SPM after 100-km SSMF with 15-dBm input power; (a) linear transmission (b) nonlinear transmission, no residual dispersion and (c) nonlinear transmission, 600-ps/nm residual dispersion. Figure 2.8 depicts an example of SPM-induced signal distortions. The eye diagrams show trans- mission over a 100-km SSMF span (γ = 1.3 km −1 W −1 , D = 17 ps/nm/km) with a 15-dBm input power. Figure 2.8b shows the impact of SPM through overshoots near the edge of the pulse. When the SPM induced phase shift is partially compensated with 600-ps/nm of chromatic dis- persion (Figure 2.8c) nearly the same eye opening is obtained as in the absence of nonlinear impairments. The balance between chromatic dispersion and SPM induced chirp can also be used to construct transmission links where the signal propagates undistorted by chromatic dispersion or fiber non- linearity [42]. This is know as soliton propagation and was first demonstrated by Mollenauer et. al. in 1980 [63]. Ideally, this would require a loss-less fiber as the fiber attenuation destroys the balance between chromatic dispersion and SPM. However, soliton propagation is also possible for lossy fiber, although it requires small amplifier spacings. Soliton propagation has been an extensive field of research throughout the 1990’s [64, 65] as it allows for error-free transmission over Trans-oceanic distances. But a drawback of transmission systems using soliton propagation is that they require a low chromatic dispersion coefficient for high bit rates, which increased inter-channel impairments in WDM transmission system [66]. In WDM transmission systems it is therefore preferable to use in-line dispersion management, which is also known as dispersion- managed soliton transmission [67]. 26 2.4. Nonlinear transmission impairments 2.4.3 Cross-phase modulation Cross phase modulation (XPM) describes the nonlinear phase change through the Kerr effect that results from the interaction with another optical pulse at a different wavelength. There is only a distinction between SPM and XPM in the case both pulses have a clearly separated spectrum, as is the case in WDM transmission systems. In Equation 2.33 the refractive index is denoted a function of two co-propagating wavelength channels [42]. ¯ n(ω, [E k [ 2 k=1,2 ) = n 0 (ω) +n 2 ([E k [ 2 +B[E 3−k [ 2 )/A e f f . (2.33) where B is a measure for the difference in polarization between the two channels. When both channels have the same polarization B is equal to 2 and when they are orthogonally polarized B is equal to 2/3. The factor two stems from the number of terms of the χ (3) susceptibility that contribute to the nonlinear polarization rotation (Equation 2.23), which double for two distinct optical frequencies compared to the single (degenerate) case [42]. The factor 1/3 results from the weaker interaction between two orthogonal polarizations. Neglecting chromatic dispersion results in expression 2.34 for the total nonlinear phase shift induced through SPM and XPM when two channels are co-propagating, φ k (z) = γ([E k (0)[ 2 +c[E 3−k (0)[ 2 ) 1−exp(−αz) α . (2.34) When two pulses at different wavelengths propagate along the fiber perfectly overlapping each other (in the absence of chromatic dispersion) the impact of XPM is similar to SPM. The XPM induced nonlinear phase shift is however more detrimental when the two pulses at different wave- lengths are partially overlapping in time. One part of the pulse will experience a nonlinear phase shift whereas the other part of the pulse will be unaffected. The nonlinear phase shift interacts with chromatic dispersion along the link, which converts the phase shifts into amplitude distor- tions. Chromatic dispersion decreases the XPM induced nonlinear phase shift as both channels have a different group velocity and therefore walk-off from each other. Consider the nonlinear phase shift that a pulse at ω 1 imposes on a pulse at ω 2 . The faster the two pulses walk-off, the smaller the difference in nonlinear phase shift will be across the pulse at ω 2 . In the extreme case, both pulses walk-off fast enough that the nonlinear phase shift is nearly constant across the pulse and the impact of XPM diminishes. The XPM efficiency is therefore related to the walk-off length L W in [m]. L W = T 0 [β 12 −β 11 [ ≈ T 0 [β 2 [∆ω , (2.35) where β 1k is the group velocity for the k th co-propagating pulse with k =1, 2, ∆ω is equal to [ω 1 − ω 2 [ and proportional to the difference in wavelength. The walk-off length is further dependent on the symbol period T 0 . This implies that impact of XPM decreases both for higher chromatic dispersion and a higher symbol rate. XPM is therefore most detrimental for narrow channels spacing or low dispersion fiber [68, 69]. For example, in an optical transmission system with 27 Chapter 2. The fiber-optic transmission channel SSMF and a 10-Gb/s symbol rate, the nonlinear impairment is XPM dominated for a 25-GHz WDM channel spacing [70] and SPM dominated for a 100-GHz WDM channel spacing. The reduced XPMefficiency between neighboring WDMchannels with an orthogonal SOP is ex- ploited in polarization interleaved transmission systems [71, 72], which reduces the XPM caused by the nearest neighbor channels. However, polarization interleaving complicates system design as it requires the transmitter to use polarization maintaining components up to the point where the orthogonally polarized WDM channels are multiplexed. Further techniques to reduce the impact of XPM-induced nonlinear impairments are optimization of the dispersion map (see Sec- tion 3.3.1) and shifting or scrambling the relative timing between adjacent WDM channels with optical delay lines [73]. In the context of optical or electrical equalization of nonlinear impairments there is a further significant difference between SPM and XPM. In the case of SPM, the source of the impairment are trailing or leading pulses at the same wavelength. The source of the impairment is thus known to an equalizer with memory, which can therefore (partially) compensate for it [74, 75]. For XPM, the source of the impairment are neighboring WDM channels that are unknown to any (practical) equalizer. In the context of equalization, XPM induced impairments therefore appear as noise. 2.4.4 Cross-polarization modulation Cross-polarization modulation (XPolM) is an extension of SPM when the two orthogonal polar- izations in the fiber are considered. Nonlinear interaction between both polarization components at the same wavelength results in coherent coupling, which can be considered as a XPM-like ef- fect. However, both polarization components carry a portion of the same signal and XPolM has therefore a similar impact as SPM [42]. This is evident by considering the nonlinear contribution to the refractive index ∆n x and ∆n y for a two-polarization model, ⎧ ⎨ ⎩ ¯ n(ω, [E x [ 2 ) = n 0 (ω) +n 2 ([E x [ 2 + 2 3 [E y [ 2 ) ¯ n(ω, [E y [ 2 ) = n 0 (ω) +n 2 ([E y [ 2 + 2 3 [E x [ 2 ). (2.36) Equation 2.36 shows that the strength of XPolM between orthogonal polarization components is a factor 2 3 of the SPM strength when only a the single polarization is considered. However, we can also observe from Equation 2.36 that the refractive index of both polarizations components combined (i.e. ¯ n(ω, [E x [ 2 )+¯ n(ω, [E y [ 2 )) is independent of the SOP. This is evident by computing the magnitude of the nonlinear refractive index for, respectively, E x = 1, E y = 0 and E x = E y = 1/2 √ 2. The total nonlinear phase shift in a single WDM channel is therefore independent of the SOP. The impact of XPolM becomes more detrimental for multiple co-propagating WDM channels. As an example we assume that a pulse train propagates at a frequency ω 1 with its power equally divided over the two orthogonal polarizations E x = E y = 1/2 √ 2. The SOP of a second co- propagating pulse train at a frequency ω 2 is such that all power propagates in one of the polari- 28 2.4. Nonlinear transmission impairments zation components E x = 1, E y = 0. The nonlinear phase shift induced on the E y component of a pulse at ω 1 is then smaller by a factor 3 compared to the E x component, which follows from Equation 2.33. This results in a change of the relative phase difference between both polariza- tion components E x and E y of the pulse, which in turn changes the SOP. Because the SOP change depends on the pulse train at ω 2 , it results in a noise-like change of the SOP and, hence, depolar- ization. This depolarization can severely degrade the efficiency of PMD compensation [76]. In the presence of PDL, the depolarization is converted into amplitude fluctuations. XPolM is particulary detrimental when a polarization sensitive receiver is used, as the depolar- ization translates into amplitude distortions when a single polarization is filtered out [77, 78]. In particular for polarization-multiplexed transmission (Chapter 7) this results in crosstalk between the two polarization tributaries. 2.4.5 Four-wave mixing Four-wave mixing (FWM) is a parametric nonlinear process which involves interaction between four optical waves, in this case different WDM channels, hence the name four-wave mixing. Two or three photons are annihilated and new photons are created at difference frequencies such that the net energy and momentum are conserved. The FWM efficiency depends on the frequency and phase matching among the four optical waves. There are two distinct four wave mixing processes. In the first process three photons are annihilated and a new photon is created at the sum frequency of the three photons (for exam- ple third-harmonic generation). The phase matching condition for this process is hard to satisfy in an optical fiber and is therefore not of significance to optical transmission systems. The second mixing process annihilates two photons and creates two photons. The frequency (left) and phase matching (right) conditions are denoted in Equation 2.37 [79]. ω 1 +ω 2 = ω 3 +ω 4 , n 1 ω 1 +n 2 ω 2 = n 3 ω 3 +n 4 ω 4 . (2.37) Where ω j is the frequency and n j the refractive index of the fiber at this frequency. The phase condition is most easily satisfied in the case ω 1 = ω 2 , which is also referred to as degenerate FWM. In this case, FWM generates two photons at the Stokes and anti-Stokes wavelengths of ω 2 , which are located at frequencies ω 3 and ω 4 . The Stokes shift ω 2 −ω 3 =ω 4 −ω 2 depends on the fiber parameters. When two WDM channels at ω 2 and ω 3 are co-propagating this results in FWM products at ω 1 = 2ω 2 −ω 3 and ω 4 = 2ω 3 −ω 2 . This is illustrated in Figure 2.9. For equally spaced WDM channels (e.g. on a 50-GHz wavelength grid) FWM has the worst impact, as the FWM products result in crosstalk for other co-propagating channels. Chromatic dispersion decreases the FWM efficiency considerable as the difference in phase ve- locity causes the phase matching condition to be only satisfied over a short transmission distance. This decreases FWM efficiency considerable and is therefore only the dominating Kerr nonlinear impairment for small WDM channel spacings and low dispersion fiber, such as DSF [80, 81]. A 29 Chapter 2. The fiber-optic transmission channel FWM Ȧ 2 Ȧ 3 Ȧ 2 Ȧ 3 Ȧ 4 Ȧ 1 Figure 2.9: Principle of four-wave mixing. potential solution to reduce the FWM efficiency is the allocation of unequal channel spacings, but this significantly reduces the number of allowable WDM channels [82, 83]. The FWM ef- ficiency is also reduced when the polarization of the neighboring WDM channels is orthogonal, as is the case for polarization interleaved transmission systems [71, 72] or when using the higher dispersion coefficient in the L-band [84]. For C-band transmission systems using SSMF, the impact of FWM can generally be neglected. 2.4.6 Intra-channel XPM and FWM The nonlinear interaction that occurs between subsequent pulses at the same wavelength is very similar to XPM and FWM, and is therefore referred to as intra-channel XPM and FWM. Intra- channel XPM (IXPM) and intra-channel FWM (IFWM) are a subdivision of SPM, with pure single pulse SPM sometimes referred to as isolated SPM (ISPM). The XPM and FWM processes explained in the previous section are inter-channel nonlinear effects, which describe the inter- action between co-propagating WDM channels. Intra-channel XPM and FWM occur mainly in transmission links with high dispersive fiber, as a single pulse is spread out over multiple time slots. IXPM and IFWM are particulary important for transmission at bit rates of 40-Gb/s or above and high dispersive fiber such as SSMF [85, 86]. For such bit rates, the signal waveforms evolves very fast when propagating along the fiber, which averages out the nonlinear interaction between symbols from the same wavelength channel as well as the interaction between co-propagating WDM channels. This transmission regime is known as pseudo-linear because, similar to a linear transmission link, the optimum residual dispersion is close to zero. Pseudo-linear transmission occurs when the normalized nonlinear length (Equation 2.28) is significantly larger than the normalized dispersion length (Equation 2.8). IFWM results in energy transfer between subsequent time slots [85, 87]. This effect is the most evident for amplitude modulated signals, as it creates ghost pulses in the time slots where a ’0’ is transmitted. The IFWM induced energy transfer further results in amplitude jitter in the ’1’ symbols. This is illustrated in Figure 2.10 where a ’0’ ’1’ ’1’ ’0’ sequence is transmitted over high dispersive fiber. Along the fiber the signal is dispersed and the pulses are spread out beyond their respective time slots. At the same time the Kerr effect causes both pulses interact with each other, which results in two FWM products. When subsequently the accumulated dispersion 30 2.4. Nonlinear transmission impairments Ȧ t t t t E t E t E t t E Ghost pulses FWM Chromatic dispersion Kerr nonlinearity Chromatic dispersion compensation Ȧ Ȧ Ȧ 0 1 1 0 0 1 1 0 Figure 2.10: Impact of intra-channel FWM (after [85]). is compensated at the receiver, the two FWM products appear as ghost pulses in the time slots where a ’0’ is originally transmitted. IXPM generates a frequency shift due to the intensity change of the overlapping pulses. Through the interaction with chromatic dispersion this frequency shift is subsequently converted into tim- ing jitter [86]. The impact of intra-channel XPM and FWM impairments in high-dispersive transmission links can be reduced through a symmetric transmission link. This is, for exam- ple, possible by evenly splitting the chromatic dispersion compensation between the transmitter and receiver [88] In addition, mid-link optical phase conjugation allows for a symmetrical link design, as discussed in Section 3.6. 2.4.7 Nonlinear phase noise Nonlinear phase noise results from the interaction between the optical signal and ASE induced power fluctuations. These power fluctuations are transformed into phase noise through interac- tion with the Kerr effect. Nonlinear phase noise was first described by Gordon and Mollenauer in 1990 and is therefore commonly referred to as the Gordon-Mollenauer effect [89]. It is only of significant importance for modulation formats that encode the information in the phase of the optical signal. Ideally, a phase modulated signal has a regular pulse shape and each pulse contains an equal amount of optical power. The nonlinear phase shift introduced through the Kerr nonlinearity is then the same for each pulse. When ASE from optical amplifiers is added to the signal along the transmission link, each pulse interferes constructively or destructively with the ASE. This results in a different power for each pulse. When the signal propagates further along the link the pulses then experiences a difference in nonlinear phase shift, which is referred to as SPM induced nonlinear phase noise [90]. Figure 2.11 illustrates this origin of nonlinear phase noise through the interaction of ASE with the Kerr effect. Several methods have been demonstrated to reduce or cancel out the impact of nonlinear phase, including optical phase conjugation [91, 92] 31 Chapter 2. The fiber-optic transmission channel Intensity n 2 Kerr effect ASE Re(E) I m ( E ) 10 -6 10 -5 10 -4 10 -3 P r o b a b i l i t y BER = 10 -4 Re(E) I m ( E ) 10 -6 10 -5 10 -4 10 -3 P r o b a b i l i t y Figure 2.11: Impact of nonlinear phase noise on optical transmission systems. and semiconductor optical amplifier based optical regeneration [93]. The constellation diagram in Figure 2.11 shows the typical nonlinear phase noise induced ying-yang shape. This correlation between signal power and nonlinear phase shift can be used to reduce the impact of SPM induced nonlinear phase noise. For example, in the receiver a phase shift can be applied to each symbol that is dependent on the intensity of the symbol. This is possible through either optical [94, 95] or electronic [96] means. Alternatively, signal processing in the receiver could take the ying-yang shape into account when making a decision on the data [95]. Nonlinear phase noise can further result from interaction through XPM. In this case the ASE that is added along the transmission link changes the power level of the co-propagating channels, which either enhances or reduces the XPM-induced nonlinear phase shift. The difference in XPM strength in turn translates into nonlinear phase noise. For XPM induced nonlinear phase noise, there is no correlation between signal power and phase shift in the constellation diagram, which makes it more difficult to compensate for. The nonlinear phase noise strength is dependent on both the fiber chromatic dispersion coefficient as well as the OSNR along the transmission link [95]. For high dispersive fiber, the power in a symbol period changes rapidly along the fiber which averages out the nonlinear phase shift contribution. The impact of nonlinear phase noise is also strongly dependent on the OSNR along the transmission link, i.e. the path-averaged OSNR. As the OSNR requirement increases for high bit rates, so will the path-averaged OSNR. This reduces the impact of nonlinear phase noise as the ASE power is not large enough to make a significant contribution to the total nonlinear phase shift. Nonlinear phase noise is therefore mainly the dominating impairment for D(Q)PSK modulation at < 20-Gb/s bit rates or transmission over low dispersion fiber, such as DSF. 32 2.4. Nonlinear transmission impairments 2.4.8 Non-elastic scattering effects The second class of nonlinear effects important to optical transmission systems are the non- elastic scattering effects. Non-elastic scattering effects depend on the interaction between the optical pulses and the silica molecules of the optical fiber. The optical pulses transfer a part of the photon energy to the dielectric medium. The most important non-elastic scatting effects in optical transmission are stimulated raman scattering (SRS) and stimulated Brillouin scattering (SBS). When a photon collides with a silica molecule of the fiber, it normally scatters through elastic Rayleigh scattering, which does not transfer any energy to the silica molecule. However, for a small fraction of the photon-molecule collisions (∼ 10 −6 ) Raman scattering occurs. The origin of Raman scattering is related to the imaginary part of the χ (3) susceptibility (see Equation 2.23, whereas the Kerr nonlinearities have their origin in the real part. Raman scattering transfers a part of the photon energy to the silica molecule which makes a transition to a higher-energy vi- brational state. In the process a lower frequency photon is generated. The frequency shift of the generated photon is dependent on the propagating material. For silica, which is not a crys- talline material, a continuous spectrum is created with a peak value around 13.2 THz ≈ 100 nm downshifted from the original frequency, this is called the Stokes band. Raman scattering can result in stimulated emission when co-propagating WDM channels are present within the Raman bandwidth. SRS is the most effective when both channels have the same polarization and the wavelength difference is close to the 100 nm Raman gain peak. The SRS efficiency dependent on the fiber type and the intensity of the incident pulse [97]. In par- ticular when the optical power is above a critical power, the SRS threshold, the Stokes band will build up nearly exponentially. For long-haul optical transmission systems the input power per channel is generally lower than the SRS threshold, hence SRS-induced impairments are normally not significant. However, SRS can be exploited to create Raman amplifiers [98], which use the fiber as a gain medium by launching a strong pump signal in the fiber. Raman amplifiers are discussed in more detail in Section 3.2.2. SRS Ȧ 1 Ȧ 2 Ȧ 3 Ȧ 4 Ȧ 1 Ȧ 2 Ȧ 3 Ȧ 4 Figure 2.12: Principle of Stimulated Raman Scattering. In WDM transmission, SRS can also occur between neighboring channels, which results in un- wanted crosstalk. This transfers energy from the high frequency channels to lower frequency channels and can result in bit-dependent [99] and time averaged SRS crosstalk [100]. Bit- dependent crosstalk behaves similarly as XPM and its impact is therefore relatively small for fibers with a high dispersion coefficient [99]. Time averaged SRS crosstalk results in a gain tilt 33 Chapter 2. The fiber-optic transmission channel in the WDM spectrum as depicted in Figure 2.12 [101]. This crosstalk can be reduced in optical transmission systems using dynamic gain equalizers (DGE) along the transmission link. Stimulated Brillouin scattering (SBS) results from the interaction between photons and acoustic waves. An optical signal traveling through the fiber generates an acoustic wave, which in turn modulates the refractive index of the optical fiber in a periodic manner. This periodic variation of the refractive index scatters the light of the incident wave through Bragg refraction. This gen- erates a backwards propagating wave, counter-directional to the optical signal. The virtual Bragg grating is moving with a certain acoustic velocity, which causes a Doppler shift of ∼10 GHz be- tween the backward reflecting wave and the optical signal [42]. The power reflected through SBS increases exponentially when the power is above the SBS threshold. SBS therefore limits the op- tical power that can be launched into the fiber. However, for optical transmission systems SBS is not of significant importance as it nearly vanishes for pulses shorter than several nanoseconds. Phase modulation of the optical signal is also an effective method to reduce the SBS efficiency. 34 3 Long-haul optical transmission systems In long-haul WDM transmission systems there are basically five dominant limitations: OSNR, optical bandwidth, chromatic dispersion, PMD and nonlinear impairments. The tolerance with respect to these limitations scales linearly, or even quadratically, with the bit rate. Hence, to build robust long-haul transmission systems at high bit rates these transmission impairments should be considered and, if possible, compensated. This chapter deals with the design of long-haul optical transmission systems and the required technologies to compensate for the dominant transmission impairments. First of all, in Sec- tion 3.1 the optical transmitter and receiver are discussed. Subsequently, in Section 3.2 the periodic amplification of optical signals is explained. Section 3.3 then describes the chromatic dispersion compensation in long-haul optical transmission systems and the design of dispersion maps. In Section 3.4 the compensation of PMD is briefly treated and Section 3.5 describes the impact of optical-add-drop multiplexing in transparent optical networks. Finally in Section 3.6, optical phase conjugation is discussed as a potential technology to compensate for nonlinear impairments. 3.1 Transmitter & receiver structure An optical transmission link can be defined as the physical medium over which an information carrying optical signal propagates between a transmitter and a receiver. In the transmitter an optical carrier, generally the output of a laser, is modulated with a bit sequence. At the receiver, the optical signal is again converted into an electrical signal using one or more photodiodes. After a binary decision, ideally, the transmitted bit sequence is again obtained. This section 35 Chapter 3. Long-haul optical transmission systems discusses the most common optical modulation principles (Section 3.1.1) and receiver structure (Section 3.1.2). Section 3.1.3 explains the use of forward error correction in optical communica- tion systems. 3.1.1 Optical modulation Optical modulation is the conversion of a signal from the electrical into the optical domain. This can be achieved by a variety of modulation technologies, which include directly modulated lasers (DML), electro-absorption modulators (EAM) and Mach-Zehnder modulators (MZM). In order to realize high-speed modulation an optical modulator should have (1) a high electro-optical bandwidth, (2) low optical insertion loss, (3) not induce undesired frequency chirp in the signal and (4) have a high enough extinction ratio. The extinction ratio is defined as the ratio of the energy in the ’0’ compared to the energy in the ’1’s. Optical modulation can be most easily realized by direct modulation of the laser drive current. A DML is a very cost-efficient modulation technique as it is compact and does not require any further optical components apart from the transmitter laser. Although DMLs have been shown to operate at bit rates up to 40 Gb/s [102, 103] their modulation bandwidth is limited. High-speed modulation of a DML introduces frequency chirp, a residual phase modulation, alongside the desired intensity modulation and reduces the extinction ratio. The frequency chirp broadens the modulated spectrum, which makes it unattractive to use DML in WDM systems. They are today mainly used in low-bit rate applications, e.g. up to 2.5 Gb/s or short-reach 10-Gb/s transmission. In addition, frequency chirp reduces the chromatic dispersion tolerance. A special application of DMLs that is better suited for high-speed modulation is the use of frequency instead of am- plitude modulation. When subsequently a narrowband optical filter is placed after the DML the frequency modulation is converted into intensity modulation with a high extinction ratio [104]. For high-speed modulation, external modulators are generally required as they result in a nearly chirp-free signal. An external modulator switches the incoming continuous-wave laser output ON or OFF, depending on the electrical drive signal applied to the modulator. An EAM mod- ulates the optical field by controlling the absorption of the device material using the externally applied voltage. Modulation with an EAM can result in an optical signal with lower chirp than a DML and a high electro-optical bandwidth can be realized [105]. However, EAMs have a wavelength dependent performance, low extinction ratio (<10 dB typical), high insertion loss (10 dB typical) and a limited optical input power. EAMs mainly find applications in low-cost 10-Gb/s transmitters but have also been used extensively in (single-channel) OTDM transmission experiments. The most widely used device for optical modulation is the MZM, first proposed by Ernst Mach [106] and Ludwig Zehnder [107]. A MZM consists of two 3-dB couplers with two intercon- necting waveguides of equal length to create an interferometer, as show in Figure 3.1. The MZM waveguides are normally made from a Lithium-Niobate (LiNbO 3 ) electro-optic crystal [108], but sometimes other materials are used such as Gallium Arsenide (GaAs) [109], and Indium Phos- phide (InP) [110]. In such an electro-optic crystal the refractive index depends on the applied 36 3.1. Transmitter & receiver structure electric field. An electrical drive signal can therefore modulate the refractive index of the crystal, which in turn changes the velocity of the light propagating through the waveguide. By choosing the electrical drive voltage level appropriately, the interference in the second 3-dB coupler can be either constructive or destructive. The difference in drive voltage which changes the interference from constructive to destructive is known as the V π of the modulator. The two waveguides of a MZM can be modulated separately, which is known as dual-drive operation and which is used in Z-cut modulators. Alternatively, both waveguides can be coupled together, which is known as single-drive operation and which is used in X-cut modulators. A typical V π for a single-drive LiNbO 3 MZM modulator is ∼4 V. In order to amplify the elec- trical drive signal to the required peak-to-peak voltage (V pp ), high power and broadband driver amplifiers are therefore required. In a dual-drive modulator the peak-to-peak voltage swing of the electrical drive signal is reduced by a factor of two when a differential drive signal is applied to both waveguides. This is attractive for high-bit rates as there is a trade-off between the electro- optical bandwidth and the V π of the MZM. A dual-drive modulator, on the other hand, has the drawback that it requires two broadband driver amplifiers to amplify the electrical drive signal to a sufficiently high peak-to-peak voltage. E in E out RZ66 V 0 Quadrature Optical phase = t T r a n s m i t t a n c e Optical phase = 0 Crest Trough (a) (b) Bias RZ50 RZ33 Electrode Waveguide 0 1 2 3 P o w e r ( m W ) -40 -20 0 20 40 Time (ps) 0 1 2 3 P o w e r ( m W ) -40 -20 0 20 40 Time (ps) 0 1 2 3 P o w e r ( m W ) -40 -20 0 20 40 Time (ps) (c) (d) (e) x y z Figure 3.1: (a) Structure of a X-cut MZM, (b) Operation of a MZM for pulse carving, (c-e) RZ eye diagrams for (c) 33%, (d) 50% and (e) 66% pulse carving. AMZMis particulary suitable for long-haul transmission as it has a high extinction ratio (>20 dB typical), low insertion loss (4 dB typical) and is (nearly) wavelength-independent. The MZM can be used to generate several different optical modulation formats, which is described in more detail in Chapter 4. Another application of a MZM is pulse carving, i.e. the conversion of a non-return-to-zero (NRZ) signal into a return-to-zero (RZ) pulsed signal. RZ pulse carving is widely used for different optical modulation formats as it is less sensitive to imperfections in the transmitter. In high bit rate optical transmitters this can help to reduce the often stringent requirement on, for example, the electro-optical bandwidth of the modulator and driver amplifier voltage swing. 37 Chapter 3. Long-haul optical transmission systems Table 3.1: DRIVE SIGNAL PROPERTIES FOR RZ PULSE CARVING WITH A MZM. RZ pulse carving Modulator Drive signal Drive duty cycle bias voltage voltage swing frequency 33% crest 2 V π 0.5 symbol rate 50% quadrature V π symbol rate 66% trough 2 V π 0.5 symbol rate The impact of transmission impairments changes significantly when comparing NRZ and RZ modulation. Because of its more regular pulse shape, RZ modulation improves the tolerance against nonlinear signal impairments. Especially for a 40-Gb/s symbol rate, i.e. transmission limited by intra-channel nonlinear impairments, there is a clear improvement in nonlinear toler- ance [111]. The main drawback of RZ modulation is the more complex transmitter structure as well as broadening of the optical spectrum. This reduces the tolerance against narrowband fil- tering, which is a significant disadvantage for spectrally efficient optical transmission or optical transmission systems with cascaded optical add-drop filtering. In addition, the broadened optical spectrum reduces the chromatic dispersion tolerance somewhat [112]. RZ pulse carving, on the other hand, improves the PMD tolerance as the ISI between adjacent bits is reduced [112, 113]. Using a MZM, three different RZ pulse shapes can be generated, as depicted in Figure 3.1. RZ pulse carving with a 50% duty-cycle is generated by driving a MZM with a sinusoidal drive signal at a frequency equal to the symbol rate. Both 33% or 66% duty-cycle are realized by driving a MZM with a sinusoidal drive signal at half the symbol rate. The drive frequency, bias voltage and drive signal voltage swing are summarized in Table 3.1. Note that RZ modulation with a 66% duty-cycle, in addition to the amplitude modulation, also encodes a 180 o phase shift between consecutive symbols. It is therefore often referred to a carrier-suppressed return-to-zero (CSRZ). RZ modulation with a duty-cycle below 33% is possible by cascading two pulse carvers with a time offset between the two drive signals. This has been used in high-bite rate OTDM transmission experiments [114]. The narrower the duty-cycle of the RZ pulse, the broader the optical spectrum and the higher the peak-to-average power. The change in pulse shape is evident from Figure 3.1c-e. Because of the more narrow optical spectrum, RZ modulation with a high duty-cycle is often preferred in WDM transmission. 3.1.2 Optical receivers The most common configuration of an optical receiver is depicted in Figure 3.2. It can be sub- divided in the lower speed optical receivers (up to ∼10-Gb/s) and high bit-rate receivers for 40-Gb/s transmission systems. Both types of optical receiver use a high-speed photodiode to convert the optical signal to the electrical domain. As a photodiode only detects the power enve- lope of the optical, any phase information is discarded from the signal. There are several types of high-speed photodiodes, but the most common one found in optical receivers is a p-i-n pho- todiode. A p-i-n photodiode is a semiconductor device that contains a p −n junction with an 38 3.1. Transmitter & receiver structure undoped (intrinsic) layer between the n (negative) and p (positive) layers. When incident light is absorbed in the depletion region of the intrinsic layer, a photocurrent is generated. Photodiodes for the 1.5µm - 1.6µm wavelengths range are normally made from indium gallium arsenide (In- GaAs). The electro-optical conversion in a photodiode cannot detect arbitrary high frequencies, and a photodiode therefore low-pass filters the signal. The electro-optical 3-dB bandwidth of a photodiode should be in excess of 70% of the symbol rate. A photodiode is further characterized by its responsivity in [A/W], which defines the efficiency with which the photodiode converts the optical signal into a photocurrent. Most p-i-n photodiodes have a responsivity of 50%-70%, but high-speed photodiodes often have a somewhat reduced responsivity. CDR PD 10 Gb/s AGC FEC & framing TDC control 40 Gb/s D E M U X CDR FEC & framing D E M U X slow PD PD EDFA Figure 3.2: Optical receiver configuration. For lower speed optical receivers, a transimpedance amplifier is typically used for automatic gain control (AGC). The transimpedance amplifier amplifies the photocurrent, which has typical peak- to-peak voltage of 10 mV for 50Ω termination, and controls the gain such that a constant output voltage is obtained. For high-speed optical receivers, the bandwidth and gain of a transimpedance amplifier can be inadequate. In this case, an optical pre-amplifier is used in the receiver to amplify the signal. In addition, 40-Gb/s receivers require tunable dispersion compensation (TDC) to optimize the accumulated dispersion, this is discussed in more detail in Section 3.3. In the clock and data-recovery (CDR), the receiver is synchronized with the signal in order to sample at the correct time instant within the symbol period. The data recovery then takes a dig- ital decision on the signal. A variable sampling threshold is normally used for data recovery, as the optimum threshold changes under the impact of transmission impairments such as chromatic dispersion and PMD. This threshold can be optimized using a feedback signal from the forward error correction (FEC) that minimizes the BER. Afterwards, FEC decoding is applied to recover errors that occurred in the received sequence and the transmitted data is extracted from the trans- port frame (e.g OTN [optical transport network] framing). The signal is then time de-multiplexed for further processing. 39 Chapter 3. Long-haul optical transmission systems 3.1.3 Forward-error correction For long-haul transmission systems, the signal quality at the receiver is normally too low to ensure error-free transmission (BER < 10 −13 ). For such systems, FEC enables the correction of bit-errors after transmission by encoding the data appropriately at the transmitter. FEC coding also increases the system robustness against signal impairments such as chromatic dispersion and PMD. FEC coding requires that some redundant information is added to the transmitted data, which is referred to as the FEC overhead. In optical communication systems the typical FEC overhead is 7%, although in submarine ultra long-haul transmission a FEC overhead of 25% is normally used. This increases the bit rate, for example, from 10 Gb/s to 10.709 Gb/s. The use of FEC results in a coding gain, which defines the difference in required OSNR for a BER of 10 −13 with and without FEC coding. The highest BER before FEC that can be corrected to a BER below 10 −13 after FEC is typically referred to as the FEC limit. When the bit-errors are not Gaussian distributed but come in error-bursts (e.g. PMD-induced) the FEC code might not be able to correct all bit-errors at the FEC limit. FEC coding therefore interleaves the data before transmission in order to obtain Gaussian-like error statistics after transmission [115]. In optical transmission experiments, the use of FEC is normally assumed by taking into account the 7% required overhead and measuring the transmission performance at the FEC limit. FEC has been used since the 1960s in radio communication, but the first application to fiber-optic transmission systems was reported by Grover in 1988 [116]. The first commercial applications of FEC were submarine optical transmission systems in the early 1990’s [117]. In particular, the Reed-Solomon(RS) code RS(255,239) has been adopted for submarine-transmission systems and has been specified in ITU-T G.975 [118]. This code is known as the first-generation FEC and provides a coding gain of up to 5.8 dB. Nowadays, the most common error correcting codes used in optical transmission are known as second-generation FEC codes. These codes consist of two interleaved codes, where the individual codes can be, for example, RS or Boss-Chaudhuri- Hocquenghem (BCH) codes or a combination of both. Such codes have a code gain of ∼8.5 dB and have been standardized in ITU-T G.975.1 [119]. An overview of FEC in optical transmission systems is given in [120], where also more advanced codes using turbo codes and soft-decision decoding are discussed. For the transmission experiments described in this thesis we assume the use of a concatenated RS(1023,1007)/BCH(2047,1952) code with 7% overhead as defined in ITU-T G.975.1 subclause I.4. This code corrects a 2.23 10 −3 BER before FEC to a 1 10 −13 BER after FEC, a coding gain of 8.3 dB. This code is widely used in transmission experiments and deployed long-haul transmission systems [121]. In some long-haul transmission experiments in the literature a more advanced code is used that achieves a coding gain of 8.8 dB with a 6.69% overhead [122, 123]. This code is defined in ITU-T G.975.1 subclause I.9 and consists of interleaved BCH(1020,988) with 10-fold iterative decoding. A4 10 −3 BERbefore FECis corrected by this code to a 1 10 −13 BER after FEC. 40 3.2. Fiber loss compensation 3.2 Fiber loss compensation As discussed in Section 2.1, optical fiber is a low-loss transmission medium that allows for considerable transmission distances without re-amplification of the signal. However, in order to realize long-haul transmission systems (1,000 km - 3,000 km) periodic amplification is required after each fiber span in order to compensate for fiber loss. The span length varies strongly in deployed transmission systems, but a typical design value is a span attenuation of 21 dB. Depending on fiber quality and splicing losses this translates into a span length between 80 km and 110 km. In between the fiber spans different amplification technologies can be used to compensate for the fiber loss. In this section we discuss doped fiber amplifiers and Raman amplification. 3.2.1 Erbium-doped fiber amplifiers In long-haul optical transmission systems, optical amplification is nearly exclusively used to am- plify the signal in between fiber spans. On of the main advantages of optical amplification over optical-electrical-optical conversion is thats it can amplify the optical signal independently of modulation format and bit rate. In addition, a single amplifier can amplify the full C-band trans- mission window. The most common type of optical amplifiers are Erbium doped fiber amplifiers (EDFA). EDFAs are constructed by doping a single mode fiber with Erbium (Er 3+ ) ions and pumping the fiber with one or more pump lasers. Early work on EDFAs was pioneered by Mears [124] and Desurvire [125] in 1987. A detailed overview of EDFA design and technologies can be found in [126]. The general structure of an EDFA is shown in Figure 3.3a. The actual optical amplification takes place in the Erbium-doped fiber with a typical length of ∼10 meters, which is pumped with light from one or more laser diodes. In Figure 3.3a the fiber is bidirectionally (forward and backward direction) pumped by two laser diodes, which is the most common for optical amplifiers that re- quire a high output power. Either co-directional or counter-directional pumping is also possible when the required output power is not too high. The input signal and output of the pump lasers is combined using a pump combiner, which allows for a low insertion loss. Optical isolators are normally required in optical amplifiers to prevent backreflections. The input isolator prevents light from the counter-directional pump or amplified spontaneous emission (ASE, defined later) to propagate backwards out of the amplifier input. The output isolator prevents that that the out- put light can be reflected back into the amplifier, which could cause lasing. The gain equalizing filter is necessary to ensure that all WDM channels are amplified uniformly and that a flat output spectrum is obtained. Gain equalization can be realized using a variety of filter technologies, such as thin-film filter [127] or long-periodicity fiber Bragg gratings [128]. The wavelength of the pump signal is either around 980 nm or 1480 nm. The energy levels (vibrational states) in Figure 3.3c are not discrete levels but rather a manifold, which is due to the non-crystalline nature of silica. Each energy level that appears as a discrete spectral line in an isolated Erbium ion is split into a manifold when silica glass is doped with the Erbium ions, this 41 Chapter 3. Long-haul optical transmission systems is known as the Stark effect. The Stark effect explains why amplification occurs in a wavelength band rather than at a single wavelength. Pumping with a 1480 nm laser excites the Erbium ions from the ground-state manifold 4 I 15/2 into the 4 I 13/2 manifold, from where they can amplify light in the 1500-nm wavelength region via stimulated emission. In the case of pumping with a 980-nm laser the ions are first exited to the 4 I 11/2 manifold, from where there is a quick (∼1µs) non-radiative transfer (relaxation) to the 4 I 13/2 manifold. The 4 I 13/2 manifold is metastable with a half-time of around 10 ms, which is known as the fluorescence time. This is orders of magnitude longer than the bit rates that are normally used in optical communication systems (i.e. 2.5-Gb/s to 40-Gb/s). An exception to this are systems that use burst-mode transmission where the burst- interval can be longer than the fluorescence time [129]. pump laser (1480 nm, 980 nm) Gain equalizing filter Isolator Er 3+ Pump combiner Isolator Wavelength (nm) G a i n ( d B ) 1530 1560 980 nm pumping 1480 nm pumping Relaxation 4 I 11/2 4 I 13/2 4 I 15/2 Spontaneous emission Stimulated emission IJ = 6.6µs IJ = 10ms (a) (b) (c) Figure 3.3: (a) schematic of an EDFA; (b) gain spectra of a C-band EDFA and (c) energy level diagram of an erbium-doped silica fiber. The principle behind optical amplification is stimulated emission. In stimulated emission, as first described by Einstein in 1917 [130], a photon from the pump signal transfers a part of its energy to the Erbium ion which makes a transition to a higher-energy vibrational state. When a photon from the input signal collides with the Erbium ion it falls back to the lower vibrational state and at the same time releases a duplicate photon with the same properties (frequency, state of polarization). In optical amplification, this process is repeated numerous times which results in an exponential increase in signal power. The typical gain of an EDFA can therefore be in excess of 40 dB. The output power of an EDFA strongly depends on the number of pump lasers and their respective pump powers. A typical value for the EDFA output power is ∼23 dBm, which is generally sufficient to amplify up to 80 WDM channels in the wavelength band between roughly 1525 nm and 1570 nm. As depicted in Figure 3.3b, the EDFA generally exhibits a gain peak around 1530 nm. The spectral gain profile can be flattened by doping the Erbium-doped fiber with co-dopants such as Aluminium Oxide (Al 2 O 3 ) [126], or through the use of gain flattening filters. 42 3.2. Fiber loss compensation Besides stimulated emission, also spontaneous emission occurs in an optical fiber amplifier. In spontaneous emission, an ion in the high energy 4 I 13/2 manifold falls back to the ground state, emitting a photon in the process. In contrast to stimulated emission, the emitted photon has an arbitrary frequency and state of polarization. As the spontaneous emission is in turn also amplified along the optical amplifier, this causes amplified spontaneous emission (ASE). ASE is the most dominant for high gain amplifiers, where a large part of the output signal can consists of ASE. The ASE generated by an optical amplifier is added to the amplified signal, which reduces the OSNR. An optical amplifier can therefore be characterized with its noise figure, which denotes the difference in OSNR between the input and output of the amplifier. A practical C-band EDFA normally has a noise figure between 4 dB and 6.5 dB. Pumping the erbium-doped fiber with a 980-nm laser allows the highest gain efficiency and lowest noise figure. With a 1480-nm pump wavelength a higher power efficiency can be achieved as no transfer to the 4 I 11/2 manifold occurs. Such a transfer reduces the power efficiency, as part of the energy is lost through relaxation when the ion falls back to the 4 I 13/2 manifold. On the other hand, stimulated emission of the 1480-nm pump wave occurs along the Erbium-doped fiber. The fraction of Erbium ions in the exited 4 I 13/2 manifold is therefore much smaller, which reduces the gain efficiency, i.e. the small-signal gain as a function of pump power. As a result, a longer Erbium doped fiber is required which generally results in a higher noise figure. Optical amplifiers for the L-band also used Erbium-doped fiber, but this requires a different optimization of the fiber length (∼ 100 m) and Erbium ion concentration. A single erbium-doped fiber can therefore not amplify both wavelength bands. The EDFA belongs to a broader family of rare-earth doped fiber amplifiers that also includes neodymium, ytterbium, praseodymium, or thulium doped fiber amplifiers [131]. Doping with other rare-earth elements can be used to construct optical amplifiers for wavelengths other than the C- or L-band. Ytterbium doping can further be used to construct Ytterbium-Erbium co-doped double-clad optical amplifiers [132, 133]. In such amplifiers the 980-nm pump is absorbed by the Ytterbium ions, which are excited to a higher vibrational state. The Ytterbium ions subsequently transfer their energy to the Erbium ions. As the Ytterbium doping density can be much larger than the Erbium doping density this allows for a higher amplifier gain. The co-doping is often combined with double-clad amplifiers. A double-clad amplifier pumps the cladding of the fiber to obtain a more equal distribution of the pump power along the fiber length. Such amplifiers can have output powers as high as 33 dBm. In Section 6.5 such an amplifier is used as pump amplifier for phase conjugation. DCM VOA Pre-amp EDFA Booster EDFA next span SSMF Figure 3.4: EDFA structure used in the long-haul optical transmission experiments. Figure 3.4 shows the typical EDFA structure used in the long-haul transmission experiments discussed in this thesis. The received optical signal is first fed into a pre-amplifier stage. A pre- 43 Chapter 3. Long-haul optical transmission systems amplifier EDFA is optimized for high gain and a low noise figure. The pre-amplifier stage can consist of two separate EDFAs with a variable optical attenuator (VOA) in between both ampli- fiers. The VOA is used to dynamically reduce the tilt in the wavelength spectrum, which can either result from SRS along the fiber or the preamplifier amplification itself. After the pream- plifier, generally, a dispersion compensation module (DCM) is used for chromatic dispersion compensation. The signal is then fed to the booster EDFA, which is optimized for high out- put power. The combination of pre-amplifier and booster stage allows the realization of both a low-noise figure and high output power. 3.2.2 Raman amplifiers A Raman amplifier is an optical amplifier based on Raman gain, which results from the effect of SRS (see Section 2.4.8). The use of SRS to construct a Raman amplifier was proposed by Stolen et. al. in 1972 [134] and demonstrated by Hegarty et. al. in 1985 [135]. The most well known type of Raman amplification is distributed Raman amplification, which uses the transmission fiber as a gain medium. A Raman amplifier can be forward (co-propagating) pumped, backward (counter-propagating) pumped or a combination of both (bi-directional). Backwards pumped Raman amplification is the most common and the power of the pump P p (z) and signal P s (z) can be expressed as follows, ⎧ ⎪ ⎨ ⎪ ⎩ P p (z) = P p (L)exp(−α p (L−z)) P s (z) = P s (0)exp(−α s z)exp _ g R A e f f P p (L) α p [exp(−α p (L−z)) −exp(−α p L)] _ (3.1) Where g R is the Raman gain coefficient in [m/W]. P p (L) is the Raman pump power in [W], which is launched counter-propagating to the optical signal from the back-end of the transmission fiber. P s in [W] is the signal power launched into the transmission fiber. The attenuation coefficients α p and α s in [Np/km] denote the fiber attenuation at the pump and signal wavelengths. The attenuation coefficients are normally different for the pump and signal, as the pump is in the 1445 nm wavelength region where the fiber attenuation is slightly higher. The Raman gain coefficient of depolarized light is 0.428 10 −13 m/W for SSMF [98]. Note that pump depletion is not included in this equation. In Figure 3.5a the optical signal power as a function of transmission distance is depicted for backwards pumped Raman amplification with A e f f = 72.8 µm 2 , α s = 0.2 dB/km, P s = 0 dBm, α p = 0.25 dB/km and P p = 24.5 dBm. This results in Raman ON/OFF gain G on/o f f of 12.4 dB. The Raman ON/OFF gain can also be denoted through G on/o f f = exp _ g R A e f f P p (L)L e f f _ = exp _ g R A e f f P p (L) α p [1−exp(α p L)] _ , (3.2) Raman amplification does not necessarily compensate the full span loss, and the remaining part can be compensated using an EDFA. This is known as hybrid EDFA/Raman amplification. This improves the OSNR compared to EDFA-only amplification as the lowest power that occurs along 44 3.2. Fiber loss compensation 0 20 40 60 80 100 -20 -15 -10 -5 0 5 Transmission distance (km) S i g n a l p o w e r ( d B m ) 0 20 40 60 80 100 -20 -15 -10 -5 0 5 Transmission distance (km) S i g n a l p o w e r ( d B m ) 0 20 40 60 80 100 -20 -15 -10 -5 0 5 Transmission distance (km) S i g n a l p o w e r ( d B m ) Backward-pumped Raman amplification Forward-pumped Raman amplification Bi-directional Raman amplification With Raman W i t h o u t R a m a n W i t h o u t R a m a n W i t h R a m a n G o n / o f f G o n / o f f G o n / o f f W i t h o u t R a m a n W i t h R a m a n A l l - R a m a n (a) (b) (c) Figure 3.5: Optical signal power as a function of the transmission distance for (a) Backward-pumped Raman, (b) Forward-pumped Raman and (c) bi-directional Raman and all-Raman amplification. All schemes use a total pump power of 24.5 dBm, except for all-Raman amplification which uses a total pump power of 26.5 dBm. the link is now much higher. The noise figure of a hybrid Raman/EDFA amplifier can be charac- terized with the effective noise figure. The effective noise figure of a Raman amplifier is defined as the noise figure that EDFA-only amplification would need to have in order to achieve the same OSNR as obtained with Raman amplification The effective noise figure of a hybrid EDFA/Raman amplifier can be as low as -3 dB [136, 137]. However, intra-band SRS between the Raman pumps increases the noise figure for lower wavelengths and a typical hybrid-EDFA/Raman amplifica- tion scheme has therefore an effective noise figure between 0 dB and 1 dB for the worst WDM channel [138]. A further possible amplification scheme is forward-pumped Raman amplification, where the sig- nal and pump are co-propagating along the fiber. This scheme is less desirable as it increases the signal power in the first part of the transmission link, which results in increased nonlinear impairments (see Figure 3.5). For the same pump power, backward and forward-pumped Ra- man amplification have the same ON/OFF Raman gain. Equation 3.2 is therefore also valid for forward-pumped Raman amplification when P p (L) is replaced with P p (0). The evolution of the signal and pump powers along the transmission fiber is now denoted through, ⎧ ⎪ ⎨ ⎪ ⎩ P p (z) = P p (0)exp(−α p z) P s (z) = P s (0)exp(−α s z)exp _ g R A e f f P p (0) α p [1−exp(−α p z)] _ (3.3) Figure 3.5b shows an example of the power evolution for the forward-pumped scheme, using the same parameters as the backward-pumped scheme. Finally, in bi-directional Raman amplifica- tion, Raman pumps are both co-propagating as well as counter-propagating with the signal. This can be used for all-Raman amplification. All-Raman amplification is depicted in Figure 3.5c, using a 23.5-dBm pump power for both co-propagating and counter-propagating directions. Be- 45 Chapter 3. Long-haul optical transmission systems cause of the high required pump powers for all-Raman amplification it is desirable to combine it with fiber types that have a high Raman gain coefficient, such as NZDSF. A Raman amplifier is very suitable for WDM transmission as the 3-dB bandwidth of the Raman gain spectrum is approximately 55 nm. To further flatten and broaden the Raman gain spectrum, multiple Raman pump laser at different wavelengths are often used. This allows for a Raman amplifier with a flat 100-nm gain spectrum [139], which is nearly equal to the Stokes shift in SSMF. A multi-pump Raman amplifier consists often of a single strong pump and several smaller pumps to equalize the gain spectrum [138]. For the transmission experiments in this thesis, Hybrid EDFA/Raman amplification is used with four Raman pumps. A 300-mW polarization- multiplexed pump at 1423 nm and depolarized pumps at 1436 nm (150 mW), 1453 nm (90 mW) and 1467 nm (150 mW) [140]. SSMF DCF Raman pumps DCF Pre-amp EDFA Booster EDFA next span Figure 3.6: Hybrid Raman/EDFA structure used in the long-haul optical transmission experiments. Figure 3.6 depicts the typical hybrid Raman/EDFA structure used in the long-haul transmission experiments discussed in this thesis. The SSMF is backward pumped with an average Raman gain between 11 dB and 14 dB, depending on the transmission fiber used in the experiment. The insertion loss of the DCF is distributed by placing a DCF module after the Raman pumps, which compensate for part of the chromatic dispersion. The remaining chromatic dispersion is compensated between the pre-amplifier and booster EDFA. Alternatively, the full chromatic dispersion can be compensated with a DCF module placed after the Raman pumps followed by only a pre-amplifier (see Section 10.6.3). Raman amplification has also some important drawback compared to EDFAs. The pump powers required for Raman amplification are typically significantly higher than the pump powers re- quired in an EDFA. This results in a more expensive amplifier design and the high pump powers can reduce the reliability of the pump lasers [138]. Finally, the distributed nature of high pump powers in Raman amplification makes handling safety precautions important. The high optical powers can cause injuries to skin and eyes and cause optical connectors to damage easily when there is dirt or dust on the connector [141, 142]. As an alternative, discrete Raman amplification can be used. In discrete Raman amplification the high optical powers are contained within the amplifier subsystem and do not propagate into the transmission fiber. Instead DCF or specially designed fiber is used as a Raman gain medium. The high Germanium doping in the core and the small effective area results in ∼7 times the Raman gain efficiency of SSMF [143]. In Sec- tion 3.3.2, discrete Raman amplification is used to investigate the feasibility of lumped chromatic dispersion compensation. 46 3.2. Fiber loss compensation 3.2.3 Optical-signal-to-noise ratio The ASE added by the optical amplifiers in a long-haul transmission link ultimately limits the feasible transmission distance. When we consider a long-haul transmission link with N spans , the total ASE power P tot ASE in [W] added by all optical amplifiers along the link equals P tot ASE = P ASE N spans . This is valid under the assumption that a single amplifier adds a noise power P ASE and that all spans have the same insertion loss. After N spans , the ratio between ASE power and signal power is known as the OSNR and is defined as, OSNR = P out put P ASE N spans = P out put 2N 0 ∆f 0 , (3.4) where P out put defines the signal power at the output of the last amplifier of the transmission link and has unit [W]. The noise power can be expressed as the noise power spectral density per polarization N 0 . For measurement purposes the OSNR is often normalized with respect to a certain optical bandwidth, usually 0.1 nm, which is expressed through the reference bandwidth ∆f 0 in [Hz]. The factor two results from the two orthogonal polarization dimensions in the fiber. Note that, although the ASE is assumed to be unpolarized, only the ASE that is polarized parallel to the signal results in signal–spontaneous beat noise upon detection with the photodiode. The ASE in the orthogonal polarization is added to the signal upon detection with the photodiode, but there is no signal–spontaneous beat noise as the ASE does not coherently interfere with the signal. It therefore worsens the OSNR tolerance with only ∼0.3 dB [10], which results from spontaneous–spontaneous beat noise. The noise power spectral density of an amplifier can be expressed as, N 0 = n sp hf 0 (G−1)N spans = n sp h f 0 (αL span −1)N spans , (3.5) where n sp is the spontaneous emission factor of a single amplifier, f 0 the reference frequency in [Hz] and h is Planck’s constant (6.626068 10 −34 m 2 kg/s). The amplifier gain G is substituted with the fiber span loss αL span under the assumption that the gain of each amplifier is equal to the span loss. The noise figure of an EDFA can then be expressed as [144], F = 2n sp (1− 1 G ) + 1 G = 2n sp (αL span −1) +1 αL span . (3.6) In the limit of high gain (G=αL span ¸10) the noise figure therefore approaches F =2n sp . This shows that even a perfect optical amplifier n sp = 1 has a noise figure of 3 dB. Combining Equations 3.4, 3.5 and 3.6 gives an expression for the OSNR as a function of the amplifier noise figure and the span loss. OSNR = P out put (αL span F −1)h f 0 ∆f 0 N spans (3.7) = αL span P input (αL span F −1)h f 0 ∆f 0 N spans ≈ P input Fh f 0 ∆f 0 N spans . 47 Chapter 3. Long-haul optical transmission systems Denoting Equation 3.7 in [dB] gives, OSNR[dB] ≈ 10log 10 ( P input N spans Fh f 0 ∆f 0 ) = P input [dBm] −10log 10 (N spans ) +58dBm−F[dB] (3.8) = P out put [dBm] −αL span −10log 10 (N spans ) +58dBm−F[dB], where −10log 10 (hf 0 ∆f 0 ) equals 58 dBm for a reference frequency f 0 of 193.4 THz (1550 nm) and a reference bandwidth ∆f 0 of 12.5 GHz (0.1 nm). We can therefore conclude that the OSNR scales linearly with P out put and inversely with the insertion loss of the fiber span. In order to increase the OSNRat the receiver, either the input power into the fiber span (which equals P out put ) has to be increased or the loss of the fiber span αL span has to be reduced. The input power is ultimately limited by degradations due to nonlinear impairments. The span loss can be reduced by spacing the amplifiers closer together, as is often done for ultra long-haul transmission systems that have to bridge transoceanic distances, or the use of Raman amplification. 3.3 Chromatic dispersion compensation Chromatic dispersion accumulates along an optical fiber which causes ISI and limits the feasi- ble transmission distance, i.e. the dispersion-limited reach. The normalized dispersion length in Equation 2.8 shows that there is a quadratic dependence between the dispersion-limited reach and the symbol rate. This is also evident from Table 3.1, which depicts the dispersion-limited trans- mission reach over SSMF. Hence, in order to realize long-haul transmission systems, chromatic dispersion compensation is required. Table 3.2: DISPERSION-LIMITED REACH FOR NRZ-OOK AND A 2-DB OSNR PENALTY. Symbol rate (Gb/s) SSMF (km) 2.7 640 10.7 40 42.8 2.5 107 0.4 0 core cladding core radius n n silica Figure 3.7: Refractive index profile of a DCF. Chromatic dispersion compensation can generally be subdivided into two categories, in-line and accumulated dispersion compensation. The bulk of the chromatic dispersion in a long-haul trans- mission link is normally compensated using in-line dispersion compensation. Several technolo- gies have been developed for in-line chromatic dispersion compensation, such as dispersion com- pensating fiber (DCF), dispersion managed cables [145], Higher-order mode DCF [146], fiber Bragg gratings and optical phase conjugation. 48 3.3. Chromatic dispersion compensation Nowadays, DCF is the standard solution to compensate for the chromatic dispersion accumulated in long-haul optical transmission systems. It yields colorless, slope-matched dispersion cance- lation with negligible cascading impairments. DCF was first proposed by Lin et. al. in 1980 [147] and demonstrated in 1992 by Dugan et. al. [148]. DCF has a smaller core effective area (∼20 µm 2 ) and different core index profile in comparison to SSMF. Figure 3.7 shows the core index profile of DCF, which normally has triple-cladding structure. The triple cladding index profile has a narrow high-index core surrounded by a deeply depressed cladding followed by a raised ring. The refractive index of the core is raised through GeO 2 doping. The small core size and triple-cladding structure forces a larger part of the optical field to propagate in the cladding, which increases the significance of waveguide dispersion and results in large negative values of D. The triple cladding design also changes the sign of the dispersion slope such that the DCF is slope-matched with the transmission fiber. State-of-the-art DCF can therefore accurately com- pensate the chromatic dispersion of all channels in the C-band. The high (GeO 2 ) doping in the core of the DCF and the fact that a larger part of the optical field propagates in the cladding slightly raises the attenuation of the DCF, which is typically close to α = 0.5 dB/km. It also makes DCF more vulnerable to core ovality than SSMF, which results in higher module PMD [149] and raises the nonlinear coefficient. An extensive overview of dispersion compensation using DCF can be found in [143]. Despite the fact that the DCF consists of several kilometers of fiber, it is normally used as disper- sion compensation module (DCM) where the fiber is coiled around a spool for discrete dispersion compensation. This is due to the higher insertion loss per kilometer and the higher complexity of cable installation, which makes it unattractive to use DCF as part of the transmission fiber. The insertion loss of state-of-the-art DCM is ∼6 dB for a module that can compensate for the chromatic dispersion of 100 km of SSMF (1700 ps/nm). Normally, a two-stage EDFA structure with mid-stage access for the DCM is used to compensate the insertion loss (see Figure 3.4). In such a two-stage amplifier, the input power into the DCF is an important design parameter. The relatively high insertion loss of the DCF must be compensated while keeping at the same time the input powers into the DCF low enough to avoid nonlinear impairments. This relative impact of nonlinear impairments can be quantized using a path-averaged nonlinearity ˆ γ. ˆ γ = γ _ z=L z=0 exp(−αz)dz, (3.9) where L is the length of the fiber and α is denoted in [Np/km]. We nowconsider 100 kmof SSMF and matching DCF and use the fiber parameters in Table 3.3. The path-averaged nonlinearity is then 24.5 dB and 25.0 dB for the SSMF and DCF, respectively. The difference between SSMF and DCF is small, because the impact of the higher DCF nonlinearity is offset through the higher DCF attenuation coefficient. The path average nonlinearity is independent of the input power, but by multiplying with the input power we obtain an expression for the total nonlinear phase shift. φ NL = φ NL,SSMF +φ NL,DCF = ˆ γ SSMF P 0,SSMF + ˆ γ DCF P 0,DCF . (3.10) The DCF-induced increase in the total nonlinear phase shift can be denoted as, ∆φ NL,DCF = φ NL,SSMF +φ NL,DCF φ NL,SSMF = 1+ ˆ γ DCF ˆ γ SSMF ∆P 0 , (3.11) 49 Chapter 3. Long-haul optical transmission systems Table 3.3: SSMF AND DCF FIBER PARAMETERS, DCF PARAMETERS ARE TAKEN FROM [143]. SSMF DCF unit Insertion loss (α) 0.2 0.5 [dB/km] Dispersion (D) 17 -170 [ps/km/nm] Nonlinearity (γ) 1.3 5.24 [W −1 km −1 ] where ∆P 0 is the difference input power between the SSMF and DCF, ∆P 0 = P 0,SSMF P 0,DCF . (3.12) This shows that when the input power difference between SSMF and DCF increases, the DCF- induced contribution to the total nonlinear phase shift diminishes. The total noise figure of a two-stage amplifier can be calculated using Friis’s formula [126]. F tot = F 1 + α DCF L DCF F 2 +1 G 1 = F 1 + α DCF L DCF F 2 +1 α SSMF L SSMF /∆P 0 (3.13) where F tot is the total noise figure of the amplifier. The noise figure of the pre-amplifier F 1 and booster F 2 are assumed to be 5.0 dB and 7.5 dB, respectively [143]. The pre-amplifier gain G 1 is equal to the SSMF span loss minus ∆P 0 . Figure 3.8 depicts the total noise figure and the increase in nonlinear phase shift for a 100 km SSMF span using the fiber parameters of Table 3.3. This shows that a smaller difference in input power leads to an increased nonlinear phase shift but a decrease in total noise figure of the two-stage EDFA. Combining the total noise figure and the increase in nonlinear phase shift gives a measure of the optimal difference in input power between SSMF and DCF. This shows that the optimum power difference is 6.5 dB, which results in a combined penalty of ∼7 dB. When dispersion compensation is not required, a single-stage EDFA with a 5 dB noise figure would in principle be sufficient to amplify the signal and no nonlinear phase shift would be accumulated in the DCF. Hence, we can conclude that DCF- based chromatic dispersion compensation results in a ∼2 dB penalty due to the combined effect of an increased nonlinear phase shift and higher effective noise figure. We note that this penalty is independent of the modulation format, as it is based on the DCF-induced increase in nonlinear phase shift and not the absolute nonlinear tolerance. This simplified analysis does not take the amplifier spectral tilt into account, which might change the choice of the SSMF and DCF input powers. The chromatic dispersion at the receiver is referred to as the accumulated dispersion. The ac- cumulated chromatic dispersion of a long-haul link is normally only roughly known as not all fiber is measured accurately before deployment. In addition, the chromatic dispersion slope, different propagation paths in a transparent optical network and temperature dependence [150] also introduce a variation in the accumulated dispersion at the receiver. For ≤10 Gb/s transmis- sion systems the accumulated dispersion tolerance is generally large enough such that a standard 50 3.3. Chromatic dispersion compensation 0 2 4 6 8 10 12 14 0 2 4 6 8 10 I n c r e a s e i n n o n l i n e a r p h a s e s h i f t ( d B ) Input power SSMF - Input power DCF (dB) T o t a l n o i s e f i g u r e ( d B ) penalty C o m b in e d (dB) Figure 3.8: Effective noise figure and increase in nonlinear phase shift as a function of the input power difference between SSMF and DCF, the solid curve shows both penalties combined. direct detection receiver can compensate for the variations that occur. For higher symbol rates (e.g. 40-Gb/s), on the other hand, the accumulated dispersion tolerance is generally too small to compensate for such variations. This can be solved by using optical modulation formats that are more tolerant to chromatic dispersion, as extensively discussed in the remainder of this the- sis. Alternatively, tunable chromatic dispersion compensation can be employed to improve the chromatic dispersion tolerance at the receiver. A number of different technologies have been proposed for tunable dispersion compensation, including Fiber Bragg gratings [151, 152], thin film etalons [153] and digital signal processing technologies. Digital signal processing such as pre-distortion and digital coherent receivers are an exception to the subdivision of in-line and accumulated dispersion compensation as they can compensate for the full dispersion of the fiber link (see Chapter 10). 3.3.1 Dispersion map In a long-haul transmission system, chromatic dispersion interacts with the SPM and XPM in- duced nonlinear phase shifts. Depending on the local dispersion along the transmission link, this can result in severe transmission impairments. It is therefore important to design the local dispersion evolution along the link, which is known as the dispersion map. C h r o m a t i c D i s p e r s i o n ( p s / n m ) Post- compensation Inline under- compensation Transmission distance (km) 0 Pre-compensation Post- compensation Figure 3.9: Degrees of freedom in the design of a dispersion map. 51 Chapter 3. Long-haul optical transmission systems Figure 3.9 visualizes the degrees of freedom that can be used in the design of a dispersion map. First of all, the pre-compensation refers to a DCM with negative dispersion that is added to pre- chirp the signal directly after the transmitter [154]. An optimized pre-compensation makes the dispersion map more symmetric with respect to the zero-dispersion point and minimizes the path- averaged pulsewidth over the high power area of the transmission system. A lower path-average pulsewidth reduces the overlapping of neighboring pulses and, hence, minimizes the distortions due to SPM-induced nonlinearities [155]. A rule of thumb for the design of the dispersion map is to choose the pre-compensation such that the path-averaged nonlinearity corrected for the sign of the local dispersion is close to zero. γ n=N spans ∑ n=1 _ z=L span (n) z=L span (n−1) sign[D local (z)]exp(−αz)dz ≈0. (3.14) When the path-average nonlinearity is close to zero it results in a transmission link where the high-power areas are nearly symmetric with respect to the zero-dispersion point. This is illus- trated in Figure 3.10a which indicates the high-power areas along the transmission link directly after each EDFA. Such a link design is possible through the use of a dispersion map that is symmetric with respect to the middle of the link [88, 156]. The second degree of freedom is the inline under-compensation, which denotes the difference between the chromatic dispersion of each span and the chromatic dispersion of the subsequent DCF module. The inline under-compensation changes the chromatic dispersion in the high power region at the beginning of each subsequent span. This averages out the interaction between the nonlinear phase shift and chromatic dispersion, as the power envelope is slightly different for each of the following high power regions. The inline under-compensation is particulary im- portant to reduce the impact of XPM, as it is similar to a path-averaged walk-off length. The XPM penalty is, on the other hand, only slightly dependent on the pre-chirp and local disper- sion [157]. Finally, the post-compensation optimizes the accumulated dispersion at the receiver. The optimal amount of post-compensation can compensate to a certain degree the SPM-induced nonlinear phase shift as discussed in Section 2.4.2. The optimization of the dispersion map for WDM transmission systems is reported in many theoretical (e.g. [158, 159]) and experimental studies (e.g.[160, 157, 161]). C h r o m a t i c D i s p e r s i o n ( p s / n m ) Transmission distance (km) 0 High-power area (a) 0 1000 2000 3000 4000 5000 0 0.2 0.4 0.6 Chromatic dispersion (ps/nm) A v e r a g e o p o w e r p e r p u l s e ( m W ) single SSMF span (b) 42.8-Gb/s 10.7-Gb/s Figure 3.10: (a) Dispersion map with indication of high-power area and (b) average standard deviation of the power in a symbol (75% symbol period) for 10.7-Gb/s and 42.8-Gb/s NRZ-OOK modulation. 52 3.3. Chromatic dispersion compensation The choice of the dispersion map is particulary important for a ∼10 Gb/s symbol rate, as the number of interacting pulses is relatively small. This is illustrated in Figure 3.10b which shows the standard deviation of the power in each pulse, averaged out over all pulses in the transmitted sequence, as a function of chromatic dispersion only. In order to exclude the pulse transitions, only the middle 75% of the time slot is used in the calculations. The standard deviation of the power increases with the accumulated chromatic dispersion as the overlapping pulses interfere with each other. For a 10.7-Gb/s symbol rate the standard deviation increase up to an accumulated dispersion of ∼2000 ps/nm and then saturates. This indicates that if the dispersion map keeps the local dispersion in high-power area below ∼2000 ps/nn the nonlinear impairments will be lower than when the chromatic dispersion is not periodically compensated. For a 42.8-Gb/s symbol rate, the standard deviation saturates for a ∼150 ps/nm accumulated dispersion. This indicates that for higher symbol rates, the number of interacting pulses rapidly increases which limits the efficiency of suppressing nonlinear impairments through the choice of the dispersion map. We note that another measure often used to characterize the impact of nonlinearities is the peak power along the transmitted sequence. The peak power shows a similar trend as the average standard deviation, but as there is no averaging in computing the peak power, it is more dependent on the length of the transmitted sequence. -10 -5 0 5 10 15 10 12 14 16 18 20 Input power (dBm) O S N R ( d B / 0 . 1 n m ) (a) BER = 10 -5 0 400 800 1200 1600 2000 10 13 16 19 22 25 Chromatic dispersion (ps/nm) O S N R ( d B / 0 . 1 n m ) (b) -5 dBm -1 dBm 1 dBm 3 dBm 5 dBm 9 dBm 11 dBm BER = 10 -5 Figure 3.11: (a) Required OSNR for 10.7-Gb/s NRZ-OOK after 2000-km transmission with a all optimized dispersion map, optimized in-line and pre-compensation, zero accumulated dispersion and zero pre, in-line and accumulated dispersion. (b) accumulated dispersion tolerance for different input powers. As an example, Figure 3.11 illustrates the impact of dispersion map optimization on the nonlinear and dispersion tolerance in a long-haul transmission system. Depicted in Figure 3.11a is the non- linear tolerance for 20x100 km transmission with a single 10.7-Gb/s NRZ-OOK channel. When no dispersion map is used and the pre-, in-line- and accumulated dispersion are all equal to zero, an input power of -1 dBm per span results in a 2-dB OSNR penalty. Optimizing the pre- and in-line compensation improves the nonlinear tolerance significantly to 6-dBm input power per span. For this link, the optimum pre-compensation is in the range -1190 ps/nm (lower powers) to -680 ps/nm (higher powers). The optimum in-line under-compensation ranges from 51 ps/nm (lower powers) to 68 ps/nm (higher powers). When furthermore the accumulated dispersion at 53 Chapter 3. Long-haul optical transmission systems the receiver is optimized, the nonlinear tolerance increases to 10 dBm per span. The optimum accumulated dispersion for different input powers per span is depicted in Figure 3.11b for a dis- persion map with -680 ps/nm pre-compensation and 68 ps/nm in-line under-compensation. This shows that in the nonlinearity-limited transmission region the accumulated dispersion can be as high as 900-ps/nm. Note that for a zero pre- and in-line compensation, optimizing the accumu- lated dispersion also improves the nonlinear tolerance (to ∼ 8 dBm, not shown). However, for WDM transmission the impact of XPM would be particulary strong in this case, which makes it less relevant. When the pre- and in-line compensation are optimized, the impact of XPM can be reduced. However, even for an optimized dispersion map the impact of XPM will considerably limit the nonlinear tolerance. In the long-haul transmission experiments described in this thesis, the dispersion map is opti- mized in order to understand its impact on the transmission properties of different modulation formats (see Chapter 6). The dispersion map is optimized by starting of with an dispersion map as would be optimal for 10.7-Gb/s NRZ-OOK modulation, and then independently varying the pre-compensation and in-line under-compensation. In deployed transmission systems, the opti- mization of the dispersion map is somewhat restricted because every span has a different length and the DCMs are only available in a certain granularity. A further requirement for optically- switched networks is that at each add-drop points the accumulated dispersion is low in order to minimize the required post-compensation. A practical chromatic dispersion map for such trans- mission systems is a double-periodic dispersion map [162]. Such a dispersion map typically has a high inline under-compensation for each span, but once every several spans the accumulated dispersion is reduced through a high inline over-compensation. 3.3.2 Lumped dispersion compensation The design of a dispersion map improves the reach in a long-haul transmission system signifi- cantly. But it also requires complex system engineering to obtain a near optimal dispersion map in deployed transmission systems. An alternative approach is the use of lumped dispersion maps, which compensate the chromatic dispersion every several spans or, in the extreme case, do not apply in-line dispersion compensation at all. For example, the dispersion compensation can be concentrated only at specific points, such as optical add-drop nodes. This allows the replacement of multiple small DCMs with a single ”large-dispersion” DCM. Furthermore, it has the advan- tage that simpler EDFAs can be used in between the dispersion compensation nodes. The use of a lumped dispersion map can potentially also improve transmission performance. When no mid-stage access are required for the EDFAs, less pump lasers are required and the EDFA can have a lower noise figure. As shown previously, this can improve the OSNR with up to 2 dB. Figure 3.12 depicts the accumulated dispersion along a transmission link for both a conventional and a lumped dispersion map. This illustrated that the local dispersion along the link is signif- icantly higher in the case of a lumped dispersion map. The higher local dispersion can reduce the nonlinear tolerance, which makes lumped dispersion compensation less interesting for ultra long-haul transmission systems or modulation formats that require careful optimization of the dispersion map. For example, for 10.7-Gb/s NRZ-OOK modulation the use of a lumped disper- 54 3.3. Chromatic dispersion compensation A c c u m u l a t e d D i s p e r s i o n ( p s / n m ) Transmission distance (km) Figure 3.12: Example of a lumped dispersion map. sion will result in a reduced nonlinear tolerance as this modulation format strongly benefits from an optimized dispersion map [163]. But 40-Gb/s transmission has shown to be highly resistant towards a large accumulated dispersion, particulary when phase shift keyed modulation formats are used [164]. To make lumped dispersion compensation practical an important consideration is the large inser- tion loss of the single centralized DCM. An efficient amplification scheme to reduce the insertion loss is backwards pumped Raman amplification, as DCF has a high Raman gain coefficient. This allow for a high ON/OFF Raman gain, in the order of 25 dB, while using only low power Ra- man pumps. A further increase in Raman gain can result in double Rayleigh scattering, which increases the noise figure [165, 166]. When hybrid EDFA/Raman amplification is used the total DCF insertion loss can be ∼30 dB, which is sufficient to compensate the chromatic dispersion of 500 km of SSMF. An alternative approach for lumped dispersion compensation would be the use of chirped FBGs. This combines a large chromatic dispersion with an insertion loss small enough to be compensated using EDFA-only amplification. An example of long-haul transmission with a lumped dispersion map is discussed in Section 6.3. 3.3.3 Chirped fiber-Bragg gratings Chirped multi-channel fiber-Bragg gratings (FBG) are an alternative to DCF for the compen- sation of chromatic dispersion in long-haul transmission links [167, 168]. A FBG is a type of distributed Bragg reflector, first demonstrated by Hill et. al. in 1978 [169]. It consists of a short segment of fiber with a periodic variation of the refractive index along the fiber core. The re- fractive index variation generates a wavelength specific dielectric mirror that reflects a particular wavelength. A FBG can therefore be used to construct a very narrow optical filter that reflects the desired wavelength and transmits all other wavelengths. When a FBG is combined with a circulator, the resulting component transmits only the desired wavelength and attenuates all oth- ers, as shown in Figure 3.14. The signal enters the circulator through port 1 and outputs it again through port 2. The FBG connected to port 2 then reflects only the desired wavelengths back into the circulator, which outputs the signal again through port 3. The refractive index profile of a FBG can have a linear variation in the grating period. Different wavelength are then reflected at different positions along the FBG, which introduces chirp into the signal. Such chirped fiber Bragg gratings can be used for dispersion compensation. A chirped 55 Chapter 3. Long-haul optical transmission systems FBG does not reflect a single wavelength, but rather reflects a range of wavelength defined by the variation of the grating period. This can be used to construct FBGs with a broad bandwidth, for example the full C-band, which can compensate the chromatic dispersion for multiple WDM channels. Alternatively, multiple short gratings can be written on top of each other to reflect multiple WDM channels with a single complex grating. Such a structure enables the manufac- turing of full C-band FBGs that can be used on a 100-GHz [170] or 50-GHz grid [171]. The amplitude response of a chirped FBG with 100-GHz channel spacing is depicted in Figure 3.13b. This shows a very flat insertion loss with a ripple of <0.5 dB across a 65-GHz bandwidth and a ∼25 dB insertion loss in between two pass-bands. FBG circulator 1 2 3 Figure 3.14: FBG with circulator. In Figure 3.13c, the phase response of a chirped FBG is depicted. A draw- back of chirped FBGs is that they suffer from distortions in their phase re- sponse, better known as the group delay ripple (GDR). The GDR is caused by imperfections in the gratings fabrication process and limits the num- ber of FBGs that can be cascaded. Figure 3.13d shows the obtained GDR when the a linear fit is subtracted from the group delay response. In [172], Scheerer et. al. showed that the penalty can be calculated from the ampli- tude and period of the GDR in the frequency domain. The main consider- ation is the ripples frequency relative to the symbol rate. High-frequency ripples, i.e. ripples with more than one ripple period within the signal bandwidth, create satellite pulses in the time domain. These satellite pulses interfere with adjacent pulses and therefore cause ISI. Low frequency ripples, with only a fraction of the ripple period within the signal bandwidth, cause pulse broadening. This pulse broadening is analog to chromatic dispersion and therefore merely changes the residual dispersion of the signal. The low-frequency ripples can 9 9 Low insertion loss Low insertion loss 9 9 Negligible nonlinearity coefficient Negligible nonlinearity coefficient 9 9 Compact size Compact size 8 8 Group delay ripple Group delay ripple 9 9 Colorless Colorless 9 9 Cascadibility Cascadibility 8 8 High insertion loss High insertion loss 8 8 High nonlinear coefficient High nonlinear coefficient Chirped Fiber Bragg Gratings Dispersion Compensating Fiber (a) -30 -20 -10 0 10 20 30 -45 -30 -15 0 15 30 45 G r o u p d e l a y r i p p l e ( p s ) Normalized frequency (GHz) Peak-to-peak GDR (d) -80 -60 -40 -20 0 20 40 60 80 -1000 -500 0 500 1000 G r o u p d e l a y ( p s ) Normalized frequency (GHz) -80 -60 -40 -20 0 20 40 60 80 -40 -30 -20 -10 0 A t t a n u a t i o n ( d B ) Normalized frequency (GHz) 65 GHz 100 GHz (b) (c) Figure 3.13: (a) Comparison between FBGs and DCF for chromatic dispersion compensation; (b) am- plitude, (c) group delay and (d) group delay ripple of a channelized chirped-FBG. 56 3.4. PMD compensation be compensated using tunable dispersion compensation. As a result, mainly the high-frequency ripples cause transmission impairments. Note that the best prediction of the penalty associated with cascaded FBGs is generally the phase ripple (PR) weighted by the signal spectrum [173]. Figure 3.13a lists the most significant differences between DCF and FBGs for dispersion com- pensation. The main advantage of FBGs is their lower insertion loss and negligible nonlinearity. This potentially allows simpler EDFA design, by cascading the FBG and transmission fiber with- out a mid-stage amplifier. Another advantage is the compact size, which enables the integration of a (tunable) FBGs in the receiver. A FBG can be made tunable through heating or stretching of the fiber grating, which enables dispersion tuning over a range of typically 800 ps/nm [174]. The main disadvantage of FBGs is the PR-related impairments. However, improved fabrication pro- cesses have gradually reduced the PR of slope-matched FBGs, which significantly increases their cascadability [175] A further reduction in PR-related impairments is possible using equalization [176], which enables ultra long-haul transmission using FBGs for dispersion compensation. In Section 6.4 the impact of PR-induced impairments are discussed for a long-haul WDM transmis- sion experiment using 10.7-Gb/s NRZ-OOK and 42.8-Gb/s RZ-DQPSK modulation. 3.4 PMD compensation As there is no easy compensation solution, PMD related penalties are among the most cumber- some for state-of-the-art long-haul optical transmission systems. However, several approaches have been proposed that either mitigated or actively compensated the impact of PMD. Passive PMD mitigation technologies include the use of robust modulation formats, as discussed further in this thesis, and FEC-supported polarization scrambling [177, 178]. Active PMD compensa- tion techniques include PSP coupling [179], the use of optical PMD compensators [180, 181] and optical [182] or electrical signal processing. An extensive overview of PMD compensation technologies is given by Sunnerud et. al. in [183]. PC ¨IJ RX DGD feedback PC ¨IJ RX DGD feedback PC ¨IJ DGD (a) (b) Figure 3.15: (a) single-stage PMD compensator; (b) two-stage PMD compensator. PSP coupling simply aligns the input SOP with the PSP of the transmission link. This is a fairly easy method to compensate for DGD, but cannot be used to compensate for second-order PMD or in the presence of strong PDL. It also requires a feedback signal from the receiver to the transmitter, which complicates system design. In addition, the time delay in a long transmission link makes it impossible to track fast polarization changes. Optical PMD compensators can ei- ther use single-stage [180] or two-stage compensation [181], as illustrated by Figure 3.15. A single stage PMD compensator consists of a polarization controller followed by either a fixed 57 Chapter 3. Long-haul optical transmission systems or tunable birefringent section. Such a PMD compensator has either two (fixed) or three (tun- able) degrees of freedom. The degrees of freedom of a PMD compensator is a good figure of merit for the complexity of the control algorithm. With a fixed single birefringent section, the amount of birefringence should match the average PMD of the link and a penalty is introduced when the compensator DGD is larger than the DGD of the transmission link. Note that a single- stage PMD compensator can only compensate for a limited amount of second-order PMD [184]. Hence, for 43-Gb/s transmission a two-stage PMD compensator is desirable. A two-stage PMD compensator (Figure 3.15b) has normally 4 degrees of freedom. This requires both a sophisti- cated control algorithm as well as a suitable choice of the feedback signal. Most two-stage PMD compensators schemes are known to have the tendency of getting trapped in suboptima [183]. An important design aspect for PMD compensators is the speed of compensation. Polarization changes in an optical fiber are normally on the scale of a few degrees per second. However under the influence of, for example, vibrations, temperature changes, human handling or wind in the case of aerial fibers, the polarization changes can reach a speed of ∼50 revolutions per second on the Poincar´ e sphere [185, 186, 187]. In order to track these polarization changes with a (θ < 10 o ) accuracy, the response time of the automatic polarization control should be in the order of 1 ms. The feedback required for optical polarization controllers makes it difficult to obtain such response times. The combined requirement of a short response time and control algorithms that do not suffer from local suboptima has stalled the deployment of optical PMD compensators in recent years. 3.5 Narrowband-optical filtering The previous three sections discussed the compensation of transmission impairments that occur in a long-haul optical transmission link. This section discusses the impact of optical narrowband filtering, a transmission impairment that typically occurs in an optical transmission network. An optical meshed network requires that signals routed through the network have the flexibility to pass multiple optical add-drop multiplexer (OADM) and photonic cross connects (PXC) nodes along the transmission link [188]. An OADM compromises different optical sub-systems to realize wavelength switching. Gen- erally, the WDM spectrum is de-multiplexed in order to block certain WDM channels and let other WDM channels pass through. This can either be achieved with a wavelength blocker or a wavelength selective switch (WSS), with the difference being that a wavelength blocker has a 1x1 structure whereas a WSS can be a NxM switch, with N and M being the number of input and output ports, respectively. Common types are a 1x4 or 1x9 WSS. The combination of a wave- length blocker with fiber-optic couplers at the input and output makes it possible to add/drop WDM channels. A wavelength blocker can be realized using planar lightwave circuits or liquid crystal technology [189], whereas a WSS is generally realized using micro-electro mechanical system (MEMS) technology [190]. 58 3.6. Optical phase conjugation -50 -30 -10 10 30 50 -40 -30 -20 -10 0 Normalized frequency (GHz) R e l a t i v e t r a n s m i t t a n c e ( d B ) 1 2 5 10 Figure 3.16: Transmittance of a 50-GHz WSS. Table 3.4: OPTICAL FILTER BAND- WIDTH OF A CASCADED 50-GHZ WSS. cascaded 3-dB 20-dB filters bandwidth bandwidth (GHz) (GHz) 1 43 59 2 39 52 5 35 45 10 32 40 The wavelength de-multiplexing that occurs in an OADM/PXC results in spectral filtering of the WDM channels. Particulary when multiple OADM/PXC are cascaded this filtering can limit the optical bandwidth to a fraction of the channel spacing. Figure 3.16 shows the measured transmittance of a state-of-the-art WSS, which has a (single-pass) 3-dB bandwidth of 43-GHz on a 50-GHz ITU grid. When the measured transmittance is cascaded multiple times to simulate cascaded filtering, the 3-dB bandwidth is reduced significantly, as depicted in Figure 3.16. Note that we here assume that all optical filters have exactly the same transmittance as a function of wavelength. In deployed optical networks, the filter transmittance of the cascaded OADM/PXC is likely to be slightly shifted in wavelength, for example, due to temperature differences or slight variations in the device specifications. This indicates that on a 50-GHz ITU grid, the available 3-dB bandwidth is approximately 35-GHz when a realistic number of 3-4 OADM/PXC is passed along the transmission link. This bandwidth is therefore a suitable figure-of-merit to determine if a modulation format can be used with a 50-GHz channel spacing. Today, state-of-the-art transmission systems have a 50-GHz WDM channel spacing. This implies a 0.8-b/s/Hz spectral efficiency for 40-Gb/s transmission. For binary formats this is close to the theoretical limit which makes it difficult to cascade multiple OADM with an acceptable OSNR penalty. The more narrow optical spectrum of multi-level modulation formats is therefore one of the more decisive advantages over binary modulation formats. In the remainder of the thesis, a WSS is included in the optical transmission experiments to emulate the strong optical filtering as it occurs in a transparent optical network. 3.6 Optical phase conjugation Nonlinear transmission impairments are clearly the most difficult transmission impairments to compensate in a long-haul transmission link. This mainly results from the lack of a technology that can inverse the nonlinear impairment, e.g. a material with a negative Kerr effect. Optical phase conjugation (OPC) is one of the technologies that can (partially) compensate for nonlinear transmission impairments. It uses the transmission fiber itself to compensate for transmission 59 Chapter 3. Long-haul optical transmission systems impairments and, in effect, invert the sign of the Kerr effect in the second half of the transmis- sion link. With OPC, the impairments that occurred before conjugation can be canceled out by impairments that occur after phase conjugation. OPC is currently not used in deployed optical transmission systems, but it is one of the most promising technologies to increase the robustness against nonlinear transmission impairments. Yariv et. al. proposed in 1979 the use of chromatic dispersion compensation by means of OPC [191]. But apart from the compensation of chromatic dispersion, OPC can also be used to com- pensate for other (deterministic) linear and nonlinear transmission impairments. This includes the compensation of SPM [192, 193], IXPM/IFWM [194, 195] and nonlinear phase noise [91]. And as OPC compensates the chromatic dispersion along a transmission link, it also allows for simpler EDFA design. The broad range of transmission impairments that can be compensated using OPC makes it a very powerful technology to extend the reach of long-haul transmission systems. This section briefly discusses the theory behind optical phase conjugation. Section 6.5 discusses long-haul transmission experiments using OPC for the compensation of transmission impairments. An in-depth description of optical phase conjugation in long-haul transmission systems can be found in [21]. 3.6.1 Periodically-poled lithium-niobate The most promising technology to realize OPC is parametric difference frequency generation (DFG) in a periodically-poled lithium-niobate (PPLN) waveguide. Several other techniques have been proposed to phase conjugate an optical signal and have been used in earlier exper- iments. This includes highly nonlinear fiber [196], a semiconductor optical amplifiers [197], silicon waveguides [198] and AlGaAs waveguides [199]. Highly nonlinear fibers, semiconduc- tor amplifiers and silicon waveguides are all media with a high χ 3 and therefore use FWM to conjugate the optical signal. As a result, the phase conjugated signal is degenerated through SPM and XPM that occur simultaneously with the FWM in a χ 3 nonlinear media. A PPLN waveguide has a high second order susceptibility χ 2 but negligible third order suscep- tibility χ 3 . Nonlinear interaction resulting from the third-order susceptibility (i.e. SPM, XPM and FWM) can therefore be neglected. Phase conjugation with a PPLN waveguide is realized by second harmonic generation (SHG) and DFG [200, 201]. The principle of the cascaded SHG and DFG process in a PPLN waveguide is illustrated in Figure 3.17. Through SHG, the pump at fre- quency ω pump is up-converted to the frequency 2 ω pump . Simultaneously DFG occurs where the second harmonic 2 ω pump interacts with the input signal ω input . The DFG generates a phase con- jugated output signal that mirrors the input signal ω input with respect to the pump signal ω pump . The frequency of the output signal is therefore ω con jugate = 2 ω pump −ω input . It is also possible to phase conjugate the signal using only DFG, in that case the pump signal should have a fre- quency 2 ω signal +∆ω [202], where ∆ω is the frequency difference between the input and phase conjugated output signal. The cascaded SHG/DFG process is instantaneous and phase sensitive in its response, which implies that OPC with a PPLN waveguide is transparent to bit rate and modulation format [203] and has a high conversion efficiency [204]. The DFG and SHG pro- cesses can conjugate signals over a broad wavelength range. For example, in [202] conversion is 60 3.6. Optical phase conjugation shown between the 1.31µm and 1.5µm band. The input signal can be a single wavelength chan- nel or multiple WDM signals. In [205], Yamawaku et. al., showed the simultaneous conversion of 103 WDM channels using a single PPLN waveguide. In an ordinary LiNbO 3 waveguide, SHG and DFG have a very low efficiency because of the phase mismatch caused by the dispersion of the lithium-niobate. For efficient SHG and DFG, this phase mismatch needs to be compensated, which is possible through quasi-phase matching (QPM). First order QPM can be realized by reversing the sign of the nonlinear susceptibility (periodically poling) with every phase matching period. Typically, the phase matching period of the periodic poling is ∼16.5µm. Note that the phase matching period fixes the wavelength of the pump signal, hence a PPLN waveguide has to be designed for a specific pump wavelength. However, slight tuning of the operating wavelength can be realized by changing the operating temperature of the PPLN waveguide. A concern of OPC using a PPLN waveguide is that it suffers from the presence of the photorefractive effect [206]. This can be mitigated by heating the PPLN waveguide. Typically, a PPLN waveguide is operated at 180 o to 200 o Celsius. Because of the high operating temperature, pigtail fibers cannot be glued to the waveguide and free-space optics have to be used to couple the light in and out of the PPLN waveguide, which complicates sub-system design. Another approach to mitigate the photorefractive effect is doping the LiNbO 3 slightly with magnesium-oxide [207]. This lowers the operating temperature to between 50 o and 90 o Celsius [194, 195], which allows gluing the fibers to the waveguide. Hence, magnesium- oxide doped PPLN waveguide are more practical for use as an optical subsystem. SHG 2Ȧpump Ȧpump DFG Ȧconjugate Ȧinput wavelength p o w e r Figure 3.17: Second harmonic generation (SHG) and difference frequency generation (DFG) in a PPLN. circ PBS PPLN TM TE TE Q TM Ȧinput Ȧpump 1 2 3 output Figure 3.18: Counter directional polarization in- dependent OPC subsystem. A PPLN waveguide is intrinsically polarization dependent, which is a significant drawback for in-line OPC in a long-haul transmission system. However, two polarization diversity schemes can be used to make the PPLN structure polarization independent. Either using a parallel [208] or a counter-directional [209] approach. In the parallel polarization-diversity scheme, the input signal is split up into two orthogonal polarization components that are separately phase conju- gated by two PPLN waveguide. The counter-directional polarization-diversity scheme, on the 61 Chapter 3. Long-haul optical transmission systems other hand, uses a single PPLN waveguide. In the transmission experiments described in Sec- tion 6.5 a counter-directional polarization-diversity structure is used, as depicted in Figure 3.17. A polarization beam splitter (PBS) splits the incoming signal with arbitrary polarization into the two orthogonal polarization modes (TM and TE). Counterclockwise rotating, the signal on the TM mode is then phase conjugated in the TM aligned PPLN waveguide, and subsequently converted to the TE mode with a TE ↔TM fusion splice. Clockwise rotating, the TE mode is first converted to the TM mode and and afterwards phase conjugated. Both counter propagating modes are again recombined with the same PBS. The pump signal ω pump is combined with the input signal ω input before the polarization-diversity structure. In order to obtain the same con- version efficiency for both the clockwise and counter-clockwise direction, the pump has to be launched at 45 o with respect to the principal axes of the PBS such that the pump power is split with a 50%−50% ratio. As both the TE and TM mode travel through the same components for the counter-direction polarization-diversity scheme, the structure has an inherently low DGD. And as long as the pump power is high enough that the DFG and SHG processes are not satu- rated, the PDL is also inherently low. The main disadvantage is the vulnerability to multiple path interference resulting from reflections and the finite extinction ratio of the PBS. 3.6.2 Compensation of transmission impairments As discussed in Section 2.4, the propagation of an optical signal can be expressed by the Non- linear Schr¨ odinger equation assuming a slowly varying envelope approximation. The complex conjugate of the Nonlinear Schr¨ odinger equation can be denoted as, ∂E ∗ ∂z = − α 2 E ∗ .¸¸. attenuation + j β 2 2 ∂ 2 E ∗ ∂T 2 . ¸¸ . dispersion + β 3 6 ∂ 3 E ∗ ∂T 3 . ¸¸ . dispersion slope − jγ[E ∗ [ 2 E ∗ . ¸¸ . Kerr nonlinearities , (3.15) where E ∗ denotes the complex conjugate of the optical field. Comparing Equations 2.21 and 3.15 shows that the contributions of the chromatic dispersion and the Kerr effect have an inverted sign. We now assume that the signal is phase conjugated in the middle of a perfectly symmetrical transmission link. In this case, impairments due to chromatic dispersion and the Kerr effect that occurred along the first part of the link are perfectly canceled out in the second part of the link. The sign of the attenuation and the dispersion slope remains unchanged and are not compensated. An important consideration for OPC-aided transmission links is that, ideally, compensation of chromatic dispersion and the Kerr effect can only be realized in a transmission link that is per- fectly symmetric with respect to the OPC unit. However, due to the attenuation of the optical fiber, the power envelope decreases exponentially with propagation distance along a single span. As a result, the transmission link will not be fully symmetric with respect to the OPC unit. The asymmetry can be reduced by using all-Raman amplification, as discussed in Section 3.2.2 [208]. However, Chowdhury et. al. showed that also with hybrid EDFA/Raman amplification, where the power profile along the link is not fully symmetric with respect to the OPC unit, significant nonlinearity compensation can be achieved [194, 195]. And in [210], Jansen et. al. showed that also with EDFA-only amplification a significant gain in nonlinear tolerance can be achieved. 62 3.6. Optical phase conjugation Compensation of the dispersion slope can be achieved by optimizing the post-compensation on a per-channel basis after transmission [211, 208, 203]. Alternatively, the third order dispersion can be compensated using a slope compensator [212]. In a long-haul transmission link, the power envelope evolution is a periodic function of the trans- mission distance. This produces a periodic variation of the fiber refractive index through the Kerr effect. This causes the transmission link to act as a very long FBG with a grating period equal to the amplifier spacing. Such a virtual grating induces a parametric gain which causes exponen- tial growth of the signals spectral sidebands [213]. This parametric gain is known as sideband instability and can be interpreted in the frequency domain as a FWM process which is quasi phase-matched through the virtual grating. The growth of the spectral sidebands in not symmet- ric with respect to the middle of the transmission link and can therefore not be fully compensate with OPC [193, 214]. Modulation instability can be mitigated with a periodic dispersion map [215], hence it is insignificant in transmission system using periodic dispersion compensation. The lumped dispersion map in OPC-aided transmission systems does not suppress modulation instability, which can therefore result in signal impairments. However, in deployed transmission links not every span will have the same length and power profile, and this significantly reduces the effectiveness of the parametric gain. In the long-haul transmission experiments described in this thesis no modulation instability impairments have been observed, which probably also results from (slight) differences in span length [203, 216]. When hybrid EDFA/Raman amplification is used in a transmission link, the noise figure of the amplifiers can vary across the C-band. This is a result of pump-to-pump interaction between the Raman pumps, which reduces the OSNR of the lower wavelength [138]. This in turn causes a wavelength-dependent performance, where the higher wavelength channels generally have a better performance than the lower wavelength channels. In an OPC-aided transmission link, wavelength conversion occurs in the middle of the transmission link. As a result, all wavelength channels propagate both in the higher and the lower wavelength band for part of the transmission distance. This can ease the design of transmission links somewhat as the wavelength dependent performance among the WDM channels is averaged out. The most significant drawback of OPC in a long-haul transmission link is its incompatibility with OADM. As an example we assume that an OPC unit is placed in the middle of a transmission link which also contains an OADM, offset from the middle of the transmission link. This implies that the dispersion of the add/drop channels will not be fully compensated by the OPC. OPC- based dispersion compensation in a transmission link with OADMs therefore requires phase conjugating the signal at multiple points in the link. Alternatively, the OPC can be only used for the compensation of nonlinear impairments and the chromatic dispersion is compensated by other means [194, 195]. 3.6.3 Nonlinear phase noise compensation The impact of nonlinear phase noise is, due to its statistical nature, one of the most difficult transmission impairments to take into account in the design of a transmission system. OPC can 63 Chapter 3. Long-haul optical transmission systems partially compensate for nonlinear phase noise impairments, as originally proposed by Lorat- tanasane and Kikuchi [193]. Figure 3.19 depicts a transmission link of 6 spans with and without mid-link OPC for nonlin- ear phase noise compensation. We assumes the every EDFA has the same output power and introduces the same amount of ASE onto the signal. The ASE generated by an EDFA adds amplitude noise to the signal. When the signal plus amplitude noise subsequently propagates over the another fiber span, it introduces a nonlinear phase shift to the signal that is dependent on the total power level (i.e. signal plus noise). The total nonlinear phase shift is defined by the number of spans that the ASE propagates along the link and therefore accumulates with ¸ρ tot,N ) =¸ρ tot,N−1 ) +N ¸ρ), where ¸ρ) is the nonlinear phase shift added in the first span and N is the n th span of the transmission link. It can be shown that this is equal to, ¸ρ tot,N ) =¸ρ) n=N ∑ n=1 n =¸ρ) N 2 (1+N). (3.16) RX TX <ȡ> 0 +1 +2 +3 +4 +5 +6 +7 <ȡtot> 0 1 3 6 10 15 21 28 RX TX <ȡ> 0 +1 +2 +3 -3 -2 -1 0 0 +1 +2 +3 +1 +2 +3 +4 <ȡtot> 0 1 3 6 4 5 9 16 OPC + + A B C D E F G (a) (b) phase conjugated terms Figure 3.19: Nonlinear phase noise compensation using optical phase conjugation (after [193]). When mid-link OPC is used in the transmission link, the nonlinear phase noise can be partly compensated. This is depicted in Figure 3.19b, which shows how the nonlinear phase noise adds up along the transmission link. As an example, we now take the amplitude noise generated by amplifier B. After amplifier B, the signal plus noise propagates over two spans before reaching the OPC unit (between amplifiers B and D), generating a nonlinear phase shift equal to 2¸ρ). The OPC unit conjugates this signal, which reverses the sign of the nonlinear phase shift but keeps the power of the signal plus noise unchanged. After the OPC unit, transmission over the two more spans (between amplifiers D and F) generates again the same nonlinear phase shift equal to 2¸ρ). However, the contribution to the nonlinear phase shift before and after the OPC have an opposite sign and therefore add up to zero. In the last two spans (between amplifier F and Rx) another nonlinear phase shift equal to 2¸ρ) is generated, which is not compensated anymore. The total nonlinear phase shift generated by the noise of amplifier B, reduces therefore from 6¸ρ) to 2¸ρ). Computing this for all amplifiers shows that the total nonlinear phase shift is reduced from 64 3.6. Optical phase conjugation 28¸ρ) to 16¸ρ)). Note that it is beneficial to place the OPC unit at 66% of the transmission link. For example, when in the example in Figure 3.19 the OPC unit is placed after then 5 th span, the total nonlinear phase shift is reduced to 7¸ρ). The nonlinear phase noise penalty is related to the nonlinear phase noise variance, rather than the average and scales with ¸ρ 2 )N 3 [193]. McKinstrie et. al. showed in [217] that with mid-link OPC the accumulated nonlinear phase noise variance becomes proportional to (2¸ρ 2 ))(N/2) 3 = ¸ρ 2 )(N 3 /4), resulting in about 6 dB phase noise suppression. When the OPC unit is placed at 66% of the transmission link, the phase noise reduction can be increased to 9.5 dB. However, the OPC can then not fully compensate for the chromatic dispersion of the link. When not every amplifier adds the same amount of noise to the signal, the optimum placement of the OPC unit changes. For example, amplitude distortions in the transmitted signal can be modeled as an amplifier with a high noise factor. The optimum placement of the OPC unit to compensate for transmitter-induced impairments is at 50% of the transmission link. This will shift the optimal position of the OPC unit more towards the middle of the link. Re(E) I m ( E ) 10 -6 10 -5 10 -4 10 -3 Re(E) I m ( E ) 10 -6 10 -5 10 -4 10 -3 /wo OPC /w OPC 50% Re(E) I m ( E ) 10 -6 10 -5 10 -4 10 -3 P r o b a b i l i t y /w OPC 66% (a) (b) (c) Figure 3.20: Simulated constellation diagrams of DPSK modulation, (a) without OPC, (b) with OPC at 50% of the transmission link and (c) with OPC at 66% of the transmission link. Figure 3.20 illustrates the compensation of nonlinear phase noise through OPC in a long-haul transmission link. Simulated is single channel DPSK transmission (see Section 4.3) over 30 x 90-km spans with a 3-dBm input power per span and the ASE added along the transmission line. The fiber attenuation is α = 0.25 dB/km, fiber nonlinearity γ = 1.3 W −1 km −1 and chromatic dispersion is neglected. Without OPC, a constellation plot is obtained that illustrates the typical ying-yang shape of a nonlinear phase noise distorted signal. This shape disappears partly or completely when OPC is used to reduce the impact of nonlinear phase noise. In particular when the OPC unit is placed at 66%, the impact of nonlinear phase noise is almost fully compensated. 65 Chapter 3. Long-haul optical transmission systems 66 4 Binary modulation formats Many different modulation formats exist that use either amplitude, phase, frequency or polariza- tion modulation to either transmit information or enhance the transmission tolerance. We focus here on the most significant binary modulation formats that are deployed in long-haul transmis- sion systems. As a reference format we use NRZ-OOK modulation, as this currently still the most widely de- ployed modulation format for terrestrial long-haul transmission systems. The other modulation formats are evaluated in comparison to OOK. First of all, Section 4.1 introduces briefly the ad- vantages and disadvantages of OOK modulation. Subsequently, Section 4.2 described duobinary modulation, which is currently the most widely used modulation format for 40-Gb/s transmis- sion. We then focus on phase shift keyed modulation formats, which is likely to replace duobi- nary modulation for long-haul 40-Gb/s transmission. Differential phase shift keying (DPSK) is discussed in Section 4.3. Finally, in Section 4.4 we describe a narrowband filtering tolerant DPSK format, known as partial DPSK. 4.1 On-off-keying From the first application of fiber optics in the middle of the 1970’s until only recently, NRZ- OOK has been the modulation format of choice for most commercial applications. NRZ-OOK is an amplitude modulation format, as it encodes the information in the amplitude of the optical field. The transmitter and receiver structure of NRZ-OOK modulation is depicted in Figure 4.1. At the transmitter, NRZ-OOK is realized by switching the output of a laser ON or OFF, de- pending on the information to be transmitted. Direct modulation can be used for NRZ-OOK 67 Chapter 4. Binary modulation formats laser data Tx PD 0 0 1 1 1 0 data Rx -100 -50 0 50 100 Frequency (GHz) -40 -30 -20 -10 0 P S D ( d B ) optional MZM clock MZM Figure 4.1: NRZ-OOK transmitter and receiver structure and simulated optical spectrum for 42.8-Gb/s NRZ-OOK. modulation, as well as external modulators. For long-haul transmission systems, external mod- ulation with a MZM is normally preferred to reduce the residual chirp in the modulated signal. The MZM modulates the output of a laser, typically a distributed feedback laser (DFB), which results in a chirp-free signal with high extinction ratio. The operation of a MZM for NRZ-OOK modulation is depicted in Figure 4.2a. The MZM is biased in the quadrature point and is driven from minimum to maximum transmittance. The electrical drive signal requires therefore a peak- to-peak amplitude of V π . Note that due to the nonlinear transmission function of the MZM, overshoots and ripples on the electrical drive signal can be suppressed during modulation. The optical spectrum of a NRZ-OOK modulated signal is depicted in Figures 4.1 and 4.2b, respectively. This shows the power spectral density (PSD) as function of optical frequency. NRZ-OOK has a strong component at the carrier frequency, which contains half the optical power and is referred to as the carrier. The spectrum further shows clock tones that are spaced at multiples of the symbol rate, but which are strongly reduced compared to the carrier component. The bandwidth of the optical spectrum is approximately twice the symbol rate. Bias V 0 Electrical drive signal Quadrature Optical phase = t T r a n s m i t t a n c e V t Optical phase = 0 Crest Trough Time Time (a) (b) (c) 93 ps P o w e r ( a . u ) 93 ps P o w e r ( a . u ) Figure 4.2: (a) Operation of the MZM for OOK modulation and eye diagrams showing, respectively, (b) 10.7-Gb/s NRZ-OOK and (c) 10.7-Gb/s RZ-OOK modulation. 68 4.2. Duobinary The simple transmitter and receiver structure of OOK modulation comes at the cost of subopti- mal transmission properties. In particular the nonlinear tolerance is low due to the strong optical carrier in OOK modulation. The nonlinear tolerance can be improved through RZ pulse carving, which results in RZ-OOK modulation [111, 218]. Without RZ pulse carving, OOK is referred to as NRZ-OOK, which is often abbreviated to NRZ. The most suitable RZ-OOK modulation format for WDM transmission is CSRZ. As discussed in Section 3.1.1, the RZ pulse caring re- sults in a 180 o phase change between consecutive symbols for CSRZ. Because of this alternating phase change, the optical field has a positive sign for half the ’1’ symbols, whereas the other half has a negative sign. This results in a zero-mean optical field envelope, which suppresses the carrier component. The zero-mean optical field also improves the nonlinear tolerance in the pseudo-linear regime where there is strong pulse overlapping. Another approach to improve the nonlinear tolerance is the use of chirped RZ-OOK modulation, also known as CRZ. In CRZ, a specific amount of phase modulation is imposed on the RZ- OOK signal [219, 220]. Chirped RZ-OOK has an increased nonlinear tolerance in comparison to RZ-OOK modulation, but at the same time the signal chirp results in spectral broadening. This implies there is a trade-off between spectral efficiency and nonlinear tolerance for CRZ, and the optimum phase modulation index therefore depends on the system properties. CRZ modulation can be generated by modulating the phase of the RZ-OOK signal using a phase modulator (PM). Note that CRZ thus requires three modulators in cascade, for data coding, pulse carving and phase modulation, respectively. This either requires careful synchronization of the three drive signals or an integrated CRZ modulator such as reported by Griffin et. al. in [221]. Because of its higher nonlinear tolerance, CRZ is used in ultra long-haul (transoceanic) transmission systems. 4.2 Duobinary Duobinary modulation is the best known example of a class of coding formats known as partial response codes, or alternatively known as phase engineering or phase coding formats. Similar to OOK, such modulation formats transmit the information in the amplitude domain and rely on straightforward direct detection at the receiver. But unlike OOK, there is predefined phase relation between consecutive bits that can be used to improve the optical filtering tolerance as well as the chromatic dispersion tolerance. Duobinary is sometimes also referred to as pseudo binary transmission (PSBT) [222]. Duobinary has originally been introduced in the 1960’s by Lender as a suitable technique to trans- mit binary data into an electrical cable with a high-frequency cutoff characteristic [223, 224]. The main characteristic of duobinary modulation is a strong correlation between consecutive bits, which results in a more compact spectrum. It can either be generated as a 3-level amplitude signal (’0’, ’0.5’, ’1’) or as a 3-level signal that combines phase and amplitude signaling (’-1’, ’0’, ’1’), which is referred to as AM-PSK modulation [224]. The first optical duobinary experi- ment using 3-level amplitude modulation was reported at 280 Mb/s by O’Mahony in 1980 [225]. However, duobinary generation through 3-level amplitude modulation results in a lower receiver 69 Chapter 4. Binary modulation formats sensitivity as the symbol distance is reduced by a factor of two [226]. Optical transmission ex- periments using AM-PSK modulation for duobinary generation have therefore gained interest in the mid-90’s [227, 228]. The use of AM-PSK duobinary generation is advantageous in optical communication as it has ideally the same or an even better OSNR requirement than OOK mod- ulation [228]. At the same time the narrower optical spectrum and strong correlation between consecutive bits result in an increased dispersion tolerance [227]. This has made duobinary mod- ulation a useful modulation format to increase the robustness of 10.7-Gb/s and 42.8-Gb/s optical transmission systems where the chromatic dispersion tolerance is a key design parameter. laser PD data Rx Precoded data Tx 1 1 1 0 0 0 -1 0 0 -1 0 1 1 1 0 0 B/4 -100 -50 0 50 100 Frequency (GHz) -40 -30 -20 -10 0 P S D ( d B ) encoder decoder ~ ~ MZM Figure 4.3: Duobinary transmitter and receiver structure and optical spectrum of 42.8-Gb/s duobinary. The transmitter and receiver structure of duobinary modulation is shown in Figure 4.3. Analo- gous to OOK modulation, the transmitter consists of a standard MZM. In addition, the electrical signal is encoded before modulation to realize the required correlation between consecutive bits that characterizes duobinary modulation. Prior to encoding, the logical signal is first pre-coded, such that at the receiver the transmitted sequence is again recovered. The pre-coder therefore implements the inverse transfer function of the encoder, modulation and decoder combined. A duobinary pre-coder can be implemented through the operation, b(k) = d(k) ⊕b(k −1). (4.1) where d(k) represents bit k of the input sequence, b(k) is the sequence after pre-coding and ⊕ is a logic exclusive OR operation. The pre-coder implementation is therefore a recursive operation, which is difficult to realize with high-speed electronics. An alternative non-recursive implementation consists of an ANDoperation of the input sequence and clock signal, followed by a toggle flip-flop (T-FF) [229]. Note that pre-coding is not required in transmission experiments that uses a PRBS to evaluate the performance, as the duobinary encoding then merely results in a cyclic shift of the input sequence. The phase coding in duobinary modulation is exemplified in Figure 4.4. A logical / 0 / is coded as a zero whereas a logical / 1 / is coded as either / −1 / or / 1 / . Consecutive logical / 1 / s have a 180 0 phase shift when they are separated by an odd number of logical / 0 / s. The duobinary signal constellation in Figure 4.4 depicts the three constellation points and the binary logical symbols that they represent. Duobinary encoding can be realized through a delay-and-add, c(k) = b(k) +b(k −1), (4.2) where c(k) is the output sequence of the encoder that is used for modulation. Note that the encoder operation converts a binary signal into a 3-level amplitude signal. To realize duobinary 70 4.2. Duobinary 1 -1 ǻij Re{E} Im{E} 0 -1 0 1 R e { E } [ s q r t ( m W ) ] 0 100 200 300 400 500 600 Time (ps) 0 0 -1 0 0 0 1 0 -1 0 0 -1 0 1 0 -1 0 0 -1-1-1-1 0 1 1 1 1 0 2E S Logical ‘1’ Logical ‘0’ Figure 4.4: Duobinary signal and signal constellation. modulation with a MZM, the electrical driving voltage should have a peak-to-peak voltage of 2V π and the MZM has to be biased in the trough point. The MZM then switches between two crest points, which have a 180 o phase difference. This effectively maps: 0 → exp( j π) = -1 1 → 0 = 0 , 2 → exp( j 0) = 1 which is equal to the duobinary partial response code. However, on itself the duobinary partial response code does not result in an improved chromatic dispersion tolerance. To improve the dispersion tolerance the spectral width has to be reduced by electrically low-pass filtering the signal with a B 0 /2 bandwidth, where the bandwidth B 0 is twice the inverse of the symbol period (B 0 = 1/T 0 ). For ’standard’ binary coding, low-pass filtering with a B 0 /2 bandwidth results in severe eye closing. This is best exemplified with a ’1 0 1’ logical sequence. Low-pass filtering results in energy leakage from the surrounding ’1’ into the middle ’0’ which closes the eye. But duobinary encoding does not allow a logical sequence ’1 0 1’ to occur, instead coding it to ’-1 0 1’ or ’1 0 -1’. The energy from the surrounding ’-1’ and ’1’ that leaks into the middle ’0’ through narrowband filtering nowdestructively interferes, which limits the eye closing. As a result, strong low-pass filtering does not impact the signal too severely. The delay-and-add operation can be replaced by low-pass filtering the signal with a B 0 /4 bandwidth. The narrowband electrical filtering results in a compact optical spectrum, which is evident from comparing the optical spectrum of duobinary modulation (Figure 4.3) and OOK modulation (Figure 4.1). Duobinary modulation with a MZM preceded by electrical low-pass filtering is depicted in Fig- ure 4.5a, and Figure 4.5b shows the eye diagram for 10.7-Gb/s duobinary modulation. Due to its simplicity this transmitter structure has become the standard duobinary implementation. The low electrical bandwidth allows for a further simplification as the MZM modulator used in duobi- nary transmitter only requires a B 0 /4 electro-optical bandwidth [230, 231]. Hence a 42.8-Gb/s duobinary transmitter can be realized using a ∼10-Gb/s modulator. At the receiver, the decoding of duobinary modulation results directly from the square-law detection [E[ 2 of the photodiode, i.e. −1 →1, 0 →0 and 1 →1. Duobinary modulation therefore uses the same direct detection receiver as NRZ-OOK modulation. The duobinary eye diagram in Figure 4.5b shows a triangular shape with residual energy in the / 0 / s. This results in a 2-3 dB back-to-back OSNR penalty compared to NRZ-OOK modula- tion. Kim et.al. showed that the OSNR requirement of duobinary can be significantly improved through narrowband optical filtering at either the transmitter or receiver [232]. The optimal op- 71 Chapter 4. Binary modulation formats Bias V 0 Electrical drive signal Quadrature Optical phase = t T r a n s m i t t a n c e 2V t Optical phase = 0 Crest Trough T i m e Time (a) (b) (c) Electrical drive signal after low pass filtering After narrowband optical filtering 93 ps 93 ps P o w e r ( a . u ) ~ ~ ~ ~ ~ 3B 0 /4 B 0 /4 Optical Filter Electrical filter Figure 4.5: (a) Operation of the MZM for duobinary modulation and (b-c) measured eye diagram shows 10.7-Gb/s duobinary (b) without and (c) with additional narrowband optical filtering. tical filter bandwidth is approximately 0.8 B 0 , with a 2 nd order Gaussian shape [233]. After narrowband optical filtering the duobinary signal becomes more NRZ-like, as evident from Fig- ure 4.5c. Figure 4.6a compares the back-to-back OSNR tolerance of duobinary, narrowband filtered duobinary and NRZ-OOK. Narrowband optical filtering at the receiver is particularly in- teresting as it filters out more noise than a broad de-multiplexing filter, which results in a ∼4 dB OSNR improvement [234]. Because of the narrower optical bandwidth the OSNR tolerance for filtered duobinary is approximately 1 dB better than NRZ-OOK [235]. The quantum limit for a theoretically optimal duobinary modulation is therefore also ∼1 dB below the quantum limit of NRZ-OOK modulation [236]. However, the theoretically obtainable performance of duobinary modulation is hard to achieve in practice. In a commercial transponder penalties often arise from variations in the electrical component bandwidth. This can be improved through the integration of a narrowband optical filter, but for a 10-Gb/s receiver this requires a very narrow optical fil- ter with a ∼8-GHz bandwidth. For a 40-Gb/s receiver, optical filtering is more practical as the required filter bandwidth scales inversely with the symbol rate. Optical filters with a 32-GHz bandwidth are readily available. The OSNR tolerance of duobinary is also improved through the use of RZ-duobinary instead of NRZ-duobinary, which can be generated using an additional pulse carver at the transmitter. However, the broader optical bandwidth of RZ-duobinary cancels out the improved chromatic dispersion tolerance that characterizes duobinary, which becomes similar to RZ-OOK modula- tion. Although the chromatic dispersion tolerance can be recovered through narrowband optical filtering at the receiver this again reduces the OSNR tolerance [237]. RZ-duobinary is therefore only sporadically used in optical transmission experiments and not in deployed transmission sys- 72 4.2. Duobinary tems. A different application of RZ-duobinary is the reduction of intra-channel impairments, in which it obtains a similar performance as CSRZ [111]. Figure 4.6b shows the chromatic dispersion tolerance of duobinary. In the absence of narrow- band optical filtering, a / w / shape is obtained in the dispersion curve. This is typical for duobinary modulation. The / w / shape disappears when the duobinary signal is narrowband optical filtered, which improves the back-to-back OSNR requirement. We note that the narrowband optical fil- tering strongly reduces the chromatic dispersion tolerance for a 2-dB OSNR penalty. However, this is not due to a reduction in the absolute dispersion tolerance but rather a side-effect of the improved back-to-back OSNR requirement. The residual energy in the / 0 / s that cause the ’w’ shape in the dispersion tolerance also reduces the DGD tolerance of duobinary modulation. In the presence of DGD the pulses spread out, which further raises the residual energy in ’0’s and results in an OSNR penalty. We note though that the SOPMD tolerance of duobinary is more beneficial; the narrow optical spectrum reduces the PSP depolarization and the large chromatic dispersion tolerance reduces the impact of PCD [238]. (a) 10 12 14 16 18 20 22 24 -11 -9 -7 -5 -4 -3 -2 OSNR (dB/0.1nm) l o g ( B E R ) (b) BER = 10 -5 -300 -200 -100 0 100 200 300 16 18 20 22 24 26 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) Figure 4.6: Simulated comparison of (a) back-to-back OSNR tolerance and (b) chromatic dispersion tolerance for 42.8-Gb/s duobinary, 42.8-Gb/s filtered duobinary 42.8-Gb/s NRZ-OOK. The opti- cal filter bandwidths are 90-GHz 3rd order Gaussian for duobinary and OOK, and 34-GHz 2nd order Gaussian for filtered duobinary. Duobinary modulation has been used extensively in long-haul transmission experiments at 10.7- Gb/s [239] and 42.8-Gb/s [240, 241, 242] bit rates. The narrower spectral width of duobinary makes it a good candidate for DWDM transmission with narrow channel spacing [243]. Hence, duobinary modulation can be used to realize 42.8-Gb/s transmission with a 50-GHz channel spacing, enabling a 0.8-b/s/Hz spectral efficiency [240, 241]. Besides duobinary modulation there are a large number of other partial response codes that offer similar properties [244]. But the simplicity of duobinary encoding through electrical low-pass filtering has made it the most widely used partial response format. Higher-level partial response (polybinary) codes generally do not offer a further improvement in the dispersion tolerance. Although such formats concentrate the power closer to the carrier, they cannot further reduce the total spectral width in comparison to a duobinary signal [245]. 73 Chapter 4. Binary modulation formats 4.3 Differential phase shift keying Both OOK and duobinary modulation encode the information in the amplitude of the optical sig- nal. Binary phase shift keying (BPSK), on the contrary, encodes the information in the signal’s phase. Because a photodiode is only sensitive to the incident optical power, phase shift keying requires demodulation at the receiver before it can be detected. Various schemes are capable of demodulating BPSK signals. Homodyne demodulation provides the best performance but is complex to realize. In optical transmission systems a low-complexity self-homodyne (interfero- metric) demodulation scheme is therefore often used [10, 246]. With self-homodyne demodula- tion, the information is encoded in the differential phase of the optical signal. Hence, the name differential BPSK, or DPSK. data Rx laser MZDI T + - PD Balanced detection (c) (d) (b) (e) 1 -1 -1 1 -1 -1 (c) (d) (b) (e) 23 ps P o w e r ( a . u ) 23 ps 23 ps 23 ps (a) precoded data Tx optional MZM clock MZM Figure 4.7: (a) Transmitter and receiver structure of RZ-DPSKand (b-e) measured eye diagrams for 42.8- Gb/s RZ-DPSK; (b) before phase demodulation, (c) constructive component, (d) destructive component and (e) after balanced detection. 1 0 1 -1 ǻij OOK: Re{E} Re{E} Im{E} Im{E} DPSK: 2 E S E S Figure 4.8: Signal constellations for binary OOK and binary DPSK modulation, both signal constella- tions have the same average optical power. The transmitter and receiver structure of DPSK modulation is shown in Figure 4.7. DPSK mod- ulation has a number of advantages over OOK modulation that makes it a suitable modulation format for robust long-haul transmission systems. The main benefit of DPSK modulation is the lower OSNR requirement when compared to OOK. This can be understood directly from the signal constellation, as visualized in Figure 4.8. In the case of OOK modulation, the difference 74 4.3. Differential phase shift keying between the two constellation points equals the signal energy E s , assuming NRZ pulse coding, an infinite extinction ratio and an average optical power 1/2 0+1/2 [E s [ 2 =1/2 [E s [ 2 . For DPSK, both constellation points have the same signal energy but a differential phase of either ∆φ = 0 or ∆φ = π. When the difference between the two constellation points equals √ 2E s the average power of DPSK is the same as for OOK, i.e. 1/2 [1/ √ 2E s [ 2 +1/2 [1/ √ 2E s [ 2 = 1/2 [E s [ 2 . However, as the symbol distance is increased with a factor √ 2 in comparison to OOK modula- tion, we obtain a ∼3-dB advantage in OSNR tolerance. Bias V 0 Electrical drive signal Quadrature Optical phase = t T r a n s m i t t a n c e 2V t Optical phase = 0 Crest Trough Time Time (b) (c) (a) 93 ps P o w e r ( a . u ) 93 ps P o w e r ( a . u ) Figure 4.9: (a) Operation of the MZM for DPSK modulation and eye diagrams before phase demodula- tion showing, respectively, (b) 10.7-Gb/s NRZ-DPSK and (c) 10.7-Gb/s RZ-DPSK modulation. 4.3.1 Transmitter structure As DPSK modulation carries the information in the optical phase, the most straightforward mod- ulator configuration is based on a phase modulator. An (ideal) phase modulator changes only the phase of the optical signal, which results in constant amplitude. However, as the electro- optical bandwidth of a practical phase modulators is limited, the 180 o phase transition is not instantaneous, which introduces chirp between symbol transitions. In the presence of chromatic dispersion and/or nonlinear impairments, this chirp limits transmission tolerances. The more practical DPSK transmitter design is, similar to OOK modulation, based on a MZM. DPSK modulation with a MZM is depicted in Figure 4.9. The MZM is biased in the trough of the modulator curve and the electrical driving voltage has a peak-to-peak voltage of, ideally, 2V π . The MZM therefore switches between two crest points, which encodes the 180 o phase jumps. This is visible in the NRZ-DPSK output signal, which shows characteristic intensity dips when the MZM switches from / −1 / to / 1 / or vice-versa. The width of the intensity dips in the NRZ-DPSK signal depends on the electro-optical bandwidth of the MZM and/or the bandwidth of the electrical drive signal. The electro-optical bandwidth of a MZM is similar to what can be 75 Chapter 4. Binary modulation formats realized for a phase modulator. But as a MZM has exact 180 o phase changes, it does not suffer from modulator induced chirp. When the DPSK modulator is followed by an additional pulse carver the NRZ pulse shape is converted to a RZ shape, similar as discussed for OOK modulation. For DPSK, pulse carving with a 66% duty-cycle does not result in alternating phase coding but merely inverts the encoded information in the DPSKsignal. It is therefore not fully correct to refer to CSRZ-DPSK, although the abbreviation is often used in the literature. Figure 4.9b and 4.9c show typical eye diagrams for 10.7-Gb/s NRZ-DPSK and RZ-DPSK, respectively. As DPSK modulation is based on differential detection, it requires pre-coding of the transmitted sequence. The pre-coder for DPSK is similar to the pre-coder required for duobinary modulation (Section 4.2,[239]). Note that the ’encoding’ of the signal is, in contrast to duobinary modulation, not realized at the transmitter but through the phase demodulation at the receiver. 4.3.2 Receiver structure In a DPSK receiver, the differential phase modulation is normally converted into amplitude mod- ulation using a Mach-Zehnder delay-line interferometer (MZDI). An MZDI demodulates the differential phase between each data bit and its successor, which implements the differential de- coding of DPSK modulation. Figure 4.10 depicts in more detail the phase demodulation with an MZDI. The optical input signal before demodulation is NRZ-DPSK modulated and has an aver- age optical power of 1 mW (Figure 4.10a). The center spectral lobe of the NRZ-DPSK optical spectrum has a width equal to twice the signal bandwidth, 2B 0 = 2/T 0 . The MZDI splits up the signal in two copies, delays one copy over a single bit period ∆T in [s] and recombines both arms to create optical interference. Note that ∆T is not necessarily equal to the symbol period T 0 (e.g. for partial DPSK). The transfer function of the MZDI is defined through, u ± (t) = r(t) ±exp( j∆φ)r(t −∆T), (4.3) where u ± (t) is the constructive and destructive component, respectively. r(t) is the input signal and ∆φ the phase difference between both interferometer arms. The phase difference is ideally ∆φ = 0±π. This can be understood by noting that for this phase shift and an unmodulated input signal, destructive interference occurs at one of the outputs and constructive interference at the other output. Hence, the output ports of the MZDI are referred to as the constructive and de- structive port, respectively. When ∆T is the delay in the interferometer arm, the constructive and destructive output ports exhibits a periodic notch response with a 3-dB bandwidth of 1/(2∆T) and a free spectral range (FSR) of 1/∆T. The constructive and destructive components obtained after demodulation are depicted in Figures 4.10b and 4.10c, respectively. Both signal components have a different optical spectra and signal structure but carry the same (but inverted) information. The optical spectrum of the constructive output port has a central lobe with a spectral width of B 0 = 1/T 0 , which results in duobinary modulation [247, 248]. In the optical spectrum of the destructive output signal the carrier frequency is suppressed, which results in an alternating mark 76 4.3. Differential phase shift keying inversion (AMI) signal. An AMI signal has a 180 o phase jump between each consecutive ’1’, which gives the characteristic RZ shape of the AMI signal. An MZDI can be realized with different technologies, for example with fiber-optic couplers [249], a fiber-Bragg grating [250] or free space technology [251]. An MZDI based on fiber- optic couplers requires active phase stabilization, as even slight changes in temperature result in a change in the differential delay of a fraction of an optical cycle. The path-length difference changes the interference between the two signals, which would degrade signal quality without an active control. An MZDI based on free-space technology is athermal and therefore does not require active phase stabilization. However, the drawback of an MZDI design without active control is that the phase difference between the two interfering arms cannot be adjusted to the center frequency of the received signal. Hence, such an MZDI must be matched to a predefined wavelength (usually the ITU grid). When the MZDI should be colorless, i.e. when it can be used for any WDM channel, this implies a fixed 50-GHz FSR, instead of 43-GHz FSR as would be optimal for a 43-Gb/s bit rate. Closely related to the phase stabilization of an MZDI, but more difficult to avoid, is the pola- rization dependent wavelength shift (PDλ). When both arms of the MZDI have a polarization dependent propagation coefficient, the periodic notch response of the MZDI is dependent on the SOP of the incoming light. As an example, we assume that the phase offset in the MZDI is mini- mized for a certain input SOP. The worst penalty then occurs when the input SOP changes to the orthogonal SOP on a time scale faster than the phase offset control loop. There is a high proba- bility this will occur, since polarization changes are generally much faster than a thermal control. The penalty that results from a PDλ can be avoided through polarization tracking, but this is impractical as it significantly raises the receiver complexity. Minimizing the PDλ is therefore one of the more important criteria in the design of an MZDI. Both the constructive and destructive output port of an MZDI carry the full information of the DPSK signal. Therefore, detecting either only the constructive or destructive output is sufficient. This is known as single-ended detection. But in order to obtain the ∼3-dB OSNR improvement of DPSK over OOK modulation, both MZDI output ports have to be detected simultaneously. This is known as balanced detection, which uses two photodiodes followed by a differential amplifier. The transfer function of a DPSK receiver, i.e. the MZDI plus balanced detection is now defined through, u(t) = [u + (t)[ 2 −[u − (t)[ 2 (4.4) = [ 1 2 r(t) +exp( j∆φ) 1 2 r(t −∆T)[ 2 −[ 1 2 r(t) −exp( j∆φ) 1 2 r(t −∆T)[ 2 , where u(t) is the output after balanced detection. This is depicted in Figure 4.10d, which shows that the peak-to-peak amplitude of the balanced output is twice that of the constructive and de- structive signal, separately. Figure 4.7 depicts measured eye diagrams for 42.8-Gb/s RZ-DPSK before demodulation and the constructive, destructive and balanced signals after demodulation. 77 Chapter 4. Binary modulation formats 0 0.5 1 -100 -50 0 50 100 Frequency (GHz) -40 -30 -20 -10 0 10 -1 0 1 R e { u ( t ) } [ m A ] 0 100 200 300 400 500 600 700 800 Time (ps) R e { u + { t ) } [ s q r t ( m W ) ] 0 100 200 300 400 500 600 700 800 -1 0 1 0 100 200 300 400 500 600 700 800 (b) -100 -50 0 50 100 Frequency (GHz) -40 -30 -20 -10 0 10 (c) -100 -50 0 50 100 Frequency (GHz) -40 -30 -20 -10 0 P S D ( d B ) (a) Optical input Constructive Destructive (1) Optical input signal (3) Alternating mark inversion (AMI) (2) Duobinary (4) Output differential amplifiers 0 0.5 1 | r ( t ) | 2 [ m W ] -40 -20 0 20 40 Time (ps) -40 -20 0 20 40 Time (ps) -1 0 1 R e { u ( t ) } [ m A ] -40 -20 0 20 40 Time (ps) -1 0 1 A m p l i t u d e [ s q r t ( m W ) ] -40 -20 0 20 40 Time (ps) 0 0.5 1 0 0.5 1 -1 0 1 1 -1 -1 1 1 1 1 1 -1 1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 -1 1 1 1 1 -1 1 0 0 1 1 1 1 1 0 -1 0 1 1 1 1 0 0 0 0 1 1 1 0 -1-1-1-1 0 1 0 1 -1 0 0 0 0 0 1 0 -1 0 0 0 0 1 -1 1 -1 0 0 0 1 0 0 0 0 -1 0 1 1 -1 1 1 1 1 1 1 -1 -1 1 1 1 1 1 -1 1 -1 1 1 1 1 -1-1-1-1-1 1 1 | r ( t ) | [ s q r t ( m W ) ] R e { u - { t ) } [ s q r t ( m W ) ] | u + ( t ) | 2 [ m W ] | u - ( t ) | 2 [ m W ] 10 ǻij ǻT + - MZDI (1) (2) (3) (4) r(t) u(t) u + (t) u - (t) 2B 0 B 0 2B 0 Figure 4.10: Phase demodulation of 42.8-Gb/s NRZ-DPSK showing the input signal before demodula- tion, as well as the spectra of the constructive, destructive and balanced outputs of the MZDI. The phase difference between the MZDI arms is equal to ∆φ = π in the example. 78 4.3. Differential phase shift keying A special application of DPSK demodulation is the optical generation of either duobinary or AMI modulation. This can be achieved using a DPSK transmitter followed by an MZDI to demodulate either the constructive or destructive component. Especially the generation of optical duobinary via this method has some practical applications. The optical duobinary signal has similar properties as the (electrical) duobinary described in Section 4.2. This can be especially interesting in transmission links where strong narrowband filtering occurs [252]. On the other hand, the transmitter is more complicated as it requires an MZDI and higher bandwidth optical and electrical components (drive amplifiers, optical modulator). 4.3.3 Back-to-back OSNR requirement The use of interferometric detection in DPSK allows for a lower-complexity receiver but requires a high OSNR to obtain the same performance as homodyne (coherent) detection. Figure 4.11 compares the theoretical performance of the different detection schemes for 10.7-Gb/s DPSK. The difference in OSNR requirement between 10.7-Gb/s DPSK with coherent and direct detec- tion is 0.6 dB for a 10 −3 BER. Differential detection is not required in a coherent receiver and this can improve the OSNR requirement with a further 0.55 dB. The total difference in OSNR requirement between 10.7-Gb/s BPSK with coherent detection and DPSK with direct detection is therefore 1.1 dB for a 10 −3 BER. 2 3 4 5 6 7 8 9 10 -10 -8 -6 -4 -3 -2 OSNR (dB/0.1nm) l o g ( B E R ) 16 14 12 10 8 Q ( d B ) FEC limit Figure 4.11: Theoretical performance of 10.7-Gb/s DPSK modulation direct detection with an MZDI, coherent detection with differential decoding, coherent detection without differential decoding. The difference is slightly dependent on the BER and it can be shown that the theoretical re- ceiver sensitivity or ’quantum limit’ at a BER of 10 −9 is 18 photons/bit for coherent BPSK and 20 photons/bit [253] for direct detection DPSK. In comparison, for OOK with direct detection the quantum limit is 38 photons/bit. Hence the theoretical sensitivity difference between OOK and DPSK modulation is 2.8 dB at low BER. Experimental verification has shown receiver sen- sitivities for direct detection DPSK of 30 photons/bit [254] and 38 photons/bit [255, 112] at a bit rate of 10 Gb/s and 42.7 Gb/s, respectively. Besides the lower OSNR requirement, coherent detection can have further advantages over in- terferometric detection in the nonlinear transmission regime. Interferometric detection compares the phase difference between two consecutive symbols; the sensitivity penalty is therefore a prod- uct of the phase error in both symbols. When one assumes an ideal transmitter and LO laser in 79 Chapter 4. Binary modulation formats coherent detection (i.e. no phase noise) the penalty only dependent on the phase error in the received symbol itself. Hence, coherent detection theoretically reduces the impact of nonlinear phase noise by a factor of two in comparison to interferometric detection [256]. The main draw- back of homodyne demodulation is the higher complexity of a coherent receiver as it requires the detection of the full optical field, including the state of polarization. Because of its relative sim- plicity, self-homodyne demodulation is therefore the preferable choice for deployed transmission systems. A practical approach for homodyne demodulation that is currently under consideration is a coherent intra-dyne receiver, which is discussed in Chapter 10. In this section we further discuss the properties of DPSK modulation using a direct detection receiver. 10 12 14 16 18 20 22 -12 -10 -8 -6 -5 -4 -3 -2 OSNR (dB/0.1nm) l o g ( B E R ) Modulation required format OSNR (dB) for 10 −3 BER RZ-DPSK, balanced 11.1 NRZ-DPSK, balanced 11.8 NRZ-DPSK, constr. 14.3 NRZ-DPSK, destr. 13.6 NRZ-OOK 15.2 Figure 4.12: Simulated OSNR requirement for 42.8-Gb/s NRZ-DPSK, balanced, 42.8-Gb/s RZ- DPSK, balanced, 42.8-Gb/s NRZ-DPSK, constructive, 42.8-Gb/s NRZ-DPSK, destructive, 42.8- Gb/s NRZ-OOK. In all cases a 90-GHz optical filter bandwidth is used The difference in OSNR requirement between DPSK and OOK modulation depends on pulse shape and receiver parameters. For the simulations depicted in Figure 4.12, the difference in required OSNR between NRZ-DPSK and NRZ-OOK is 3.4 dB. The >3-dB penalty is a result of the broad 90-GHz optical filter bandwidth used in the simulations. For DPSK modulation, the transfer function of the MZDI narrowband filters the signal which reduces the spontaneous- spontaneous beat noise in the signal. For OOK, on the other hand, the OSNR requirement is higher as the spontaneous-spontaneous beat noise is not filtered out. It is further observed that the constructive and destructive components of the NRZ-DPSK signal differ by 0.7 dB in OSNR requirement. This is a consequence of the RZ pulse shape of the destructive (AMI) components in comparison to the NRZ-pulse shape of constructive (duobinary) component. For the same reasons, a 0.7 dB difference in OSNR is observed between NRZ-DPSK and RZ-DPSK. The difference between NRZ-DPSKand the constructive/destructive component is 2.5 dBand 1.8 dB, respectively, for a 10 −3 BER but increases for lower BER. We note that with narrowband optical filtering the comparison changes as each of the signal has a different optimal filter bandwidth. However, a 90-GHz filter bandwidth is a reasonable assumption for transmission systems with a 100-GHz channel spacing. 80 4.3. Differential phase shift keying 4.3.4 Receiver imperfections Imperfection in the phase demodulation have a significant impact on the optical performance characteristics of a DPSK receiver [257, 258]. A direct detection DPSK receiver can be impaired through, for example, an amplitude or time imbalance between the constructive and destructive outputs. The amplitude imbalance results in a shift of the optimum threshold whereas the time imbalance offsets the constructive and destructive components, resulting in a skewed eye dia- gram. Furthermore, the phase differences and bit-delay between the signal and its delayed copy upon interfere within the MZDI are important to consider. The bit-delay in the MZDI is an im- portant aspect for partial DPSK, and is therefore discussed extensively in the next section. We note that although the simulated results are for a 42.8-Gb/s symbol rate, most of the receiver imperfections are bit rate independent. -1 -0.5 0 0.5 1 13 14 15 16 17 Balanced detector amplitude imbalance (a.u.) R e q u i r e d O S N R ( d B / 0 . 1 n m ) 2.6 dB (a) BER = 10 -5 -60 -40 -20 0 20 40 60 13 14 15 16 17 18 19 20 MZDI phase mismatch (degrees) R e q u i r e d O S N R ( d B / 0 . 1 n m ) (b) BER = 10 -5 Figure 4.13: Simulated DPSK receiver imperfections, (a) amplitude imbalance and (b) phase mismatch; 42.8-Gb/s NRZ-DPSK, 42.8-Gb/s RZ-DPSK. Figure 4.13a shows the amplitude imbalance between the constructive and destructive compo- nent. An amplitude imbalance results from a difference in the pigtail or connector loss in one of the two arms, or a difference in conversion efficiency between the two photodiodes. The amplitude imbalance is defined as [257], α = [u + [ 2 −[u − [ 2 [u + [ 2 +[u − [ 2 , (4.5) where [u − [ 2 and [u + [ 2 are the averaged output powers of both photodiodes before balanced de- tection. The amplitude imbalance varies between α =±1 and is in the extremes equal to single- ended detection of either the constructive or destructive component. For NRZ-DPSK, the curve is slightly asymmetric, which results from the difference in OSNR requirement between the con- structive component (dominant for α < 0) and destructive component (dominant for α > 0). For RZ-DPSK, the difference is negligible as both components have a similar OSNR requirement. The simulated penalty is with 2.6 dB slightly lower than the 2.8-dB penalty that one would ex- pect from theory, which is caused by the higher BER (10 −5 ) used in the simulations. An α = 0.2 81 Chapter 4. Binary modulation formats results in a 0.5-dB penalty, which equals approximately a 1.5 dB difference between the two outputs of the MZDI. The phase offset penalty results from a phase difference upon interference between the two arms of the MZDI, as ∆φ = 0 is optimal. For an OSNR penalty of 1 dB, the allowable phase offset is about 20.5 o (see Figure 4.13b). Note that the penalty is independent of the pulse coding (RZ or NRZ). A phase offset in the MZDI can be induced through (1) wavelength drift of the transmitter laser, (2) temperature drift of the MZDI and (3) polarization-dependent wavelength shift of the MZDI [259]. The phase offset in degrees is related to the laser wavelength through, ∆φ = 360 ∆f ∆T, (4.6) where ∆f is the laser frequency drift in [Hz]. To counter a temperature or laser wavelength drift, the required tracking speed is generally slow and in the seconds range. A (slow) thermal control can therefore be used to change the phase difference between the two arms and as a control signal, the RF power after balanced detection can be measured [260]. When a phase offset is present in the MZDI, the constructive and destructive component are not anymore fully orthogonal to each other, i.e. [u + [ 2 ≈−[u − [ 2 . The substraction of the constructive and destructive component through balanced detection then result in a lower RF power. Hence, a phase offset in the MZDI lowers the RF power obtained after balanced detection and maximizing the RF power will minimize the phase offset in the MZDI. -200 -100 0 100 200 14 16 18 20 22 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) BER = 10 -5 (a) (b) 0 5 10 15 20 14 16 18 20 22 Differential group delay (ps) R e q u i r e d O S N R ( d B / 0 . 1 n m ) BER = 10 -5 Figure 4.14: (a) chromatic dispersion and (b) DGD tolerance for 42.8-Gb/s NRZ and RZ-DPSK; 42.8- Gb/s NRZ-DPSK, after balanced detection, 90-GHz filter 42.8-Gb/s RZ-DPSK, 90-GHz filter. 42.8- Gb/s NRZ-DPSK, destructive component, 60-GHz filter 42.8-Gb/s NRZ-DPSK, constructive component, 40-GHz filter. 4.3.5 Chromatic dispersion & DGD tolerance The chromatic dispersion tolerance of DPSK modulation is depicted in Figure 4.14a. This shows that the dispersion tolerance differs between the destructive and constructive component of DPSK. This difference can be explained by the line coding in both components. Due to its 82 4.4. Partial DPSK duobinary coding, the constructive component has similar properties as duobinary modulation. This improves the dispersion tolerance, although the tolerance is somewhat lower compared to conventional duobinary. The destructive component, on the other hand, has a reduced dispersion tolerance. This results from the RZ-shape of the signal, which broadens the optical spectrum. Note that the optical filter bandwidth for both the constructive and destructive component is different and has been optimized. The chromatic dispersion tolerance after balanced detection is determined by both components. However, together with narrowband filtering (not shown) the dispersion tolerance becomes similar to the tolerance of the constructive component. When we furthermore compare the dispersion tolerance of RZ-DPSK with NRZ-DPSK, a significant reduction is evident. This results from the broader optical spectrum of the RZ signal. In addi- tion, there is no significant difference between the constructive and destructive component for RZ-DPSK. Figure 4.14b shows the DGD tolerance for 42.8-Gb/s NRZ-DPSK and RZ-DPSK. For a RZ pulse shape, there is less ISI for small amounts of DGD because the pulses spread out but not yet interfere with the neighboring pulses. Hence, we find a 9 ps and 10 ps DGD tolerance (1-dB OSNR penalty) for NRZ-DPSK and RZ-DPSK, respectively. For larger amounts of DGD the tolerance of both RZ and NRZ is similar, as the DGD tolerance is mainly determined by the symbol rate. 4.4 Partial DPSK Ideally, 42.8-Gb/s modulated signals can be deployed in transmission systems with a 50-GHz channel spacing. But when OADM/PXCs are passed along the transmission link this result in severe narrowband optical filter, and the optical bandwidth can be reduced to ∼35 GHz. For 42.8-Gb/s NRZ-DPSK modulation this result in high OSNR penalties, which limits the number of add-drop nodes that can be passed When a NRZ-DPSK signal is narrowband filtered, the constructive component remains nearly unaffected because most of the energy is close to the carrier. In addition, the constructive com- ponent has a duobinary line coding which significantly improves its tolerance to narrowband filtering. For the destructive component, on the other hand, most of the energy is relatively far away from the carrier. Narrowband filtering therefore reduces the power in the destructive com- ponent, which becomes distorted. As a result, the signal after balanced detection is asymmetric and the optimum threshold shift towards the constructive component. The use of a shortened MZDI in the DPSK receiver, which has a ∆T < T 0 bit-delay between both arms, improves the narrowband filtering tolerance. This is known as partial DPSK, and was first demonstrated in 2003 by Yoshikane et. al. [261]. Figures 4.15a and 4.15b depicts the concept of partial DPSK and the OSNR requirement as a function of the bit-delay, respectively. This shows that for 42.8-Gb/s NRZ-DPSK there is a strong asymmetry with respect to the 1- bit delay. For ∆T < T 0 , the signal and its delayed copy are only partially overlapping upon interference, which results in deterministic interference at the beginning and end of the symbol 83 Chapter 4. Binary modulation formats delay mismatch 0.65 - bit delay signal delayed over 0.65 x T 0 input signal 1 -1 1 1 -1 1 -1 1 1 -1 (a) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 14 16 18 20 MZDI bit-delay (AT/T 0 ) R e q u i r e d O S N R ( d B / 0 . 1 n m ) BER = 10 -5 (b) Figure 4.15: (a) phase demodulation with < 1-bit delay, (b) OSNR penalty for different MZDI bit-delays 42.8-Gb/s NRZ-DPSK, 90-GHz filter bandwidth 42.8-Gb/s RZ-DPSK, 90-GHz filter bandwidth 42.8-Gb/s NRZ-DPSK, 35-GHz filter bandwidth. period. After balanced detection the electrical signal appears, apart froma negative offset, similar to a duobinary signal. This is evident from Figure 4.16, which shows simulated eye diagrams of the balanced output for several MZDI bit-delays. The shortened bit-delay in the MZDI results in a somewhat higher OSNR requirement. This is explained by the observation that the constructive and destructive components are not fully orthogonal anymore, which results in a lower signal power after balanced detection. For ∆T ¸ T 0 , the destructive component fades out and the penalty is solely determined by the constructive component. For ∆T > T 0 , the symbol transition of the delayed copy occurs in the middle of the symbol period which results in crosstalk. The penalty reduces for ∆T ¸T 0 and is close to zero for ∆T ∼2T 0 as the symbol transitions are again aligned with each other [262]. The impact of a shortened bit-delay on the narrowband filtering tolerance is showin Figure 4.15b. Depicted is the penalty for 42.8-Gb/s NRZ-DPSK with a 35-GHz, 3 rd order Gauss filter as a -100 -50 0 50 100 Frequency (GHz) -40 -30 -20 -10 0 10 P S D ( d B ) -40 -20 0 20 40 Time (ps) -1 0 1 1.0-bit delay 0.65-bit delay 0.5-bit delay 0.34-bit delay -100 -50 0 50 100 Frequency (GHz) -100 -50 0 50 100 Frequency (GHz) -100 -50 0 50 100 Frequency (GHz) -40 -20 0 20 40 Time (ps) -40 -20 0 20 40 Time (ps) -40 -20 0 20 40 Time (ps) R e { E } ( m A ) constr. destr. Figure 4.16: Impact of < 1-bit MZDI delay. The upper row show the optical spectra (0.1-nm res.) of the constructive and destructive output port. The lower row show the electrical signal after balanced detection. 84 4.4. Partial DPSK function of the MZDI bit-delay. For a 1 bit-delay, a 16.0-dB OSNR is required, a 1.9-dB OSNR penalty. When the bit-delay is reduced, the narrowband filtering penalty reduces accordingly, with a minimum penalty for a 0.65 bit-delay. Note that for a 0.65 bit-delay there is a negligible difference in OSNRrequirement between NRZ-DPSK with (35 GHz) and without (90 GHz) opti- cal filtering. This is particulary interesting from a system design point of view, as no performance variation has to be accounted for. We further observe that with narrowband filtering, the bit-delay can be reduced to zero with only a minor penalty. In this case the DPSK signal is demodulated through narrowband optical filtering [263]. The improved narrowband filtering tolerance for a shortened bit-delay is best explained with the optical spectra of the constructive and destructive component, as shown in Figure 4.16. When the bit-delay is decreased, the 3-dB bandwidth of the MZDIs periodic notch response broadens. As a result, a larger part of the signals energy passes through the constructive port. The destructive component, on the other hand, is attenuated and fades out for shorter bit-delays. The optical narrowband filtering mainly affects the destructive component, which is attenuated anyway through the demodulation with a shortened MZDI. The constructive component (with the duobinary line coding) becomes the dominant signal compo- 0.4 0.6 0.8 1 1.2 1.4 -200 -100 0 100 200 MZDI bit-delay ( AT/T 0 ) C h r o m a t i c d i s p e r s i o n ( p s / n m ) 14 14 15 15 15 15 16 16 16 16 17 17 17 17 17 (a) 0.4 0.6 0.8 1 1.2 1.4 20 30 40 50 60 70 80 90 MZDI bit-delay (AT/T 0 ) O p t i c a l f i l t e r b a n d w i d t h ( G H z ) 14 14 14 14 15 15 15 15 16 16 16 16 16 17 17 17 17 17 (b) 0.4 0.6 0.8 1 1.2 1.4 -200 -100 0 100 200 MZDI bit-delay (AT/T 0 ) C h r o m a t i c d i s p e r s i o n ( p s / n m ) 15 15 16 16 14 15 14 (c) 0.4 0.6 0.8 1 1.2 1.4 20 30 40 50 60 70 80 90 MZDI bit-delay ( AT/T 0 ) O p t i c a l f i l t e r b a n d w i d t h ( G H z ) 14 14 14 15 15 15 15 16 16 16 16 17 17 17 17 (d) Figure 4.17: Chromatic dispersion (a,c) and optical filter bandwidth (b,d) tolerance for NRZ-DPSK (a,b) and RZ-DPSK (c,d) as a function of MZDI differential delay. The contour plots show the required OSNR for a 10 −5 BER. 85 Chapter 4. Binary modulation formats nent, which in turn reduces the narrowband filtering penalties. As a result, partial DPSK is the DPSK format of choice for deployed transmission systems. The improvement in optical filter tolerance for 42.8-Gb/s NRZ-DPSK with a shortened MZDI is discussed in [264, 265]. For RZ-DPSK, the penalty is more or less symmetrical with respect to the 1 bit-delay. A shortened bit-delay results in a signal that has similar properties as RZ-duobinary, including a broad optical spectrum. No significant improvement in narrowband filtering tolerance is therefore observed at low OSNR penalties [266]. Finally, we note that the chromatic dispersion tolerance and the filter bandwidth are dependent on each other as well as on the MZDI bit-delay. This is depicted in Figure 4.17. When narrowband optical filtering or a shortened MZDI are considered separately, an OSNR penalty is observed for NRZ-DPSK. For an OSNR requirement of 16-dB (2.5-dB penalty), the narrowband filter tol- erance is 35-GHz. However, combined with a shortened 0.65 bit-delay MZDI the narrowband filter tolerance is improved to 24 GHz. At the same time, the chromatic dispersion tolerance increases from 80-ps/nm to 95-ps/nm, for an 16-dB required OSNR. We note that this is com- puted with a 60-GHz optical filter bandwidth. When the shortened bit-delay is combined with narrowband filtering, the tolerance can be further increased. For RZ-DPSK (Figure 4.17c-d), the dependence is significantly reduced. Only for high OSNR penalties a similar improvement in narrowband filtering tolerance is observed. The observed ’w’-shape in the dispersion tolerance for small bit-delays confirms that the signal is similar to duobinary in the absence of narrowband filtering. 86 5 Differential quadrature phase shift keying For high-speed optical transmission systems, multi-level modulation formats are a logical up- grade to either increase the spectral efficiency above 1-b/s/Hz, or to improve the robustness against transmission impairments. A significant number of different multi-level modulation for- mats have been proposed, using either modulation in the amplitude, phase or polarization domain [267, 245, 268]. In order to minimize the OSNR requirements and maximize nonlinear tolerance for long-haul transmission systems, especially modulation formats based on either phase and/or polarization modulation appear to be the most suitable. Phase modulated formats have only mod- estly worse OSNR requirements compared to DPSK [10]. As well, the lack of a strong optical carrier reduces the generation of XPM when compared to amplitude modulation formats [269]. The higher OSNR requirement, as well as the reduced nonlinear tolerance of multi-level modu- lation in the amplitude domain [270] makes it impractical for long-haul transmission. The use of polarization as a selective agent is discuses in Chapter 7 The multi-level modulation format that received the most interest in recent years is return-to-zero differential quadrature phase shift keying (RZ-DQPSK). This chapter discusses the properties of DQPSK modulation. In Section 5.1 the structure of a DQPSK transmitter and receiver are explained. Subsequently, in Section 5.3 the properties of DQPSK modulation are discussed, including the tolerance against narrowband filtering, chromatic dispersion and PMD. Section 5.4 analyzes the nonlinear tolerance of DQPSK modulation and in Section 5.5 we discuss in detail the use of multi-level random sequences for evaluation of DQPSK transmission performance. In Chapter 6 we subsequently focus on long-haul transmission using DQPSK modulation. 1 The results described in this chapter are published in c11, c24, c35, c42, c50, c53 87 Chapter 5. Differential quadrature phase shift keying 5.1 Transmitter & receiver structure Figure 5.1 depicts the signal constellations of both binary DPSK and quaternary DQPSK modu- lation. Comparing DPSK and DQPSK modulation, it is evident that the number of constellation points is doubled and the distance between the constellation points is halved. Taking, for exam- ple, ’00’ as a reference, then the symbols ’01’, ’10’ and ’11’ correspond to a phase difference π/2, π and 3π/2, respectively. At the same symbol rate, DQPSK therefore doubles the total bit rate. However, as the distance between the constellation points is halved it requires, at least, a 3-dB higher OSNR for the same BER. More commonly, DQPSK is used at half the symbol rate of binary modulation to obtain the same total bit rate. DQPSK has then, ideally, no OSNR penalty in comparison to DPSK modulation. 1 -1 ǻij Re{E} Im{E} DPSK: 2 E s 1 DQPSK: E s Re{E} Im{E} ǻij 1 symbol/bit 2 symbol/bit j -1 -j Figure 5.1: Signal constellations for binary DPSK and quaternary DQPSK modulation. DQPSK modulation can be realized using a variety of modulator configurations. The most com- mon DQPSK modulator configuration is depicted in Figure 5.2 using a so called ’Super Mach- Zehnder’ structure as first introduced by Griffin et. al. [271]. In such a parallel DQPSK modu- lator, the signal is split and each tributary is, in effect, DPSK modulated. DQPSK modulation is subsequently obtained by interfering the two tributaries with a suitable chosen phase shift (either −π/2 or π/2). Two independent electrical drive signals are fed to the DQPSK modulator and only binary drive signals are required. This has the advantage that standard drive amplifiers at half the bandwidth of DPSK modulation can be used to amplify the electrical drive signals to a 2V π voltage swing. The eye diagram in Figure 5.2 shows a double intensity dip when the MZM switches over either ∆φ = π/2 or ∆φ = π, this is characteristic for DQPSK modulation with a parallel modulator. Other modulator configurations for DQPSK modulation include a MZM and phase modulator in series [272], a single phase modulator with a 4-level drive signal [273, 274] and two EAMs in a three-arm interferometer structure [275]. Figure 5.3 depicts the signal constellation for sev- eral of the DQPSK modulator configurations. The main drawback of using a phase modulator for DQPSK modulation is the higher residual chirp in the signal, which reduces the tolerance against chromatic dispersion and nonlinear impairments [273, 274]. We note that modulation with a parallel DQPSK modulator also result in residual chirp, but in somewhat reduced amounts as it occurs only during the symbol transitions. The higher signal chirp is also evident from the signal constellations of both the MZM and phase modulator in series as well as the 4-level phase modulator. RZ pulse carving reduces the residual chirp in the modulated signal and is 88 5.1. Transmitter & receiver structure t/2 MZ MZ ǻij = t/2 ǻij = 0 ǻij = t Parallel DQPSK modulator Constellation diagram DQPSK eye diagram Figure 5.2: Operation of the ’super’ Mach-Zehnder structure for DQPSK modulation. therefore desirable for DQPSK modulation. The performance of all three modulation structures is nearly identical for 33% RZ pulse carving [273]. This is illustrated by optical time-division- multiplexing experiments where a MZM plus phase modulator has been used for DQPSK mod- ulation with excellent performance [276]. -1 0 1 -1 0 1 I (normalized) Q ( n o r m a l i z e d ) -1 0 1 -1 0 1 I (normalized) Q ( n o r m a l i z e d ) -1 0 1 -1 0 1 I (normalized) Q ( n o r m a l i z e d ) (a) (b) (c) Figure 5.3: Simulated signal constellations for DQPSK modulation with (a) a parallel ’Super Mach- Zehnder’ structure, (b) a cascaded MZM and PM and (c) a PM with 4-level drive signal. The thick line shows the signal in the middle 50% of the symbol period. Figure 5.4 depicts the transmitter and receiver structure using a parallel DQPSK modulator. In most reported transmission experiments, two separate MZDIs are used in the receiver to convert the modulation from the phase to amplitude domain. Although it is also possible to demodulate both tributaries at the same time using a 1x4 star coupler [277, 278], or a 90 o hybrid with one of its inputs delayed over one symbol period [279]. When two separate MZDI interferometers are used, the phase shift between the two arms of the MZDI is +45 o and −45 o to demodulated the in- phase (I) and quadrature (Q) component, respectively. A phase control for DQPSK demodulation is described in [280]. Each MZDI has a constructive and destructive output and therefore 4 photo- diodes are required for balanced detection of DQPSK. For experimental evaluation of DQPSK modulation, a pseudo random quaternary sequence (PRQS) can be used to ensure that all possible sequences up to a given length are tested (see Section 5.5). The data sequences obtained after balanced detection are, due to the differential demodulation in the 1-bit delay MZDI, a mix of the two transmitted data sequences. Either pre-coding or post-coding is therefore required to evaluate DQPSK modulation. For experimental evaluation the BER tester is normally programmed for the expected output sequence (post-coding). This limits the PRBS length to ∼ 2 15 −1 because 89 Chapter 5. Differential quadrature phase shift keying laser Prec. data I Prec. data Q ʌ/2 MZ MZ “Super Mach-Zehnder” structure T + - T + - MZDI In-phase (ǻij= ʌ/4) Quadrature (ǻij= -ʌ/4) PD data u Rx data v Rx j j 1 -j -1 -j (b) (c) (d) (e) (a) 47ps 47ps 47ps 47ps P o w e r ( a . u ) DQPSK precoder u v clock MZM optional Figure 5.4: (a) Transmitter and receiver structure of RZ-DQPSK, (b-e) Measured eye diagrams showing; (b) 42.8-Gb/s NRZ-DQPSK, (c) 42.8-Gb/s NRZ-DQPSK after phase demodulation, (d) 42.8-Gb/s RZ- DQPSK, (e) 42.8-Gb/s RZ-DQPSK after phase demodulation. programming the expected output sequence makes longer sequences impractical. Each bit I(k) and Q(k) in the post-coded sequences is dependent on four bits of the transmitted sequence, u(k), v(k), u(k −1) and v(k −1). The post-coded bits for a parallel DQPSK modulator are given by, I(k −1) = 1 2 _ u(k −1) ⊕u(k) + v(k −1) ⊕v(k) (5.1) − u(k −1) ⊕v(k) + v(k −1) ⊕u(k) _ Q(k −1) = 1 2 _ u(k −1) ⊕u(k) + v(k −1) ⊕v(k) (5.2) + u(k −1) ⊕v(k) − v(k −1) ⊕u(k) _ In a commercial transponder, on the other hand, pre-coding of the transmitted sequence is re- quired [281, 282, 283]. Each bit of the pre-coded sequence is dependent on the bits u(k), v(k), I(k −1) and Q(k −1). This shows that each pre-coded bit depends on its predecessor, which im- plies that a high-speed feedback is required that operates at the symbol rate. Such a high-speed feedback path can be avoided by using toggle flip-flops, as shown by Serbay et. al. in [281]. Alternatively, a parallel implementation can be used to reduce the speed of the feedback path 90 5.1. Transmitter & receiver structure [283]. The pre-coded bits of a parallel DQPSK modulator are given by [271], I(k) = _ I(k −1) ⊕Q(k −1) _ _ I(k −1) ⊕v(k) _ (5.3) + _ I(k −1) ⊕Q(k −1) _ _ I(k −1) ⊕u(k) _ Q(k) = _ I(k −1) ⊕Q(k −1) _ _ I(k −1) ⊕u(k) _ (5.4) + _ I(k −1) ⊕Q(k −1) _ _ I(k −1) ⊕v(k) _ which can be re-written as [283], I(k) = u(k) v(k) I(k −1) + u(k) v(k) Q(k −1) (5.5) + u(k) v(k) I(k −1) + u(k) v(k) Q(k −1) Q(k) = u(k) v(k) Q(k −1) + u(k) v(k) I(k −1) (5.6) + u(k) v(k) I(k −1) + u(k) v(k) Q(k −1) Figure 5.4 further shows the measured eye diagrams for NRZ- and RZ-DQPSK modulation be- fore and after demodulation. This shows a relatively broad ’1’-rail in the NRZ-DQPSK modu- lated eye diagram due to amplitude noise. The amplitude noise results from modulator imperfec- tions. Typical modulator imperfections result from mismatches between the V π of the modulator and the 2 V π amplitude swing of the driver amplifiers. But for a parallel DQPSK modulator, in particular the phase and amplitude mismatches between the two DPSK modulated tributaries is important. Such imperfections depend on the specifications of the modulator, but can be min- imized by controlling the bias voltage of the three interferometers within a parallel DQPSK modulator. In the transmission experiments reported here these bias voltages are set manually, but for a commercial transponder they have to be controlled, for example, by minimizing the power envelope variance. In this case three different pilot tones can be used, where each pilot tone separately controls one of the three bias voltages. Alternatively, an additional light source at the modulator output can be used to implement a control of the bias voltages by minimizing the power of the backward propagating light [284]. The broadened ’1’-rail in a DQPSK signal can be partially suppressed through RZ pulse-carving, but the amplitude of the pulse remains noisy. We note that the amplitude noise in the signal is not clearly evident in the back-to-back OSNR requirement, but results in an increased impact of nonlinear phase noise along the transmission link. 91 Chapter 5. Differential quadrature phase shift keying 5.2 Back-to-back OSNR requirement The OSNR requirement of DQPSK modulation is, ideally, the same as for DPSK modulation at the same total bit rate. However, for direct detection receivers the OSNR requirement dif- fers between both modulation formats as DQPSK suffers from a higher MZDI demodulation penalty. The higher OSNR requirement for DQPSK demodulation can be explained as follows. For DPSK, the constructive component is duobinary modulated and the destructive component is AMI modulated. In an ideal DPSK receiver, both components are (nearly) orthogonal to each other. For DQPSK modulation both the constructive and destructive outputs are neither duobi- nary or AMI modulated. This is clearly visible in Figure 5.7 which depicts eye diagrams of the constructive and destructive components as well as the (slightly skewed) eye diagram after bal- anced detection for the in-phase tributary of 42.8-Gb/s RZ-DQPSK modulation. The constructive and destructive components show a ghost pulse in the ’0’, which in a sense results from crosstalk of the other tributary. The crosstalk is removed through balanced detection as the ghost pulse is subtracted from the other component. This causes a loss of signal power, which translates into a higher OSNR requirement. Figure 5.5 shows the measured OSNR requirement for 42.8-Gb/s RZ-DQPSK modulation, with 21.4-Gb/s RZ-DPSK as a reference. This indicates that the difference in OSNR requirement be- tween RZ-DPSK and RZ-DQPSK is BER dependent. For a 10 −9 BER the difference is 6.2 dB, whereas for a 10 −3 BER the difference reduces to 4.4 dB. When we do not take the 3-dB dif- ference into account that results from doubling the bit rate, a measured penalty is left that varies between 1.4 dB and 3.2 dB. Figure 5.6 depicts this excess OSNR penalty for both the measure- ments as well as simulations. The measured penalty is slightly higher than the penalty predicted by simulations, which is ∼0.6 dB for a BER close to the FEC limit and increases to 1.6 dB for a 10 −9 BER. The difference between simulated and measured penalty results from transmitter and receiver imperfections. 6 8 10 12 14 16 18 20 22 -12 -10 -8 -6 -5 -4 -3 -2 OSNR/0.1nm(dB) l o g ( B E R ) 16 14 12 10 8 Q ( d B ) FEC limit 6.2 dB 4.4 dB Figure 5.5: Measured BER versus OSNR for 42.8-Gb/s RZ-DQPSK, In-phase 42.8-Gb/s RZ- DQPSK, Quadrature 21.4-Gb/s RZ-DPSK. -12 -10 -8 -6 -4 -2 0 1 2 3 4 log(BER) A O S N R ( d B ) 0.6 dB 1.7 dB Figure 5.6: OSNR difference between DPSK and DQPSK modulation at a 42.8-Gb/s bit rate; simulated measured. 92 5.3. Transmitter & receiver properties P o w e r ( a . u ) 47 ps (a) P o w e r ( a . u ) 47 ps (b) P o w e r ( a . u ) 47 ps (c) Figure 5.7: Measured eye diagrams for the in-phase tributary of 42.8-Gb/s RZ-DQPSK with 34-GHz optical filtering, (a) destructive, (b) constructive and (c) after balanced detection. The higher OSNR requirement of DQPSK modulation can be computed using Equation 4.4. As an example, we assume that the input signal is an ideal unmodulated signal, r(t) = 1, and that the phase shift in the MZDI is ideal, i.e. ∆φ = π/4. The output signal after balanced detection can then be denoted as, u(t) =[ 1 2 + 1 2 exp( j π 4 )[ 2 −[ 1 2 − 1 2 exp( j π 4 )[ 2 = √ 2. (5.7) In comparison, for DPSK modulation, i.e. ∆φ = 0, this gives u(t) = 1. The difference is equal to 1.5 dB when converted to logarithmic units. For homodyne demodulation in a coherent receiver, DPSK and DQPSK modulation have the same OSNR requirement. Figure 5.8 depicts the BER as a function of OSNR for self-homodyne demodulation of DQPSK and homodyne demodulation of DQPSK and QPSK. For a 10 −3 BER the difference between coherent and interferometric detection is 1.85 dB for DQPSK. Compar- ing DQPSK with coherent QPSK detection the OSNR difference increases to 2.4 dB, as the differential decoding of DQPSK doubles the BER. We note that the curve for 42.8-Gb/s DQPSK modulation with interferometric detection is computed using Monte-Carlo simulations. The sim- ulation assumes ideal signal constellations and matched filtering at the receiver to match with the theoretical performance of the coherent detection schemes. Note that the simulated penalty is slightly higher than the difference between the theoretical curves in Figure 5.8 as we assume ideal matched filtering. The excess OSNR penalty of DQPSK demodulation with an MZDI can be compensated using electrical post-processing algorithms such as multi-symbol phase estima- tion (see Chapter 9). 5.3 Transmitter & receiver properties Similar to DPSK, a direct detection DQPSK receiver is vulnerable to receiver impairments such as amplitude or time imbalance between the photodiodes and an offset in the phase and time- delay of the MZDI. The eye diagrams in Figure 5.10 show the impact of some of the receiver impairments on the demodulated signal after balanced detection. Figure 5.9a depicts the tol- erance of NRZ-DQPSK against phase offsets in the MZDI, with NRZ-DPSK as a reference. 93 Chapter 5. Differential quadrature phase shift keying Q ( d B ) 7 8 9 10 11 12 13 14 15 -10 -8 -6 -4 -3 -2 OSNR (dB/0.1nm) l o g ( B E R ) 16 14 12 10 8 FEC limit Figure 5.8: Theoretical performance of 42.8-Gb/s DQPSK with conventional direct detection, co- herent detection with differential decoding, 42.8-Gb/s QPSK with coherent detection. Because the phase difference between the constellation points is halved, DQPSK is about a fac- tor of three more sensitive than DPSK to MZDI phase offsets. For a 1-dB OSNR penalty, the allowable phase offset is 6.5 o for a DQPSK signal compared to 20.5 o for DPSK [285]. When the penalty is expressed as a percentage of the bit rate, as for example used by Kim and Winzer in [259], the phase offset tolerance is a factor of six lower due to the factor of two difference in symbol rate. Measurements of the phase offset penalty in [259] shows a slightly larger penalty which most likely results from transmitter impairments. Figure 5.9b depicts the impact of an offset in the MZDI differential delay. The penalty as a function of differential delay offset is very similar to DPSK modulation. For a <1-bit delay MZDI the partially deterministic interference results in a smaller penalty than for a >1-bit delay where three symbols are interfering and the symbol transition of the delayed symbol falls within the symbol period. Although the use of a <1-bit delay MZDI improves the narrowband filtering tolerance somewhat [286, 287], its effectiveness is reduced through the mixing of the duobinary and AMI component in the MZDI. This indicates that partial-DQPSK does not to provide a significant benefit over DQPSK modulation. 5.3.1 Narrowband optical filtering One of the more important advantages of DQPSK modulation over binary modulation formats is its robustness against narrowband filtering in densely spaced WDM transmission. Figures 5.11a and 5.11b show for 42.8-Gb/s RZ-DQPSK the tolerance towards narrowband optical filtering for back-to-back simulations and measurements, respectively. The receiver structure in the simula- tions is modeled to match the experimental receiver, with a 3 rd order Gaussian optical filter and a 15-GHz 5 th order Bessel electrical low-pass filter. The BER is computed with the eigenfunc- tion evaluation method [288]. The OSNR at the receiver is set to 17 dB in the measurements and 15 dB in the simulation, which results for both cases in a BER of approximately 4 10 −6 . Comparing Figures 5.11a and 5.11b show a similar tendency but a different optimal filtering bandwidth of 32 GHz (experimental) and 45 GHz (simulations), respectively. We conjecture that the more narrow filtering bandwidth is beneficial in the measurements because it removes im- pairments in the optical signal resulting from imperfections in the modulator. In the simulations an ideal RZ-DQPSK signal is used and hence no modulator imperfections are taken into account. 94 5.3. Transmitter & receiver properties R e q u i r e d O S N R ( d B / 0 . 1 n m ) -60 -40 -20 0 20 40 60 13 14 15 16 17 18 19 20 21 MZDI phase mismatch (degrees) 41 o 13 o BER = 10 -5 (a) 0.4 0.6 0.8 1 1.2 1.4 13 14 15 16 17 18 19 20 21 MZDI differential delay (AT/T 0 ) R e q u i r e d O S N R ( d B / 0 . 1 n m ) BER = 10 -5 (b) Figure 5.9: Simulated (a) MZDI phase mismatch and (b) MZDI differential delay mismatch; 42.8- Gb/s NRZ-DQPSK, 42.8-Gb/s NRZ-DPSK. P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps (a) (b) (c) Figure 5.10: Measured eye diagrams for the quadrature tributary of 42.8-Gb/s RZ-DQPSK with 100- GHz optical filtering, (a) amplitude imbalance, (b) time imbalance and (c) phase offset. The modulator imperfections are also evident from the eye diagrams depicted in Figure 5.12a, which show the amplitude fluctuations in the broadened ’1’-rail of the optical signal. Note that the eye diagrams are measured at high OSNR, so that practically no ASE is present. With nar- rowband filtering (36 GHz) the amplitude fluctuations are reduced, as evident from Figure 5.12b. The ’0’ level is broadened due to ISI, but this does not impact the signal quality after the MZDI. Hence, narrowband optical filtering results in a performance improvement for a filtering band- width down to ∼ 34 GHz. For an even narrower filtering bandwidth, the additional ISI causes performance impairments. However, only a 1-dB penalty is measured for a 24-GHz filtering bandwidth (Figure 5.12c). This indicates that 42.8-Gb/s RZ-DQPSK is compatible with a nar- row channel spacing down to 25 GHz. In [289], it has been shown that 21.4-Gb/s RZ-DQPSK is compatible with a 12.5-GHz WDM grid and in [290] the performance of 85.6-Gb/s RZ-DQPSK on a 50-GHz WDM grid is measured. For optical meshed networks, as discussed in Section 3.5, the available optical bandwidth after cascaded optical filtering is approximately 35-GHz. This shows that 42.8-Gb/s RZ-DQPSK modulation is well suited for optical meshed networks [291]. Besides the optical filter bandwidth, the filters center frequency is an important parameter to take into account. An offset between the filters center frequency and the optical spectrum result in asymmetric filtering. For most optical filters the center frequency will change slightly over the 95 Chapter 5. Differential quadrature phase shift keying 10 20 30 40 50 60 70 80 90 9 11 13 15 3-dB Filter bandwidth (GHz) Q ( d B ) -3 -4 -5 -7 l o g ( B E R ) FEC limit (a) 10 20 30 40 50 60 70 80 90 9 11 13 15 3-dB filter bandwidth (GHz) Q ( d B ) -3 -4 -5 -7 l o g ( B E R ) FEC limit (b) Figure 5.11: (a) simulated and (b) measured narrowband filtering penalty for 42.8-Gb/s RZ-DQPSK. P o w e r ( a . u ) 47 ps (a) P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps (b) (c) Figure 5.12: Measured eye diagrams for 42.8-Gb/s RZ-DQPSK before (upper row) and after (lower row) phase demodulation for (a) 50-GHz filtering (b) 36-GHz filtering and (c) 24-GHz filtering. course of the filters lifetime. This can, for example, results from temperature induced changes or component aging. Furthermore, in the case of cascaded optical filters, every filter can have a slightly different center frequency. Figure 5.13a shows the measured tolerance with respect to filter center frequency offset. For a broad 50-GHz optical filter, the allowable frequency offset window with a penalty below 1 dB is as large as 32-GHz. This shows that 42.8-Gb/s RZ-DQPSK modulation on a 50-GHz WDM grid is still very tolerant to de-tuning of the optical filter [292]. The depicted measurements are for a single WDM channel. When other channels would be present at a 50-GHz channels spacing, the filter offset results in crosstalk as some energy of the other channel is passed through. Note that for a center frequency offset of up to ±10 GHz, the performance slightly improves. This is similar as observed for narrowband optical filtering and we attribute this to a reduction in modulator imperfections. When the optical filter bandwidth is reduced, the tolerance to center frequency offsets is con- sequently lowered. An important consideration is therefore the tolerance for filter bandwidths in the range of 35 to 40 GHz, as this is typical for cascaded optical filtering on a 50-GHz grid. Figure 5.13a shows that for a 37.5-GHz optical filter bandwidth the allowable filter offset range 96 5.3. Transmitter & receiver properties -20 -10 0 10 20 6 8 10 12 14 Center frequency offset (GHz) Q ( d B ) -2 -3 -4 -6 l o g ( B E R ) FEC limit (a) (b) 1554 1554.5 1555 Wavelength (nm) -60 -50 -40 -30 -20 -10 0 R e l a t i v e P o w e r ( d B ) 0 GHz 10 GHz 20 GHz P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps (c) (d) (e) Figure 5.13: (a) measured filter center frequency offset for 42.8-Gbit/s RZ-DQPSK for a 3-dB filter bandwidth of 50 GHz, 37.5 GHz and 25 GHz; (b-e) 42.8-Gb/s RZ-DQPSK after passing through a 40-GHz 3-dB bandwidth filter for different offsets from the center frequency, (b) measured spectra and eye diagrams for an offset of (c) 0 GHz; (d) 10 GHz and (e) 20 GHz. is still ∼10 GHz with a penalty below 1 dB. The impact of asymmetric filtering is also evident from the measured spectra and eye diagrams in Figures 5.13b and 5.13c-e. For a 10-GHz center frequency offset, mainly the ’0’ level in between two symbols is broadened due to ISI, but no significant degradation is observed in the middle of the symbol period. Combined, a 37.5-GHz optical filter bandwidth and 10-GHz center frequency offsets tolerance should be sufficient to counter the (random) drift in center frequency of a number of cascaded 50-GHz optical filters (with 42-GHz 3-dB bandwidth) over the course of their lifetime. 5.3.2 Chromatic dispersion & DGD tolerance A further advantage of DQPSK over DPSK modulation is the higher tolerance against linear transmission impairments, such as chromatic dispersion and PMD. Figure 5.14a shows simula- tions that compare the chromatic dispersion tolerance of 42.8-Gb/s NRZ-DPSK, NRZ-DQPSK and duobinary modulation. For DQPSK, the increased tolerance against chromatic dispersion results from the doubled symbol period as well as the more narrow optical spectrum. When we compare 42.8-Gb/s NRZ-DPSK and NRZ-DQPSK, the chromatic dispersion tolerance increases from 96 ps/nm to 221 ps/nm for a 1-dB OSNR penalty, a factor of 2.3. This is lower than the factor of four that one would expect by simply scaling the symbol rate. The difference results 97 Chapter 5. Differential quadrature phase shift keying -400 -200 0 200 400 14 16 18 20 22 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) BER = 10 -5 (a) R e q u i r e d O S N R ( d B / 0 . 1 n m ) 0 10 20 30 40 14 16 18 20 22 Differential group delay (ps) BER = 10 -5 (b) Figure 5.14: Simulated comparison of (a) chromatic dispersion and (b) DGD tolerance; 42.8-Gb/s NRZ-DQPSK, 42.8-Gb/s NRZ-DPSK, 42.8-Gb/s filtered duobinary. Table 5.1: CHROMATIC DISPERSION TOLER- ANCE FOR A 1-DB OSNR PENALTY. Optical NRZ RZ filter [GHz] [ps/nm] [ps/nm] DPSK 90 96 63 DQPSK 42 221 226 Duobinary 90 350 - Duobinary 32 157 - Table 5.2: DGD TOLERANCE FOR A 1-DB OSNR PENALTY. PMD-LIMITED REACH FOR 0.1−ps/ √ km PLUS 0.3-PS OF DGD PER SPAN. DGD PMD-limited tolerance reach [ps] [km] NRZ-DPSK 9.5 650 NRZ-DQPSK 18.5 1,800 Duobinary 6 300 from the residual chirp in the signal, which decreases the chromatic dispersion tolerance. This can be reduced through 50% RZ pulse carving, which improves the chromatic dispersion toler- ance. When we now compare 42.8-Gb/s RZ-DPSK and RZ-DQPSK, the chromatic dispersion tolerance increases from 63 ps/nm to 226 ps/nm for a 1-dB OSNR penalty, a factor of 3.6. This is summarized in Table 5.1. In order to compare NRZ-DQPSK with duobinary modulation, the optical filter bandwidth plays a critical role. Without narrow-band optical filtering, duobinary has a larger chromatic dispersion tolerance but also an increased OSNR requirement. With optimal narrowband filtering (32-GHz), duobinary has a somewhat lower chromatic dispersion tolerance for a 1-dB OSNR penalty. Figure 5.14b shows the DGD tolerance for the same modulation formats. The DGD tolerance is, in contrast to the chromatic dispersion tolerance, mainly dependent on the symbol period. This gives DQPSK modulation a clear advantage over either DPSK or duobinary modulation. For a 1-dB OSNR penalty, the DGD tolerance equals 18.5 ps, which translates into a ∼6-ps PMD tolerance. We now consider a link with 0.1-ps/ √ km PMD coefficient for the transmission fiber and 0.3-ps DGD for each span to account for PMD in the EDFAs and DCF. This gives a 1,800-km feasible transmission distance for DQPSK, which compares favorably with other 42.8- 98 5.4. Nonlinear tolerance Gb/s modulation formats as denoted in Table 5.2. In particular the feasible PMD-limited reach of duobinary modulation is limited in comparison to both DPSK and DQPSK modulation, as discussed in Section 4.2. 5.4 Nonlinear tolerance The smaller phase difference between the constellation points in DQPSK modulation results also in a reduced nonlinear tolerance. Particulary the SPM-induced nonlinear phase shift has a more severe impact on DQPSK modulation compared to DPSK. This is illustrated in Figure 5.16 by comparing the nonlinear tolerance of 10.7-Gb/s RZ-DPSK and 21.4-Gb/s RZ-DQPSK on a 800- km SSMF transmission link. In this experiment, the outputs of 1 to 9 ECL on a 50-GHz grid (center wavelength at 1550.9 nm) are combined in a 16:1 coupler. A MZM driven with a 10.7-Gb/s clock signal is used for pulse-carving. The second modulator is a standard MZM driven with a 2 31 −1 PRBS for 10.7- Gb/s DPSK modulation or a parallel DQPSK modulator for 21.4-Gb/s DQPSK modulation. In this case, two 10.7-Gb/s 2 15 −1 PRBS sequences with a relative delay of 5 bits for de-correlation of the bit sequences are used for modulation of the DQPSK signal. Before transmission, the channels are de-correlated with -510 ps/nm of pre-compensation. The transmission line consists of eight 100 km spans of SSMF with EDFA amplification in between the spans, as depicted in Figure 5.15. After each span the chromatic dispersion is compensated with an average under- compensation of 78.4 ps/nm. The loss of the SSMF spans and DCF varied between 21 dB ... 24 dB and 8 dB ... 11 dB, respectively. At the receiver a 37-GHz CSF selects the desired WDM channel and the accumulated dispersion is compensated to approximately 0 ps/nm. Subsequently, the OSNR is set such that a 10 −9 back-to-back BER is obtained, which is 10.9 dB and 15.9 dB for 10.7-Gb/s RZ-DPSK and 21.4-Gb/s RZ-DQPSK, respectively. We now take a 10 −5 BER as a measure for the nonlinear tolerance in Figure 5.16. For the single-channel case, the nonlinear tolerance reduces from 12.8 dB for 10.7-Gb/s RZ-DPSK to 6.2 dB for 21.4-Gb/s RZ-DQPSK, a difference of 6.6 dB. For WDM transmission, the impact of XPM reduces the difference between both modulation formats. With a 50-GHz WDM channel spacing and 9 co-propagating channels the nonlinear tolerance is 4.5 dB (DQPSK) and 8.3 dB (DPSK), respectively. The 4.5 dB lower nonlinear tolerance indicates a severe XPM penalty for DPSK. For DQPSK modulation, on the other hand, the difference between single-channel and 50-GHz spaced WDM transmission is only slightly over 1 dB, and this includes degradations due 100km SSMF Post- compensation Pre- compensation 8x DCM TX RX ~ ~ ~ 25-GHz CSF TDC DCM Figure 5.15: Experimental setup 99 Chapter 5. Differential quadrature phase shift keying 0 2 4 6 8 10 12 14 16 8 10 12 14 16 Input power (dBm/ch/span) Q ( d B ) -2 -3 -4 -5 -6 -8 -10 l o g ( B E R ) FEC limit (a) 4.5dB -2 0 2 4 6 8 10 12 14 16 8 10 12 14 16 Input power (dBm/ch/span) Q ( d B ) -2 -3 -4 -5 -6 -8 -10 l o g ( B E R ) FEC limit 6.6 dB (b) S i n g l e D P S K c h a n n e l 1 0 . 7 - G b / s Figure 5.16: Measured nonlinear tolerance for 800-km transmission (a) 10.7-Gb/s RZ-DPSK and (b) 21.4-Gb/s RZ-DQPSK with single channel, 9 channels on a 50-GHz grid, 5 channels on a 100- GHz grid and 3 channels on a 200-GHz grid. to amplifier gain tilt. We can therefore conclude that RZ-DQPSK is strongly SPM-limited, even at a 10.7-Gb/s symbol rate, whereas RZ-DPSK is largely XPM limited. We note that 21.4-Gb/s RZ-DPSKmodulation will have a reduced nonlinear tolerance compared to 10.7-Gb/s RZ-DPSK, and hence the comparison is here somewhat undue. However, at the same bit rate, i.e. 42.8-Gb/s DPSK compared to 42.8-Gb/s DQPSK, the difference in nonlinear tolerance is still ∼2-3dB. The small inter-channel impairments that are observed for DQPSK in Figure 5.16 are not the result of a high XPM tolerance. On the contrary, the denser signal constellation of DQPSK in comparison to DPSK modulation makes it more sensitive to XPM-induced distortions. An important consideration for 42.8-Gb/s RZ-DQPSK modulation is therefore the impact of co- propagating 10.7-Gb/s NRZ-OOK channels, as first observed by Spinnler et. al. in [293]. Such a configuration might occurs when a deployed system, carrying 10.7-Gb/s NRZ-OOK channels, is upgraded to a 42.8-Gb/s bit rate. As this is an important aspect for the deployment of 42.8-Gb/s DQPSK transmission, it has been extensively studied in the literature [294, 295, 296, 297]. Fig- ure 5.17 shows the impact of XPM-induced impairments using signal constellations. Simulated is a 2000-km transmission link with -2-dBm input power per channel. In the case of DQPSK- only transmission, a very similar constellation diagram is obtained with either single-channel or five WDM channels on a 50-GHz grid. However, when the four co-propagating channels are 10.7-Gb/s NRZ-OOK modulated, the XPM impact is much stronger. In particular the signal constellation before phase demodulation is clearly degraded through a pattern-dependent XPM- induced phase shift. We can therefore conclude that 42.8-Gb/s RZ-DQPSK is XPM rather than SPM limited with co-propagating 10.7-Gb/s NRZ-OOK channels. The strong XPM impact can be reduced through a lower input power. This is however difficult, and often impossible, as the system design of the deployed NRZ-OOK channels is based on high input powers (typically 3 dB per channel). Alternatively, the wavelength spacing between the DQPSK and NRZ-OOK channels can be increased to ≥100 GHz. Figure 5.17 further shows that the phase distortions are strongly reduced through differential demodulation, which indicates a strong correlation between the XPM-induced phase shift of consecutive symbols. This is important for digital coherent re- ceivers, as discussed in Chapter 10, which do not necessarily use differential demodulation. 100 5.5. Pseudo random quaternary sequences -150 -100 -50 0 50 100 150 -40 -30 -20 -10 0 Frequency (GHz) P S D ( d B ) -150 -100 -50 0 50 100 150 -40 -30 -20 -10 0 Frequency (GHz) P S D ( d B ) -150 -100 -50 0 50 100 150 -40 -30 -20 -10 0 Frequency (GHz) P S D ( d B ) -1 0 1 -1 0 1 I (normalized) Q ( n o r m a l i z e d ) -1 0 1 -1 0 1 I (normalized) Q ( n o r m a l i z e d ) -1 0 1 -1 0 1 I (normalized) Q ( n o r m a l i z e d ) -1 0 1 -1 0 1 I (normalized) Q ( n o r m a l i z e d ) -1 0 1 -1 0 I (normalized) Q ( n o r m a l i z e d ) -1 0 1 -1 0 1 I (normalized) Q ( n o r m a l i z e d ) 1 Optical spectra Constellation before demodulation Constellation after demodulation (a) (b) (c) Figure 5.17: Simulated impact of XPM on 42.8-Gb/s RZ-DQPSK; (a) single-channel 42.8-Gb/s RZ- DQPSK, (b) 5 co-propagating 42.8-Gb/s RZ-DQPSK channels and (c) a 42.8-Gb/s RZ-DQPSK center channel with 4 co-propagating 10.7-Gb/s NRZ-OOK channels. 5.5 Pseudo random quaternary sequences We now discuss in more detail the impact of the pseudo-random bit sequence in DQPSK trans- mission experiments. Binary modulation formats are routinely modeled using a PRBS, but for quaternary modulation formats no such standard exists. For DQPSK modulation, two bit streams at half the bit rate are fed to the modulator. In transmission experiments, generally, the same data stream is used twice with a relative delay for de-correlation. To assess the linear and nonlinear transmission properties of DQPSK, inter-symbol interference as occurs along the transmission line should be properly modeled. For example in [298], Wickhamet. al. showed that for transmis- sion systems limited by intra-channel nonlinear impairments the bit pattern length can be critical in correctly evaluating the transmission performance. For DQPSK modulation, the transmission performance is best assessed by using pseudo-random quaternary sequences (PRQS). 101 Chapter 5. Differential quadrature phase shift keying A pseudo-random sequence should, ideally, contain all possible combinations of symbols up to a given length. Assume a sequence to have length k n , where k is the alphabet size and n an integer value. A pseudo random sequence (also know as de Bruijn sequence) can then be defined as a sequence that contains all possible combinations of symbols up to length n (subsequences) exactly once. Note that De Bruijn sequences are equal to standard PRBS with length k n −1 with the exception that the subsequence with n consecutive zeros is omitted. Two PRBS with a cyclic shift for de-correlation can be multiplexed to construct a 4-level sequence. However, this results in a sequence with length 4 n/2 = 2 n which is generally not a pseudo-random sequence, i.e. it does not contain all possible subsequences up to length n/2. 1 10 20 30 40 50 64 -8 -7 -6 -5 -4 Cyclic shift (symbols) l o g ( B E R ) PRBS 2 6 (a) 1 50 100 150 200 256 -8 -7 -6 -5 -4 Cyclic shift (symbols) l o g ( B E R ) PRBS 2 8 (b) 1 100200 300 400 500 600 700 800 900 1024 -8 -7 -6 -5 -4 Cyclic shift (symbols) l o g ( B E R ) PRBS 2 10 (c) Figure 5.18: Simulated BER for 42.8-Gb/s NRZ-DQPSK after 1140 km for all possible cyclic shifts and (a) PRBS 2 6 , (b) PRBS 2 8 ,(c) PRBS 2 10 , doted lines denote in-phase and quadrature tributaries, solid line denote the average of both tributaries. Comparing multi-level (k >4) modulation with binary modulation, the required sequence length to consider all possible subsequences of a given length n grows exponentially. Hence, for multi- level modulation formats it becomes difficult in both simulations as well as experimental verifi- cation to correctly model the interaction of long bit patterns. To verify the impact of bit pattern dependence we now simulated the influence of different 4-level sequences on 42.8-Gb/s NRZ- DQPSK transmission. We use NRZ rather than RZ-DQPSK modulation here as RZ carving would somewhat mask the impact of bit-sequence dependence. Single channel transmission over 12x95-km (1140 km) of SSMF is simulated with a pre-compensation of 680-ps/nm, 85- ps/nm/span in-line under-compensation and zero residual dispersion. The input power is 4 dBm per channel into the SSMF and -1 dBm into the DCF. At the receiver, the signal is filtered with a 45-GHz optical Gauss filter, phase demodulated with an MZDI, differentially detected and subse- quently filtered with a 17-GHz electrical Bessel filter. The OSNR is set to 18.3 dB, which results in a back-to-back BER of 10 −9 . The BER is computed using a Karhunen-Loeve series expansion 102 5.5. Pseudo random quaternary sequences [299]. Figure 5.18 shows the obtained BER after transmission for different bit pattern lengths. For each bit pattern length, two PRBS (u and v) are used to modulate the in-phase and quadrature component of the DQPSK signal. The bit pattern dependence is observed by cyclically shift- ing both sequences with respect to each other and computing the BER for each cyclic shift. As evident from Figure 5.18 this results in significant performance differences, clearly indicating that the choice of bit pattern severely affects the obtained transmission performance. Comparing Figure 5.18a-c shows that a shorter bit pattern length result on average in a lower BER. For a longer bit pattern length (e.g. 1024 symbols) the variation in BER as a function of the cyclic shift is reduced, but differences of more than an order of magnitude are still apparent. This shows that even for long sequences an arbitrary cyclic shift can potentially result in inaccurate modeling of transmission penalties. PRBS 2 8 50 100 150 200 250 0 20 40 60 80 100 Cyclic shift (symbols) F r a c t i o n o f a l l p o s s i b l e s u b s e q u e n c e s ( % ) 4 8 12 16 20 24 90 100 Figure 5.19: Fraction of existing sequences with length 4 as a function of the cyclic shift. 64 128 256 512 1024 -7 -6 -5 -4 Sequence length (symbols) l o g ( B E R ) 14 13 12 Q ( d B ) PRBS PRQS Figure 5.20: Worst-case, median and best-case BERs for all cyclic shifts compared to the BER of a PRQS. The observed transmission performance difference can be avoided by a proper choice of the bit pattern. For this purpose we analyze which fraction of all possible 4-level subsequences with length n/2 exists as a function of the cyclic shift between the two PRBS sequences u and v with length 2 n . Figure 5.19 shows the obtained results for a PRBS length of 2 8 and a subsequence length of 4. It is evident that all possible subsequences of length 4 exist only when v is cyclically shifted over ±4 symbols with respect to u. It can be shown that for a 2 n PRBS and a cyclic shift of ±n/2 symbols (for n is even) always a PRQS with length 4 n/2 is obtained. Note that shifting v over -n/2 symbols is equal to shifting v over +n/2 symbols and inverting it. This gives a straightforward and simple method to generate true PRQS for the simulation and experimental verification of 4-level modulation formats such as DQPSK 1 . This method can also be extended to create pseudo-random sequences for modulation formats with k > 4, such as polarization- multiplexed DQPSK modulation (see Chapter 8). From Figure 5.18 we now take the worst-case, median and best-case obtained BER for all possible cyclic shifts between u and v larger than two (to ensure all symbol transitions exist), as depicted in Figure 5.20. The proposed PRQS results in a BER close to the median value over all possible cyclic shifts. This indicates that such sequences are suitable for the assessment of DQPSK transmission performance. For a bit 1 The use of PRQS for DQPSK modulation is based on more recent work and is therefore not used in most of the transmission experiments discussed in this thesis. An exception is the transmission experiment discussed in Section 10.6.3. 103 Chapter 5. Differential quadrature phase shift keying pattern length larger than 256 symbols the median value is relatively constant, which indicates this bit pattern length is sufficient to properly determine transmission penalties. We note that PRQS can also be generated using 4-level generator polynomials [300], similar to the method used for PRBS. 5.6 Summary & conclusions DQPSK modulation is one of the most suitable multi-level modulation formats for long-haul transmission links. As it encodes 2 bits per symbol, it allows for a higher spectral efficiency and a higher tolerance towards linear transmission impairments compared to binary modulation formats. The most significant properties of DQPSK modulation can be summarized as follows: → DQPSK modulation is possible using a variety of modulator architectures, of which the parallel ’Super Mach-Zehnder’ structure is most widely used. An important considera- tion for the choice in modulator architecture is the residual frequency chirp in the mod- ulation signal. In addition, DQPSK modulation has an increased transponder complexity compared to DPSK or duobinary modulation. This makes a higher degree of optical inte- gration attractive for DQPSK modulation. → DQPSK is normally demodulated with two separate MZDI with a ±π/4 phase shift be- tween both arms. Due to the suboptimal phase demodulation, DQPSK has a higher OSNR requirement in comparison to DPSK modulation. Near the FEC limit, the difference is limited to approximately 1 dB. → The narrowband filtering tolerance is one of the most significant advantages of DQPSK in comparison to binary modulation formats. No significant narrowband filtering penalty is evident down to a 28-GHz filter bandwidth. On a 50-GHz grid, DQPSK further allows for a 10-GHz filter offset with an OSNR penalty smaller than 1-dB. → The chromatic dispersion tolerance of DQPSK modulation is lowered due to the residual chirp in the modulated signal. This residual frequency chirp can be reduced through RZ pulse carving, which potentially makes the tolerance comparable to DPSK at the same symbol rate. For 50% RZ-DQPSK modulation the chromatic dispersion tolerance is ap- proximately a factor of three higher when compared to DPSK at the same bit rate. → DQPSK modulation has a doubled PMD tolerance compared to DPSK modulation. This negates the need for active PMD compensation on fibers with even moderately high PMD. → DQPSK modulation is strongly limited by inter-channel nonlinear impairments. This significantly reduces the nonlinear tolerance of DQPSK modulation compared to DPSK modulation. For a 10.7-Gbaud symbol rate, the difference is approximately 4 dB for a 50-GHz WDM system. At the same bit rate the difference in nonlinear tolerance is 2-3 dB. 104 6 Long-haul DQPSK transmission The previous chapter focused on the properties of DQPSK modulation in comparison to binary modulation formats. In this chapter we focus in more detail on the properties of DQPSK in long-haul transmission. In particular, we discuss the optimization of the dispersion map and the use of different technologies for chromatic dispersion compensation. First of all, in Section 6.1 we discuss an ultra long-haul transmission experiment using 21.4-Gb/s RZ-DQPSK modulation. Subsequently, in Section 6.2 the bit rate is doubled and we focus on long-haul transmission with 42.8-Gb/s RZ-DQPSK modulation. The second part of this chapter focuses on alternative dispersion compensation technologies for long-haul transmission systems. In Section 6.3 we simplify dispersion compensation using a lumped dispersion map. This allows for simplified EDFAs in most of the transmission link, at the cost of a less optimized dispersion map that somewhat reduces the nonlinear tolerance. In Section 6.4, chirped-FBGs are discussed as a means of dispersion compensation in more cost- sensitive transmission systems. Here, we particulary focus on the impact of phase ripple induced impairments on 42.8-Gb/s RZ-DQPSK modulation. Subsequently, Section 6.5 focuses on the combination of DQPSK modulation and OPC-supported long-haul transmission. We shows that OPC can enable both lumped dispersion compensation as well as a significant increase in trans- mission distance through the compensation of intra-channel nonlinear impairments. Finally, in Section 6.6 we compare some of the DQPSK transmission experiments that have been reported in the literature. 1 The results described in this chapter are published in c1, c5, c8-c10, c12, c27, c32-c33, c38, c40-c41, c44, c46, c51 105 Chapter 6. Long-haul DQPSK transmission 6.1 21.4-Gb/s RZ-DQPSK transmission Figure 6.1 depicts the experimental setup for ultra long-haul 21.4-Gb/s RZ-DQPSK modulation. At the transmitter, the outputs of 44 DFB lasers on a 50 GHz ITU grid are multiplexed using an AWG. Subsequently, two cascaded modulators are used for RZ pulse-carving with a 50% duty cycle and DQPSK modulation. The parallel DQPSK modulator is driven with two 10.7- Gb/s PRBS with length 2 15 −1 and shifted over 5 bits for de-correlation. The transmission link consists of three 94.5 km spans of SSMF, with an average span loss of 21.5 dB. Using hybrid EDFA/Raman amplification, with an average 11-dB ON/OFF Raman gain from counter- directional pumping, the SSMF span loss is compensated. After each span a DCF module is used to compensate for the chromatic dispersion. Approximately 20% of the DCF is placed between the Raman pump and the first amplifier stage to balance the DCF insertion loss. In order to emulate ultra long-haul transmission, the signal is re-circulated and passes multiple times through the same transmission link. Two optical switches are used to control the propaga- tion of the signal. When the first switch (Tx switch) is open, an optical burst from the transmitter enters the re-circulating loop. Afterwards, the first switch closes and the second switch (Loop switch) is opened which allows the optical burst signal to propagate around the re-circulating loop. Once the signal has propagated over the predetermined transmission distance (a multiple of the re-circulating loop length) a trigger signal to the receiver starts the measurements. Af- terwards, the first switch opens again and another optical burst starts to propagate around the re-circulating loop. The re-circulating loop further contains a loop-synchronous polarization scrambler (LSPS) in order to obtain the correct polarization distribution and a WSS to emulated cascaded optical fil- tering and power equalization. At the receiver, a 25-GHz CSF selects the desired WDM channel. Afterwards, the accumulated dispersion is optimized on a per-channel basis. The signal is then fed into a one-bit (∆T = 94ps) MZDI and subsequently detected with a balanced photodiode. The transmission performance is evaluated using a BER tester programmed for the expected output sequence. Loop switch ~ ~ ~ 25-GHz TDC CSF RX TX ì1 ì44 A W G 94.5 km SSMF 3x WSS LSPS Pre- compensation Raman Tx switch DCM DCM EDFA Figure 6.1: Experimental setup for long-haul 21.4-Gb/s RZ-DQPSK transmission. In order to maximize transmission performance, the SSMF input power, inline-under compensa- tion and pre-compensation are optimized after 4,500-km transmission. The input power is set to 106 6.1. 21.4-Gb/s RZ-DQPSK transmission -4 dBm/channel; the pre-compensation to -850 ps/nm and the inline-under compensation is fixed at 80 ps/nm/span. Subsequently each parameter is varied to assess its influence on the trans- mission performance (Figure 6.2). The optimum input power per channel is lowered through the hybrid EDFA/Raman amplification and has its optimum at -4 dB/channel. For lower input powers, transmission is OSNR limited, whereas for higher input powers the penalty is dominated by nonlinear impairments. However, the transmission performance is relatively tolerant to power variations as the input power can be varied between -7 dBm and -1 dBm for a 1-dB Q-factor penalty. Secondly, we optimize the pre-compensation. This has only a minor impact on the transmission performance, but we observe that a higher amount of pre-compensation is slightly better. Next, we optimize the inline under-compensation per span. A clear penalty is evident for low inline under-compensation per span as this results in an enlarged impact of XPM due to insufficient spreading between the channels [301]. For an inline under-compensation higher than >60 ps/nm/span the performance differences are insignificant. -9 -7 -5 -3 -1 1 -2 -3 -4 -5 -6 -7 Input power (dBm/ch/span) l o g ( B E R ) 14 12 10 8 Q ( d B ) (a) (b) -100 -300 -500 -700 -900 -1,100 -2 -3 -4 -5 -6 -7 Pre-compensation (ps/nm) l o g ( B E R ) 14 12 10 8 Q ( d B ) 10 30 50 70 90 110 130 -2 -3 -4 -5 -6 -7 Inline under-compensation (ps/nm/span) l o g ( B E R ) 14 12 10 8 Q ( d B ) (c) Figure 6.2: BER as function of (a) input power per channel, (b) pre-compensation and (c) inline-under compensation; with λ = 1533.7 nm, λ = 1549.7 nm, λ = 1553.5 nm. Using the optimized parameters, the BER of a typical channel (in-phase tributary, 1550.7 nm) is assessed as a function of the transmission distance (Figure 6.3a). For shorter distances, the log(BER) increases linearly with an exponential increase in transmission distance. After 5,000- km transmission, the measured log(BER) deviates from the linear increase due to the accumu- lated nonlinear impairments. We conjecture that this accelerated BER increase results partially from the impact of SPM-induced nonlinear phase noise which is more significant at low OSNR, as previously observed in [302]. This limits the feasible transmission distance in this configu- ration to 7,100 km. We note that the optimum input power per channel will be slightly lower after transmission over 7,100 km compared to 4,500 km. A lower input power would therefore 107 Chapter 6. Long-haul DQPSK transmission somewhat improve the feasible transmission distance beyond the limit measured here as less non- linear impairments accumulate and transmission is more limited by the OSNR. In Figure 6.3b the BER of both the in-phase and quadrature components of all 44 WDM channels is assessed after 7,100 km. It can be seen that the performance is similar for all WDM channels and no spectral dependence is measured. The highest measured BER is 1.6 10 −3 after 7,100-km transmission, which is a 0.4-dB Q-factor margin with respect to the FEC limit 1 . 2000 4000 6000 8000 10000 8 10 12 14 16 Distance (km) Q ( d B ) -3 -4 -5 -6 -8 l o g ( B E R ) (a) FEC limit 1530 1535 1540 1545 1550 1555 8 9 10 11 12 Wavelength (nm) Q ( d B ) -3 -4 l o g ( B E R ) FEC limit (b) Figure 6.3: (a) Measured BER as a function of transmission distance (b) BER of all channels after 7,100-km transmission (25 re-circulations); In-phase tributary, Quadrature tributary. 6.2 42.8-Gb/s RZ-DQPSK transmission RZ-DQPSK modulation is the most promising for a 42.8-Gb/s bit rate (21.4-Gbaud symbol rate). This enables robust 42.8-Gb/s transmission on a 50-GHz wavelength grid, as is used by the majority of the deployed transmission systems. In addition, at a 21.4-Gbaud symbol rate, the bandwidth requirement for the electrical components in the transponder is still modest. In this section we optimize the power and dispersion map for 42.8-Gb/s RZ-DQPSK modulation and analyze the long-haul transmission performance. Figure 6.4 depicts the transmitter and receiver structure for 42.8-Gb/s RZ-DQPSK modulation. The WDM channels are modulated using two parallel modulator chains for separate modulation of the even and odd channels. Each RZ-DQPSK modulator chain consists of a MZM for RZ pulse-carving, followed by a parallel DQPSK modulator. The pulse-carver MZM is driven with a 21.4-GHz clock signal to carve out pulses with a 50% duty cycle. The 21.4-Gb/s electrical bit sequences for DQPSK modulation is created by electrically multiplexing two 10.7-Gb/s PRBS signals with a length of 2 15 −1 and a relative delay of 16 bits. The 21.4-Gb/s data stream is subsequently split and fed to both inputs of the 42.8-Gb/s DQPSK modulator with a relative delay of 10 bits. After modulation, the spectral width of an unfiltered 42.8-Gb/s RZ-DQPSK signal is >50 GHz. Optical filtering is therefore required to reduce the linear crosstalk between neighboring WDM channels. Here, the channels are filtered when the odd and even WDM channels are combined in the 50-GHz interleaver. 1 The absolute performance is expressed here in terms of the BER, whereas a penalty or margin is expressed in terms of the Q-factor, see Appendix B for the difference. 108 6.2. 42.8-Gb/s RZ-DQPSK transmission T MZDI PD + - CR 1:2 (a) (b) clock 21.4G data I 21.4G data Q ì2 ì18 A W G ʌ/2 MZ MZ I N T RZ-DQPSK Tx – even channels RZ-DQPSK Tx – odd channels PBS MZM BERT Figure 6.4: Experimental setup for long-haul 42.8-Gb/s RZ-DQPSK transmission (a) transmitter and (b) receiver. In this experiment, 18 WDM channels are multiplexed on a 50-GHz ITU grid, as depicted in Figure 6.5a. The 18 WDM channels are divided over the lower and higher part of the C-band, 9 channels in the lower part of the C-band (from 1534.25 nm to 1537.40 nm) and 9 channels in the higher part of the C-band (from 1549.32 nm to 1552.52 nm). The two separate wavelength bands are used here to investigate the presence of wavelength dependent performance differences due to a change in amplifier noise figure or gain tilt across the C-band. For this purpose, the BER is measured for the center channels of both the higher and lower wavelength band (1535.9 nm and 1551.0 nm). In order to model worst-case nonlinear interaction between the WDM channels, a PBS after the interleaver ensures that all WDMchannels are co-polarized. The re-circulating loop setup is the same as used in the 21.4-Gb/s RZ-DQPSK transmission experiment (see Figure 6.1). At the receiver, the chromatic dispersion is optimized on a per-channel basis and a narrowband 25-GHz CSF is used to select the desired WDM channel. Note that the 25-GHz bandwidth of the optical filter results in a 1-dB OSNR penalty. Subsequently, the signal is split and one part is used for clock-recovery. The other part is fed to a two-bit (∆T = 94 ps) MZDI, followed by balanced detection. The use of a two-bit instead of a one-bit MZDI might result in slightly higher penalties [262] but it is used here to simplify the post-coding of the DQPSK sequences. After balanced detection, the signal is de-multiplexed to 10.7-Gb/s with a 1:2 de-multiplexer and evaluated using a BER tester programmed for the expected bit sequence. With a two-bit MZDI, the BER tester requires only programming for the expected 10.7-Gb/s tributary instead of the multiplexed 21.4-Gb/s signal. As the BER is measured using a 10.7-Gb/s BER tester this considerably simplifies the DQPSK post-coding. The performance of the two tributaries is averaged through loop operation; hence it is sufficient to measure only one 10.7-Gb/s tributary of the 21.4-Gb/s signal. Figure 6.5 shows the optimization of the dispersion map for 42.8-Gb/s RZ-DQPSK after 2,260- km transmission. First of all, the measured BER as a function of the input power per channel is depicted in Figure 6.5b. The inline under-compensation is set to ∼33 ps/nm/span and the pre- compensation is fixed at -1020 ps/nm. For high input powers a slight performance difference is measured between both channels. This is due to amplifier gain tilt and intra-band SRS, which increases the noise factor of the lower wavelengths. The optimal input power is found to be -3.5 dBm per channel. Subsequently, the inline under-compensation per span is optimized, as shown in Figure 6.5c. The inline under-compensation is changed by stepwise substituting the DCF spools in the link such that the average inline under-compensation increases or decreases. A pre-compensation of -1020 ps/nm is used as well as a -3.5-dBm channel input power. For a 109 Chapter 6. Long-haul DQPSK transmission 1535 1540 1545 1550 1555 -30 -20 -10 0 Wavelength (nm) R e l a t i v e p o w e r ( d B ) (a) -8 -6 -4 -2 0 8 9 10 11 12 13 Input power (dBm/ch/span) Q ( d B ) -2 -3 -4 -5 -6 l o g ( B E R ) (b) -100 -50 0 50 100 150 200 8 9 10 11 12 13 Inline under-compensation (ps/nm/span) Q ( d B ) -2 -3 -4 -5 -6 l o g ( B E R ) (c) -2000 -1500 -1000 -500 0 8 9 10 11 12 13 Pre-compensation (ps/nm) Q ( d B ) -2 -3 -4 -5 -6 l o g ( B E R ) (d) -200 -100 0 100 200 -6 -5 -4 -3 -2 Accumulated dispersion (ps/nm) l o g ( B E R ) 13 12 11 10 9 8 Q ( d B ) (e) 1000 2000 3000 4500 6000 800010000 8 10 12 14 Transmission distance (km) Q ( d B ) -3 -4 -5 -6 l o g ( B E R ) FEC limit (f) Figure 6.5: Dispersion and power map optimization for 42.8-Gb/s RZ-DQPSK after 2,260 km, (a) Op- tical spectra of the 18 WDM channels, (b-e) BER as a function of (b) input power per channel, (c) pre-compensation, (d) inline under-compensation per span, (e) accumulated dispersion and (f) trans- mission distance; λ = 1535.9 nm, In-phase tributary, λ = 1535.9 nm, Quadrature tributary, λ = 15551.0 nm, In-phase tributary, λ = 1551.0 nm, Quadrature tributary, 21.4-Gb/s RZ-DQPSK. lower under-compensation the walk-off between the WDM channels is reduced which clearly raises the transmission penalty. The optimal value is found to be an inline under-compensation of ∼60 ps/nm/span. A further increase in inline under-compensation decreases the measured performance only by a small amount, which indicates a large tolerance for 42.8-Gb/s RZ-DQPSK modulation towards suboptimal dispersion maps. Next, Figure 6.5d plots the BER performance as a function of pre-compensation. In this experiment the input power is again set to -3.5 dBm per channel and the inline under-compensation is fixed at ∼60 ps/nm/span. Similar to the measured results for 21.4-Gb/s RZ-DQPSK, the amount of pre-compensation has no strong influence on the transmission performance. Only when the pre-compensation value is close to zero, insufficient pulse spreading occurs and the measured performance decreases. The optimal pre-compensation is -1020 ps/nm. 110 6.3. Lumped dispersion compensation The optimal dispersion map for 42.8-Gb/s RZ-DQPSK modulation is similar to other modulation formats as well as to the optimum values found in the previous section for 21.4-Gb/s RZ-DQPSK transmission. This indicates that 42.8-Gb/s RZ-DQPSK should be compatible with a dispersion maps optimized for 10.7-Gb/s NRZ-OOK legacy transmission systems. Figure 6.5e shows the BER after 2,260-km as a function of the accumulated dispersion excursion. For a 1-dB and 2-dB Q-factor penalty, the chromatic dispersion window is in excess of 160 ps/nm and 250 ps/nm, respectively. This is somewhat lower as the simulated back-to-back tolerance in Figure 5.14a, which probably results from the accumulation of nonlinear impairments after 2,260-km trans- mission. Figure 6.5f depicts the measured BER of both center channels (1535.9 nm and 1551.0 nm) as a function of the transmission distance. Up to a 2,500 km transmission distance the log(BER) degrades in a linear fashion. But for longer transmission distances, the log(BER) degradation accelerates due to the accumulation of nonlinear impairments. For a 10 −3 BER, the feasible transmission distance is therefore approximately 3,500 km. Compared to the reach of 21.4-Gb/s RZ-DQPSK, which is depicted as a reference, this is a reduction by a factor 2.3 in feasible transmission distance. After 2,260-km transmission the measured BER is 9 10 −5 , which gives a ∼2.4-dB margin with respect to the FEC limit. 6.3 Lumped dispersion compensation In order to explore the possibility of simplified dispersion management, we now discuss 42.8- Gb/s RZ-DQPSKtransmission with a lumped dispersion map. In this experiment 16 DFBoutputs are combined on a 50-GHz ITU grid, from 1549.0 nm to 1555.0 nm. The transmitter and receiver structure that is used for 42.8-Gb/s RZ-DQPSK modulation is identical to the one described in Section 6.2, with the exception that a 34-GHz CSF is now used to de-multiplex the WDM channels. This improves the back-to-back OSNR requirement with ∼1 dB. Raman WSS LSPS Pre- compensation Post- compensation 11x 94.5km SSMF 3x DCF -4783 ps/nm Raman even ch. 100GHz ITU odd ch. 100GHz interleaved Tx switch Loop switch ~ ~ ~ 34-GHz CSF TDC PBS RX TX TX I N T EDFA Figure 6.6: Re-circulating loop setup with lumped dispersion compensation. Figure 6.6 depicts the re-circulating loop setup. Before entering the re-circulating loop, the WDM channels are de-correlated with -1020 ps/nm of pre-compensation. The re-circulating loop consists of three 94.5-km spans of SSMF with an average span loss of 21.5 dB. A Hybrid 111 Chapter 6. Long-haul DQPSK transmission Raman/EDFA structure with backward pumping is used for signal amplification with an average ON/OFF Raman gain of ∼11 dB. The chromatic dispersion of the three 94.5-km SSMF spans combined (-4783 ps/nm), is compensated using DCF placed after the third span. The DCF in- sertion loss is compensated using backwards Raman pumping with an ON/OFF Raman gain of 18 dB. As the combined loss of DCF and Raman coupler is 17.6 dB, the dispersion compensa- tion has effectively no insertion loss. However, in order to avoid nonlinear impairments in the DCF, the input power is ∼5 dB reduced with respect to the SSMF. Hence, the total gain of the EDFA/Raman amplification for dispersion compensation is 23 dB. Note that the Raman pump powers launched into the DCF are significantly lower than the pump powers used for Raman amplification in the SSMF. -100 -50 0 50 100 150 200 250 300 8 9 10 11 12 Inline under-compensation per recirculation (ps/nm) Q ( d B ) -3 -4 l o g ( B E R ) (a) -9 -7 -5 -3 -1 1 8 9 10 11 12 Input power (dBm/ch) Q ( d B ) -3 -4 l o g ( B E R ) (b) Figure 6.7: Measured BER after 2,550km transmission versus (a) inline under-compensation and (b) input power variation; lumped dispersion map, periodic dispersion map. Figures 6.7a and 6.7b show the dependence of the transmission performance on the inline under- compensation per recirculation and input power, respectively. The BER is measured for the center channel at 1552.12 nm and after 2,550-km transmission. From Figure 6.7a it is clear that even though the accumulated dispersion is only compensated every 285 km, the influence of the inline under-compensation on the measured BER is still significant. This can be attributed to a reduction of XPM-induced impairments from co-propagating channels. The worst perfor- mance is obtained with full dispersion compensation after every three spans, which results in approximately a 2-dB penalty. When either inline under- or over-compensation is used, the performance improves and optimal performance is obtained for an inline under-compensation of more than 60 ps/nm. Figure 6.7b shows the input power variation for a 107-ps/nm inline under-compensation per re-circulation. 42.8-Gb/s RZ-DQPSK with a periodic dispersion map, as described in the previous section, is shown as a reference. Note that the transmission distance is slightly different in both experiments (2,260 km and 2,550 km). The optimal input power is -4 dBm and -3.5 dBm for the lumped and periodic dispersion map, respectively. The 0.5 dB difference indicates that the lumped dispersion map suffers from a somewhat larger influence of nonlinear impairments. However, with the lumped dispersion map the number of EDFA’s in the re-circulating loop is reduced (single-stage versus double-stage amplifiers). This slightly in- creases the OSNR at the receiver. Hence, there is a trade-off between nonlinear tolerance and OSNR requirement and only a negligible difference in BER is measured between the lumped and periodic dispersion map. 112 6.4. Chirped-FBGs based dispersion compensation Figure 6.8a shows the BER as a function of transmission distance for both the periodic and lumped dispersion map. The dispersion map and input powers are separately optimized for the periodic and lumped dispersion map. From this comparison we conjecture that the use of a lumped dispersion map does not reduce the transmission performance of 42.8-Gb/s RZ-DQPSK modulation. This indicates that more cost effective dispersion management is feasible by ac- cumulating the DCF at specific points and using single-stage amplifiers in the remainder of the transmission link. Figure 6.8b shows the measured BER for all 16 channels after 3,100-km trans- mission. The worst-case WDM channel still has a ∼1 dB margin with respect to the FEC limit. 500 1000 2000 3000 4500 8 10 12 14 16 Transmission distance (km) Q ( d B ) -3 -4 -5 -6 -8 l o g ( B E R ) FEC limit (a) 1548 1550 1552 1554 1556 8 9 10 11 12 Wavelength (nm) Q ( d B ) -3 -4 l o g ( B E R ) FEC limit (b) Figure 6.8: Measured BER (a) as a function of transmission distance and (b) for all 16 WDM channels after 3,100-km transmission; Lumped map, In-phase tributary, Lumped map, Quadrature tributary, Periodic map, In-phase tributary, Periodic map, Quadrature tributary. 6.4 Chirped-FBGs based dispersion compensation Cost-sensitive optical transmission systems nowadays might use chirped-FBGs for dispersion compensation. As discussed in Section 3.3.3, the low insertion loss and negligible nonlinear- ity of a FBG allow for a simpler EDFA structure. But the accumulation of phase ripple (PR)- induced transmission impairments limit the feasible transmission distance. This is particulary important for 42.8-Gb/s transmission systems, where the PR-induced transmission impairments might make it difficult to realize long-haul transmission. For chirped-FBGs that have a chan- nelized dispersion compensation profile, as discussed here (see Figure 3.14), the broad optical spectrum can further increase the penalty because the FBGs incur narrowband filtering and have an increased PR near the edge of the pass-band. It is therefore advantageous to use a 42.8-Gb/s modulation format with a relatively narrow optical spectrum such as 42.8-Gb/s RZ-DQPSK. This has the further advantage that the PR penalty is generally smaller for phase modulated formats in comparison to amplitude modulation [303]. This section describes a long-haul transmission experiment using 42.8-Gb/s RZ-DQPSK modulation. In order to assess the impact of using cas- caded FBGs for chromatic dispersion compensation we compare long-haul transmission with either FBGs or DCF based chromatic dispersion compensation. In the transmitter, 32 DFB outputs are combined on a 100-GHz ITU grid, from 1538.2 nm to 1563.0 nm. The channel spacing is limited to 100 GHz because of the channelized profile of 113 Chapter 6. Long-haul DQPSK transmission the FBGs. The 32 WDM channels are 42.8-Gb/s RZ-DQPSK modulated with the transmitter discussed in Section 6.2 and the re-circulating loop setup as shown in Figure 6.9. It consist of 6 x 95-km SSMF spans with an average span loss of 19.5 dB. The span loss is ∼2 dB lower in this experiment compared to the previous experiments as no Raman coupler are included. The chromatic dispersion is compensated with chirped-FBGs and a double periodic dispersion map is used in the transmission experiments. This has the advantage that the accumulated dispersion after every six spans is close to zero. The double-periodic dispersion map is realized using a FBG-based DCM with -1020 ps/nm of chromatic dispersion (at 1550 nm) before the first span, which at the same time is also used as pre-compensation. The FBG-based DCM have an average insertion loss of 2 dB and an average GDR of 0.074rad with a standard deviation of 0.02rad. As the motivation of this experiment is the feasibility of FBG-based dispersion compensation for cost-effective transmission systems, EDFA-only amplification is used (see Section 3.2.2). The SSMF input power is ∼0.5 dBm per channel, which is found to be the optimum for this configuration. When DCF-based DCMs are used for chromatic dispersion compensation, the input power into the DCF is ∼7 dB reduced with respect to the SSMF input power. The FBG and transmission fiber are not cascaded here because the EDFA used in this experiment are optimized for DCF-based dispersion compensation. The use of a double-stage EDFAs structure is therefore necessary to control the tilt of the WDM spectrum. At the receiver the desired WDM channel is selected using a narrowband 34-GHz CSF and the residual chromatic dispersion is per channel optimized with a (DCF/SSMF-based) TDC. Afterwards, the signal is fed into the 42.8-Gb/s RZ- DQPSK receiver discussed in Section 6.2. 2x 95 km SSMF DGE LSPS 6x FBG DCM FBG circ circ DCM EDFA WSS LSPS Tx switch Loop switch ~ ~ ~ 34-GHz TDC CSF RX TX Figure 6.9: Re-circulating loop setup with FBG-based dispersion compensation. To analyze the impairments that result from cascaded FBGs, the performance for all 32 WDM channels is measured after two circulations (1140 km). First, in-line dispersion compensation with only FBG-based DCMs is considered. The 6 in-line DCMs in the re-circulating loop have either a chromatic dispersion of -1345 ps/nm (5x) or -1681 ps/nm (1x). Hence, after two re- circulation a total number of 14 FBGs is cascaded. Figure 6.10a depicts the measured BER for all WDM channels. The PR penalty is clearly visible through the large (3.0 dB) spread in perfor- mance between the 32 WDM channels. For cascaded FBGs the PR can add up constructively or destructively, as a results some WDM channels will be affected significantly where other WDM channels show only minor PR related impairments. However, despite the significant PR-induced penalty the measured BER is below the FEC limit for all channels. 114 6.4. Chirped-FBGs based dispersion compensation Figure 6.11 shows measured eye diagrams before and after phase demodulation (Quadrature trib- utary). After transmission, the combination of residual dispersion and PR impairments results in a WDM channel dependent eye shape. The eye diagram in Figure 6.11b shows a more severe PR penalty (BER 1.5 10 −4 ) than the eye diagram in Figure 6.11c (BER 1.9 10 −5 ). Note that in the experiment the residual dispersion is optimized on a per-channel basis to minimize the BER. The measured difference in optimal post-compensation between the channels shown in Figures 6.11b and 6.11c is approximately 220 ps/nm. This indicates that the residual dispersion optimization can be important to reduce the PR associated penalty [303, 304]. In deployed systems this would require per-channel tunable dispersion compensation at the receiver, for example through the use of a thermally-tuned FBG [151, 152]. Note that in the absence of PR impairments the residual dispersion would be close to zero. 1535 1540 1545 1550 1555 1560 1565 8 10 12 14 16 Wavelength (nm) Q ( d B ) -3 -4 -6 -8 l o g ( B E R ) FEC limit (a) 1535 1540 1545 1550 1555 1560 1565 8 10 12 14 16 Wavelength (nm) Q ( d B ) -3 -4 -6 -8 l o g ( B E R ) FEC limit (b) l o g ( B E R ) 1535 1540 1545 1550 1555 1560 1565 8 10 12 14 16 Wavelength (nm) Q ( d B ) -3 -4 -6 -8 FEC limit (c) Figure 6.10: Measured BER for 32 WDM channels after 1140-km (12 x 95 km) of SSMF using dispersion compensation with (a) only FBGs, (b) mixed DCF and FBGs and (c) only DCF; In-phase tributary, Quadrature tributary. Next, every second FBG-based DCMs is replaced with DCF-based DCMs and the measured per- formance for all WDMchannels is depicted in Figure 6.10b. The in-line dispersion compensation now consist of FBG-DCMs (-1345 ps/nm, 3x) and DCF (-1512 ps/nm, 3x). The smaller number of cascaded FBG clearly improves the transmission performance. This reduces the spread be- tween the WDM channels to below 1.5 dB and decreases the average BER to 1.2 10 −5 , which re- sults in nearly a 3 dB margin with respect to the FEC limit. Finally, Figure 6.10c shows the mea- sured performance when all FBG DCMs are replaced by DCF except for the pre-compensation DCM. The in-line dispersion map consists now of DCF modules with either -1345 ps/nm (3x) or -1512 ps/nm (3x) of chromatic dispersion. Using DCF-only for dispersion compensation further reduces the spread between adjacent WDM channels to approximately 1 dB, but the average 115 Chapter 6. Long-haul DQPSK transmission BER is 2.8 10 −5 , slightly higher compared to the mixed FBG/DCF in-line dispersion compen- sation. This is a results of the performance difference between the lower and higher part of the WDM spectrum. We conjecture that this difference is due a spectral tilt, which increases the power of the channels in the upper part of the WDM spectrum. The higher power increases nonlinear impairments, which in turn increases the measured BER. This illustrates that the lower insertion loss and nonlinearity of FBG-based inline dispersion compensation can simplify EDFA spectral tilt control. We can now compute the Q-factor penalty from using FBGs instead of DCF-based dispersion compensation. The Q-factor of the best-case channel with DCF for dispersion compensation is 13.0 dB and the Q-factor of the worst-case WDM with FBG-based dispersion compensation is 9.6 dB. This translates into a Q-factor penalty per FBG of 0.24 dB. Although this penalty is clearly overestimated, long-haul transmission with only FBGs for in-line dispersion compensa- tion might not be feasible. This particularly results from the small margins available with 42.8- Gb/s transmission, which makes it difficult to allocate a 2-dB penalty to PR-related impairments. However, a smaller number of FBGs (up to ∼10) result in an acceptable penalty, comparable to or smaller than the increased nonlinear penalty when DCF is used for in-line dispersion compen- sation. P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps P o w e r ( a . u ) 47 ps (a) (c) (b) Figure 6.11: Eye diagrams showing the signal before phase demodulation (upper row) and the quadra- ture tributary after demodulation (lower row). Back-to-back (a) and after 1140 km transmission for λ = 1553.3 nm (b) and λ = 1538.2 nm (c). 6.4.1 Wavelength de-tuning Figure 6.10 depict the measured BER when the WDM channel is centered on the ITU grid, whereas PR-induced penalties can change significantly with only a small change in center wave- length [305]. We now assess the impact of laser de-tuning on the PR-induced penalties. Fig- ure 6.12 depicts the measured BER as a function of the wavelength de-tuning. Note that the 116 6.4. Chirped-FBGs based dispersion compensation channelized WSS used in the re-circulating loop has a 42-GHz 3-dB bandwidth, which is more narrow than the 65-GHz 3-dB bandwidth of a single FBG. The wavelength de-tuning range is thus in principe not limited by the bandwidth of the channelized FBGs. To measure the penalty as a function of wavelength de-tuning, both the wavelength of the transmitter laser and the center wavelength of the receiver-side CSF are changed. Figure 6.12a shows the measured BER for the WDM channel at 1538.2 nm, which suffers only from a small PR penalty whereas the chan- nel at 1544.5 nm is severely affected (Figure 6.12b). However, both channels show that the PR penalty can easily change with up to 3 dB within a ±5-GHz de-tuning range. Note though that a typical laser wavelength drift over the system lifetime would be ±1.5 GHz. As evident from Figure 6.12b, the measured BER increases to above the FEC limit within the de-tuning range. But the PR-induced penalty is artificially enlarged in these results as each of the FBGs is passed twice within the re-circulating loop. When independent FBGs are cascaded, the peak-to-peak PR would increase statistically in comparison to a linear addition when the same FBGs are passed multiple times. Hence, the peak-to-peak PR will be higher for a re-circulating loop with two re-circulations in comparison to straight-line transmission. For two re-circulations, the peak-to- peak PR increases by a factor of √ 2, but the difference is OSNR penalty can be more significant. The impact of using a re-circulating loop in the evaluation of PR-induced penalties is discussed in more detail in the next section. -10 -5 0 5 10 6 8 10 12 14 Detuning from ITU grid (GHz) Q ( d B ) -2 -3 -4 -5 -6 l o g ( B E R ) ì = 1538.2 nm (a) FEC limit -10 -5 0 5 10 6 8 10 12 14 Detuning from ITU grid (GHz) Q ( d B ) -2 -3 -4 -5 -6 l o g ( B E R ) ì = 1544.5 nm (b) FEC limit Figure 6.12: Measured BER versus wavelength detuning from the ITU grid after 1140-km, for the WDM channels at (a) 1538.2 nm and (b) 1544.5 nm; In-phase tributary, Quadrature tributary 6.4.2 10.7-Gb/s NRZ-OOK In order to analyze the PR-induced penalties that occur when multiple FBG are cascaded, we now discuss a long-haul transmission experiment using 10.7-Gb/s NRZ-OOK modulation and chirped-FBGs for dispersion compensation. In this experiment, the same 32 channels are used as in the previous section (from 1538.2 nm to 1563.0 nm) and the transmitter and receiver structure are depicted in Figure 6.13. The same re-circulating loop setup is used here as described in the previous section (Figure 6.9), with the difference that the number of spans in the re-circulating loop is increased to 8. For the in-line dispersion compensation, the DCMs have a chromatic dispersion equivalent to 80 km (1345 ps/nm, 5x) or 100 km of SSMF (1681 ps/nm, 3x). The SSMF input power is increased to ∼3 dBm per WDM channel, which is consistent with the input powers that are used in deployed 10.7-Gb/s transmission systems. At the receiver the 117 Chapter 6. Long-haul DQPSK transmission desired WDM channel is selected using a 18-GHz CSF and the residual chromatic dispersion is per channel optimized with a (DCF/SSMF-based) TDC. Afterwards, the signal is fed to a standard 10.7-Gb/s receiver (Rx), which consists of a photo-diode, CDR and BER tester. 10.7G data MZM ì1 ì32 A W G PD BERT (a) (b) CDR Figure 6.13: Transmitter and receiver structure for 10.7-Gb/s NRZ-OOK. Figures 6.14a and 6.14b show the measured BER after 3,040-km and 3,800-km of transmission, cascading 36 and 45 FBGs, respectively. The impact of PR-related impairments is apparent through the large ∼5 dB spread in performance between the WDM channels whereas the spread would be in the range of ∼1 dB for a similar DCF-based transmission experiment. By measuring a large number of WDM channels a certain measured of statistics for the PR penalties is obtained. This shows that after 3,040-km transmission the measured BER is below 10 −4 for the worst channel, which gives a 2.5 dB margin with respect to the FEC limit. And even for a 3,800-km transmission distance, the measured BER is below the FEC limit for all 32 WDM channels. Figure 6.15 shows in the upper row the measured eye diagrams after 3,800-km transmission. The eye diagrams at (a) 1543.7 nm and (b) 1551.7 nm show WDM channels where the PR has a relatively small influence. On the other hand, for the channels at (c) 1552.5 nm and (d) 1554.1 nm the PR has evidently a more severe impact, limiting the feasible transmission distance to 3,800 km. The lower row in Figure 6.15 shows the eye diagrams for the same WDM channels when the amplitude and phase response of the cascaded FBGs are simulated. In the simulations the measured amplitude and phase response of the FBGs from the transmission experiment are used, but no transmission is simulated (”back-to-back”). Hence, the simulation shows only the PR related impairments resulting from the cascaded FBGs. Both the simulated and measured eye diagrams in Figure 6.15 show a strong broadening of the ’1’ rail through phase distortions. Based on this similarity we conjecture that the phase distortion in the measured eye diagrams result mainly from PR-induced penalties. We now compute the OSNR penalty between FBG and DCF-based dispersion compensation. After transmission the average OSNR is 19.7 dB and 18.8 dB, for respectively a 3,040-km and 3,800-km transmission distance. For comparison, back-to-back the required OSNR is 9.7 dB and 15.3 dB for a 10 −3 and 10 −9 BER, respectively. The OSNR penalty is now computed by subtracting the required back-to-back (B2B) OSNR for the measured BER from the measured OSNR after transmission, ∆OSNR = OSNR Rx −OSNR B2B (BER Rx ). (6.1) We compute this way the OSNR penalty for the best-case and worst-case measured BER, which gives a variation in OSNR penalty between 4 dB and 8.5 dB after 3,040 km transmission. After a 3,800 km transmission distance, the OSNR penalty range increases and we measure penalties 118 6.4. Chirped-FBGs based dispersion compensation 1535 1540 1545 1550 1555 1560 1565 8 10 12 14 16 Wavelength (nm) Q ( d B ) -3 -4 -6 -8 -10 l o g ( B E R ) FEC limit 2.5 dB margin (a) 1535 1540 1545 1550 1555 1560 1565 8 10 12 14 16 Wavelength (nm) Q ( d B ) -3 -4 -6 -8 -10 l o g ( B E R ) (b) FEC limit Figure 6.14: Measured BER for 32 WDM channels after (a) 3,040-km and (b) 3,800-km transmission. P o w e r ( a . u ) 93 ps P o w e r ( a . u ) 93 ps P o w e r ( a . u ) 93 ps P o w e r ( a . u ) 93 ps (a) (b) (c) (d) Figure 6.15: upper row: Eye diagrams after 3,800 km with small (a and b) and large (c and d) PR related penalties, lower row: simulated back-to-back eye diagrams using measured amplitude and phase response, (a) 1543.7 nm; (b) 1551.7 nm; (c) 1552.5 nm; (d) 1554.1 nm. between 5 dB and 10 dB. When we now assume that the OSNR penalty is only related to PR- induced impairments, we can compute the OSNR penalty per FBG. Dividing the penalty through the number of FBGs passed along the transmission link, we obtain an OSNRpenalty per cascaded FBG between 0.11 dB and 0.24 dB. Figure 6.16b shows the BERincrease with transmission distance for a number of WDMchannels, including channels that suffer from small as well as large PR penalties. The Q-factor decrease with ∼6.5 dB when the transmission distance is doubled, in comparison to 3 dB for an ideal (linear) transmission line 2 . Hence, we can conclude that the PR related impairments become more severe with an increasing number of cascaded FBGs. However, in the re-circulating loop experiment, the measured penalty is artificially increased due to the cascade of the same FBGs for each re-circulation. This is visualized through simulations in Figure 6.16b and 6.16c, which show the growth of the peak-to-peak GDR (GDRpp) when an increasing number of FBGs is cascaded. The mean value and the standard deviation of the GDRpp are computed from a large number (> 100) of measured FBGs for statistical averaging. Both the mean GDRpp and the mean GDRpp plus twice the standard deviation (2 σ) are shown. In Figure 6.16b we assume 2 This is slightly different in a nonlinear transmission link. If the Q-factor is assessed as a function of the trans- mission distance for a fixed input power, the decrease is ∼2.2 dB for a doubling in transmission distance. 119 Chapter 6. Long-haul DQPSK transmission that arbitrary FBGs are cascaded, as occurs in field deployment. The PR of the cascaded FBGs is then uncorrelated and grows statistically (square-root) [305]. However, in this transmission experiment 8 FBGs are cascaded in a re-circulating loop and the optical signal is thus passed multiple times through the same FBG. Consequently, the peak-to-peak GDR grows linearly, tremendously worsening the associated penalty. Figure 6.16c depicts the case when 8 arbitrary FBG are cascaded in a re-circulating loop. Hence, we conjecture that for arbitrary cascaded FBGs the drop-off with transmission distance is less steep and a significant larger number of FBGs can be cascaded with acceptable PR-induced impairments. 1500 2000 3000 4000 6000 7 9 11 13 15 Transmission distance (km) Q ( d B ) -2 -3 -4 -6 -8 l o g ( B E R ) 1551.7nm 1552.5nm FEC limit (a) 0 10 20 30 40 0 50 100 150 200 250 300 Number of FBGs G r o u p d e l a y r i p p l e ( p s ) Square root fit (b) 0 10 20 30 40 0 50 100 150 200 250 300 Number of FBGs G r o u p d e l a y r i p p l e ( p s ) Linear fit (c) Figure 6.16: (a) Measured BER versus transmission distance for a channel with small (1551.7 nm) and large (1552.5 nm) PR penalties as well as several arbitrary WDM channels. Peak-to-peak group-delay ripple (b) when arbitrary FBGs are cascaded and (c) when 8 FBGs are cascaded in a re-circulating loop; mean GDRpp, mean GDRpp + 2 σ. The transmission experiment shows that the PR of state-of-the-art FBGs is small enough for dispersion compensation in a long-haul transmission link. In a straight-line, where the PR of the cascaded FBGs adds randomly, the worst-case OSNR penalty per FBG is ∼0.1 dB when we assume that a larger number of FBGs are cascaded. When we allow a maximum 2-dB penalty re- sulting from PR-induced impairments this implies that FBG fabrication technology has matured into an appealing alternative for cost-sensitive long-haul links, up to approximately 2000 km. However, the penalties associated with cascading an even large number of FBGs (> 30) implies that FBGs are not yet suitable for ultra long-haul applications. In addition, the penalty we find here assume per-channel optimization of the accumulated dispersion. Without tunable dispersion compensation the OSNR penalty per FBG will be higher. We note that it is not straightforward how the PR related penalty scales as a function of the bit rate. The FBG peak-to-peak ripple amplitude is a much larger fraction of the bit period for 42.8- Gb/s modulated signals in comparison to 10.7-Gb/s modulation. The ripple period on the other hand is usually well below the modulation frequency for 42.8-Gb/s modulation, which reduces the ripple impact [172]. In [152] it was shown that the PR penalty is somewhat larger for a 42.8-Gb/s compared to a 10.7-Gb/s bit rate, but the difference is relatively small. Comparing the PR-induced penalty for 10.7-Gb/s NRZ-OOK and 42.8-Gb/s RZ-DQPSK appears to support this conclusion. 120 6.5. OPC-supported long-haul transmission 6.5 OPC-supported long-haul transmission DQPSK has a somewhat lower nonlinear in comparison to DPSK modulation, as observed in Section 5.4. This makes OPC of particular interest to DQPSK modulation, as it can be used to improve the nonlinear tolerance and thereby increases the feasible transmission reach. In this section we therefore discuss OPC-aided long-haul transmission experiments using RZ-DQPSK modulation and compare it with the DCF-aided transmission experiment discussed in Section 6.1. The experimental setup of the OPC-aided transmission link is depicted in Figure 6.17a, the link with DCF for dispersion compensation in Figure 6.1. In both experiments, the same transmitter and receiver structure is used. 6.5.1 21.4-Gb/s RZ-DQPSK transmission In this transmission experiment, 44 wavelengths on a 50-GHz ITU grid are 21.4-Gb/s RZ- DQPSK modulated. The wavelengths range from 1532.3 nm to 1540.6 nm in the lower part of the C-band and from 1546.1 nm to 1554.5 nm in the upper part of the C-band. After half the re-circulations (18x), the signals are optically phase conjugated. Mid-link OPC is realized here with a re-entrant re-circulating loop structure, as depicted in Figure 6.17a. The re-circulating loop is split in two branches, with one branch containing the OPC subsystem. The other branch contains only a VOA to match the output power of both branches . After half the re-circulations, the loop switch is closed and the re-entrant switch is opened for one re-circulation. This feeds the phase conjugated signal into the loop, which then propagates for another 18 re-circulations. The OPC subsystem first removes the 22 channels in the lower part of the C-band, which range from 1532.3 nm to 1540.6 nm, as these channels are only used to balance the amplifiers in the re-circulating loop. Subsequently, the remaining 22 channels, from 1546.1 nm to 1554.5 nm, are optical phase conjugated. The OPC subsystem that is used in this experiment is based on the counter-propagating polarization-diversity scheme discussed in Section 3.6.1 and has a measured PDL of less than 0.4 dB. In order to reduce the photo-refractive effect in the PPLN waveguide, it is operated at 202.3 o Celsius. QPM inside the PPLN waveguide is realized by reversing the sign of the nonlinear susceptibility every 16.3µm. The OPC subsystem is pumped, after amplification to ∼26 dBm, with the output of an ECL at 1543.4 nm. The input power of the WDM channels is approximately 10 dBm per channel at the input of the polarization diversity structure. The optical spectrum at this point is depicted in Figure 6.17b, which consists only of the 22 WDM channels in the upper part of the C-band. The optical spectrum at the output of the OPC subsystem consists of the pump signal, input signals and phase conjugated signals, as depicted in Figure 6.17c. The phase conjugated signals are present mirrored with respect to the pump and range from 1532.3 nm to 1540.6 nm. The conversion ef- ficiency of the PPLN waveguide, i. e. the difference between the input signal and the conjugated signal at the output of the OPC subsystem, is 9.2 dB. This is shown in Figure 6.17c, where the conversion efficiency is the difference between the lower (after OPC) and upper (before OPC) wavelength band. The insertion loss of the OPC subsystem and subsequent filters is comparable 121 Chapter 6. Long-haul DQPSK transmission 1530 1535 1540 1545 1550 1555 -70 -60 -50 -40 -30 -20 -10 0 10 Wavelength (nm) R e l a t i v e P o w e r ( d B ) 1530 1535 1540 1545 1550 1555 -60 -50 -40 -30 -20 -10 0 10 Wavelength (nm) R e l a t i v e P o w e r ( d B ) EDFA Loop switch ~ ~ ~ 25-GHz TDC CSF RX TX (a) ì1 ì44 A W G 94.5 km SSMF 3x WSS LSPS Pre- compensation Raman VOA OPC subsystem B S F ~ ~ ~ PBF B S F Re-entrant switch Tx switch 1530 1535 1540 1545 1550 1555 -40 -30 -20 -10 0 10 Wavelength (nm) R e l a t i v e P o w e r ( d B ) (b) (c) (d) 9.2 dB Figure 6.17: (a) Experimental setup for OPC-aided long-haul 21.4-Gb/s RZ-DQPSK transmission; (b) spectra at the input of the OPC subsystem; (c) spectra at the output of the OPC subsystem and (d) received spectra after 10,200-km transmission (all spectra 0.01 nm res. bw.) to a single fiber span (with hybrid EDFA/Raman amplification), and the OPC has therefore no significant impact on the OSNR after transmission. After the OPC subsystem, the pump signal is suppressed through a pump block filter (PBF) and the original input signals are removed using a band selection filter (BSF). Finally, the input channels, ranging from 1546.1 nm to 1554.5 nm, are recombined with the phase conjugated channels to balance the amplifiers when the signal propagates for another 18 re-circulations through the re-circulating loop. In the OPC-aided transmission experiment, the optimal SSMF input power is -3 dBm per chan- nel. This is 1 dB higher than the optimal input power in the transmission experiment with DCF- based dispersion compensation. Figure 6.18 depicts the BER as a function of the transmission distance. For the OPC-aided transmission experiment the in-phase tributary at 1535.1 nm is mea- sured, whereas for the configuration with DCF the in-phase tributary at 1550.7 nm is depicted. At shorter distances, the Q-factor of the configuration with DCF is about 0.5 dB lower than that of the OPC-aided transmission system. But after 5,000-km transmission, the performance of the DCF configuration deviates from the linear increase in log(BER) whereas the OPC based performance is virtually unaffected. As RZ-DQPSK is mainly limited by single channel impair- ments this likely results from SPM induced nonlinear impairments and the impact of nonlinear phase noise. In the absence of OPC, the nonlinear impairments are not compensated, which re- sults in worsening of the performance after 5,000-km transmission. As well, an extra penalty arises in this experiment due to transmitter-side imperfections of the parallel DQPSK modula- tor. The amplitude fluctuations result in signal dependent nonlinear phase shift variations, which 122 6.5. OPC-supported long-haul transmission l o g ( B E R ) 1000 2000 4000 6000 10000 8 10 12 14 16 Transmission distance (km) Q ( d B ) -3 -4 -5 -6 -7 -8 -9 FEC limit Figure 6.18: BER of a typical channel as a func- tion of the transmission distance, with OPC and without OPC. 1528 1530 1532 1534 1536 1538 1540 1542 8 9 10 11 12 13 Wavelength (nm) Q ( d B ) 7980 km 10200 km FEC limit -3 -4 -5 l o g ( B E R ) Figure 6.19: BER of all channels after trans- mission for the OPC-aided configuration; 10,200 km, In-phase, 10,200 km, Quadrature, 7,980 km, In-phase, 7,980 km, Quadrature. P o w e r ( a . u ) 93 ps P o w e r ( a . u ) 93 ps (a) (b) Figure 6.20: Eye diagrams after 10,200-km transmission (a) before demodulation; (b) after demodu- lation, Quadrature. causes additional nonlinear phase noise impairments along the transmission link. In the OPC- aided transmission experiment, mid-link OPC reduces both conventional SPM-induced nonlinear impairments as well as the increased nonlinear phase noise due to modulator imperfections. Fig- ure 6.20 depicts the measured eye diagrams after 10,200 km transmission, before as well as after phase demodulation. The BER of all WDM channels after 7,980 km (28 circulations) and 10,200 km (36 circula- tions) is depicted in Figure 6.19. The performance is only evaluated for the 22 phase conjugated channels. In order to conjugate the other 22 channels, a second OPC subsystem would be re- quired. After 7,980 km there is an average 2 dB margin with respect to the FEC limit. And even after 10,200 km transmission all WDM channels are well below the FEC limit. Note that for a 10,200 km transmission distance, the single OPCunit compensates for an accumulated chromatic dispersion of over 160,000 ps/nm. When we compare mid-link OPC and the configuration with DCF for dispersion compensation, the transmission reach of 21.4-Gb/s RZ-DQPSK is 10,200 km and 7,200 km, respectively. This indicates that the use of a single mid-link OPC unit increases the transmission distance by 44%. 123 Chapter 6. Long-haul DQPSK transmission 6.5.2 42.8-Gb/s RZ-DQPSK transmission The concept of mid-link OPC for simultaneous chromatic dispersion and nonlinearity compen- sation is even more promising for higher bit rates. As an increase in bit rate severely reduces the feasible transmission distance, the gain in transmission reach provided through OPC can be an enabling technology for long-haul transmission. We now discuss a transmission experiment where mid-link OPC is combined with 42.8-Gb/s RZ-DQPSK modulation. In this transmission experiment, 52 wavelengths on a 50-GHz ITU grid are used, ranging from 1530.8 nm to 1540.6 nm in the lower wavelength band and from 1546.1 nm to 1556.1 nm in the higher wavelength band. The channels are 42.8-Gb/s RZ-DQPSK modulated using the transmitter architecture discussed in Section 6.2 and the re-circulating loop has the same configuration as shown in Figure 6.17a. The input power per channel into the SSMF is -2.9 dBm in the OPC-aided configuration, compared to -3.5 dBm for the configuration with DCF for dispersion compensation. The channels are first de-correlated with -2040 ps/nm of pre-compensation before entering the re-circulating loop. The signal then propagates for 8 re-circulations (2270 km) around the re-circulating loop. Mid-link, the signals are fed through the re-entrant branch of the loop and the signal is phase conjugated using the same polarization- diversity OPC subsystem as described in the previous section. The conversion efficiency is with 7.2 dB slightly higher in this experiment, which results from further optimization as well as a higher pump power (27 dBm). After phase conjugation, the signal is transmitted for another 8 circulations around the re-circulating loop and subsequently fed into the 42.8-Gb/s RZ-DQPSK receiver. The optical spectrum at the receiver is depicted in Figure 6.21b. 1530 1535 1540 1545 1550 1555 -50 -40 -30 -20 -10 0 Wavelength (nm) R e l a t i v e P o w e r ( d B ) 1530 1535 1540 1545 1550 1555 -40 -30 -20 -10 0 Wavelength (nm) R e l a t i v e P o w e r ( d B ) (c) (d) (e) P o w e r ( a . u ) 46 ps P o w e r ( a . u ) 46 ps P o w e r ( a . u ) 46 ps (a) (b) 7.2 dB Figure 6.21: (a) Optical spectrum after the PPLN subsystem, (b) Optical spectrum at the receiver after 4,500-km transmission, (c) eye diagram before demodulation without narrowband filtering, (d) eye dia- gram before demodulation with narrowband filtering and (e) eye diagram after demodulation (all spectra 0.01nm res.bw.). 124 6.5. OPC-supported long-haul transmission Figure 6.21c depicts the measured eye diagram after 4,500-km transmission when the nearest neighbors are switched off and the signal is not passed through the 25-GHz CSF. Although the low OSNR after transmission (∼15.5 dB) is evident from the eye diagram, the RZ shape is clearly recognizable. When the nearest neighbors are switched on and the signal passes at the receiver through the 25-CSF, the eye diagram in Figure 6.21d is obtained. The narrowband optical filtering is clearly visible in the eye diagram. As discussed in Section 5.3.1, narrowband filtering with a 25-GHz bandwidth results in approximately a 1-dB penalty. Figure 6.21e depicts the eye diagram after phase demodulation and balanced detection. The measured performance as a function of transmission distance is depicted in Figure 6.22. For this measurement, the same 18 WDM channels are used as in the configuration with the periodic dispersion map. In this case the upper 9 channels are phase conjugated (from 1549.32 nm to 1552.52 nm), and the additional 9 channels (from 1534.25 nm to 1537.40 nm) are used to bal- ance the amplifiers. Reducing the number of WDM channels resulted in a slight improvement in transmission performance because the more narrow spectrum requires less gain tilt compensa- tion in the EFDA, which improves the amplifier noise figure. The measured difference between the 9 channel and 52 channel WDM spectrum is approximately 1 dB in Q-factor. For the cen- ter channel (at 1535.8 nm), the BER is measured as a function of transmission distance from 1,700 km up to 5,700 km. Figure 6.22 further depicts the BER versus transmission distance of 42.8-Gb/s RZ-DQPSK with a periodic DCF-based dispersion map. When we compare the performance of both configurations, a clear advantage is evident for mid-link OPC. Similar to the 21.4-Gb/s RZ-DQPSK experiment, we measure for the mid-link OPC a linear dependency between transmission distance and log(BER), which indicates that the nonlinear impairments are (partially) compensated. This increases the feasible transmission distance from 3,500 km with a periodic dispersion map to 6,000 km with the mid-link OPC. Hence, a single OPC provides a >50% improvement in transmission reach. 500 1000 2000 4000 6000 -9 -8 -7 -6 -5 -4 -3 Transmission distance (km) l o g ( B E R ) 16 14 12 10 8 Q ( d B ) FEC limit Figure 6.22: BER of a typical channel as a func- tion of transmission distance; without OPC and with OPC. 1530 1532 1534 1536 1538 1540 1542 8 9 10 11 12 Wavelength (nm) Q ( d B ) -3 -4 l o g ( B E R ) FEC limit Figure 6.23: BER of the in-phase and quadrature tributary after 4,500 km for the OPC-aided config- uration; In-phase, Quadrature. 125 Chapter 6. Long-haul DQPSK transmission The WDM performance with mid-link OPC is evaluated after 4,500-km transmission for the 26 phase conjugated WDM channels. In Figure 6.23, the BER of both the in-phase and quadrature channels are depicted. Both tributaries show a similar average BER, with a slightly better perfor- mance for the in-phase tributary due to modulator imperfections. The BER of the worst measured channel is 1.3 10 −3 ; hence all measured channels are below the FEC limit. The received OSNR of all channels after 4,500-km transmission is approximately 15.5 dB averaged over all WDM channels, which corresponds to a 2-dB OSNR penalty compared with the back-to-back perfor- mance. This indicates that there is only a minor impact of nonlinear distortions, and we observe no evidence of severe nonlinear phase noise impairments. Hence, OPC effectively improves the nonlinear tolerance and thereby extends the reach of 42.8-Gb/s RZ-DQPSK transmission. 6.6 Comparison of DQPSK transmission experiments The previously discussed long-haul transmission experiments focus on the feasible transmission distance near the FEC limit. However, deployed transmission systems operate often with a con- siderable margin with respect to the FEC limit. This is used to account for chromatic dispersion and PMD penalties as well as aging, component variations and temperature differences. In addi- tion, the vast majority of the deployed transmission system uses EDFA-only amplification. Figure 6.24 shows two 42.8-Gb/s RZ-DQPSK transmission experiments with a ∼3-dB margin with respect to the FEC limit. Both experiments are discussed in more detail in Section 6.4 and Section 8.2, respectively. The transmission experiment in Figure 6.24a uses EDFA-only amplification, whereas in Figure 6.24b hybrid EDFA/Raman amplification is used. This shows that the use of hybrid EDFA/Raman amplification increases the feasible transmission distance with ∼60%. This percentage can be used as a figure of merit to estimate the feasible transmis- sion distance for the other transmission experiments discussed in this chapter when EDFA-only amplification would be used. We note that in the first experiment a 100-GHz channel spacing is used, but due to the small impact of XPM on DQPSK modulation this will not significantly affect the comparison. The transmission experiment in Figure 6.24a shows that a ∼1000-km reach is feasible for 42.8- Gb/s RZ-DQPSK modulation with EDFA-only amplification and a 3-dB margin with respect to the FEC limit. For long-haul transmission systems that can use hybrid EDFA/Raman amplifica- tion the feasible transmission distance can be extended to around 1,700 km. Table 6.1 summarizes some of the long-haul transmission experiments that have been reported in recent years using >40-Gb/s DQPSK modulation. In [291], Gnauck et. al. were the first to show that 42.8-Gb/s RZ-DQPSK enabled long-haul transmission with a 0.8-b/s/Hz spectral efficiency in the presence of strong optical filtering. But the lower nonlinear tolerance of RZ- DQPSK coupled with the higher OSNR requirement, severely restricts the feasible transmission distance when compared to DPSK modulation. For example, comparing the long-haul trans- mission experiments using 42.8-Gb/s RZ-DPSK modulation in [306] and 42.8-Gb/s RZ-DQPSK modulation in [122], the feasible transmission distance is reduced from 6,120 km to 4,080 km. 126 6.6. Comparison of DQPSK transmission experiments 1535 1540 1545 1550 1555 1560 1565 8 10 12 14 16 Wavelength (nm) Q ( d B ) -3 -4 -5 -6 -8 l o g ( B E R ) FEC limit 1,140 km transmission (a) 1535 1540 1545 1550 1555 1560 1565 8 10 12 14 16 Wavelength (nm) Q ( d B ) -3 -4 -5 -6 -8 l o g ( B E R ) FEC limit 1,700 km transmission (b) Figure 6.24: Long-haul 42.8-Gb/s RZ-DQPSK transmission, (a) BER after 1,140-km transmission with EDFA-only amplification (b) BER after 1,700-km with hybrid EDFA/Raman amplification; In-phase tributary, Quadrature tributary. Hence, the OSNR requirement (1 dB) and lower nonlinear tolerance (2-3 dB) result on average in a 50% reduction in feasible transmission distance. However, the nonlinear tolerance of RZ- DQPSK can potentially be improved through all-Raman amplification [122], CRZ modulation [307], bit-wise alternating polarization (APol) [307] or optical phase conjugation (OPC) [308]. Note that bit-wise alternating polarization or phase modulation results in spectral broadening, which reduces the feasible spectral efficiency and therefore offsets one of the main advantage of DQPSK modulation. Finally, in [294] a field trail using 43-Gb/s DQPSK modulation was reported with full implementation of the transmitter and receiver control circuits. A commercial 43-Gb/s RZ-DQPSK transponder is discussed by Hoshida et. al. in [309]. For the next generation of 100-Gb/s transmission systems, the lower symbol rate of DQPSK modulation is of particular interest. Binary modulation formats are challenging to use at such bit rates, as the required bandwidth of the electrical components in the transponder is difficult and costly to realize. As shown by Winzer et. al. in [15], 107-Gb/s DQPSK transmission can enable long-haul transmission with a 1.0-b/s/Hz spectral efficiency. The performance of 100- Gb/s DQPSK modulation is currently limited by the immature components, predominantly the DQPSK modulator, in the transponder. However, this performance is likely to increase in the near future as components are better optimized for the required ∼55-Gbaud symbol rate. The disadvantage of 100-Gb/s DQPSK modulation is the limited transmission reach. When we assume the use of EDFA-only amplification and taking into account a 3 dB margin with respect to the FEC limit, even for an optimized 100-Gb/s DQPSK signal, the feasible transmission distance is not likely to exceed ∼600 km. In [310], a field trail was reported using 107-Gb/s DQPSK modulation to cover a 500 km distance, albeit using all-Raman amplification. A further drawback of 100-Gb/s DQPSK modulation is its spectral width, which makes it unsuitable for a 50-GHz channel spacing. When used with a 100-GHz channel spacing, the advantage over 40-Gb/s transmission with a 50-GHz channel spacing is limited, particulary as there is a considerable difference in feasible transmission reach. We note that 100-Gb/s DQPSK modulation can be compatible with a 50-GHz wavelength grid using asymmetric interleavers [311]. Asymmetric interleavers have a broad and a narrow pass-band, which allows to use modulation formats with different spectral width for the odd and even wavelength grid. 127 Chapter 6. Long-haul DQPSK transmission Table 6.1: SELECTED LONG-HAUL (> 1,000 KM) TRANSMISSION EXPERIMENTS USING DIRECT DE- TECTED >40-GB/S RZ-DQPSK MODULATION. year bit # of Spectral Distance Spans (km) / Remarks Company / rate WDM efficiency (km) fiber type Ref (Gb/s) channels (b/s/Hz) 2004 42.7 25 0.8 2,800 100 EDFA/Raman Lucent SSMF [291] 2005 42.8 26 0.8 4,500 93.5 EDFA/Raman TU/e, Siemens SSMF OPC [308] 2005 43 151 0.8 4,080 65 all-Raman Alcatel -D/+D/-D [122] 2006 42.8 18 0.8 2,800 93.5 EDFA/Raman TU/e, Siemens SSMF [312] 2006 42.7 28 0.3 6,550 45 EDFA-only Tyco -D/+D/-D APoL/CRZ [307] 2006 43 1+38 - 1,047 ∼90 EDFA-only Ericsson, SSMF field-trail CoreOptics [294] 2006 107 10 0.66 2,000 100 EDFA/Raman Lucent NZDSF [14] 2007 107 10 1.0 1,200 100 EDFA/Raman Alcatel-Lucent NZDSF NRZ [15] 6.7 Summary & conclusions In this chapter, we described a number of long-haul transmission experiments using RZ-DQPSK modulation. → In an ultra long-haul transmission experiment using 21.4-Gb/s RZ-DQPSK modulation, the feasible transmission distance is 7,100-km. This shows that ultra-long haul trans- mission with a 0.4-b/s/Hz spectral efficiency is possible using only 10-Gb/s optical and electrical components and a 50-GHz channel spacing. → For 42.8-Gb/s RZ-DQPSK transmission we obtain a feasible transmission distance of 2,800 km with a 0.8-b/s/Hz spectral efficiency. The re-circulating loop used in the trans- mission experiment contains a narrowband optical filtering nodes with 42-GHz bandwidth. This shows that a large number of cascaded optical filtering nodes can be passed in a long- haul transmission link using 42.8-Gb/s RZ-DQPSK modulation. → Both for a 21.4-Gb/s and 42.8-Gb/s bit rate, the optimized dispersion map for DQPSK modulation is comparable to a dispersion map optimized for 10.7-Gb/s NRZ-OOK modu- lation as used in most deployed transmission systems. 128 6.7. Summary & conclusions → For deployed transmission systems with EDFA-only amplification and a 3 dB margin with respect to the FEC limit, a ∼1000 km transmission reach seems feasible for 42.8-Gb/s RZ-DQPSK modulation. We further discussed long-haul transmission experiments using a number of different technolo- gies for chromatic dispersion compensation. → Lumped dispersion compensation requires only minor changes to the transmission link design. The lumped dispersion map discussed here compensates the DCF insertion loss with backwards-pumped raman amplification. A single DCM unit can then compensate the chromatic dispersion between two OADM nodes (up to ∼ 500 km) and simpler ED- FAs can be used in the remainder of the link. The long-haul transmission experiments shows that a high accumulated chromatic dispersion does not severely affect the nonlin- ear tolerance of 42.8-Gb/s RZ-DQPSK. When 10.7-Gb/s NRZ-OOK modulated channels are co-propagating on the same link, the lumped dispersion map might result in a lower nonlinear tolerance. → Fiber Bragg gratings (FBG) have a low insertion loss (2 dB to compensate for 100 km of SSMF) and negligible nonlinearity. The FBG can therefore be cascaded with trans- mission fiber, which negates the need for inter-stage access in the EDFA. The use of chirped-FBGs for dispersion compensation results in PR-induced impairments that limit the feasible transmission distance. This PR-related penalty can be significantly reduced by optimizing the chromatic dispersion at the receiver. When the accumulated dispersion is optimized, the cascade of a large number of FBGs results in an OSNR penalty of ∼0.1 dB per FBG. This implies that FBG-based dispersion compensation can be used for links up to 2000 km with 10.7-Gb/s NRZ-OOK modulation. For 42.8-Gb/s RZ-DQPSK the penalty per FBG is only slightly higher than for 10.7-Gb/s NRZ-OOK modulation, but the smaller available margin for 42.8-Gb/s makes it challenging to use FBG-based dispersion compen- sation at this bit rate. → Optical phase conjugation (OPC) allows the compensation of both chromatic dispersion and intra-channel nonlinear impairments in a long-haul transmission link. OPC is mod- ulation format and bit rate transparent and a single device can conjugate multiple WDM channels. In a long-haul transmission experiment with 42.8-Gb/s RZ-DQPSK, the use of a single mid-link OPC unit increases the feasible transmission distance with >50% when compared to a conventional transmission link with an optimized periodic dispersion map. This indicates that use of OPC extends the feasible transmission reach and enables trans- mission links without any periodic dispersion compensation. It can therefore be instru- mental in the realization of long-haul transmission systems with a high spectral efficiency. The results discussed in Chapters 5 and 6 shows that DQPSK modulation has a number of sig- nificant advantages over binary modulation formats in terms of chromatic dispersion and PMD tolerance, as well as spectral efficiency. On the other hand, the higher OSNR requirement and lower nonlinear tolerance somewhat restrict the feasible transmission distance. In summary, 129 Chapter 6. Long-haul DQPSK transmission 43-Gb/s DQPSK modulation seems to be particulary promising for transmission systems that require a high tolerance against transmission impairments rather than maximize the transmission reach. The compensation of nonlinear impairments through, for example, optical phase con- jugation might be instrumental in realizing ultra long-haul transmission with 43-Gb/s DQPSK modulation. 130 7 Polarization-multiplexing So far, we have limited the discussion to modulation formats that employ either the amplitude or phase dimension to transmit information. A different approach towards multi-level modula- tion formats is the use of the polarization dimension of the optical signal. In comparison to the extensive use of amplitude or phase shift keying in fiber-optic research, modulation using the po- larization dimension has attracted only modest attention. This is mainly due to the fact that such modulation formats require a polarization sensitive receiver. Polarization-multiplexed (POL- MUX) transmission, sometimes also referred to as polarization division multiplexing (PDM), is the most widely used polarization-sensitive modulation format. It transmits two independent tributaries in each of the orthogonal polarizations and can therefore be used to double the spec- tral efficiency in comparison to single polarization modulation. In addition, POLMUX signaling reduces the symbol rate by a factor of two when compared with binary modulation formats at the same total bit rate. This can be useful to increase both linear and nonlinear transmission tolerances. For instance, POLMUX-DPSK features a comparably high chromatic dispersion tol- erance and narrow spectral width as DQPSK modulation, but at the same time has a lower OSNR requirement and higher SPM tolerance. Evangelides et. al. first proposed in 1992 the use of polarization-multiplexing in long-haul transmission systems using soliton transmission [313]. Later on, different groups used POLMUX signaling in transmission experiments as a means to increase the bit rate in a single wavelength channel [314, 315]. This ultimately resulted in a transmission experiment where POLMUX- DQPSK was used to transmit 2.56-Tb/s in a single wavelength channel [276]. After the advent of WDM transmission systems, POLMUX signaling has mainly be used to double the spectral efficiency for high-capacity WDM transmission experiments. In 1996, Chraplyvy et. al. used POLMUX transmission to demonstrate for the first time a 1-Tb/s transmission capacity [316]. 1 The results described in this chapter are published in c13, c16-c18, c37, c48-c49, c55 131 Chapter 7. Polarization-multiplexing Later on, POLMUX signaling has been used in a number of record-capacity breaking laboratory experiments [317, 318, 319, 320, 321, 34] and field trails [322]. However, such record-capacity breaking experiments are generally limited to comparably short transmission distances. This is in part due to the sensitivity of POLMUX to PMD-related impairments in long-haul transmission systems. POLMUX is only one representative of a broader family of polarization sensitive modulation for- mats, which includes bit-wise alternating-polarization (APol) modulation and polarization-shift- keying (PolSK). APol modulation can be used either with a polarization sensitive or polarization insensitive receiver. The main advantage of POLMUX over APol modulation is the potentially higher spectral efficiency. POLMUX, on the other hand, has a more complicated transmitter and receiver structure. PolSK uses the SOP of the signal to encode the information rather then multi- plexing two orthogonal polarizations. It therefore requires an even more complicated transmitter and receiver structure, but can potentially provide an even higher spectral efficiency. Due to the random birefringence in optical fibers, a polarization sensitive receiver requires po- larization de-multiplexing at the receiver. This can be realized either in the optical or electrical domain. This chapter discussed POLMUX modulation with a direct detection receiver, i.e. with polarization de-multiplexing in the optical domain. Chapter 10 will consider digital coherent detection, which opens up the possibility of electrical polarization de-multiplexing. Because POLMUX signaling transfers the information in the polarization of the optical signal, it is more sensitive to polarization related impairments. In particular, optical polarization de-multiplexing reduces the PMD tolerance, which makes this a key issue to consider. This chapter therefore focuses on the interaction between PMD and various signal impairments. In Section 7.1 we introduce the concept of POLMUX mathematically and show that up to three channels can be multiplexed. Subsequently, Section 7.2 discusses the transmitter and receiver architecture required for POLMUX signaling. Section 7.3 then reviews the tolerance of POL- MUX signaling with respect to linear transmission impairments with a focuss on PMD related impairments. Finally, Section 7.4 analyzes the impact of single-channel and WDM nonlinear impairments on POLMUX signaling. 7.1 Principle of polarization-multiplexing The possibility to multiplex two channels in the polarization domain is intuitive when considering the two degenerate polarization modes of an optical fiber. Mathematically, the possibility of multiplexing using the polarization as a selective agent can be derived by considering the matrix multiplication that is required for polarization (de-)multiplexing. We assume therefore that the signals E 1 , E 2 , ..., E k , in total K logical channels, are multiplexed and transmitted over an optical fiber. The K signals have an equally spaced linear SOP, θ k = (k −1) π K . (7.1) 132 7.1. Principle of polarization-multiplexing In the receiver the intensity received for channel k after a polarizer with polarization angle θ k is given by Malus law [43] and can be denoted through E / k , E / k = 1 K K ∑ n=1 E n cos 2 [θ k −θ n ] = 1 K K ∑ n=1 E n cos 2 [(k −n) π K ], (7.2) where the summation over the K channels describes the amount of energy of input channel E k that contributes to E / k . Hence, a KK matrix A K characterizes the received signal for all channels by denoting the transferred power from the input to the output signals. It is straightforward that proper decoding of the transmitted signal at the receiver is only possible when this matrix can be inverted. The possibility of transmitting K signals multiplexed in the polarization domain is therefore dependent on the existence of an inverse matrix A −1 K . It can be shown that the inverse matrix A −1 K only exists when the determinant of matrix A K is nonzero [323]. This is possible when K ≤3. First, we look at the case that two channels are multiplexed in the polarization. The channel matrix A 2 is then given by Equation 7.3 A 2 = ⎛ ⎝ 1 2 cos 2 (0) 1 2 cos 2 (− π 2 ) 1 2 cos 2 ( π 2 ) 1 2 cos 2 (0) ⎞ ⎠ = _ 1 0 0 1 _ . (7.3) Where it should be noted that A 2 equals A −1 2 . This shows that multiplexing two channels in the polarization is possible with each channel having a linear polarization. When we extend this to multiplexing three channels in the polarization domain, the transfer matrix A 3 and its inverse A −1 3 are denoted by, A 3 = 1 3 ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ 1 1 4 1 4 1 4 1 1 4 1 4 1 4 1 ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ , A −1 3 = 1 3 ⎛ ⎝ 10 −2 −2 −2 10 −2 −2 −2 10 ⎞ ⎠ . (7.4) The negative elements in the inverse matrix A −1 3 shows that not all of the three channels can have a linear SOP. The three-fold multiplexing is therefore only possible by employing the elipticity of the transmitted signals, i.e. the phase difference between the polarization states [324]. This is in a sense very similar to PolSK, although only binary signals are multiplexed at the transmitter. The distribution on the Poincar´ e sphere for two and three-fold POLMUX signaling is visualized in Figure 7.1, which shows that for three-fold POLMUX the symbol are also spaced more closely together. This results in a slightly higher OSNR requirement for the same total bit rate. The maximum of three multiplexed channels can also be related to the generalized description of a two-by-two Jones matrix. This describes the polarization change in an optical device, including optical fiber. In its most general form the Jones matrix is denoted through [325], _ cosθ exp( jφ) −sinθ exp(−jψ) sinθ exp( jψ) cosθ exp(−jφ) _ , (7.5) 133 Chapter 7. Polarization-multiplexing (a) (b) Figure 7.1: Poincar´ e sphere for (a) two-fold and (b) three-fold polarization-multiplexing, each polariza- tion tributary is DQPSK modulated where θ, φ and ψ are independent real variables. This also implies that in the case of three- fold multiplexing in the polarization domain, not all channels have a linear SOP. Multiplexing three channels in the polarization domain is generally not used in optical transmission because it would require careful control of the relative phase differences between the polarization states. For two-fold multiplexing, on the other hand, only the linear part of the SOP has to be controlled. In addition, the impact of PMD and fiber nonlinearities in realistic optical fiber links are likely to make three-fold multiplexing impractical. We therefore focus in the remainder of this thesis on POLMUX signaling with two orthogonal polarization channels. 7.2 Transmitter & receiver structure Following Equation 7.3, two channels can be multiplexed using linear, but orthogonal, SOPs. In this section we discuss the transmitter and receiver structure required for POLMUX signaling with two orthogonal polarizations. Figure 7.2 depicts the basic layout of a POLMUX transmitter and receiver. The transmitter can either use a single laser source or two different laser sources, but a single laser source is generally used as this is more cost-effective and prevents impairments through beating between the two lasers in the presence of PMD [326]. The output of the laser source is split into two branches, with a MZM in each branch to modulate the orthogonal signal components with independent electrical drive signals. Afterwards a PBS recombines the two polarization tributaries channels into a single POLMUX channel. Note that the laser output, PBS and modulators should use polarization maintaining fiber to ensure that both polarization tributaries have an equal optical power. Figure 7.2 depicts the transmitter and receiver structure for POLMUX-RZ-OOK modulation, as well as eye diagrams for (N)RZ-OOK and (N)RZ-DPSK with POLMUX signaling. Fig- 134 7.2. Transmitter & receiver structure clock data H data V PBS polarization control feedback PC MZM laser MZM MZM PBS PD data V PD data H (0,1) (0,1) (1,1) (0,0) (1,1) (1,0) 93 ps P o w e r ( a . u ) P o w e r ( a . u ) 93 ps 93 ps P o w e r ( a . u ) 93 ps P o w e r ( a . u ) (b) (c) (d) (e) (a) optional Figure 7.2: Transmitter and receiver structure for POLMUX modulation; 21.4-Gb/s back-to-back eye diagrams for (b) POLMUX-NRZ-OOK, (c) POLMUX-RZ-OOK, (d) POLMUX-NRZ-DPSK and (e) POLMUX-RZ-DPSK. 2 POLMUX-DPSK: E s POLMUX-OOK: (0,0) (0,1) (1,0) (1,1) E s 2E s (-1,-1) (1,1) (-1,1) (1,-1) Figure 7.3: Signal constellations for POLMUX-OOK and POLMUX-DPSK modulation. ure 7.3 depicts the signal constellation for POLMUX-OOK and POLMUX-DPSK modulation. This shows that combined with DPSK modulation, POLMUX-DPSK is still a constant intensity modulation format. POLMUX-OOK modulation, on the other hand, results in a ’quasi’ 3-level amplitude signal. POLMUX signaling requires a polarization-sensitive receiver in order to separate both polariza- tion tributaries. The optical polarization de-multiplexing consists of a PBS preceded by an au- tomatic polarization control. After polarization de-multiplexing, two conventional polarization- independent receivers can be used. As discussed in Section 2.3, the birefringence in an optical fiber results in a random and time-variant SOP at the receiver. When the polarization axis of the PBS are not aligned with the two polarization tributaries, a misalignment penalty occurs. This misalignment penalty as a function of the angle θ is depicted in Figure 7.4 for linearly polar- ized 21.4-Gb/s POLMUX-NRZ modulation. This shows that a 4.5 o and 9 o misalignment angle between the PBS axis and the polarization tributaries results in a 1-dB and 2-dB OSNR penalty, respectively. Note that the penalty curve for both polarization tributaries is asymmetric because the misalignment results in crosstalk that adds either constructively or destructively with the sig- nal on the orthogonal polarization. Destructive crosstalk results in a higher OSNR penalty. When 135 Chapter 7. Polarization-multiplexing the polarization of both polarization tributaries is not linear but elliptical, the crosstalk interferes only partially. Averaged over time, the randomly varying interference results in a noise-band that characterize suboptimal polarization de-multiplexing. This is evident by comparing the optical signals in Figures 7.4b and 7.4c. -30 -20 -10 0 10 20 30 15 17 19 21 23 25 u (degrees) R e q u i r e d O S N R ( d B / 0 . 1 n m ) BER = 10 -5 (a) (b) (c) 1 ns P o w e r ( a . u ) 1 ns P o w e r ( a . u ) Figure 7.4: (a) OSNR penalty versus misalignment angle θ for 21.4-Gb/s POLMUX-NRZ-OOK with the 0 o tributary and the 90 o tributary; measured optical signals show de-multiplexing (b) without crosstalk and (c) with crosstalk. The automatic polarization control in front of the PBS should be both accurate to minimize the de-multiplexing penalty, and fast in order to track the randomly changing polarization that can occur in optical fibers (see Section 3.4). The tracking speed of an automatic polarization control for polarization de-multiplexing needs to be faster than the tracking speed required for PMD compensation in a polarization insensitive receiver. To limit the OSNR penalty to < 0.5 dB the de-multiplexing needs to have an accuracy of θ < 2 o , compared to approximately θ ≤10 o for a polarization insensitive receiver. The response time of the automatic polarization control should therefore be in the order of 200 µs when we assume that a full revolution around the Poincar´ e sphere can occur in 20 ms [185, 186, 187]. In order to track the polarization, the automatic po- larization control requires a feedback signal that provides a measure of the interference between the two polarization tributaries. A number of feedback principles have been proposed in the literature. Including the use of pilot tones [322, 327], FEC error counting, different line rates for each polarization tributary [328] or the magnitude of the clock recovery output [77, 316]. The most practical approach is to add a low-frequency phase modulated pilot tone to one of the polarization tributaries [327]. The phase modulation varies the crosstalk between constructive and destructive interference which, after filtering and signal processing in order to integrate over time, provides a measure for the degree of misalignment. 136 7.3. Transmitter & receiver properties 7.3 Transmitter & receiver properties The lower symbol rate of POLMUXsignaling compared to binary modulation formats, combined with the impact of optical polarization de-multiplexing has a significant impact on the tolerance against linear transmission impairments. The chromatic dispersion tolerance and OSNR require- ment are improved. But polarization related signal impairments, such as PMD and PDL, are more critical. This section discusses the tolerance of POLMUX signaling with respect to OSNR (Section 7.3.1), PMD (Section 7.3.2), chromatic dispersion (Section 7.3.3) and polarization de- pendent loss (Section 7.3.4). 7.3.1 Back-to-back OSNR requirement The use of different multi-level modulation formats such as amplitude phase shift keying and DQPSK (with direct detection) results in a >3 dB increase in OSNR for a doubling in the bit rate. One of the main advantages of POLMUX signaling is therefore that it allows a doubling of the bit rate with a ≤3 dB increase in OSNR requirement. This is valid under the assumption that without POLMUX signaling a polarization-insensitive receiver is used. The combination 4 6 8 10 12 14 16 18 20 -12 -10 -8 -6 -4 -3 -2 OSNR/0.1nm(dB) l o g ( B E R ) 16 14 12 10 8 Q ( d B ) FEC limit NRZ modulation (a) 4 6 8 10 12 14 16 18 20 8 10 12 14 16 OSNR (dB/0.1nm) Q ( d B ) -2 -3 -4 -6 -8 -10 -12 l o g ( B E R ) FEC limit RZ modulation (b) Figure 7.5: Measured OSNR requirement for (a) NRZ and (b) RZ modulation; 10.7-Gb/s OOK, 10.7-Gb/s DPSK, 21.4-Gb/s POLMUX-OOK, 10.7-Gb/s POLMUX-DPSK and 21.4-Gb/s DQPSK. of POLMUX signaling with different binary modulation formats is depicted in Figure 7.5a and the OSNR requirements for a 10 −3 and 10 −9 BER are listed in Table 7.1. At a 10 −9 BER the required OSNR for NRZ-OOK and POLMUX-NRZ-OOK is respectively 15.7 dB and 18.4 dB. The 2.7-dB difference in OSNR requirement results from a 3-dB penalty due to the doubled bit rate and a 0.3-dB improvement which results from the use of a polarization sensitive receiver. The OSNR tolerance improves with ∼0.3 dB in a polarization sensitive receiver because the ASE in the orthogonal polarization is filtered out, which worsens the OSNR tolerance through spon- taneous–spontaneous beat noise in a polarization insensitive receiver. Note that the advantage of using a polarization sensitive receiver increases slightly for higher BER, where the impact 137 Chapter 7. Polarization-multiplexing Table 7.1: MEASURED OSNR TOLERANCE FOR DIFFERENT MODULATION FORMATS AT 10 GBAUD (BER 10 −3 AND 10 −9 ) single polarization POLMUX (10.7-Gb/s) (21.4-Gb/s) NRZ-OOK 9.7 / 15.7 12.2 / 18.4 RZ-OOK 8.7 / 14.2 11.2 / 17.2 NRZ-DPSK 7.1 / 11.7 9.0 / 14.3 RZ-DPSK 6.8 / 10.9 9.0 / 13.7 single polarization 21.4-Gb/s) RZ-DQPSK 10.1 / 15.9 of spontaneous–spontaneous beat noise is stronger for a polarization independent receiver. The difference between NRZ-DPSK and POLMUX-NRZ-DPSK is only 1.9 dB at a 10 −3 BER. This lower difference might result from the absence of a PDλ induced penalty in the polarization sen- sitive DPSK receiver. As a polarization sensitive receiver filters out the orthogonal polarization, the PDλ of the MZDI is irrelevant. It indicates that the advantage of a polarization sensitive re- ceiver is somewhat higher for D(Q)PSK compared to OOK modulation. We note that for DPSK modulation there is some measurement uncertainty as the drift of both polarization and MZDI phase offset is controlled manually in the experiment. For a high BER this measurement uncer- tainty is averaged out, but for 10 −9 BER it results in some residual penalty, which explains the smaller difference between OOK and DPSK at low BER. Figure 7.5b compares the OSNR tolerance of 21.4-Gb/s POLMUX-RZ-DPSK with 21.4-Gb/s RZ-DQPSK. This shows that POLMUX modulation allows for a 1.1 dB improvement in OSNR requirement compared to direct detection RZ-DQPSK. The improved OSNR requirement is a combination of the use of a polarization sensitive receiver and the absence of a phase demodula- tion penalty as observed for direct detection DQPSK. 7.3.2 Polarization-mode dispersion In the absence of PMD and nonlinear impairments both orthogonal polarization modes do not interact with each other. In this case POLMUXcan truly be considered a transparent multiplexing technique. Even in the presence of random fiber birefringence, the SOP is only rotated and both polarization modes remain orthogonal to each other. However, in the presence of PMD, the coupling between the polarization modes will generally result in a transmission impairment for POLMUX signaling. Only when the POLMUX tributaries are exactly coupled into the PSP’s of the fiber, the DGD results only in a time delay and no de-multiplexing penalty occurs. 138 7.3. Transmitter & receiver properties (a) BER = 10 -5 0 20 40 60 80 0 2 4 6 8 10 Differential Group Delay (ps) R e q u i r e d O S N R ( d B / 0 . 1 n m ) 93 ps P o w e r ( a . u ) 93 ps P o w e r ( a . u ) 93 ps P o w e r ( a . u ) (c) (e) (d) Polarization rotation + DGD Inverse polarization rotation (b) Figure 7.6: (a) Simulated OSNR penalty versus DGD for 10.7-Gb/s NRZ-OOK, 21.4-Gb/s POLMUX-NRZ-OOKand 21.4-Gb/s NRZ-OOK; (b) polarization changes within a symbol period result- ing due to DGD; (c-e) measured eye diagrams for 21.4-Gb/s POLMUX-NRZ-OOK with (c) back-to-back, (d) with 40-ps DGD and (e) with 40-ps DGD after polarization de-multiplexing. PSP coupling is however not realistic for a deployed transmission systems and the polarization de-multiplexing will therefore introduce a DGD induced penalty. This is most easily understood by noting that DGD results in ISI between neighboring bits. For POLMUX signaling this results in higher penalties because the DGD changes the SOP along the symbol period, which results in amplitude fluctuations when the tributaries are polarization de-multiplexed. This is illustrated in Figure 7.6b for a ’010’ sequence in both polarization tributaries. When DGD is added to the POLMUX signal, the part of the signal in the slower PSP is delayed. If the POLMUX tributaries are not coupled into the PSPs, the ISI results in mixing of the tributaries at the leading and falling edges of the symbol. At the receiver, the polarization tracking aligns the polarization tributaries again with the PSPs. But the polarization control cannot correct for polarization changes on the time scale of a single symbol period. We assume therefore that the polarization control will align the polarization in the middle part of the symbol period, which contains the majority of the pulse energy, to the axis of the PBS. The part of the pulse at the leading and falling edge which has been coupled to the orthogonal polarization will then appear as a ghost pulse. For other sequences (e.g. ’011’ or ’110’), the ghost pulse will interfere either constructively or destructively with the trailing or leading pulse, which results in over- and undershoots. The over- and undershoots are in effect crosstalk between the polarization tributaries. The measured eye diagrams in Figure 7.6c- e clearly show the DGD induced over- and undershoots in a 21.4-Gb/s POLMUX-NRZ-OOK signal with 40-ps DGD. 139 Chapter 7. Polarization-multiplexing Figure 7.6a shows a comparison between the DGD tolerance of 10.7-Gb/s NRZ-OOK and 21.4- Gb/s POLMUX-NRZ-OOK for a worst-case 45 o offset with respect to the PSP’s. Although POLMUXis more sensitive to PMD-induced impairments, the difference with single polarization modulation is relatively small. This can be understood by noting that the crosstalk occurs mainly at the rising and falling edge of the pulse and not in the middle of the symbol period. The allowable DGD for a 2-dB OSNR penalty reduces from 42 ps to 34 ps for POLMUX signaling, while the bit rate is doubled. In comparison, when the symbol rate is doubled the DGD tolerance is reduced by a factor of two (e.g. for 21.4-Gb/s NRZ-OOK). This indicates a clear advantage of POLMUX signaling over an increase in symbol rate. (a) (b) Figure 7.7: Simulated scatter plots showing the penalty for different average PMD (a) 10-Gb/s NRZ- OOK and (b) 20-Gb/s POLMUX-NRZ-OOK. We now extend the discussion to randomly distributed PMD. Figure 7.7 shows the distributions obtained with 10-Gb/s NRZ-OOK and 20-Gb/s POLMUX-NRZ-OOK with different amounts of average PMD. The PMD is generated with a wave-plate model that uses 100 randomly oriented wave-plates. In the wave-plate model, the average PMD per wave-plate is constant whereas the coupling angles between the 100 wave-plates change for each of the 10,000 simulations, this approximates a Maxwellian PMD distribution [329]. To quantify the PMD penalty, the optical EOP is used. This gives a performance indication with less computational effort, but the resulting penalty is approximately a factor of 2-3 smaller than the OSNR penalty [330]. The difference results from the use of the optical EOP to quantify the penalty rather than the OSNR requirement, which is based on the error probability in the electrical signal. To compute the OSNR requirement, the signal is low-pass electrical filtered with 0.7B bandwidth, which shift the DGD induced over- and undershoot more towards the middle of the symbol. In Figure 7.7, the worst-case penalty for a 12-ps average PMD is approximately a 0.35 dB EOP. When we adapt this to OSNR penalties (3x) and scale it to a 21.4-Gb/s bit rate to account for FEC, the worst- case penalty is approximately 1.1 dB. This indicates that 21-4-Gb/s POLMUX-NRZ-OOK has a ∼11-ps PMD tolerance for a 1-dB OSNR penalty. The results depicted in Figure 7.6 show a 34- ps DGD tolerance for a 1-dB OSNR penalty. When we take into account that the average PMD tolerance for a 10 −5 outage probability is approximately a factor of three lower than the DGD tolerance, this also translates into a ∼11-ps PMD tolerance. Using the same approach to compute the PMD tolerance of 10.7-Gb/s NRZ-OOK, we find a 16-ps tolerance for a 1-dB OSNR penalty. The impact of DGDbecomes more complicated when other impairments are present in the signal. A good example is the inter-symbol delay between both polarization tributaries (see Figure 7.8b). We can consider the case when both POLMUX tributaries are exactly interleaved. In the absence of DGD, both tributaries are orthogonal and the offset between the two polarization tributaries 140 7.3. Transmitter & receiver properties (a) 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 Inter-symbol delay (normalized) O S N R p e n a l t y ( d B / 0 . 1 n m ) BER = 10 -5 ǻT -150 -100 -50 0 50 100 150 0 0.5 1 1.5 Time (ps) P o w e r ( m W ) -150 -100 -50 0 50 100 150 0 0.5 1 1.5 Time (ps) P o w e r ( m W ) (b) (c) (d) Figure 7.8: (a) Simulated OSNR penalty versus the inter-symbol delay between the POLMUX tributaries with 34-ps of DGD; (b) definition of the inter-symbol delay between the POLMUX tributaries; (c-d) simulated eye diagrams for 20-Gb/s POLMUX-NRZ-OOK with (c) tributaries aligned and (d) tributaries interleaved. does not result in an OSNR penalty. But when DGD is added to the signal, the crosstalk between both polarization tributaries occurs not anymore at the leading and falling edge of the symbol, but is shifted to the middle of the symbol period [331]. This is depicted in Figure 7.8a for worst-case coupling of the POLMUX tributaries in between the PSP. When both polarization tributaries are synchronized, 25 ps of DGD results in a 1-dB OSNR penalty. When, on the other hand, the polarization tributaries are time-interleaved, the OSNR penalty increases to more than 4 dB. This shows that in order to minimize the OSNR penalty, both polarization tributaries should be synchronized such that the rising and falling edges of the pulse occurs at the same time. The alignment of both tributaries can be easily realized by a proper design of the transmitter, but signal impairments such as chromatic dispersion and nonlinear impairments have a similar effect on the PMD tolerance. The interaction between these transmission impairments will be discussed in the remainder of this chapter. In addition to ISI between consecutive symbols, DGD induces also a periodic change of the SOP [332]. The polarization control at the receiver aligns the signal such that crosstalk is minimized. In effect the SOP of the carrier wavelength, which contains the majority of the transmitted power, is aligned with the axes of the PBS. In the presence of DGD this results in crosstalk between both polarization channels for all other components of the signal spectrum, i.e. depolarization. The impact of DGD induced depolarization is illustrated in Figure 7.9. A DGD equal to one symbol period is added to a (single-polarization) NRZ-OOK signal which is coupled exactly in between both PSP’s. Afterwards the signal is passed through a polarizer, which shows the depolarization in the signal. Note that the periodicity between the minima in the optical spectrum in [THz] is equal to the inverse of the DGD in [ps]. The impact of SOPMD on POLMUX signaling is similar, as it also incurs a wavelength dependent change in the SOP. For high symbol rates (and hence a broad optical spectrum) the wavelength dependent polari- zation change can be dominating. The difference in PMD tolerance between POLMUX and 141 Chapter 7. Polarization-multiplexing DGD equal to T 0 Polarization filter 2B 0 Figure 7.9: Depolarization when a signal is passed through a polarizer in the presence of a DGD equal to the symbol period. non-POLMUX therefore increases for higher symbol rates. Especially at a high symbol rate (e.g. 40 Gbaud), depolarization can become the dominant impairment and significantly worsens the PMD tolerance of POLMUX signaling [326, 333, 334]. On the other hand, for POLMUX signal- ing at a 10.7-Gbaud symbol rate, the contribution of time domain ISI is normally dominant (in the absence of DGD compensation). This difference is for example evident by comparing the PMD induced penalties with and without POLMUX signaling for 10-Gb/s NRZ-OOK, as discussed here, with the results reported by Nelson and Kogelnik in [326]. They investigate POLMUX signaling combined with 40-Gb/s RZ-OOK modulation and find a reduction in PMD tolerance up to a factor of 5 compared to single-polarization modulation. 7.3.3 Chromatic dispersion The lower symbol rate of POLMUX signaling compared to binary modulation formats improves the chromatic dispersion tolerance with a factor of 4. This is evident from the comparison in Figure 7.10a, which shows a nearly identical chromatic dispersion tolerance for 10.7-Gb/s NRZ- OOK and 21.4-Gb/s POLMUX-NRZ-OOK, but a sharply reduced tolerance for 21.4-Gb/s NRZ- OOK. -2000 -1000 0 1000 2000 0 2 4 6 8 Chromatic dispersion (ps/nm) O S N R p e n a l t y ( d B / 0 . 1 n m ) (a) BER = 10 -5 0 500 1000 1500 0 10 20 30 40 Chromatic dispersion (ps/nm) D i f f e r e n t i a l g r o u p d e l a y ( p s ) 16 16 18 18 18 20 20 20 20 22 22 22 22 (b) BER = 10 -5 Figure 7.10: (a) Simulated OSNR penalty versus chromatic dispersion; 10.7-Gb/s NRZ-OOK, 21.4- Gb/s POLMUX-NRZ-OOK, 21.4-Gb/s NRZ-OOK and 21.4-Gb/s POLMUX-NRZ-OOK with 34-ps of DGD. (b) OSNR penalty versus chromatic dispersion and DGD. 142 7.3. Transmitter & receiver properties However, when we consider PMD and chromatic dispersion simultaneously, the dispersion tol- erance is somewhat reduced. The over- and undershoots in the signal that normally occur near the symbol transition are now broadened and shift more towards the middle of the symbol pe- riod. In Figure 7.10b the required OSNR is depicted as a function of both chromatic dispersion and DGD. This clearly indicates that both signal impairments are strongly correlated. For a 2- dB OSNR penalty, either 650-ps/nm of chromatic dispersion or 34-ps of DGD can be tolerated. When on the other hand both signal impairments are present simultaneously, 340-ps/nm of chro- matic dispersion and 20-ps of DGD together result in a 2-dB OSNR penalty. The combined penalty is further evident from Figure 7.10a, when comparing the tolerance without DGD and with 34-ps of DGD (2-dB OSNR penalty). In comparison, for single polarization modulation both signal impairments can be considered nearly independently of each other. 7.3.4 Polarization dependent loss For polarization insensitive receivers PDL is a relatively insignificant impairment, as only large amount of PDL results in a noticeable penalty (see Section 2.3.3). For POLMUX signaling, on the other hand, the impact of PDL is more detrimental as it effects the orthogonality between both tributaries. To simplify the discussion on PDL, we assume here for the moment a single PDL element. The PDL induced penalty in POLMUX signaling then depends on the alignment between the POLMUX tributaries and the axis of the PDL element. With a 0 o offset between the POLMUX tributaries and the axis of the PDL element, the PDL attenuates one tributary and leaves the other tributary unaffected. This is shown in Figure 7.11b. At the receiver, and assuming a constant total signal power, this reduces the OSNR of one tributary while increasing the OSNR of the other tributary. The OSNR for each of the POLMUX tributaries can then be denoted as, ∆OSNR best−case = 10log 10 ( 2 S+1 ) ∆OSNR worst−case = 10log 10 ( 2S S+1 ) , (7.6) where 0 < S < 1 denotes the PDL-induced attenuation in linear units. In the absence of PDL, S equals 1. The performance of the worst-case POLMUX tributary is generally used as a measure of the OSNR penalty. In this case a 2-dB OSNR penalty is obtained for ∼3.5 dB of PDL. PDL results in depolarization of the signal when the POLMUX tributaries are 45 o offset with respect to the axis of the PDL element. Figure 7.11c illustrates this by showing the impact of PDL-induced depolarization on the signal constellation. The POLMUX tributaries are no longer orthogonal to each other, which results in crosstalk upon polarization de-multiplexing. Normally, a polarization-sensitive receiver demultiplexes the POLMUX tributaries using only a single PBS. But this is suboptimal when the signal is severely depolarized due to PDL. A lower de-multiplexing penalty is then obtained when each of the polarization tributaries is de- multiplexed with a separate polarizer and polarization control [313, 316]. If we assume that in the absence of PDL the optimum de-multiplexing angles are θ = 0 o and θ = 90 o , respectively, 143 Chapter 7. Polarization-multiplexing the two polarizers should filter the signal with an angle, θ = 180 o π ( π 4 ±arctan( √ S)). (7.7) Even in the presence of severe PDL, this separates the two POLMUX tributaries without any crosstalk. However, there still is an OSNR penalty when two separate polarizers are used. This penalty is a result of the smaller fraction of the total signal power that now passes through the polarizers, which lower the signal power by >>3 dB. The noise power, on the other hand, is reduced with only 3-dB when the signal passes through the polarizer. The combination of a lower signal power but constant noise power results in a reduced OSNR. This assumes that the noise in unpolarized, which results in the worst-case penalty. The OSNR decrease is negligible when the noise is polarized through the PDL. Figure 7.11a depicts the impact of PDL-induced depolarization when unpolarized noise is assumed, both with a single PBS and with separate polarizers. This shows that PDL-induced depolarization results in a slightly lower OSNR penalty than PDL-induced attenuation of one of the polarization tributaries. We note that the case of two separate polarizers applies to the digital coherent receiver discussed in Chapter 10. BER = 10 -5 (a) 0 2 4 6 8 10 0 2 4 6 8 10 Polarization dependent loss (dB) O S N R p e n a l t y ( d B / 0 . 1 n m ) 40 50 60 70 80 90 Depolarization (degrees) PDL PDL PDL with no offset PDL with 45 o offset (b) (c) Figure 7.11: (a) Simulated OSNR tolerance versus polarization dependent loss, all curves show the worst-case of both POLMUX tributaries; (b, ) impact of PDL parallel to one of the polarization tribu- taries; (c) impact of PDL with a 45 o offset to the polarization tributaries with separate polarizers ( ) and for a single PBS ( ). The impact of PDL in a long-haul transmission link is more difficult to estimate as it also interacts with other transmission impairments such as PMD. We therefore only consider here the impact of PDL-induced depolarization on a POLMUX signal, which is likely to be the dominant PDL- related impairment. Figure 7.11 then shows that if we take 3 dB of PDL as a typical value for a long-haul link, the OSNR penalty due to depolarization is limited to 2-dB. 144 7.4. Nonlinear tolerance 7.4 Nonlinear tolerance We now extend the discussion on POLMUX signaling to include nonlinear transmission impair- ments. Section 7.4.1 discusses the nonlinear tolerance of POLMUX signaling in the absence of co-propagating WDM channels. Subsequently, Section 7.4.2 studies in more detail the inter- action between PMD and single-channel nonlinear impairments. We then focus on POLMUX signaling in a WDM transmission system. In WDM systems, POLMUX signaling suffers from polarization scattering through XPM-induced depolarization, which is analyzed in Section 7.4.3. Finally, Section 7.4.4 introduces polarization-interleaved POLMUX transmission as a concept to reduce the impact of XPM-induced depolarization. 7.4.1 Self-phase modulation The nonlinear interaction between both orthogonal polarization modes at the same wavelength results in XPolM. For modulation formats that do not modulate the polarization of the optical signal, both polarization modes carry a portion of the same signal and the XPolM interaction is similar to SPM. For POLMUX signaling, on the other hand, XPolM results in a crosstalk between both tributaries that is more similar to XPM. 2 4 6 8 10 12 14 16 18 8 10 12 14 16 Input power (dBm/ch) Q ( d B ) -2 -3 -4 -6 -8 l o g ( B E R ) FEC limit Figure 7.12: Measured single channel nonlinear tolerance for 10.7-Gb/s RZ-DPSK, 10.7-Gb/s RZ- OOK, 21.4-Gb/s POLMUX-RZ-OOK, 21.4-Gb/s POLMUX-RZ-DPSK. We now assess the nonlinear tolerance of POLMUX signaling on an 800-km transmission link, which is depicted in Figure 5.15. The outputs of 1 to 9 ECL on a 50-GHz grid (center wave- length at 1550.9 nm) are combined in a 16:1 coupler. A MZM driven with a 10.7-Gb/s clock signal is used for pulse-carving and a 10.7-Gb/s 2 31 −1 PRBS is used to drive a second MZM for modulation. The second MZM generates either OOK or DPSK modulation, depending on the bias voltage and drive signal amplitude swing applied to the modulator. The signal is sub- sequently polarization-multiplexed by splitting the signal, delaying one tributary by 23 ns and then recombining both tributaries with orthogonal polarizations. The 800-km transmission link 145 Chapter 7. Polarization-multiplexing consists of 8x100-km SSMF spans and the dispersion map is described in Section 5.4. At the receiver a 37-GHz CSF selects the desired WDM channel. The signal is then manually pola- rization de-multiplexed using a PBS preceded by a polarization controller (PC). For RZ-DPSK the detector consists of a 1-bit MZDI followed by balanced detection and for RZ-OOK direct detection is used. Figure 7.12 shows the single channel 1 nonlinear tolerance of 10.7-Gb/s NRZ-OOK and 10.7- Gb/s NRZ-DPSK with both single polarization and POLMUX signaling. Without POLMUX signaling, a slightly higher nonlinear tolerance is measured for DPSK compared to OOK mod- ulation. And when the signals are polarization-multiplexed, there is no significant change in the nonlinear tolerance for either OOK or DPSK modulation. This similarity in nonlinear toler- ance can be understood when we take into account that POLMUX signaling divides the channel power over both polarization modes. Because the SOP of the signal changes on the bit-level, the average propagating power is equally divided over both orthogonal PSP. Substituting the power per polarization channel into Equation 2.36 indicates that the nonlinear phase shift in a single channel is the same for both POLMUX signaling and single polarization modulation. The non- linear phase shift is therefore not related to the power per polarization channel, but to the power per wavelength channel, as is also the case in the absence of POLMUX signaling. However, the interaction between the nonlinear phase shift and chromatic dispersion is slightly different. When the signal is not coupled into the PSP’s, the propagating signal in each of the polarization modes is a mix between both POLMUX tributaries. When we take POLMUX-NRZ-OOK mod- ulation as an example, this implies that a quasi ’3-level’ amplitude modulated signal propagates along the fiber. Due to the interaction with chromatic dispersion, the nonlinear penalty for such a ’3-level’ signal will generally be slightly higher compared to a conventional NRZ-OOK signal. 7.4.2 Self-phase modulation & PMD As a next step, we consider the impact of PMD on the single channel nonlinear tolerance. In conventional transmission systems, the impact of PMD on the nonlinear tolerance is small. A significant amount of PMD can even reduce nonlinear impairments to a certain degree [335]. However, as the PMD-induced penalty is normally much larger than the improvement in nonlin- ear tolerance, it is desirable to avoid PMD in the transmission link. In POLMUX transmission the interaction between PMD and nonlinear impairments results unfortunately in increased trans- mission impairments. This is illustrated through the simulated eye diagrams in Figure 7.13. The SPM-induced nonlin- ear impairments shift the DGD-induced over- and undershoots more to the middle of the symbol period. As a result, both impairments combined results in higher penalties as when they would occur separately. For 10-Gb/s NRZ-OOK, on the contrary, we observe no significant penalty for the same amount of DGD and nonlinear phase shift, as evident from Figure 7.13. 1 Single channel refers to a single wavelength channel. 146 7.4. Nonlinear tolerance (b) (c) (a) (d) 100 ps P o w e r ( a . u ) 100 ps P o w e r ( a . u ) 100 ps P o w e r ( a . u ) 100 ps P o w e r ( a . u ) Figure 7.13: Simulated eye diagrams for (a) 20-Gb/s POLMUX-NRZ-OOK with 40 ps of DGD, (b) 20- Gb/s POLMUX-NRZ-OOK after transmission over 100-km SSMF with 15-dBm input power (c) 20-Gb/s POLMUX-NRZ-OOK after transmission and with 40 ps of DGD, (d) 10-Gb/s NRZ-OOK after transmis- sion and with 40 ps of DGD. (a) (b) (c) Figure 7.14: Statistical simulation results for 10-Gb/s NRZ-OOK and 20-Gb/s POLMUX-NRZ-OOK; (a) Monte-Carlo simulation (10,000 simulations) of the probability distribution for 8-ps, 12-ps and 16-ps of PMD, dots denote linear and circles denote nonlinear simulations for a 100-km link and 15-dBm input power. (b-c) PMD scatter plots for a 100-km link and 12-ps of average PMD with (b) 10-Gb/s NRZ-OOK and (c) 20-Gb/s POLMUX-NRZ-OOK. The precise interaction between DGD and fiber nonlinearity is rather difficult to quantize as it depends on the evolution of the SOP along the fiber. As an alternative, the interaction between PMD and nonlinear impairments is quantified using statistical simulations. Figure 7.14 shows statistical simulations of the combined penalty for 10-Gb/s NRZ-OOK and 20-Gb/s POLMUX- NRZ-OOK modulation. Only the interaction between nonlinearity and DGD is considered, ASE noise is neglected in the simulations and the performance is evaluated using the EOP. A sin- gle 100-km SSMF fiber span is simulated with -510-ps/nm pre-dispersion and zero accumulated dispersion. The input power is equal to 15 dBm into the SSMF and 5.5 dBm into the DCF. Dif- ferent amount of PMD are added distributed along the SSMF through random coupling between the wave-plates. The fiber parameters for the SSMF and DCF are depicted in Table 7.2. At the receiver, the polarization channels are de-multiplexed using a PBS. We assumes here perfect alignment between the SOP at the carrier frequency and the axis of the PBS. In addition, the worst-case EOP of both POLMUX tributaries is used. 147 Chapter 7. Polarization-multiplexing Table 7.2: SIMULATED FIBER PARAMETERS. SSMF DCF unit Insertion loss (α) 0.2 0.5 dB/km Dispersion (D) 17 -102 ps/km/nm Dispersion slope (S) 0.057 -0.34 ps/km/nm 2 Nonlinearity (γ) 1.3 2.95 1/W/km The linear and nonlinear simulation for an average PMD of 8 ps, 12 ps, and 16 ps are depicted in Figure 7.14a. For the linear simulations, only a small penalty is obtained. The penalty is Maxwellian distributed and shows a longer tail for higher average PMD. In the nonlinear simula- tions the worst-case penalty is significantly increased beyond the penalty for the linear case. As an example we consider the simulation with 16-ps average PMD, where the worst-case PMD- only penalty extends to 1.1 dB. But combined with nonlinear impairments, the worst-case penalty equals 2.5 dB whereas the mean nonlinear penalty is only 0.4 dB. This interaction is also evident from a comparison between Figures 7.14b and 7.14c. Whereas we observe a clear correlation between PMD and nonlinear impairments for 20-Gb/s POLMUX-NRZ-OOK, the penalty for 10-Gb/s NRZ-OOK is uncorrelated or decreases slightly with higher PMD. When we take the worst-case penalty from the statistical simulations as a measure, the interaction between nonlin- ear impairments and PMD results in a ∼2 dB decrease in nonlinear tolerance. Next, a fixed set of coupling angles between the birefringent wave plates is used and the strength of the birefringence is varied to simulate different amounts of DGD. The polarization channels are launched with a worst-case 45 o misalignment angle with respect to the PSP. This simplifica- tion allows for significantly reduced computation effort in the study of the interaction between DGD and nonlinearity. For a fixed DGD and input power a single EOP is now obtained instead of a probability distribution. Note that the results only represent an average case with respect to DGD and nonlinear tolerance due to the fixed evolution of the SOP along the fiber link. For the selected set of coupling angles the SOPMD is 0.228 ps 2 for a 1-ps DGD, and can therefore be neglected. Figure 7.15 shows the EOP as a function of both DGD and input power into the SSMF. In order to compare penalties, both 20-Gb/s POLMUX-NRZ-OOK (Figure 7.15a) as well as NRZ-OOK transmission with 10 Gb/s and 20 Gb/s (Figures 7.15b and 7.15c) are shown. First of all, we compare 10-Gb/s NRZ-OOK and 20-Gb/s POLMUX-NRZ-OOK. In this case the simulations show a clear reduction in both nonlinear and DGD tolerance. In the absence of nonlinear interaction, the DGD tolerance is respectively 54 ps and 42 ps for a 1-dB EOP. The nonlinear tolerance in the absence of DGD decreases from 17.5 dBm to 16.2 dBm, which is comparable to the measurements in Figure 7.12. As well, and similar to the previously discussed statistical simulations, the penalty increases when both DGD and nonlinear impairments are present. This contrasts with 10-Gb/s NRZ-OOK modulation where no interaction between DGD and nonlinear impairments is observed. Although a comparison between 20-Gb/s POLMUX- NRZ-OOK and 10-Gb/s NRZ-OOK gives insight in how POLMUX signaling changes the trans- mission penalties, it is more realistic to compare the penalties at the same total bit rate, i.e. 20-Gb/s POLMUX-NRZ-OOK with 20-Gb/s NRZ-OOK. This results in a very different com- parison between the DGD and nonlinear tolerances. Similar to Figure 7.6, the DGD tolerance 148 7.4. Nonlinear tolerance of NRZ-OOK is approximately halved and the nonlinear tolerances decrease even more when the symbol rate is doubled. Consequently, 20-Gb/s POLMUX-NRZ-OOK has a clear advantage over 20-Gb/s NRZ-OOK in both DGD and nonlinear tolerances. The DGD tolerance of 20-Gb/s POLMUX-NRZ-OOK is 42 ps compared with 26 ps for 20-Gb/s NRZ-OOK and the nonlinear tolerance equals 16.2 dBm and 11.9 dBm, respectively. We note that this difference in nonlinear tolerance gives only an indication and might change slightly when long-haul transmission with an optimized dispersion map is considered. 10 20 30 40 50 D G D ( p s ) 1 1 1 2 2 3 3 5 5 10 10 (a) 11 13 15 17 19 Input power (dBm) 10 20 30 40 50 D G D ( p s ) 0.5 0.5 1 1 2 2 2 3 (b) 11 13 15 17 19 Input power (dBm) 0.5 (c) 11 13 15 17 19 10 20 30 40 50 Input power (dBm) D G D ( p s ) 1 2 3 3 5 5 5 10 10 10 10 1 1 1 2 2 2 3 3 3 5 10 10 20 30 40 50 D G D ( p s ) (d) 11 13 15 17 19 Input power (dBm) Figure 7.15: Simulated EOP as a function of DGD and input power for transmission over 100 km of SSMF, (a) 20-Gb/s POLMUX-NRZ-OOK, (b) 10-Gb/s NRZ-OOK, (c) 20-Gb/s NRZ-OOK and (d) 20-Gb/s POLMUX-NRZ-OOK with DGD compensation. We now investigate the de-multiplexing penalties when the DGD is compensated at the receiver. First-order PMD compensation is used, i.e. the DGD at the carrier frequency is reduced to zero, and any influence of higher-order PMD is not compensated. In this case, Figure 7.15d shows that no penalties are associated with the de-multiplexing of the polarization multiplexed channels. The nonlinear tolerance is comparable to the case without DGD compensation (Figure 7.15a) and no further penalties are observed up to a 50-ps DGD. This confirms that the increased penalties in POLMUX signaling result from the polarization de-multiplexing at the receiver and do not result from nonlinear interaction along the transmission link. This implies that for a DGD compensated transmission link, PMD and nonlinear effects can be treated independently, similar as observed in Figures 7.15b and 7.15c for NRZ-OOK. A final consideration is that PMD compensation normally uses the DOP as a feedback signal. In a POLMUX transmission system, the PMD compensation cannot be based on DOP measurement as the time-averaged DOP is close to zero. An alternative feedback signal that has been reported for POLMUX signals is the monitoring of spectral components in the electrical spectrum [336]. Alternatively, the impact of PMD can be compensated using a digital coherent receiver, as discussed in Chapter 10. 149 Chapter 7. Polarization-multiplexing 7.4.3 Cross polarization modulation We now extend the discussion to POLMUX-specific inter-channel nonlinear impairments. In POLMUX transmission systems, XPM-induced XPolM results in a polarization dependent non- linear phase shift. This nonlinear phase shift depends on the transmitted bit-sequence in the co-propagating channels which leads to a noise-like change of the SOP, and hence depolariza- tion. Due to the polarization sensitive receiver, the depolarization is converted into crosstalk between the POLMUX tributaries. This was first observed for two co-propagating polarization- multiplexed solitons by Mollenauer et. al. in [77]. The nonlinear induced depolarization does not affect polarization insensitive modulation formats, as the penalty occurs only in the receiver when the POLMUX tributaries are de-multiplexed [78]. In order to study the effects of XPM-induced XPolM, we compare the nonlinear tolerance for transmission with and without POLMUX signaling. The nonlinear tolerance is measured for RZ- OOK or RZ-DPSK nodulation with different numbers of co-propagating channels and different channel spacings. The experimental setup consists of an 800-km transmission link, as discussed in Section 5.4. Figures 7.16a-d shows the BER as a function of the channel input power with co-propagating channels on a 50-GHz ITU grid. First of all, we compare single channel and WDM transmission with 9 co-propagating channels for RZ-OOK and RZ-DPSK. This shows that the nonlinear tolerance decreases with 2.4 dB and 4.8 dB, respectively, which results mainly from XPM impairments between the co-propagating WDM channels. Linear crosstalk between neighboring channels can also contribute slightly to the penalty as the channels are multiplexed using a 16:1 coupler, which does not filter out the out-of-band components. This comparison shows that at a 10.7-Gb/s symbol rate, RZ-DPSK is more affected by XPM impairments than RZ-OOK. This is straightforward when we take into account that for DPSK, the XPM-induced nonlinear phase shift results in a direct penalty. For OOK, on the other hand, the XPM-induced nonlinear phase shift results only indirectly in a transmission penalty through the interaction with chromatic dispersion. We note that for RZ-DPSK, the large inter-channel penalty could partially be a result of the high input powers used in this comparison, which enhances the influence of nonlinear phase noise. Next, we compare the nonlinear tolerance of RZ-OOK and POLMUX-RZ-OOK, which is shown in Figures 7.16a and 7.16c, respectively. For RZ-OOK, the nonlinear tolerance decreases with 2.4 dB when we compare single channel transmission with 9 co-propagating WDM channels on a 50-GHz grid. On the other hand, for POLMUX-RZ-OOKmodulation the decrease equals 6.7 dB. This indicates a strong impact of XPM-induced XPolM impairments for POLMUX-RZ-OOK modulation. Where RZ-OOK is mainly limited by (intra-channel) SPM, POLMUX-RZ-OOK is clearly limited by inter-channel nonlinear impairments. A comparison between RZ-DPSK (Fig- ure 7.16b) and POLMUX-RZ-DPSK (Figure 7.16d), on the other hand, shows only an additional 0.9-dB penalty. This is related to the more symmetric signal constellation of POLMUX-DPSK, which reduces the impact of XPolM. In summary; RZ-OOK has a higher nonlinear tolerance when compared to RZ-DPSK on a 50-GHz WDM grid. But for POLMUX signaling, the im- pact of XPolM results in a lower nonlinear tolerance for POLMUX-RZ-OOK when compared to POLMUX-RZ-DPSK. 150 7.4. Nonlinear tolerance 0 2 4 6 8 10 12 14 16 8 10 12 14 16 Input power (dBm/cd/span) Q ( d B ) -2 -3 -4 -5 -7 -9 -12 l o g ( B E R ) FEC limit 1.1dB (a) 0 2 4 6 8 10 12 14 16 8 10 12 14 16 Input power (dBm/ch/span) Q ( d B ) -2 -3 -4 -5 -7 -9 -12 l o g ( B E R ) 4.0dB (b) 0 2 4 6 8 10 12 14 16 8 10 12 14 16 Input power (dBm/ch/span) Q ( d B ) -2 -3 -4 -5 -7 -9 -12 l o g ( B E R ) FEC limit 6.7dB (c) (d) 0 2 4 6 8 10 12 14 16 8 10 12 14 16 Input power (dBm/ch/span) Q ( d B ) -2 -3 -4 -5 -7 -9 -12 l o g ( B E R ) 5.7dB FEC limit Figure 7.16: Measured nonlinear tolerance after 800-km for (a) 10.7-Gb/s RZ-OOK, (b) 10.7-Gb/s RZ- DPSK, (c) 21.4-Gb/s POLMUX-RZ-OOK and (d) 21.4-Gb/s POLMUX-RZ-DPSK with single channel, 3 WDM channel, 50-GHz spacing, 5 WDM channel, 50-GHz spacing, 9 WDM channel, 50-GHz spacing. Figures 7.17e-h compares the influence of different channel spacings with 3 co-propagating channels on a 50-GHz, 100-GHz and 200-GHz WDM grid. For both RZ-OOK (Figure 7.17e) and RZ-DPSK (Figure 7.17f), the penalty is sharply reduced for a channel spacing larger than 50 GHz. With POLMUX-RZ-OOK (Figure 7.17g) and POLMUX-RZ-DPSK (Figure 7.17h), on the other hand, a reduced nonlinear tolerance is also observed when the co-propagating channels are spaced 100-GHz and 200-GHz away. In particular POLMUX-RZ-OOK shows still a sig- nificant penalty (2.9 dB) between single channel and 3 co-propagating channels on a 200-GHz grid. For RZ-OOK, on the other hand, almost no difference is measured between 3 channels on a 200-GHz grid and single-channel transmission. This larger bandwidth is typical for XPolM- induced depolarization in POLMUX transmission. In conventional transmission systems, where the receiver is not polarization sensitive, a low-pass behavior characterizes the influence of XPM [337] and therefore results in a penalty which scales strongly with the channel spacing. Whereas XPM is normally not significant for a channel spacing in excess of 100-GHz (for SSMF and 10-Gbaud), XPolM can be a significant impairment for channel spacing up to 200-GHz. The difference in nonlinear penalty as a function of channel spacing is less significant for RZ-DPSK and POLMUX-RZ-DPSK, which confirms the observation that DPSK is mainly XPM and not XPolM limited. We note that this results in particulary large transmission impairments when a D(Q)PSK signal co-propagates with an OOK modulated channel. This case is discussed in Section 10.6.2. 151 Chapter 7. Polarization-multiplexing 0 2 4 6 8 10 12 14 16 8 10 12 14 16 Input power (dBm/cd/span) Q ( d B ) -2 -3 -4 -5 -7 -9 -12 l o g ( B E R ) FEC limit 1.1dB (a) 0 2 4 6 8 10 12 14 16 8 10 12 14 16 Input power (dBm/ch/span) Q ( d B ) -2 -3 -4 -5 -7 -9 -12 l o g ( B E R ) 4.0dB (b) 0 2 4 6 8 10 12 14 16 8 10 12 14 16 Input power (dBm/ch/span) Q ( d B ) -2 -3 -4 -5 -7 -9 -12 l o g ( B E R ) 5.3dB (c) 2.9dB 0 2 4 6 8 10 12 14 16 8 10 12 14 16 Input power (dBm/ch/span) Q ( d B ) -2 -3 -4 -5 -7 -9 -12 l o g ( B E R ) 5.2dB (d) 2.0dB Figure 7.17: Measured nonlinear tolerance after 800-km for (a) 10.7-Gb/s RZ-OOK, (b) 10.7-Gb/s RZ- DPSK, (c) 21.4-Gb/s POLMUX-RZ-OOK and (d) 21.4-Gb/s POLMUX-RZ-DPSK with single channel, 3 WDM channel, 50-GHz spacing, 3 WDM channel, 100-GHz spacing, 3 WDM channel, 200-GHz spacing. 7.4.4 Polarization-interleaved POLMUX systems The impact of XPolM-induced transmission penalties can be reduced through orthogonal pola- rization interleaving of adjacent POLMUX channels. Interleaved POLMUX transmission de- terministically spreads out the SOP of the channels over the Poincar´ e sphere, by changing the SOP of the even wavelength channels with respect to the uneven channels. Polarization inter- leaved POLMUX transmission therefore bears a strong similarity to conventional polarization interleaved transmission, where adjacent WDM channels are transmitted in orthogonal SOPs [71, 72]. In polarization interleaved POLMUX systems, a signal is transmitted in both orthogonal SOPs of each co-propagating wavelength channel, as illustrated in Figure 7.18. The decrease in trans- mission penalties is based on the observation that the sum of the Stokes vectors of two co- propagating wavelength channels is constant during transmission, which cancels the influence of XPolM. Using the Manakov Equation [338], one can show that the nonlinear polarization shift induced on a pulse in channel ω 1 through a second co-propagating pulse in channel ω 2 is equal to, S ω 1 z = 8 9 γP 0 (S ω 1 xS ω 2 ), (7.8) where S n denotes the Stokes vector of channel n, P 0 is the channel input power and z the trans- mission distance. Assuming a sum vector S 0 with S 0 = 1 2 (S ω 1 +S ω 2 ) it can be shown that this is 152 7.4. Nonlinear tolerance equal to, S ω 1 z = 16 9 γP 0 (S ω 1 xS 0 ), (7.9) which only depends on S ω 1 and the sum vector S 0 . When the two pulses in channels ω 1 and ω 2 have an orthogonal SOP, the sum vector S 0 equals zero and the nonlinear polarization shift only depends on the pulse in channel ω 1 itself. Using a similar argument it can be shown that also for multiple co-propagating channels polarization interleaving minimizes the variance in nonlinear polarization shift. ’00’ ’01’ ’11’ ’10’ ’00’ ’01’ ’11’ ’10’ ’00’ ’01’ ’11’ ’10’ ’00’ ’01’ ’11’ ’10’ Channel Ȧ 1 Channel Ȧ 1 Channel Ȧ 2 Channel Ȧ 2 Non-interleaved 90° polarization interleaved Figure 7.18: Principle of interleaved POLMUX transmission. ì1 ì9 A W G MZM POL-MUX delay V H VOA PC PC I N T I N T PC Interleaving 100km SSMF DCM PBS PC ~ ~ ~ 25-GHz CSF RX data POL- deMUX PC Figure 7.19: Experimental setup for interleaved POLMUX transmission. We experimentally verify the principle of interleaved POLMUX transmission with the setup de- picted in Figure 7.19. The output of up to 9 DFB lasers, spaced on a 50-GHz grid, are 10-Gb/s NRZ-OOK modulated (PRBS 2 31 -1). Afterwards, the signals are polarization-multiplexed to 20-Gb/s POLMUX-NRZ-OOK. The WDM channels are polarization interleaved by splitting the channels into two subsets using a 50-GHz interleaver and afterwards recombining the channels with a second 50-GHz interleaver. The SOP of the POLMUX channels are adjusted using the polarization controllers in between both interleavers. As it is difficult to measure the SOP dif- ference between the WDM channels, we adjust the SOP of one of the channel subsets such that the measured BER is minimized. In effect, the polarization interleaving rotates the linear polari- zation components of the even WDM channels 90 o with respect to the uneven WDM channels. The signals are then transmitted over 100 km of SSMF and matching DCF, where the same in- put power is used for both SSMF and DCF to generate sufficient nonlinear impairments. After transmission, a 25-GHz CSF filters out the center channel and the signal is manually polarization de-multiplexed with a PBS preceded by a polarization controller. Afterwards, the signal is fed into a direct detection receiver and the nonlinear tolerance is measured for the center channel at 1551.6 nm. In Figure 7.20a, the impact of polarization interleaving on 10-Gb/s NRZ-OOK is depicted. This show an improvement of 0.9 dB and 0.5 dB for 3 and 5 co-propagating channels, respectively 153 Chapter 7. Polarization-multiplexing 5 6 7 8 9 10 11 12 13 -9 -7 -5 -4 -3 -2 Input power (dBm/ch) l o g ( B E R ) 16 14 12 10 8 Q ( d B ) FEC Limit (a) 2 4 6 8 10 12 -9 -7 -5 -4 -3 -2 Input power (dBm/ch) l o g ( B E R ) 16 14 12 10 8 Q ( d B ) FEC Limit (b) 5 6 7 8 9 10 11 12 13 -9 -7 -5 -4 -3 -2 Input power (dBm/ch) l o g ( B E R ) 16 14 12 10 8 Q ( d B ) FEC Limit (c) Figure 7.20: Measured nonlinear tolerance after 100-km for (a) 10-Gb/s NRZ-OOK and (b-c) 20-Gb/s POLMUX-NRZ-OOK with 3 channel 50-GHz spacing, 3 channel 50-GHz spacing, interleaved, 9 channel 50-GHz spacing, 9 channel 50-GHz spacing, interleaved, 3 channel 300-GHz spacing, 3 channel 300-GHz spacing, interleaved. (at 10 −5 BER). This improvement results mainly from a reduction in XPM impairments between the co-propagating channels. For 20-Gb/s POLMUX-NRZ-OOK, as depicted in Figure 7.20b, a much lower nonlinear tolerance is measured compared to 10-Gb/s NRZ-OOK. The difference between 3 and 9 co-propagating channels is more significant here than previously discussed (Figure 7.16c), as there is no dispersion map used here to reduce the impact of XPM. For 3 co- propagating channels, polarization interleaving increases the nonlinear tolerance with 1.2 dB. But when the number of co-propagating channels increases, the beneficial influence of polarization interleaved transmission decreases as channels spaced further away contribute to the XPolM penalty. The influence of the channel spacing is evident from the measurement results depicted in Figure 7.20c, which compares a 50 GHz and a 300-GHz channel spacing for 3 co-propagating channels. When the channel spacing is increased, the nonlinear tolerance improvement reduces from 1.2 dB to 0.2 dB. The efficiency of interleaved POLMUX transmission is relatively small compared to the XPolM penalty. This is mainly due to the impact of DGD and SOPMD, which changes the SOP as a function of wavelength. In particular for WDM channels that are spaced further apart, the or- thogonality between the WDM channels is maintained only over a short transmission distance. This reduces the benefit of polarization interleaving, as it requires an accurate alignment of the SOP of the WDM channels. We can therefore conclude that polarization interleaved POLMUX transmission does not sufficiently reduce the impact of XPolM to be practical in long-haul trans- mission systems. 154 7.5. Summary & conclusions 7.5 Summary & conclusions In this chapter we analyzed and compared the transmission tolerances of POLMUX signaling with polarization insensitive modulation formats. This shows that for most linear and nonlinear transmission impairments separately, POLMUX signaling significantly increases the transmis- sion tolerance when compared to binary modulation at the same bit rate. → A polarization-sensitive receiver improves the OSNR requirement by filtering out the noise in the orthogonal polarization. For POLMUX-OOK modulation, the difference is ∼2.7 dB for a doubling in the total bit rate. In comparison to DQPSK modulation, POLMUX-DPSK modulation has a 1.1 dB advantage in OSNR requirement. → PMD results in crosstalk between the POLMUX tributaries due to over- and undershoots near the edge of the pulse. But at the same bit rate, the PMD tolerance of POLMUX signaling is significantly higher in comparison to binary modulation formats. → The lower symbol rate increases the chromatic dispersion tolerance by a factor of 4 in the absence of a PMD. However, the combination of chromatic dispersion and PMD, shifts the DGD induced edge over- and undershoots from the edge to the center of the pulse. This reduces the tolerance by ∼30% (2-dB OSNR penalty) in comparison to single-polarization transmission at the same symbol rate. → For POLMUX signaling, PDL can either result in an OSNR fluctuation for one of the tribu- taries or a loss of orthogonality between the tributaries. A 3-dB PDL results approximately in a 2-dB worst-case OSNR penalty. → At a 10-Gbaud symbol rate, the single-channel nonlinear tolerance is comparable with and without POLMUX signaling. In the presence of PMD, the nonlinear tolerance de- creases due to the cumulative edge effects of DGD and SPM. Statistical simulations show for this case a reduction in nonlinear tolerance with up to ∼2 dB in comparison to single- polarization transmission at the same symbol rate. In addition we find that for WDMtransmission systems, the impact of XPolMresults in a reduced nonlinear tolerance for POLMUX transmission systems. → The XPolM-induced nonlinear phase shift result in a noise-like change in the SOP. This causes crosstalk between the POLMUX tributaries after the polarization sensitive receiver. → For POLMUX-OOK modulation, the impact of XPolM results in a reduction of the non- linear tolerance with 4-5 dB in comparison to WDM transmission without POLMUX sig- naling (10 Gbaud, 50-GHz grid). This makes POLMUX-OOK modulation generally im- practical for long-haul transmission. → POLMUX-DPSK modulation has a more symmetric signal constellation, which reduces the impact of XPolM. It suffers therefore only a ∼1 dB penalty from XPolM impairments. 155 Chapter 7. Polarization-multiplexing This indicates that POLMUX-DPSK can be a suitable modulation format for long-haul transmission systems. POLMUX-DPSK has a 3-dB advantage in nonlinear tolerance com- pared to DQPSK modulation at a 10-Gbaud symbol rate and 50-GHz channel spacing. → Deterministically spreading the SOP of co-propagating WDM channels reduces the impact of XPolM. Polarization interleaving of the WDM channels therefore, ideally, cancels out the XPolM penalty. However, the orthogonality between the co-propagating channels is lost through PMD, which decreases the efficiency of polarization interleaving. The interaction between PMD, chromatic dispersion and nonlinear impairment complicates sys- tem design for POLMUX transmission systems. This is undesirable for long-haul transmission systems which, if possible, have to be designed with simple engineering rules. It is therefore at- tractive to apply PMD compensation for POLMUX transmission systems, either through optical or electrical means. When the PMD-related impairments are compensated, the high transmis- sion tolerances combined with the doubled spectral efficiency of POLMUX signaling make it an attractive option for high-capacity transmission systems. However, optical compensation of PMD might not be practical due to high polarization tracking speeds that are required. The use of phase modulation reduces the impact of XPolM and makes POLMUX signaling practical for long-haul transmission systems. 156 8 Polarization-multiplexed DQPSK Future state-of-the-art optical transmission systems are expected to transmit high bit rates in even more densely spaced WDM channels. However, as shown in the previous chapter the use of multi-level modulation formats is challenging for long-haul transmission systems. It can result in reduced transmission reach through higher OSNR requirements and a lower nonlinear tolerance. This requires transmission formats with a narrow optical bandwidth while maintaining sound linear and nonlinear transmission tolerances to enable long-haul transmission with >1 b/s/Hz. Chapters 5 and 7 have discussed, respectively, DQPSK modulation and POLMUX signaling as possible approaches to double the spectral efficiency over binary modulation. To further increase the number of bits per symbol, orthogonal coding can be used to exploit two or more degrees of freedom at the same time. An example of orthogonal coding that combines amplitude and phase shift keying is amplitude differential phase shift keying [339]. The simulta- neous modulation of the amplitude, phase and polarization dimensions of an optical signal has al- lowed multi-level modulation at high bit rates with up to 5 and 6 bits per symbol [340, 341]. This chapter combines DQPSK modulation and POLMUX signaling to realize modulation with 4 bits per symbol. Such a high-density signal constellation opens up the possibility for a ≥1.6 b/s/Hz spectral efficiency in long-haul transmission systems. Section 8.1 describes the transmitter and receiver structure of POLMUX-RZ-DQPSK modula- tion, the OSNR requirement as well as the tolerance against narrowband filtering. Subsequently, Section 8.2 discusses long-haul POLMUX-RZ-DQPSK transmission with a 1.6-b/s/Hz spectral efficiency. We particulary focus on the influence of interleaved polarization multiplexing, which presents a trade-off between the nonlinear and PMD tolerance. In Section 8.3 we then compare the high-spectrally efficient transmission experiments that have been studied in the literature. 1 The results described in this chapter are published in c7, c36 157 Chapter 8. Polarization-multiplexed DQPSK 8.1 Transmitter & receiver structure A POLMUX-DQPSK transmitter consists of two DQPSK transmitters which are afterwards mul- tiplexed on the two orthogonal polarizations of the signal. This results in a transmitted signal, r(t) = _ E h E v _ = _ √ P h exp( j[ω 0 t +ϕ h (t)]) √ P v exp( j[ω 0 t +ϕ v (t)]) _ . (8.1) As POLMUX-DQPSK modulation encodes the information in the differential phase ∆φ, we can also denote the signal as, r(t) = _ √ P h exp( j[ω 0 t +ϕ +∆ϕ h (t)]) √ P v exp( j[ω 0 t +ϕ +∆ϕ v (t) +∆ψ]) _ , (8.2) where ϕ is the absolute phase of the transmitter laser and ∆ψ is the phase difference between both orthogonal polarization components. The information is carried in ∆ϕ h (t) and ∆ϕ v (t) which are independent of each other and take a value from the set [0, π/2, π, 3π/2]. Assuming ϕ and ∆ψ are equal to zero this gives √ P h exp( j∆ϕ h (t)) = h I (t) + j h Q (t) as the complex envelope of the horizontal polarization components and √ P v exp( j∆ϕ v (t)) = v I (t) + j v Q (t) as the complex en- velope of the vertical polarization component. The signals in each of the 4 signaling dimensions can therefore be defined as, h I (t) = ℜ¦E h ¦ =ℜ¦ _ P h exp( j∆ϕ h (t))¦ h Q (t) = ℑ¦E h ¦ =ℑ¦ _ P h exp( j∆ϕ h (t))¦ (8.3) v I (t) = ℜ¦E v ¦ =ℜ¦ _ P v exp( j∆ϕ v (t))¦ v Q (t) = ℑ¦E v ¦ =ℑ¦ _ P v exp( j∆ϕ v (t))¦. 1 Re{E h } Im{E h } ǻij h j -1 -j 1 Re{E v } Im{E v } ǻij v j -1 -j X X Figure 8.1: 2-dimensional signal constellation diagram for POLMUX-DQPSK modulation Figure 8.1 shows the signal constellation diagram for POLMUX-DQPSK, as a DQPSK modu- lated signal on each of the two orthogonal polarizations. Each DQPSK signal encodes 2 bits per symbol, which results in a total 2 2 = 4 bits per symbol for POLMUX-DQPSK modulation. This can be slightly counterintuitive, as the constellation diagram in Figure 8.1 shows only 8 158 8.1. Transmitter & receiver structure signal points. As an alternative representation, Figure 8.2 depicts both orthogonal polarizations combined in a single constellation diagram. The signal constellation diagram is now shown as a 4-dimensional hypercube. Different hypercubes can be used to represent the signal constellation but we use here a torus, which is the product of two coplanar circles. We use here one circle to denote exp( j∆ϕ h ), whereas the other circle denotes exp( j∆ϕ v ). Assuming that ∆ψ is equal to zero, the signal constellation can be defined in a three-dimensional coordinate system (x, y, z) as, x(∆ϕ h , ∆ϕ v ) = [R+r cos(∆ϕ v )] cos(∆ϕ h ) y(∆ϕ h , ∆ϕ v ) = [R+r cos(∆ϕ v )] sin(∆ϕ h ) (8.4) z(∆ϕ h , ∆ϕ v ) = r sin(∆ϕ v ), where R and r, with R > r defines the distance from the center of the tube to the center of the torus and the radius of the tube, respectively. Note that when visualized on a Poincar´ e sphere, the constellation diagram of POLMUX-DQPSK modulation consist of 4 signal points as only the phase difference between both polarization modes is denoted (i.e. ∆ϕ v −∆ψ −∆ϕ h , see Figure 7.1a). x y z Figure 8.2: 4-dimensional signal constellation diagram for POLMUX-DQPSK modulation The transmitter and direct detection receiver structure for POLMUX-RZ-DQPSK modulation are both depicted in Figure 8.3. For RZ modulation, the output of the laser is first RZ pulse carved. Afterwards, the signal is split and each of the tributaries is DQPSK modulated with a parallel DQPSKmodulator. With a PBS, both tributaries are then multiplexed together on orthog- onal polarizations. Hence, a total of 4 independent binary electrical data streams are modulated onto the POLMUX-DQPSK signal. We note that all fibers in the transmitter would normally be polarization-maintaining. The polarization rotation for one of the DQPSK tributaries is shown explicitly here, but is normally integrated into the PBS. At the receiver, the signal is first split into two orthogonal polarization tributaries with a polariza- tion controller followed by a PBS. Each of the polarization tributaries is split again with a 3-dB 159 Chapter 8. Polarization-multiplexed DQPSK laser Prec. data HA Prec. data HB ʌ/2 MZ MZ T + - T + - MZDI PD data HA data HB (j,-j) (j,-1)(1,-1) (-j,-j) (-1,j) (-j,1) PC PBS MZM Prec. data VA Prec. data VB ʌ/2 MZ MZ PBS clock T + - T + - data VA data VB TEQTM optional ǻij=+ʌ/4 ǻij=+ʌ/4 ǻij=+ʌ/4 ǻij=+ʌ/4 Figure 8.3: Transmitter and receiver structure for POLMUX-(RZ)-DQPSK modulation fused-fiber coupler and all four tributaries are fed to separate MZDIs. The MZDIs demodulate the in-phase and quadrature tributaries of each of the polarization components which is followed by balanced detection. This shows that the number of optical components in both the transmitter and receiver is significant for POLMUX-RZ-DQPSK modulation. Hence, to make such a modu- lation format more practical further optical integration of the components is a prerequisite. This would for example be possible using InP technology, which enables multiple components on a single optical dei [342, 278, 343]. 8.1.1 Back-to-back OSNR requirement Figure 8.4 depicts the configuration of the 85.6-Gb/s POLMUX-RZ-DQPSK transmitter and re- ceiver as used in the experimental verification. For simplicity, the transmitter and receiver struc- ture is somewhat different from the one discussed in Section 8.1. At the transmitter, the output signals of 40 DFB lasers, aligned on a 50-GHz ITU grid between 1548.15 nm and 1563.88 nm, are modulated using two parallel modulator chains for separate modulation of the even and odd wavelength channels. The RZ-DQPSK modulator is the same as discussed in Section 6.2. After DQPSK modulation, the even and odd channels are combined with a 50-GHz interleaver, having a 3-dB bandwidth of 44 GHz. Subsequently, the channels are fed to a polarization-multiplexing stage. The signal is power split to create two tributaries (Hand V), which are delayed with 16.6 ns relative to each other. One branch of the polarization-multiplexing stage contains an optical switch and phase modulator. The optical switch can be triggered (switch 1) to change between POLMUX-RZ-DQPSK, and (single polarization) RZ-DQPSK modulation for the reference mea- surements. The phase modulator (PM) causes synchronization loss in tributary V when switched on (switch 2), and is hence used to identify which polarization tributary is measured. Note that it is switched off in the actual measurement and has no influence on the discussed results. The tributaries H and V are recombined with orthogonal polarizations in a PBS to generate 85.6-Gb/s POLMUX-RZ-DQPSK modulation. The two polarization tributaries can be bit-aligned or they can be offset from each other. This is discussed in more detail in Section 8.2.1. 160 8.1. Transmitter & receiver structure POL-MUX POL-DEMUX PBS switch-1 MZDI CR BERT DE MUX ì2 ì40 A W G RZ-DQPSK Tx – even channels RZ-DQPSK Tx – odd channels I N T PBS delay V H VOA 21.4G data A 21.4G data B 21.4G clock ʌ/2 MZ MZ MZM PM Switch -1 Switch -2 PD T + - PC RZ-DQPSK Rx (a) (b) Figure 8.4: Experimental setup: (a) transmitter and (b) receiver. Figure 8.5 shows the back-to-back OSNR requirement of 42.8-Gb/s RZ-DQPSK and all four tributaries of 85.6-Gb/s POLMUX-RZ-DQPSK modulation. The simulated back-to-back OSNR requirements are shown as a reference. For both simulations and experiments the respective op- timized filter bandwidths discussed in the Section 5.3.1 are used. The required OSNR for a 10 −3 BER is 13.0 dB and 15.8 dB for 42.8-Gb/s RZ-DQPSK and 85.6-Gb/s POLMUX-RZ-DQPSK, respectively. Hence, 85.6-Gb/s POLMUX-RZ-DQPSK requires a 2.8 dB higher OSNR with re- spect to 42.8-Gb/s RZ-DQPSK. This sensitivity reduction is similar to the reduction observed in Section 7.3.1 and results from a 3-dB penalty due to the doubled bit rate and a 0.2-dB benefit which originates from the polarization sensitive receiver. In the simulations, the required OSNR is 11.8 dB and 14.6 dB for 42.8-Gb/s RZ-DQPSK and 85.6-Gb/s POLMUX-RZ-DQPSK, re- spectively. Hence, the simulative and experimentally measured OSNR requirement are in good agreement and show only a 1.2 dB difference due transmitter and receiver impairments (for a 10 −3 BER). For a fixed OSNR, the back-to-back Q-factor difference between RZ-DQPSK and POLMUX-RZ-DQPSK equals 2.4 dB and 3.0 dB for measurements and simulations, respec- tively. 10 12 14 16 18 20 22 24 26 6 8 10 12 14 16 OSNR/0.1nm(dB) Q ( d B ) -2 -3 -4 -6 -8 -10 -12 l o g ( B E R ) 42.8-Gbit/s RZ-DQPSK 85.6-Gbit/s POLMUX RZ-DQPSK 2.8 dB 2.4 dB Figure 8.5: Measured (points) and simulated (lines) back-to-back sensitivity for 42.8-Gb/s RZ- DQPSK (dashed line) and 85.6-Gb/s POLMUX- RZ-DQPSK (dotted line). 1556 1556.5 1557 -30 -20 -10 0 Wavelength (nm) R e l a t i v e P o w e r ( d B ) (a) (d) (c) (b) Figure 8.6: High resolution optical spectrum with: (a) single channel, (b) transmitted spectrum (c) received spectrum before the CSF (d) received spectrum after the CSF. 161 Chapter 8. Polarization-multiplexed DQPSK 8.1.2 Narrowband optical filtering In order to transmit 85.6-Gb/s POLMUX-RZ-DQPSK with a 50-GHz channel spacing, the band- width of the optical filters is important to consider. The narrowband filtering tolerance of 85.6- Gb/s POLMUX-RZ-DQPSK is similar to 42.8-Gb/s RZ-DQPSK as both modulation formats are DQPSK modulated and have the same symbol rate. Figure 8.6 shows in more detail the narrow- band filtering as it occurs along the transmission line in the long-haul transmission experiment discussed later in this chapter. Spectra (a) shows the single channel optical spectrum of 85.6- Gb/s POLMUX-RZ-DQPSK before optical filtering. A comparison of spectra (a) and (b) shows the influence of the 50-GHz interleaver at the transmitter. The optical filtering in the in-line WSS reduces the optical bandwidth with every pass through the re-circulating loop. The transmittance spectrum of the in-line WSS used in the experiment is shown in Figure 3.16. The in-line spectral filtering is evident by comparing the spectral dip between WDM channels in spectra (b) after the 50-GHz interleaver and spectra (c) after 6 passes through the re-circulation loop. At the receiver, the WDM signal is de-multiplexed using a CSF with a 34-GHz 3-dB bandwidth, further narrow- ing the optical bandwidth. Spectra (d) is obtained after de-multiplexing of the WDM channels. It shows that the spectral width of the received signal after 6 passes through the re-circulating loop is similar to the back-to-back optimized de-multiplexing filter bandwidth of 34-GHz. This indicates that 85.6-Gb/s POLMUX-RZ-DQPSK can be transmitted over multiple cascaded add- drop nodes on a 50-GHz WDM grid. This enables a high 1.6-b/s/Hz spectral efficiency while maintaining a sound tolerance with respect to narrowband optical filtering. 6x 94.5 km SSMF Raman Post- compensation Pre- compensation 3x DCM DCM TDC TX RX WSS LSPS Tx switch Loop switch 40 x 85.6-Gb/s POLMUX-RZ-DQPSK ~ ~ ~ 34-GHz CSF (a) (b) Figure 8.7: (a) re-circulating loop setup, (b) optical spectrum after transmission. 8.2 Long-haul transmission In this section we discuss a long-haul transmission experiment with 85.6-Gb/s POLMUX-RZ- DQPSK modulation on a 50-GHz WDM grid. The re-circulating loop consists of three 94.5- km spans of SSMF with an average span loss of 21.5 dB. Before transmission the channels are de-correlated with -1020 ps/nm of pre-compensation. The inline under-compensation per span is 33.5 ps/nm (at 1550 nm), which is close to the optimum for 42.8-Gb/s RZ-DQPSK as discussed in Section 6.2. The input power into the SSMF is -3 dBm per WDM channel and a 162 8.2. Long-haul transmission hybrid backward pumped Raman/EDFA structure is used for signal amplification with an average ON/OFF Raman gain of ∼11 dB. A LSPS with a deterministic sequence of polarization states equal to the number of re-circulations is used in the re-circulating loop. The polarization in each re-circulation of the loop is thus randomized with respect to the other re-circulations, averaging out PMD and PDL influences. However, the LSPS does not influence the polarization at the receiver and is as such not used to de-multiplex the polarization tributaries. Power equalization of the WDM channels is provided by the WSS, configured as a channel-based DGE. The optical spectrum at the receiver is depicted in Figure 8.7b. Using a TDC, the accumulated dispersion at the receiver is optimized on a per-channel basis. Subsequently, the desired channel is selected with a narrowband 34-GHz CSF and afterwards fed into the receiver (depicted in Figure 8.3b). The signal is first manually polarization de-multiplexed using a PC followed by a PBS. Afterwards, the signal is fed into the conventional 42.8-Gb/s DQPSK receiver as discussed in Section 6.2. 500 1000 2000 3000 4000 8 10 12 14 16 Transmission distance (km) Q ( d B ) -3 -4 -5 -6 -8 l o g ( B E R ) FEC limit 2 . 2 d B 8 5 . 6 - G b / s P O L M U X - R Z - D Q P S K 4 2 . 8 - G b / s R Z - D Q P S K (a) 1545 1550 1555 1560 1565 8 9 10 11 12 13 14 15 Wavelength (nm) Q ( d B ) -3 -4 -6 -8 l o g ( B E R ) 2.2 dB 85.6-Gb/s POLMUX-RZ-DQPSK 42.8-Gb/s RZ-DQPSK FEC limit (b) Figure 8.8: (a) Measured BER as a function of transmission distance, (b) Measured BER of all 40 WDM channels after 1,700 km, for RZ-DQPSK In-phase, Quadrature and POLMUX-RZ-DQPSK In-phase, pol.H, Quadrature, pol.H, In-phase, pol.V, Quadrature, pol.V. To analyze the suitability of the 85.6-Gb/s POLMUX-RZ-DQPSK modulation format for long- haul transmission, the performance is assessed as a function of the transmission distance. This is depicted in Figure 8.8b. Initially the measured log(BER) shows a linear increase with an ex- ponential increase in transmission distance. After 2,000 km it deviates from the linear increase due to an increased impact of nonlinear impairments such as SPM and nonlinear phase noise. A similar performance decrease is observed for 42.8-Gb/s RZ-DQPSK modulation and it can thus be concluded that no POLMUX specific impairments are measured. The 2.4-dB back-to-back difference in Q-factor between 42.8-Gb/s RZ-DQPSK and 85.6-Gb/s POLMUX-RZ-DQPSK is slightly reduced to 2.2 dB. This is likely a result of the lower peak power in comparison to RZ- DQPSK, which results in an improved nonlinear tolerance. We note though that the difference is small and can also partially result from measurement inaccuracies. The lack of POLMUX spe- cific impairments such as XPM induced cross polarization modulation confirms that 85.6-Gb/s POLMUX-RZ-DQPSK is strongly limited by single-channel impairments and that the influence of XPM-induced depolarization is minimal. 163 Chapter 8. Polarization-multiplexed DQPSK Figure 8.8a shows the BER for all WDM channels and tributaries for both 42.8-Gb/s RZ-DQPSK and 85.6-Gb/s POLMUX-RZ-DQPSK. After 1,700-km transmission, all 40 RZ-DQPSK chan- nels have more than 3-dB margin with respect to the FEC limit. For 85.6-Gb/s POLMUX-RZ- DQPSK the worst channel is more than 1 dB above the FEC limit. The small performance variance among the WDM channels indicates that there is no strong wavelength dependency across the upper part of the C-band. 8.2.1 Interleaved vs. bit-aligned polarization-multiplexing The optical inter-pulse delay is defined as the delay between both polarization tributaries within one symbol period (see Section 7.3.2). It can be changed such that both tributaries are either bit-aligned or interleaved. The difference in inter-pulse delay can be denoted by the optical extinction ratio before polarization de-multiplexing and phase demodulation, which is defined as the peak power divided by the minimum power in the eye diagram. In Figure 8.9 the influence of the inter-pulse delay on the optical extinction ratio is depicted for 85.6-Gb/s POLMUX-RZ- DQPSK. In the case both polarization tributaries are interleaved, a quasi CW signal is obtained and the extinction ratio is close to zero. When the polarization tributaries are bit-aligned on the other hand, the RZ pulse shape of RZ-DQPSK is to a high degree maintained and a high extinction ratio is measured, as evident from the eye diagrams in Figure 8.9. -20 -10 0 10 20 30 0 2 4 6 8 10 Normalized optical delay (ps) E x t i n c t i o n r a t i o ( d B ) (a) (b) (c) (c) (b) (a) Figure 8.9: Extinction ratio of the 85.6-Gb/s POLMUX-RZ-DQPSK signals before polarization de- multiplexing and phase demodulation as a function of the normalized inter-pulse delay. For RZ pulse carved signals, it can be particulary interesting to interleave both polarization tribu- taries as this lowers the peak power of the signal and therefore improves the nonlinear tolerance. It is observed in the transmission experiment that interleaving the polarization tributaries reduces nonlinear impairments considerably; a maximum 2 dB difference in Q-factor is measured. On the other hand the influence of PMD related impairments is enhanced for interleaved polarization tributaries, as shown in Section 7.3.2. In the experimental results reported here, the inter-pulse delay is set in between both extremes, partly because the quasi CW signal of interleaved po- larization tributaries caused instable operation of the phase-locked loop based clock-recovery. 164 8.2. Long-haul transmission Additionally, the performance fluctuations might be attributed to the reduced PMD tolerance of 85.6-Gb/s POLMUX-RZ-DQPSK with interleaved tributaries. Setting the inter-pulse delay in between both extremes resulted in more stable operation but a ∼0.5 dB decrease in measured Q-factor. With a simulative comparison the influence of the inter-pulse delay on the PMD and nonlinear tolerance of POLMUX-RZ-DQPSK is discussed in more detail. 8.2.2 Differential group delay The polarization de-multiplexing in the POLMUX receiver, results in a penalty when the signal polarization is not constant (1) over the symbol period or (2) across the optical spectrum. A DGD results in a polarization change across the symbol period, which causes over- and under- shoots near the edges of the symbol. For high bit rates, the impact of SOPMD is also important to consider as it results in a polarization change along the optical bandwidth. For 85.6-Gb/s POLMUX-RZ-DQPSK the influence of a wavelength dependent polarization mismatch should be relatively small due to the 21.4-Gb/s symbol rate. In particular the difference between inter- leaved and bit-aligned POLMUX is not likely to be significantly affected by higher order PMD, because the inter-pulse delay has no influence on the optical spectrum. We therefore restrict our comparison here to the DGD tolerance, which is modeled as linear birefringence. For the POLMUX signals, the simulated DGD is chosen such that the output SOP equals the input SOP. This is true when the DGD times the center frequency (193.1 THz) is an integer multiple [331]. In the simulations the penalties are denoted through the EOP. Hence, it does not include the difference in OSNR requirement for the various modulation formats. In addition, the EOP is normalized with respect to the back-to-back EOP. For RZ-DQPSK the results shown here are the worst-case (maximum) EOP obtained from the in-phase or quadrature channel. In the case of POLMUX signaling, the generated RZ-DQPSK signal is split, delayed over 17 bits and recom- bined with orthogonal polarizations, the denoted EOP is the maximum EOP obtained among the 4 tributaries. Figure 8.10a shows the simulated DGD tolerance for both cases, with 42.8-Gb/s RZ-DPSK and 42.8-Gb/s RZ-DQPSK as a reference. Comparing the DGD tolerance of 42.8-Gb/s RZ- DPSK and 42.8-Gb/s RZ-DQPSK shows an increase in DGD tolerance with about a factor of two for 42.8-Gb/s RZ-DQPSK [122]. For 85.6-Gb/s POLMUX-RZ-DQPSK the DGD tolerance is strongly dependent on the inter-pulse delay between the two polarization tributaries. When the polarization tributaries are bit-aligned the DGD tolerance is only slightly worse than 42.8-Gb/s RZ-DPSK, for the doubled bit rate. For interleaved polarization tributaries, on the other hand, the DGD tolerance is further reduced by about a factor of two in comparison to bit-aligned 85.6- Gb/s POLMUX-RZ-DQPSK. In this case the misalignment between the received polarization and the axis of the PBS does not occur in between two symbols, as is the case for bit-aligned polarization tributaries, but in the middle of the symbol period. The reduced DGD tolerance of interleaved POLMUX-RZ-DQPSK is even more evident from Figure 8.10b, which depicts the penalty versus the inter-symbol delay between the polarization tributaries in the presence of 8.0 ps of DGD. This clearly shows a relatively low penalty for aligned polarization tributaries and a large increase in penalty when the tributaries are interleaved. The inset eye diagrams show 165 Chapter 8. Polarization-multiplexed DQPSK 0 10 20 30 40 50 0 2 4 6 8 DGD (ps) n o r m a l i z e d E O P ( d B ) (a) 0 10 20 30 40 50 0 1 2 3 4 5 6 Optical delay (ps) n o r m a l i z e d E O P ( d B ) (b) Figure 8.10: (a) Simulated comparison of the DGD tolerance with 42.8-Gb/s RZ-DPSK, 42.8- Gb/s RZ-DQPSK 85.6-Gb/s POLMUX-RZ-DQPSK, bit-aligned 85.6-Gb/s POLMUX-RZ-DQPSK, interleaved; (b) normalized EOP as a function of the inter-pulse delay for 85.6-Gb/s POLMUX-RZ- DQPSK with 8-ps DGD. Dotted lines denote tributaries whereas the denote worst case result among all tributaries. Table 8.1: SIMULATED LINK AND RECEIVER PARAMETERS. Link parameters unit Transmission length 8 x 100 km Amplification EDFA - Pre-compensation -510 ps/nm Inline under-compensation 90 ps/nm Post-compensation 0 ps/nm the additional degradation for interleaved polarization tributaries. When the tributaries are bit- aligned the DGD mainly results in jitter between consecutive symbols and the penalty is below 1 dB. For interleaved polarization tributaries on the other hand, severe overshoots are evident in the middle of the eye diagram which clearly shows the cause of the reduced DGD tolerance. This increases the EOP to in excess of 4 dB. 8.2.3 Nonlinear tolerance The more constant intensity level of interleaved POLMUX-RZ-DQPSK modulation reduces the impact of nonlinear impairments through a lower peak power. To show the relation between nonlinear tolerance and inter-pulse delay we simulate single-channel transmission over an 8x100- km link of SSMF. The simulation parameters of the transmission link are listed in Table 8.1 whereas the fiber parameters are the same as denoted in Table 7.2. In the simulated transmission link, the polarization is randomized through random coupling between wave-plates every 1 km. EDFA-only amplification is used and the dispersion map is chosen such that it is typical for a transmission link optimized for 10-Gb/s bit rate. 166 8.2. Long-haul transmission 42.8-Gb/s RZ-DPSK 42.8-Gb/s RZ-DQPSK After pol-demux before phase demodulation After phase demodulation and balanced detection 23 ps P o w e r ( a . u ) 47 ps 23 ps P o w e r ( a . u ) 47 ps 85.6-Gb/s bit-aligned POLMUX RZ-DQPSK 85.6-Gb/s interleaved POLMUX RZ-DQPSK Before pol-demux 47 ps P o w e r ( a . u ) 47 ps 47 ps 47 ps 47 ps 47 ps Figure 8.11: Simulated eye diagrams; before polarization de-multiplexing as well as before and after phase demodulation and balanced detection. Figure 8.11 depicts the simulated eye diagrams for the four considered modulation formats with a 9-dBm input power into each span. This relatively high input power is chosen here to point out the difference in nonlinear tolerance between the modulation formats. The received eye diagram of bit-aligned and interleaved POLMUX-RZ-DQPSK before polarization de-multiplexing shows the RZ and quasi CW shape, respectively. After polarization de-multiplexing, increased broad- ening of the ’1’-rail is evident for bit-aligned POLMUX, whereas for interleaved POLMUX a much cleaner RZ shape is obtained. After phase demodulation and balanced detection the in- creased eye closing is evident, showing the lower nonlinear tolerance for bit-aligned POLMUX. The variance of the ’1’ rail in the eye diagrams after polarization de-multiplexing is comparable for bit-aligned POLMUX-RZ-DQPSK and 42.8-Gb/s RZ-DPSK. However, for RZ-DPSK the phase demodulation is more ideal in comparison to RZ-DQPSK. This results in an eye diagram after balanced detection that is wide open despite the broadened ’1’-rail in the phase domain. The nonlinear tolerance of 42.8-Gb/s RZ-DPSK is therefore clearly higher than for both POL- MUX and single polarization RZ-DQPSK, which is in agreement with the measured results in Section 6. The eye diagram of 42.8-Gb/s RZ-DQPSK shows a strong timing jitter, which is not as evident in the POLMUX eye diagrams. The reduced jitter for POLMUX-RZ-DQPSK might be due to a more constant spread of the optical power over both polarization modes. From the eye diagrams after balanced detection, it follows that the nonlinear tolerance of interleaved 85.6-Gb/s POLMUX-RZ-DQPSK is slightly better than 42.8-Gb/s RZ-DQPSK. For bit-aligned POLMUX-RZ-DQPSK, on the other hand, the nonlinear tolerance is somewhat reduced com- pared to 42.8-Gb/s RZ-DQPSK. This indicates that, although the bit rate is doubled, the nonlin- 167 Chapter 8. Polarization-multiplexed DQPSK ear tolerance could be improved using POLMUX signaling. This also confirms the observation in the experimental results that 85.6-Gb/s POLMUX-RZ-DQPSK has a slightly higher nonlinear tolerance in comparison to 42.8-Gb/s RZ-DQPSK. Figure 8.12a shows the nonlinear tolerance of the four considered modulation formats. For a normalized EOP penalty of 2 dB, the differ- ence in input power between 42.8-Gb/s RZ-DPSK and 42.8-Gb/s RZ-DQPSK is 2.5 dB. For 85.6-Gb/s POLMUX-RZ-DQPSK with respect to 42.8-Gb/s RZ-DQPSK the nonlinear tolerance is increased with 1.0 dB for interleaved polarization tributaries and decreased with 1.8 dB for bit-aligned polarization tributaries. 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 Input power (dBm/ch/span) n o r m a l i z e d E O P ( d B ) (a) 0 10 20 30 40 50 0 1 2 3 4 5 6 Optical delay (ps) n o r m a l i z e d E O P ( d B ) 85.6-Gbit/s POLMUX-RZ-DQPSK 42.8-Gbit/s RZ-DQPSK (b) Figure 8.12: (a) Simulated comparison of the nonlinear tolerance for 800-km transmission with 42.8-Gb/s RZ-DPSK, 42.8-Gb/s RZ-DQPSK 85.6-Gb/s POLMUX-RZ-DPSK, bit-aligned 85.6- Gb/s POLMUX-RZ-DPSK, interleaved; (b) normalized EOP versus inter-pulse delay for a 9-dBm input power. Dotted lines denote tributaries whereas denote worst case result among all tributaries. Figure 8.12b shows a similar observation when the inter-pulse delay is varied. A severe bit- pattern dependence is observed in the simulations due to the limited length of the De Bruijn sequence. Therefore simulations have been conducted with different delay between the two po- larization tributaries (13, 16, 17, 21 symbols), and worst-case results are denoted here. The dotted horizontal line denotes the penalty obtained for 42.8-Gb/s RZ-DQPSK modulation. The trade-off between nonlinear and DGD tolerance for interleaved in comparison to bit-aligned POLMUX- RZ-DQPSK has significant implications for the use of POLMUX-RZ-DQPSK as a modulation format for long-haul transmission. The use of ultra-low PMD fiber would be required to enable long-haul transmission with interleaved POLMUX-RZ-DQPSK and benefit from its higher non- linear tolerance. In the absence of PMD compensation, only the DGD tolerance of bit-aligned POLMUX-RZ-DQPSK seems to be large enough to enable medium or long-haul transmission with realistic fiber PMD coefficients. Together with PMD compensation, interleaved POLMUX- RZ-DQPSK transmission can be used to enable long-haul transmission with a high spectral ef- ficiency. Since POLMUX signaling requires anyhow polarization control at the receiver the additional effort of PMD compensation does not significantly increase the transponder complex- ity. In addition, a digital coherent receiver can realize both polarization control as well as PMD compensation simultaneously. 168 8.3. Transmission with a high spectral efficiency 8.3 Transmission with a high spectral efficiency We now consider the feasibility of high-spectrally efficient transmission in more detail. For binary modulation formats, experimental long-haul transmission results have been reported with a spectral efficiency of 0.8 b/s/Hz. Using terrestrial length fiber spans, a transmission distance of 2,700-km [344] and 3,200-km [345] is feasible for duobinary and RZ-DPSK, respectively. For shorter span length, as common for undersea deployment, transmission distances up to 8,200-km have been bridged [346]. For RZ-DQPSK modulation with a 0.8-b/s/Hz spectral efficiency, long- haul transmission has been reported over 2,800-km (see Chapter 6 and [291]) using terrestrial length fiber spans and over 4,080-km with shorter fiber spans [122], respectively. This shows that a spectral efficiency <1-b/s/Hz can be realized in long-haul transmission systems using a number of different modulation formats. A higher spectral efficiency of 1-b/s/Hz can be realized using DQPSK modulation and a direct detection receiver [15]. In [290], Yoshikane et. al. showed the feasibility of 1.6-b/s/Hz spec- tral efficiency using narrowband filtered RZ-DQPSK. However, RZ-DQPSK modulation has to be severely bandlimited to reach a 1.6-b/s/Hz spectral efficiency, which might not be practical in the presence of optical add-drop multiplexing. Most other transmission experiments with a high spectral efficiency have been reported using POLMUX-RZ-DQPSK modulation, i.e. at 1.6 b/s/Hz [347, 348, 349, 350, 351], 2.0 b/s/Hz [352, 321, 353], 2.5 b/s/Hz [354] and 3.2 b/s/Hz [34]. The transmission experiments are listed in Table 8.2. In order to realize a >1-b/s/Hz spectral efficiency, a suitable choice of both the channel spacing and bit rate is necessary. For a 10...12.5-Gbaud symbol rate [348, 352, 354], the main challenge to obtain a high spectral efficiency is the (de-)multiplexing of the ≤25-GHz spaced WDMchannels. This requires narrow (de-)multiplexing filters with a near rectangular bandwidth profile at the transmitter, receiver and add-drop points along the link. Using less optimal filters results in linear crosstalk between neighboring WDM channels as well asymmetric filtering due to the limited wavelength stability of the laser sources. In addition, for closely spaced WDM channels the XPM induced crosstalk can be a significant source of transmission impairments. On the other hand, the OSNR requirement, chromatic dispersion and PMD tolerance are more relaxed for a ∼10-Gbaud symbol rate. At a 40...55-Gbaud symbol rate, multiplexing and de-multiplexing is significantly relaxed as only a 100-GHz [347, 349, 321] channel spacing is required. In addition, the wider channel spacing and higher symbol rate increase the walk-off between WDM channels, making intra-channel nonlinearities the dominant transmission impairment. On the other hand, the reduced chromatic dispersion and PMD tolerance at a >40-Gbaud symbol rate will require tunable compensators for most long-haul transmission systems. In particular, the need for active PMDcompensation makes it difficult to realize POLMUX signaling at such a symbol rate. The higher symbol rate poses furthermore challenges to the electrical components in the transmitter (MZM, phase modulator) and receiver, which often have a limited bandwidth. In addition, the OSNR requirement and nonlinear tolerance might limit the feasible transmission distance. 169 Chapter 8. Polarization-multiplexed DQPSK Table 8.2: SELECTED TRANSMISSION EXPERIMENTS WITH A SPECTRAL EFFICIENCY ≥1.6-B/S/HZ. UNLESS NOTES OTHERWISE ALL EXPERIMENTS USE POLMUX-DQPSK MODULATION. year bit # of Spectral Distance Spans (km) / Remarks Company / rate WDM efficiency (km) fiber type Ref (Gb/s) channels (b/s/Hz) 2001 160 40 1.6 80 40 EDFA-only NICT -D/+D [347] 2003 40 8 1.6 200 100 EDFA-only U. Kiel, Siemens SSMF [348] 2004 85.4 64 1.6 320 80 EDFA/Raman KDDI SSMF RZ-DQPSK [290] 2004 50 14 2.0 400 100 EDFA-only CeLight SSMF [352] 2005 40 3 2.5 200 100 EDFA/Raman U. of Tokyo DSF [355] 2005 160 8 1.6 324 81 EDFA/Raman U. Paderborn SSMF [349] 2006 85.6 40 1.6 1,700 94.5 EDFA/Raman TU/e, Siemens SSMF [350] 2007 222 102 2.0 240 80 EDFA/Raman NTT NZDSF [321] 2007 170.8 160 3.2 240 80 EDFA/Raman Alcatel-Lucent, NICT, SSMF Sumitomo [34] 2007 111 10 2.0 2,375 95 EDFA/Raman CoreOptics, TU/e, SSMF Siemens [353] 2007 85.6 160 1.6 2,550 65 all-Raman Alcatel-Lucent +D/-D/+D [351] The majority of the deployed WDM transmission systems uses a channel spacing of 50-GHz. A symbol rate around 20...30 Gbaud [350, 351, 353] is therefore the most suitable choice to realize high-spectrally efficient transmission with a sound tolerance towards (de)-multiplexing and optical filtering on a 50-GHz WDM grid. As shown in this chapter, the 21.4-Gbaud symbol enables long-haul transmission due to a combination of component maturity and low OSNR re- quirement. The nonlinear tolerance of a 20...30 Gbaud symbol rate also compares favorably with lower symbol rates, as intra-channel nonlinear impairments are generally dominant for SSMF-based transmission systems. This limits the penalty due to either XPM or XPolM, hence avoiding POLMUX-specific nonlinear impairments. Although, for other fiber types with a lower chromatic dispersion coefficient (e.g NZDSF) inter-channel nonlinear impairments might still be significant. In [34], Gnauck et. al. showed that a 3.2-b/s/Hz spectral efficiency can be realized using 170.8- Gb/s POLMUX-DQPSK modulation and a 50-GHz channel spacing. This indicates that future 170 8.4. Summary & conclusions high-capacity optical transmission systems might use a spectral efficiency well above 2-b/s/Hz. However, this will likely require the use of modulation formats with more than 4 bits per sym- bol in order to realize a sound tolerance to narrowband optical filtering. A potential candidate for modulation with more than 4 bits per symbol is orthogonal frequency division multiplexing (OFDM). As OFDM inherently uses multi-level signals at the transmitter, it is more straight- forward to use more dense signal constellations. For example in [356] Jansen et. al. showed OFDM-based POLMUX-QPSK modulation and in [357], Schmidt et. al. showed the implemen- tation of 4 and 5 bits per symbol using (single-polarization) quadrature amplitude modulation. 8.4 Summary & conclusions Using direct detected 85.6-Gb/s POLMUX-RZ-DQPSK modulation the feasibility of high spec- trally efficient long-haul transmission is discussed in this chapter. This shows that the transmis- sion characteristics of POLMUX-RZ-DQPSK modulation are well suited for long-haul transmis- sion as long as PMD is not the dominant transmission impairment. → An OSNR requirement of 15.8-dB is measured for 85.6-Gb/s POLMUX-RZ-DQPSK modulation combined with a direct detection receiver (10 −3 BER). The theoretical OSNR requirements for 85.6-Gb/s POLMUX-RZ-DQPSK modulation is 14.6 dB. → An optical filter bandwidth of 34-GHz is found to be optimal for 85.6-Gb/s POLMUX-RZ- DQPSK modulation. This enables long-haul transmission with cascaded optical filtering in a 50-GHz wavelength grid, realizing a 1.6-b/s/Hz spectral efficiency. → For POLMUX modulation, the inter-pulse delay has a significant impact on both the DGD tolerance as well as the impact of intra-channel nonlinear impairments. When both POL- MUX tributaries are bit-aligned the DGD tolerance is maximized. In contrast, when both tributaries are interleaved the nonlinear tolerance is increased by about 2 dB. This allows an increase in nonlinear tolerance when POLMUX signaling is used to double the bit rate. → Using POLMUX-RZ-DQPSK modulation combined with a direct detection receiver, long- haul transmission with a 1,700-km feasible transmission distance and 1.6-b/s/Hz spectral efficiency is discussed. This shows that long-haul transmission with a >1-b/s/Hz spectral efficiency is feasible over a long-haul transmission distance. 171 Chapter 8. Polarization-multiplexed DQPSK 172 9 Digital direct detection receivers As discussed in Chapters 4 to 8, the choice of the optical modulation format can substantially increase the transmission tolerances in long-haul transmission links. However, no modulation format has the ideal combination of transmission properties. For example, POLMUX-DPSK modulation has an excellent OSNR requirement and nonlinear tolerance but suffers from a re- duced PMD tolerance. DQPSK modulation, on the other hand, supports a high PMD tolerance but has a reduced OSNR requirement and lower tolerance against nonlinear impairments. It is therefore advantageous to combine robust optical modulation formats with analog or digital sig- nal processing, as this can further improve transmission tolerances and can negate some of the drawbacks of the modulation format. Digital signal processing can be applied either at the transmitter to pre-distort the optical signal or at the receiver. At the transmitter, digital signal processing can be used to electronically pre- compensate for chromatic dispersion [358, 359], intra-channel nonlinear impairments [360, 361] or both impairments simultaneously [362]. The main drawback of pre-distortion is the significant reduction in nonlinear tolerance that occurs when chromatic dispersion is fully compensated at the transmitter [363]. Although intra-channel nonlinear impairments can be compensated using pre-distortion, this is not possible for inter-channel nonlinear impairments. In addition, pre- distortion can not compensate for PMD, which can be a limiting transmission impairment in high bit rate long-haul transmission. This makes pre-distortion a less likely candidate for high bit-rate systems. In this chapter we therefore focus on digital signal processing at the receiver. In the receiver, the applications of digital signal processing are more extensive and includes the compensation of chromatic dispersion, PMD, nonlinear impairments as well as electrical pola- rization de-multiplexing and improvements in the back-to-back OSNR requirement [364]. To 1 The results described in this chapter are published in c3, c19, c23, c39, c43 173 Chapter 9. Digital direct detection receivers realize most of these receiver-side digital signal processing applications with a minimal perfor- mance penalty, the full optical field has to be transferred to the electrical domain. This is the case for a (digital) intra-dyne coherent receiver, as will be discussed in Chapter 10. However, digital signal processing is not limited to coherent receivers. In direct detection receivers, only the am- plitude information is transferred to the electrical domain. This reduces the efficiency of digital signal processing, but it can still allow for a significant increase in transmission robustness. A number of different signal processing algorithms can be used together with direct detection receivers, for example: → Linear feed-forward or decision-feedback equalizers → Nonlinear equalizers → Optical field reconstruction algorithms → Maximum likelihood sequence estimation (MLSE) In order to compensate for signal distortions, an equalizer can be used that approximates the in- verse of the channel impulse response. The simplest equalizer structure is a linear feed-forward or decision-feedback equalizer [365, 366, 367]. However, such a linear equalizer can only com- pensate for limited signal distortions as a direct detection receiver is inherently nonlinear due to the squaring function of the photodiode. This can be alleviated through the use of nonlinear equalizers, as shown by Xia et. al. in [368] using structures based on nonlinear Volterra theory. Optical field reconstruction algorithms do not equalize signal impairments but rather generate an improved decision variable. Such algorithms use the amplitude information from the in-phase and quadrature tributary to (partially) reconstruct the optical field in the receiver. This includes multi-symbol phase estimation (MSPE) and field reconstruction based on the inverse tangent of the direct detected components [369]. Once the optical field is reconstructed in the receiver, linear equalizers can be used with higher efficiency. In Section 9.1, MSPE is discussed as a means to improve the OSNR requirement and nonlinear tolerance of D(Q)PSK modulation. MLSE is another approach to increase the tolerance against linear and nonlinear transmission impairments. It improves the decision variable by basing it on a sequence of symbols rather than on a single symbol. MLSE is a more complex, but also a more versatile approach to distortion compensation than a linear equalizer. The use of MLSE can improve the tolerance against chro- matic dispersion, PMD and narrowband filtering [19, 20, 370]. In addition, it can under certain conditions improve the tolerance towards nonlinear transmission impairments [74, 75]. MLSE has shown to provide excellent performance when combined with NRZ-OOK and duobinary modulation [371]. In Section 9.2 we discuss the application of MLSE to DPSK and DQPSK modulation. 174 9.1. Multi-symbol phase estimation 9.1 Multi-symbol phase estimation In a direct detection D(Q)PSK receiver, the received signal is demodulated using one or more MZDIs. As discussed in Chapters 4 and 5, this demodulation is suboptimal and results in an OSNR penalty when compared to a coherent receiver. MSPE is a signal processing algorithm that can be used to overcome some of the drawbacks of direct detection and achieve an OSNR requirement close to theoretical optimal performance. It is based on techniques previously pro- posed for wireless communications [372, 373, 374]. In addition, MSPE can reduce impairments due to nonlinear phase noise and therefore improve the nonlinear tolerance. Section 9.1.1 introduces the concept of MSPE and Section 9.1.2 discusses the MSPE algorithm. The improvement in back-to-back OSNR requirement is subsequently discussed for 10.7-Gb/s DPSK and 42.8-Gb/s DQPSK (Section 9.1.3). In Section 9.1.4 we analyze the implications of a finite laser linewidth to the MSPE demodulation scheme. Finally, in Section 9.1.5 we focuses on reducing the nonlinear phase noise penalty using MSPE demodulation. 9.1.1 Multi-symbol phase estimation MSPE generates an improved decision variable in the electrical domain by using not only the last received symbol but a sequence of the latest received symbols. As this improved decision variable is based on a long sequence of previous symbols, the phase noise in the individual symbols is averaged out. The main difference of the MSPE in comparison to conventional MZDI-based demodulation schemes is therefore that the improved decision variable is less degraded by phase noise. Ideally, the improved decision variable is only impaired by the phase noise of the last received symbol x(k) instead of the last two symbols as is the case with the decision variable x(k)x ∗ (k −1) in a conventional direct detection receiver. Note that this is equal to coherent detection, where the decision variable is also based only on the last received symbol x(k). Hence, MSPE potentially closes the performance gap between direct detection and coherent detection. MSPE demodulates the signal by comparing each symbol from the DPSK signal with the pre- vious symbol of the demodulated sequence. Since the previous symbol is itself based on its predecessor a decision variable is generated that is based on a long sequence of received sym- bols. In other words, MSPE uses the received in-phase and quadrature components to generate a decision variable that depends recursively on the past received symbols. The recursive algorithm gives a correction term which is added to the conventional decision variable to generate an im- proved decision variable. In order to make the scheme adaptive and prevent an infinite memory, a forgetting factor w slowly fades out the contribution from previous symbols. Because MSPE is based on interferometric phase demodulation and does not involve a local oscillator, the for- getting factor w can be chosen relatively close to 1 without any performance impairments. The scheme proposed in [374] is based on coherent detection and as such suffers a penalty due to the phase drift of the local oscillator, which limits the highest acceptable value of w. In [375, 376] a similar approach is discussed, which used MZDIs with different bit-delays to generate a more accurate phase estimation in the optical domain. 175 Chapter 9. Digital direct detection receivers Figure 9.1 shows the receiver structure that is required for MSPE demodulation. In order to generate the improved decision variable, the MSPE demodulation scheme requires the phase information in the electrical domain. However, as no coherent detection is applied, the phase information cannot be directly transferred to the electrical domain. This is solved by detecting both the in-phase and quadrature component of the received symbol, which together also contain the phase of the received signal. Hence, two MZDIs are necessary with a π/2 difference in the phase shift between both arms. This is can be either a −π/4 and π/4 phase difference as in a conventional DQPSK receiver or a 0 and π/2 phase difference for the two MZDIs, respectively. T + - T + - MZDI PD data A Rx data B Rx Recursive algorithm Figure 9.1: MSPE receiver structure for either DPSK or DQPSK modulation. The MSPE algorithm can also be used for modulation formats that combine phase and amplitude modulation. This requires a third branch in the receiver with a single-ended photodiode to detect the intensity of the optical field [377]. 9.1.2 The MSPE algorithm The recursive MSPE algorithm is now based on the following principle. Consider a received signal, r(t) = √ P s exp( j[ω 0 t +ϕ(t)]), (9.1) where √ P s exp( jϕ(t)) =x I (t)+ j x Q (t) is the complex envelope of the signal x(t) in the absence of phase noise. After balanced detection and electrical low-pass filtering two components u I (t) and u Q (t) are obtained containing the in-phase and quadrature components, respectively: _ u I (t) =ℜ¦x(t)x ∗ (t −∆T)¦ u Q (t) =ℑ¦x(t)x ∗ (t −∆T)¦. (9.2) This can be realized with two MZDIs, one with a phase shift between the arms of ∆φ = 0 and one with a phase shift of ∆φ = π/2 For simplicity we now introduce a time discrete notation where t = kT 0 +t / , with −T 0 /2 ≤ t / ≤ T 0 /2. Considering the optimal sampling point in the bit interval we assume t / = 0 and the signals are further denoted as time discrete samples. The recursive algorithm now replaces the conventional decision variable x(k)x ∗ (k −1) with the improved decision variable x(k)z ∗ (k −1) [374], where x(k) is the currently received symbol. z(k) is a recursive component, z(k −1) = x(k −1) +w exp(+jc(k −1)) z(k −2), (9.3) 176 9.1. Multi-symbol phase estimation where 0 ≤w ≤1 is the forgetting factor. The binary factor c(k −1) rotates the previous symbol z(k −2) to align it with x(k −1). However, Equation 9.3 can only be implemented together with coherent detection because not x(k), but only x(k)x ∗ (k −1) is available after demodulation with an MZDI. As a result, Equation 9.3 cannot be directly implemented. The recursive component z(k) in Equation 9.3 is therefore replaced by the following approximation, y(k) = u I (k) +w u(k) exp(−jc(k −1)) y(k −1), (9.4) where u(k) = u I (k) + j u Q (k). Note that the term exp(−jc(k −1)) is a straightforward multipli- cation with either −1 or 1, depending on the binary value of c(k −1). We now show that a similar OSNR requirement can be expected for a receiver that uses either the algorithm in Equations 9.3 or 9.4. When we assume that the MSPE receiver demodulates the correct symbol we can express y(k −1) as, ˜ y(k −1) = y(k −1) exp(−jc(k −1)). (9.5) Equation 9.4 can then be written (for DPSK modulation) as, y(k) = u I (k) +w u(k) ˜ y(k −1). (9.6) The output of the MZDI u(k) equals x(k)x ∗ (k −1) which changes Equation 9.6 into, y(k) =ℜ¦x(k)x ∗ (k −1)¦+w x(k)x ∗ (k −1) ˜ y(k −1). (9.7) We can unroll the recursion in Equation 9.6, but for simplicity we assume that for symbol y(k−1) the conventional and improved decision variable are equal, e.g. y(k −1) = u(k −1) = x(k − 1)x ∗ (k −2). Using this approximation in Equation 9.7 results in, y(k) ≈ℜ¦x(k)x ∗ (k −1)¦+w x(k)x ∗ (k −1) ˜ x(k −1) ˜ x ∗ (k −2), (9.8) where ˜ x(k) = x(k) exp(−jc(k)). This gives, y(k) ≈ℜ¦x(k)x ∗ (k −1)¦+w x(k) ˜ x ∗ (k −2), (9.9) The improved decision variable thus consists partly of the most recent symbol x(k) and a contri- bution from the previous symbols x(k −1) and ˜ x(k −2). In Equation 9.3 there is no contribution from previous symbols, and it therefore results in the theoretically optimal performance. The contribution from the previous symbols in Equation 9.4 somewhat impacts the performance of the MSPE algorithm, and this causes the slight difference in OSNR requirement that we will find between MSPE and the theoretically optimal performance of a coherent receiver. In Figure 9.2 the principle of MSPE is visualized using a signal constellation diagram after in- terferometric demodulation. Combining the in-phase and quadrature components, each received symbol can be considered as a vector in the complex phase plane. In a conventional direct de- tection receiver, the binary decision would be ’0’ for ℜ¦u(k)¦ < 0 and ’1’ for ℜ¦u(k)¦ > 0. 177 Chapter 9. Digital direct detection receivers u(k) u(k-1) u(k-2) y(k) Re{u(k)} Im{u(k)} Figure 9.2: Generation of the improved decision variable. The MSPE algorithm now constructs an improved decision variable y(k) using the sequence of received symbols in Figure 9.2 such that, y(k) = ℜ¦u(k)¦ + w u(k) ℜ¦u(k −1)¦ (9.10) − w 2 u(k −1) ℜ¦u(k −2)¦ + w 3 u(k −2) ℜ¦u(k −3)¦ + ... The MSPE demodulation scheme can be implemented with either analog, as discussed here, or digital signal processing [378]. In the case of digital signal processing, the most straightforward implementation is to convert the decision variables u I (k) and u Q (k) into digital samples. Note that the performance of the MSPE demodulation scheme with a digital implementation depends on the granularity of the ADCs, which is not consider here. An analog implementation of the MSPE demodulator for DPSK modulation is shown in Figure 9.3. This implementation requires a complex four-quadrant multiplication, an attenuation to implement the forgetting factor w and a delay line with a bit-delay ∆T to multiply u(k) with the previous decision variable x(k −1). The improved decision variable c(k) is obtained from the real part of the improved decision variable x(k) after binary decision with a D-flip-flop (D-FF). Note that the upper MZDI on itself demodulates the in-phase tributary of the DPSK signal, which gives the conventional decision variable u I (k) and is therefore equivalent to a conventional direct detection DPSK receiver. 9.1.3 MSPE demodulation for 10.7-Gb/s DPSK & 42.8-Gb/s DQPSK Figure 9.4a shows the improvement in OSNR requirement with MSPE demodulation when only Gaussian noise is present. Simulations are based on the Monte-Carlo approach with a random bit sequence of 5 10 6 bits. The simulated BER is compared for a 10 −4 BER because lower BERs are impractical to simulate using the Monte-Carlo approach. The sensitivity improvement due to MSPE increases for higher values of the forgetting factor w, approaching the performance of coherent detection with differential decoding. For a 10 −4 BER, the difference between MSPE (w = 0.9) and conventional direct detection is ∼0.5 dB. The difference between MSPE (w = 0.9) and differential coherent detection is negligible, effectively closing the gap in OSNR requirement between coherent detection and direct detection. 178 9.1. Multi-symbol phase estimation A|=0 D- FF +/-1 multiplier + + + - AT w +/-1 multiplier x(k) u Q (k) u I (k) Re{y(k)} Complex four quadrant multiplier output c(k) Im{y(k)} MZDI T + - PD ~ ~ A|=t/2 MZDI T + - PD ~ ~ AT w Figure 9.3: Implementation of the MSPE algorithm for DPSK. 2 3 4 5 6 7 8 -6 -5 -4 -3 -2 OSNR (dB) l o g ( B E R ) 13 12 11 10 9 8 Q ( d B ) FEC limit 0.5 dB (a) (b) 8 10 12 14 -6 -5 -4 -3 -2 OSNR (dB/0.1 nm) l o g ( B E R ) 13 12 11 10 9 8 Q ( d B ) FEC limit 1.8 dB Figure 9.4: Performance of (a) 10.7-Gb/s DPSK and (b) 42.8-Gb/s DQPSK modulation with MSPE for Gaussian noise and several values of the forgetting factor w; conventional direct detection MSPE with w = 0.2, MSPE with w = 0.5, MSPE with w = 0.9, differential coherent detection The MSPE demodulation scheme can be easily extended to DQPSK modulation. An analog im- plementation of the MSPE demodulator for DQPSK modulation is shown in Figure 9.5. Similar to a conventional direct detection DQPSK receiver, two MZDIs are necessary to demodulate the signal. In comparison to the MSPE implementation for DPSK, the quadrature part of the signal is used to obtain the second output c Q (k) from the imaginary part of the improved decision variable y(k). The ±1 multipliers are exchanged with a complex ±1 multiplier because both the c I (k) and c Q (k) outputs have to be taken into account and c(k) now takes a value of the set ¦1, j, −1, −j¦. Note that the forgetting factor w now has to be scaled with a factor √ 2. The optical components necessary to realize the MSPE demodulation scheme are the equal to a conventional DQPSK re- ceiver. Hence, the overhead of using MSPE in combination with DQPSK modulation is limited to (potentially inexpensive) electronic signal processing. Figure 9.4b shows the performance of the MSPE demodulation scheme with DQPSK modulation when only Gaussian noise is present. Similar to the results for DPSK modulation, Monte-Carlo 179 Chapter 9. Digital direct detection receivers A|=0 D- FF + + + - AT x(k) u Q (k) u I (k) Re{y(k)} Complex four quadrant multiplier output - I c Q (k) Im{y(k)} MZDI T + - PD ~ ~ A|=t/2 MZDI T + - PD ~ ~ AT w + + - + ¥2 w ¥2 D- FF output - Q Complex +/- 1 multiplier c I (k) Figure 9.5: Implementation of the MSPE algorithm for DQPSK. simulations are used and every point is simulated with a 2 10 6 symbols long random sequence. The performance gain with MSPE demodulation is considerably larger due to the larger theo- retical difference between coherent and direct detection DQPSK. For MSPE with w = 0.9, the difference amounts to 1.8 dB for a 10 −4 BER, which is only a 0.2-dB difference with respect to coherent detection (with differential decoding). When one considers that the same optical components and nearly the same signal processing is required for MSPE with either DPSK or DQPSK modulation, DQPSK seems to be the most logical application of MSPE demodulation. 9.1.4 Laser linewidth requirements PSK modulation is generally sensitive to phase noise, for example, resulting from a finite laser linewidth. With conventional direct detection, only the phase difference between two subsequent symbols determines the sensitivity penalty. This makes direct detection robust against phase noise. At a 10.7-Gb/s bit rate and for a 0.5-dB OSNR penalty the transmitter laser requires a linewidth less than 30-MHz linewidth [379]. Savory and Hadjifotiou derived for a similar penalty the maximumallowable linewidth with DQPSKmodulation and a self-homodyne receiver, which equals 8 MHz [380]. Standard DFB lasers can have a linewidth in the order of 1-3 MHz [381], which is sufficient for both DPSK and DQPSK direct detection at a 10.7-Gb/s bit rate. MSPE uses a sequences of symbols to compute the improved decision variable. When the phase noise between those symbols is uncorrelated (zero mean) the estimate will be improved by using more symbols. However, the phase noise resulting from a finite laser linewidth is correlated and therefore does not average out when more symbols are taken into account. The phase noise of a Lorentzian-shaped laser linewidth can be described as a random walk Wiener process using φ PN (t) = m=t ∑ m=−∞ ν m , (9.11) 180 9.1. Multi-symbol phase estimation where ν m are independently Gaussian distributed random variables with zero mean and variance σ 2 = 2π∆νT 0 . ∆ν is the beat linewidth, which is the sum of the 3-dB linewidth of the signal and LO lasers, and T 0 is the symbol period [382]. In the time discrete simulations the laser linewidth is now modeled as random walk phase noise [383]. φ PN (t) = φ PN (t −T 0 ) +N(0, 2π∆νT 0 ), (9.12) where N(0, σ 2 ) is a Gaussian distribution random variable. The phase-noise degraded signal is then defined according to, s PN (t) = s(t)exp[iφ PN (t)]. (9.13) With MSPE demodulation, the number of symbols that is taken into account to compute the decision variable depends strongly on the forgetting factor. When the laser linewidth is not neg- ligible, the forgetting factor is upper bounded. A too high linewidth will result in a performance penalty because linewidth-induced phase noise reduces the accuracy of the improved decision variable. Figure 9.6a shows the performance of MSPE as a function of laser linewidth for 10.7- Gb/s DPSK. A laser linewidth lower than ∼4 MHz is required for a w = 0.9 forgetting factor. This is a significant reduction in comparison to conventional direct detection, but the tolerance is still sufficient to use a typical DFB laser. For 42.8-Gb/s DQPSK modulation the linewidth requirements are significantly higher, as shown in Figure 9.6b. For a w = 0.9 forgetting factor the maximum allowable linewidth is now 1.5 MHz (for a 1-dB penalty). However, when a w ∼ = 0.8 forgetting factor is used the linewidth tolerance increases to ∼3 MHz. And for a 2-dB penalty, the linewidth requirement increases to 10 MHz by sufficiently lowering the forgetting factor to w = ∼ = 0.5. Hence, it can be beneficial to make the forgetting factor w adaptive in order to obtain the maximum performance for a certain laser linewidth. We can compare the linewidth tolerance of MSPE with (analog) coherent detection. For coherent detection, a too high laser linewidth results in phase noise degradations through beating between transmitter and local oscillator (LO) laser. Coherent detection therefore, generally, requires a much narrower linewidth compared to direct detection. For 10-Gbaud (D)PSK modulation and a 0.5-dB sensitivity penalty, Norimatsu derived in [384] that both transmitter and LO laser require a laser linewidth below 8 MHz. For coherent detection of QPSK, the allowable laser linewidth is reduced even further. In [385], Barry and Kahn reported that a beat linewidth lower than 500 kHz is required (at 5-Gbaud and for a 0.5-dB penalty). This implies that both the transmitter and LO laser require a laser linewidth narrower than 250 kHz. When we scale this to a 42.8-Gb/s bit rate, we obtain 500 kHz or 1 MHz for 10-Gbaud POLMUX-QPSK and 20-Gbaud QPSK modulation, respectively. This tolerance is not sufficient to use standard DFB lasers and an analog coherent receiver requires therefore ECL. With ECL a linewidth below200 kHz is feasible [386]. However, such lasers are generally not used in conventional optical transponders as it is difficult to realize full C-band tunable ECL. Digital coherent detection is largely similar in terms of its tolerance against laser linewidth. For 42.8-Gb/s POLMUX-QPSK with a digital coherent receiver, a beat linewidth of 1.4 MHz is reported for a 1-dB OSNR penalty at 10 −3 BER [382]. Scaling this to a 20-Gbaud symbol rate gives a beat linewidth of 2.8 MHz, which is similar to the requirement for MSPE. With the exception that MSPE uses only a transmitter laser whereas for digital coherent detection the 181 Chapter 9. Digital direct detection receivers beat linewidth is divided over the LO and transmitter laser. Another detection scheme that is very tolerant to laser linewidth is proposed in [387], where a LO is used in combination with differential detection. However this scheme comes at the cost of an >3 dB increase in OSNR requirement. -2 10 -1 10 0 10 1 10 2 -5 -4 -3 Laser Linewidth (MHz) l o g ( B E R ) 12 11 10 9 8 Q ( d B ) FEC limit (a) 10 -1 10 0 10 1 10 2 -7 -6 -5 -4 -3 -2 Laser Linewidth (MHz) l o g ( B E R ) 14 13 12 11 10 9 8 Q ( d B ) FEC limit (b) Figure 9.6: Performance of (a) 10.7-Gb/s DPSK and (b) 42.8-Gb/s DQPSK modulation with MSPE for different laser linewidth and several values of the forgetting factor w; conventional direct detection, MSPE with w = 0.2, MSPE with w = 0.5, MSPE with w = 0.8, MSPE with w = 0.9. 9.1.5 Nonlinear phase noise compensation Besides a finite laser linewidth, nonlinear phase noise can also degrades signal quality in PSK systems, as discussed in Section 2.4.7. The reduction of nonlinear phase noise through MSPE results from the recursive decision variable, which averages out the phase uncertainty over a long sequence of received symbols. With MSPE, the decision variable ideally only depends on a single symbol x(k) instead of x(k)x ∗ (k−1) as for interferometric demodulation. MSPE therefore potentially halves the magnitude of nonlinear phase noise, which can significantly reduce the associated penalty. Another advantage of the nonlinear phase noise reduction through MSPE is that it is unimportant what the source of the phase noise is. Compensation schemes that use the correlation between intensity and nonlinear phase shift in the received symbol are restricted to compensation of SPM induced nonlinear phase noise. However, MSPE reduces the influence of phase noise in general; as long as the noise sequence is uncorrelated and has a zero-mean distribution. Hence, the impact of XPM induced nonlinear phase noise is also reduced through the use of MSPE. This can for example be important for D(Q)PSK transmission in the presence of co-propagating OOK modulated channels [293]. Figure 9.7a shows for 10.7-Gb/s DPSK the performance improvement of MSPE in the presence of nonlinear phase noise. Simulated is single channel transmission over 30 x 90-km spans with the ASE added along the transmission line. Fiber attenuation is α = 0.25 dB/km and fiber non- linearity γ = 1.3 W −1 km −1 , the influence of dispersion is neglected for simplicity [95]. In order to change the OSNR, the noise figure of the in-line amplifiers along the link is changed. For low 182 9.1. Multi-symbol phase estimation -6 -4 -2 0 2 4 6 8 4 6 8 10 12 14 16 18 R e q u i r e d O S N R ( d b / 0 . 1 n m ) Input power (dBm/span) 0.5 dB 1.8 dB BER = 10 -4 (a) -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 R e q u i r e d O S N R ( d B / 0 . 1 n m ) Input power (dBm/span) BER = 10 -4 2.1 dB 1.8 dB (b) Figure 9.7: Nonlinear tolerance of (a) 10.7-Gb/s DPSK and (b) 42.8-Gb/s DQPSK with MSPE and several values of the forgetting factor w; conventional direct detection MSPE with w = 0.2, MSPE with w = 0.5, MSPE with w = 0.9, differential coherent detection. input power the simulated OSNR requirement differs 0.5 dB between MSPE and conventional direct detection, which is also observed in the back-to-back case. When the input power is in- creased to 2.1 dBm per span, the required OSNR for the conventional direct detection receiver is 8.7-dB (3-dB penalty). However, for MSPE (w=0.9) the required OSNR is only 6.9 dB, which gives a 1.8 dB improvement over conventional direct detection. Alternatively, we can define the nonlinear tolerance as the input power for which a 3-dB OSNR penalty is obtained. In this case MSPE increases the nonlinear tolerance from 2.1 dBm to 3.6 dBm per span. For 42.8-Gb/s DQPSK transmission, the performance of MSPE in the presence of nonlinear phase noise is shown in Figure 9.7b. The link parameters used in the simulation are the same as for 10.7-Gb/s DPSK. The MSPE improvement with (w = 0.9) for a 10 −4 BER is with 2.1 dB comparable to the performance gain in the presence of only Gaussian noise. This can be understood from the con- stellation diagrams in Figure 9.8, which show a 10.7-Gb/s DPSK and 42.8-Gb/s DQPSK signal with nonlinear phase noise. The same link parameters are used as in Figure 9.7, with a 3-dBm input power per span. The received OSNR is 5.6 dB and 13.1 dB, respectively, which result back- to-back in a BER of 10 −4 . Comparing the two constellation diagrams shows a significantly larger nonlinear phase noise impact in the case of 10.7-Gb/s DPSK, despite the fact that the nonlinear phase shift is the same for both cases. The more pronounced impact of nonlinear phase noise for 10.7-Gb/s DPSK modulation is a result of the lower OSNR along the link. This indicates that the lack of an improvement in nonlinear tolerance through MSPE demodulation is a result of the smaller impact of nonlinear phase noise for 42.8-Gb/s DQPSK modulation. Comparing Figures 9.7a and 9.7b further shows that the different in nonlinear tolerance between DPSK and DQPSK is 0.8 dB (for a 3-dB OSNR penalty). This indicates that the larger difference observed in Section 5.4 results from the interaction between fiber nonlinearity and chromatic dispersion, rather than from nonlinear phase noise. We note that the simulations discussed here do not include chromatic dispersion and therefore only the reduction in nonlinear phase noise is observed. When chromatic dispersion is included, the improvement in nonlinear tolerance can be more significant, as experimentally shown by Lui 183 Chapter 9. Digital direct detection receivers Re(E) I m ( E ) 10 -6 10 -5 10 -4 10 -3 Re(E) I m ( E ) 10 -6 10 -5 10 -4 10 -3 P r o b a b i l i t y (a) (b) P r o b a b i l i t y Figure 9.8: Simulated constellation diagrams of (a) DPSK and (b) DQPSK modulation with nonlinear phase noise. et. al. in [378]. A further improvement in nonlinear tolerance might be realized by combining MSPE with a nonlinear phase noise compensation scheme that employs the correlation between intensity and nonlinear phase shift. This has been shown to provide an improvement of the nonlinear tolerance when a digital coherent receiver is used [256]. 9.2 Maximum likelihood sequence estimation Arguably the most important application of signal processing in an optical receiver is increasing the tolerance with respect to (linear) transmission impairments such as chromatic dispersion and PMD. This allows for simpler system design and can alleviate the need for optical compensa- tion of these transmission impairments. A maximum likelihood sequence estimation (MLSE) receiver searches for the transmitted sequence that has the highest probability of producing the received sequence. Such a receiver is therefore the theoretically optimal receiver for a transmis- sion channel with ISI. In Section 9.2.1 we introduce the principle of MLSE and a Viterbi receiver. Subsequently, in Sec- tions 9.2.2 and 9.2.3 we discuss the performance of MLSE with OOK and DPSK modulation, respectively. To improve the performance of MLSE with DPSK modulation, either joint-decision MLSE (Section 9.2.4) or partial DPSK (Section 9.2.6) can be used. Finally, for DQPSK modu- lation we discuss in Section 9.2.7 the use of joint-symbol MLSE. 9.2.1 The MLSE algorithm Figure 9.9a shows a received OOK modulated sequence with significant chromatic dispersion induced pulse broadening. The amplitude of the middle ’0’ of a ’101’ sequence (at 4T) is broad- ened through the ISI of the trailing and leading ’1’s. This implies that the ’0’ amplitude dif- fers depending on the two surrounding symbols and will be higher for a ’101’ than for a ’001’ sequence (e.g. at 6T). As this difference is deterministic, the receiver can assign a different 184 9.2. Maximum likelihood sequence estimation probability to each of the possible received sequences as a function of the received amplitude in the ’0’. This can be described using conditional probability density functions (PDF), with the surrounding symbols as the condition. The accuracy in which the PDF models the channel characteristics is determined by the channel memory, e.g. the number of surrounding symbols that is taken into account. For example, if the PDF takes only the two surrounding symbols into account, it assumes that the channel has an impulse response of three symbol periods. Time T 2T 3T 4T 5T 6T 7T 010 110 > 100 101 > 0 0 1 1 1 0 0 A m p l i t u d e (a) 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 000 0 0 1 111 0 1 1 1 0 0 1 01 0 1 0 1 10 State Transition T 2T nT (b) Figure 9.9: (a) Deterministic ISI resulting from chromatic dispersion and (b) trellis diagram with 4 states. To discuss the concept of MLSE we first consider a channel with no memory. The signal’s alphabet A = ¦A 1 , A 2 , . . . , A N ¦ consists of N possible symbols and each symbol is transmitted with an equal probability 1/N. Note that the alphabet size is defined through the bits per symbol of the modulation format (e.g. 2 for OOK/DPSK and 4 for DQPSK). The received sequences is a vector r(k), which contains K samples taken from the continuous received signal r(t) at sample points t = kT 0 +t / , with −T 0 /2 ≤t / ≤T 0 /2. The a posteriori probability P(A i [r k ) can now be defined as the probability that the symbol A i is transmitted when the sample r k is detected. The optimal decision then looks for the symbol that has the maximum a posteriori probability among all of the symbols in the alphabet A, P(A i [r k ) > P(A j [r k ) ∀ i ,= j. (9.14) This is known as the a posteriori probability, because the decision is made after receiving the sample r k [388]. According to Bayer’s theorem of probability, the a posteriori probability can be written as, P(A i [r k ) = P(r k [A i ) P(A i ) P(r k ) . (9.15) The terms P(r k ) and P(A i ) are equal for all a posteriori probabilities and can therefore be ne- glected. This simplifies Equation 9.14 to, ˆ A = argmax i (P(r k [A i )) ∀ i = 1, 2, . . . , N, (9.16) where P(r k [A i ) is the probability that r k is received when the symbol A i is transmitted. The term argmax(P(r k [A i )) defines the value of A i that maximizes P(r k ). For example, for a binary signal A =¦0, 1¦ the decision can then be written as, ˆ A = _ 0 P(r k [A 0 ) > P(r k [A 1 ) 1 otherwise (9.17) 185 Chapter 9. Digital direct detection receivers This is equal to the decision of a conventional CDR receiver as discussed in Section 3.1.2. An MLSE receiver does not consider only the received symbol, but rather the received sequence in order to obtain the maximum a posteriori probability decision. This can be written as, ˆ S = argmax i ( K ∏ k=1 P(r k [A k i )) ∀ i = 1, 2, . . . , N, (9.18) where ˆ S is the sequence with the maximum a posteriori probability and A k i is the set of all the possible symbols representing sample r(k). This can be simplified by changing the multiplication into a summation by taking the natural logarithm function of the a posteriori probability. The natural logarithm function is monotonic and Equation 9.18 can now be rewritten as, ˆ S = argmax i ( K ∑ k=1 ln[P(r k [A k i )]) ∀ i = 1, 2, . . . , N. (9.19) Equation 9.19 implies that N K sequences have to be taken into account to determine the maxi- mum a posteriori probability. This increases exponentially with the length of the sequence and the alphabet size, which is not practical. The MLSE estimation process is therefore based on the Viterbi algorithm as first proposed by Forney in 1972 [389]. The Viterbi algorithm can be repre- sented by means of a trellis diagram that consists of N L states and N L+1 states transitions, where N is the alphabet size and L is the memory length. Each transition m i (k) in the trellis diagram is associated with one of the PDFs of the channel. Figure 9.9b shows an example of a trellis dia- gram for a two bit channel memory and binary modulation. The trellis diagram has 2 2 possible states and 2 3 state transitions. After sample k is received and quantized with quantization level r k , the channel histogram is used to find the conditional probability P(r k [S i ) associated with each of the channels conditional PDFs. For instance, for L = 2 the transition ’010’ is associated with the PDF P(r k [010), which is the probability that the sample r k represents a ’1’ symbol, preceded and followed by ’0’ symbols. This means that a received ’1’ has four different conditional PDF functions. To make the optimum decision on a received symbol, MLSE requires that the PDFs correctly represent the distortions in the optical channel. This is possible by training the MLSE with a known sequence. Alternatively, blind estimation can be used through feedback signals from the forward error correction or more advanced blind channel estimation algorithms [390]. Once the PDFs are obtained this information can be used to calculate the metrics of the trellis’s state tran- sitions. This is possible through different algorithms of which we use here both the histograms method and the Gaussian model method. The histograms technique builds discrete PDFs for all of the possible transitions in the trellis diagram, which are quantized with a vertical resolution of Q bits. Subsequently, the a posteriori probabilities for each state transition at each quantization level P(r[S i ) are determined, which gives the PDFs or histograms [391]. The histograms are stored in a look-up table, which contains a total of 2 Q N L+1 values. The look-up tables are then used to compute the metric for each of the transitions in the trellis. For example, the metric of the state transition m i (k) can be expressed as, m i (k) = m j (k −1) +ln[P(r k [S i )], (9.20) 186 9.2. Maximum likelihood sequence estimation where m j (k −1) is the metric of the transition that leads to state S i . For each of the N L states in the trellis, the metrics of the N incoming paths are compared and the path with the highest metric survives, while the others are canceled out. Repeating this procedure for K samples results in N L surviving paths, each having a different total metric and a different path through the trellis. The trellis path of the sequence with the maximum probability is considered to represent the maximum likelihood sequence. This implies that using the Viterbi algorithm, the complexity is reduced from searching through N K down to K N L+1 sequences. Figures 9.10a and 9.10b depict two examples of histograms, for back-to-back and 2000 ps/nm of chromatic dispersion, respectively. The y-axis shows the transitions in the trellis diagram for a channel with a 2-symbol memory, where the x-axis represents the quantization bins for a 4-bit vertical resolution. The z-axis shows the probability for each quantization bin/transition. Q u a n tiza tio n b in s 5 10 15 0 0.02 0.04 0.06 P r o b a b i l i t y 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 T r a n s i t i o n X Y Z (a) 5 10 15 0 0.05 0.1 P r o b a b i l i t y 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 T r a n s i t i o n Q u a n tiza tio n b in s X Y Z (b) Figure 9.10: MLSE histograms for (a) 0-ps/nm chromatic dispersion and (b) 2000-ps/nm chromatic dispersion. The Gaussian model method uses a somewhat simpler channel model as it assumes that the PDF functions associated with a specific channel have Gaussian distributions. This method determines the sequence that maximizes the Gaussian a posteriori probability defined as, ˆ S = argmax i K ∑ k=1 ln( 1 √ 2πσ i exp(− (r k −µ i ) 2 2σ 2 i )) ∀ i = 1, 2, . . . , N, (9.21) where µ i is the mean of the Gaussian PDF associated with state transition m i , and σ i is the PDF variance. When the variance of all PDFs is assumed to be equal, Equation 9.21 can be simplified into, ˆ S = argmin i K ∑ k=1 (r k −µ i ) 2 ∀ i = 1, 2, . . . , N. (9.22) The Gaussian model method assumes that the sample belongs to the state S i of which the mean is nearest to the received sample r k [392]. Minimizing the sum of these distances for K successive samples maximizes the probability that the sequence has been correctly estimated. Only the 187 Chapter 9. Digital direct detection receivers mean of each of the PDFs is now extracted from the training sequence and a total of N L+1 values are stored in the look-up table. Hence, the Gaussian model method is somewhat less complex in comparison to the histogram technique. The assumption that all PDFs have the same variance is generally valid in the presence of significant signal distortions. An additional property of electronic equalization is that only limited signal distortions can be tolerated using baud rate sampling (1 sample per symbol)[392]. It is therefore advantageous to sample at a multiple of the baud rate in an MLSE receiver. Equations 9.19 and 9.20 then changes into, ˆ S = argmax i K ∑ k=1 H ∑ h=1 ln[P(r h,k [A k i )] ∀ i = 1, 2, . . . , N (9.23) m i (k) = m j (k −1) + H ∑ h=1 ln[P(r h,k [S i )], (9.24) where H is the number of samples per symbol. Note that this increases the size of the look- up table but does not change the size of the trellis. Sampling at twice the baud rate (H=2) is generally used in the literature. An MLSE receiver with two-fold over-sampling can tolerate an arbitrary amount of chromatic dispersion given that it uses a sufficiently large channel memory, as shown by Poggiolini et. al. in [393]. For MLSE receivers without over-sampling, the dispersion tolerance can be increased through narrowband optical filtering in the receiver [394, 395]. 9.2.2 MLSE combined with OOK For 10.7-Gb/s OOK modulation, MLSE can substantially increase the tolerance against linear transmission impairments [19]. This is verified using the experimental setup depicted in Fig- ure 9.11. At the transmitter side, a MZM is driven with a 10.7-Gb/s 2 31 −1 PRBS to generate NRZ-OOK modulation. Chromatic dispersion between -4500 ps/nm and 4500 ps/nm is subse- quently added to the signal using SSMF and DCF of different lengths, while a low input power (<5 dBm) is used to avoid nonlinear impairments. The DGD is measured by splitting the sig- nal in two orthogonal polarizations with equal power and recombining them with a time delay between 0 ps and 200 ps. At the receiver, the signal is filtered with a CSF having a 27-GHz 3-dB bandwidth. After detection with a single-ended photodiode, either a conventional threshold CDR or an MLSE receiver is used. The real-time MLSE receiver has a 3-bit ADC with a two- fold over-sampling rate of 21.4 Gsample/s and a 2-bit channel memory [19]. The channel model is based on the analysis of amplitude histograms. Figures 9.11b and 9.11c depict the CDR and MLSE receiver, respectively. Figure 9.12a shows the measured chromatic dispersion tolerance of the MLSE receiver com- pared with the CDR receiver. The chromatic dispersion tolerance of 10.7-Gb/s NRZ-OOK is ±800 ps/nm for a 2-dB OSNR penalty. But combined with the MLSE receiver, the tolerance increases to ±2000 ps/nm for a 2-dB OSNR penalty. Hence, the MLSE receiver outperforms the threshold CDR receiver by more than a factor of two. Figure 9.12b shows that the use of an MLSE receiver also significantly improves the DGD tolerance. However, the most significant 188 9.2. Maximum likelihood sequence estimation improvement occurs only when the allowable OSNR penalty is in excess of 6 dB where the DGD tolerance is doubled. For a 2-dB OSNR penalty the allowable DGD is 60 ps, a 30% improvement over a conventional CDR receiver. (b) ~ ~ ~ 27-GHz CSF VOA CD DGD PD BERT CDR PD BERT ~ ~ MLSE A/D ~ ~ (a) (c) r(t) r(t) r(t) laser data Tx MZM Figure 9.11: (a) Experimental setup, (b) conventional CDR receiver and (c) MLSE receiver. -4500 -3000 -1500 0 1500 3000 4500 6 8 10 12 14 16 18 20 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) (a) BER = 10 -3 (b) BER = 10 -3 0 20 40 60 80 100 120 140 160 180 6 8 10 12 14 16 18 20 Differential group delay (ps) R e q u i r e d O S N R ( d B / 0 . 1 n m ) Figure 9.12: Measured OSNR requirement versus (a) chromatic dispersion and (b) differential group delay; DPSK with balanced detection and CDR receiver, OOK with CDR receiver, DPSK with balanced detection and MLSE receiver, OOK with MLSE receiver. 9.2.3 MLSE combined with DPSK The improved chromatic dispersion and DGD tolerance of an MLSE receiver would be ideally combined with DPSK modulation. This would combine the high tolerance against linear impair- ments of MLSE with the improved OSNR requirement and nonlinear tolerance of DPSK. The experimental setup depicted in Figure 9.16 is used to evaluate MLSE with DPSK modulation and Figure 9.12a depicts the measured dispersion tolerance of MLSE combined with DPSK modulation. This shows that the improvement in dispersion tolerance that is observed for OOK is not replicated for DPSKmodulation. When we compare the performance of DPSKwith a CDR and MLSE receiver, no performance improvement is measured between 0 ps/nmto 1600 ps/nmof chromatic dispersion. For higher chromatic dispersion the improvement is small and approaches the results obtained with NRZ-OOK modulation. This shows that the 3-dB benefit of DPSK with 189 Chapter 9. Digital direct detection receivers Probability Probability Probability Im Re Eye diagram after balanced detection N o r m a l i z e d v o l t a g e N o r m a l i z e d v o l t a g e N o r m a l i z e d v o l t a g e PDF histograms Signal constellation Im Re Im Back- to-back 2400-ps/nm chromatic dispersion 140-ps DGD (a) (b) (c) Figure 9.13: Simulated PDF histograms of signal samples, measured eye diagrams at the output of the balanced photodiode and signal constellation for (a) back-to-back, (b) 2400-ps/nm chromatic dispersion and (c) 140-ps differential group delay. balanced detection fades away when chromatic dispersion is the dominant impairment, even when used together with an MLSE receiver. The insignificant advantage of MLSE combined with DPSK modulation was also reported in [396]. In contrast, Figure 9.12b shows that when the DGD tolerance is considered, the 3-dB benefit of DPSK remains when using an MLSE receiver. Figure 9.13 shows measured eye diagrams at the output of the balanced photodiode in the pres- ence of significant chromatic dispersion and DGD. The eye diagrams are complemented with simulated PDF histograms of the signal samples and the simulation parameters are set according to the measurement conditions. Figure 9.13a shows that back-to-back the eye diagram is wide open and the samples have a high probability in the normalized voltage range around 1 and -1. As chromatic dispersion becomes more dominant, the majority of the samples shift towards the middle of the histogram. This is particulary true for the destructive signal component, which confirms the difference in dispersion tolerance of the constructive and destructive components as discussed in Section 4.3.5. For 2400-ps/nm chromatic dispersion, the samples are concentrated with a high probability around a voltage of -0.5 and 0.2, reducing the symbol distance that is the basis for the 3-dB OSNR benefit of DPSK. For DGD, on the other hand, Figure 9.12c shows that for 140 ps the eye is highly distorted which confirms the high measured OSNR penalty. However, in contrary to chromatic dispersion there is still a high probability that the samples occur around ±1 in the histogram. Hence, the constructive and destructive outputs of the MZDI are correlated to a lesser degree which preserves more of the symbol distance, and therefore the 3-dB OSNR benefit of DPSK. 190 9.2. Maximum likelihood sequence estimation BER = 10 -4 -3000 -2000 -1000 0 1000 2000 3000 8 10 12 14 16 18 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) (a) 93 ps P o w e r ( a . u ) 93 ps 93 ps P o w e r ( a . u ) 93 ps Back-to-back 1510 ps/nm (b) Figure 9.14: (a) Experimental comparison of DPSK with single-ended or balanced detection input to the MLSE receiver; destructive, constructive, balanced detection and (b) measured eye diagrams com- paring constructive (upper row) and destructive (lower row) components back-to-back and with chromatic dispersion. To better understand the ineffectiveness of MLSE with DPSK modulation, we measure the dis- persion tolerance of the constructive and destructive ports, separately (Figure 9.14a). The de- structive component clearly shows a smaller dispersion tolerance than the constructive compo- nent. This is similar to the difference in chromatic dispersion tolerance as observed with a CDR receiver (see Section 4.3.5). Hence, the duobinary modulation of the constructive components improves the dispersion tolerance, whereas the AMI modulation on the destructive components broadens the optical spectrum and results in a lower dispersion tolerance. Figure 9.14b show measured eye diagrams of the constructive and destructive components for back-to-back and with 1900 ps/nm of chromatic dispersion. This confirms that in the presence of chromatic dispersion the destructive component is, in comparison to the constructive component, more severely dis- torted. The lower dispersion tolerance of the destructive component closes the eye diagram after balanced detection, which reduces the MLSE performance. However, this does not explain why, in the presence of >1200 ps/nm chromatic dispersion, the OSNR requirement with balanced de- tection is worse compared to the constructive component. We conjecture that this results from a correlation between the constructive and destructive components in the presence of chromatic dispersion. As a result of this correlation, the constructive and destructive component partially cancel each other out with balanced detection. This reduces the signal power, which in turn results in a higher OSNR requirement. 9.2.4 Joint-decision MLSE To overcome the low chromatic dispersion tolerance of D(Q)PSK combined with MLSE, Caval- lari et. al. proposed in [397] the use of joint-decision MLSE (JD-MLSE). JD-MLSE is character- ized by having more than one input into the MLSE receiver in order to provide it with additional information about the signal. A joint-decision MLSE can thus be considered as a two input, 191 Chapter 9. Digital direct detection receivers single output receiver. In the case of DPSK modulation, the two inputs of the JD-MLSE are the constructive and destructive output ports of the MZDI. The JD-MLSE therefore maximizes the a posteriori probability, ˆ S = argmax i K ∑ k=1 ln[P(u − k , u + k [S i )], (9.25) where u − k and u + k represent the constructive and destructive components of the demodulated DPSK signal that are used as input sequences of the JD-MLSE. P(u − k , u + k [S i ) is the a posteriori probability that samples u − k and u + k are received when the state S i is transmitted [397]. The principle of JD-MLSE is similar to the histograms method, since both methods build discrete PDFs containing the probability of occurrence for each state transition. But the JD-MLSE con- structs N L+1 3-dimensional discrete PDFs instead of the conventional 2-dimensional PDFs used in the histograms method. This increases the size of the look-up table, which now has to store the 3-dimensional PDFs, to a total of 4 Q N L+1 values. JD-MLSE therefore requires a significantly larger look-up table to compute the trellis metrics. In addition, more information is necessary to compute the PDFs with a high enough accuracy. This increases the required training sequence length or the accuracy of the blind estimation algorithms. On the other hand, the trellis diagram has the same complexity for the conventional MLSE with balanced detection (B-MLSE) and JD-MLSE. The computational effort required for the JD-MLSE is therefore comparable to the B-MLSE based on histograms (except for slightly higher memory requirements due to the larger number of PDFs). In addition slightly more hardware is required, as two ADC are necessary to convert the received signals into the digital domain. 5 10 15 5 10 15 0 0.01 0.02 0.03 0.04 X Y Z Q u a n t i z a t i o n b i n s f o r i n p u t 1 Q u a n tiz a tio n b in s fo r in p u t 2 Figure 9.15: Joint-decision MLSE histogram for transition ’010’ with 2000-ps/nm chromatic dispersion. Figure 9.15 shows a 3-dimensional PDF for the ’010’ state transition with a two bits memory length. The x-axis represents the quantization bins for the first input, where the y-axis represents the quantization bins for the second input. The z-axis gives the probability for each point in this 2-dimensional plane. Obviously, when the two input signals are the same, the PDF will be symmetric with respect to the x and y-axis. However, when two different signals (carrying the same information) are input into the JD-MLSE, another degree of confinement is added to the conditional PDF. 192 9.2. Maximum likelihood sequence estimation 9.2.5 Joint-decision MLSE combined with DPSK We now evaluate the impact of JD-MLSE on DPSK modulation using the experimental setup shown in Figure 9.16 1 . It is similar as discussed in Section 9.2.2 with the exception that a 50-GHz CSF filter is used in the receiver, this slightly increases the back-to-back OSNR requirement. + - ~ ~ + - MLSE A/D CDR MLSE ~ ~ A/D ~ ~ A/D ~ ~ ~ ~ MLSE A/D (b) (c) (d) (e) BERT BERT BERT BERT (a) ~ ~ ~ 50-GHz CSF VOA SSMF or DCF A|=0 r(t) MZDI T laser data Tx MZM PD u - (t) u + (t) u - (t) u + (t) u - (t) u + (t) u - (t) or u + (t) u - (t) u + (t) Figure 9.16: (a) Experimental setup and (b-e) different receiver configurations; (b) CDR receiver, (c) MLSE with balanced detection, (d) MLSE with single-ended detection and (e) joint-decision MLSE. At the receiver, the signal is input into either a threshold CDR receiver or a DSO. The band- width of the DSO is 8 GHz and it samples at a sampling rate of 20 Gsample/s. To obtain exactly 2 samples/symbol, the stored signal is re-sampled to a sample rate of 21.4 Gsample/s. Subse- quently, the signal is re-timed using the digital filter and square timing recovery algorithm, as discussed in Section 10.3.1. After re-timing, the signal is sampled at −T 0 /4 and +T 0 /4, where T 0 is the symbol period. Using off-line processing, MLSE is applied to the sequences stored with the DSO. The MLSE has a 4-bit quantization resolution and 4-state Viterbi decoder. To determine the MLSE performance, data sequences of 1 10 6 bits are processed by the MLSE al- gorithm, which gives an accuracy of 99.99% for a BER of 10 −3 [398]. The measured dispersion tolerance for both the conventional CDR receiver, B-MLSE as well as JD-MLSE are depicted in Figure 9.17. The balanced MLSE show no significant improvement in dispersion tolerance over the conventional CDR receiver, which is similar to results obtained in the previous section with the real-time MLSE (see Figure 9.12). Only for large accumulated dispersion we find a difference between the real-time MLSE and off-line MLSE. This is attributed to the re-timing required for the off-line MLSE, which is sub-optimal in the presence of large signal distortions. The JD-MLSE used here has a 2-symbol memory and it builds therefore eight 3-dimensional his- tograms similar to the one shown in Figure 9.15. Figure 9.17a compares the chromatic dispersion tolerance of the B-MLSE and JD-MLSE. This shows a clear advantage for the JD-MLSE, which nearly doubles the chromatic dispersion tolerance over both the B-MLSE as well as the CDR receiver. For a 2-dB OSNR penalty the measured chromatic dispersion tolerance is 2000 ps/nm 1 A real-time JD-MLSE receiver was not available in this experimental evaluation and the measurements dis- cussed here are therefore ’off-line’. In the off-line measurements, a set of data is stored using a DSO (Tektronix TDS 6804B) and afterwards post-processed on a desktop computer. 193 Chapter 9. Digital direct detection receivers -3000 -2000 -1000 0 1000 2000 3000 6 8 10 12 14 16 18 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) BER = 10 -3 (a) BER = 10 -3 -3000 -2000 -1000 0 1000 2000 3000 6 8 10 12 14 16 18 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) (b) Figure 9.17: (a) DPSK with different MLSE configurations and (b) comparison between OOK and DPSK modulation; DPSK with balanced detection and CDR receiver, OOK with CDR receiver, DPSK with balanced detection and MLSE receiver, OOK with MLSE receiver, DPSK with joint-decision MLSE receiver. for the JD-MLSE, compared to only 1100 ps/nm for the CDR and B-MLSE receivers. In Fig- ure 9.17b, the chromatic dispersion tolerance obtained for 10.7-Gb/s OOK and 10.7-Gb/s DPSK is compared when JD-MLSE is used for the DPSK receiver. This shows that JD-MLSE preserves the 3-dB difference in OSNR requirement between OOK and DPSK in the dispersion-limited regime. 9.2.6 MLSE combined with partial DPSK A different approach to improve the chromatic dispersion tolerance of DPSK modulation and MLSE is the use of partial DPSK. As shown in Section 4.4, the use of MZDI with a delay of less that one bit can considerably increase the chromatic dispersion tolerance. In this section we show that combined with MLSE the improvement is further enhanced. Figures 9.18a and 9.18b depict the simulated influence of the MZDI bit-delay on the chromatic dispersion tolerance of the CDR and MLSE receiver, respectively. The simulations use a similar configuration as shown in Figure 9.16. A 2 7 bits long 10.7-Gb/s PRBS sequence is repeated 4 times to obtain a total block length of 2 9 bits, which is then used to construct a DPSK modulated signal. To determine the chromatic dispersion tolerance, this signal is multiplied with the impulse response of the desired amount of chromatic dispersion. At the receiver, a data sequence with a length of 10 6 bits is constructed from the received 2 9 bits by using the overlap-and add-method [398]. Additive white Gaussian noise is added to the signal, which is subsequently filtered with a 2 nd -order Gaussian shaped 50-GHz filter. To determine the impact of partial DPSK, the MZDI bit-delay is varied from 0.5 T 0 to 1.0 T 0 bit in steps of 0.1 T 0 . After balanced detection, the electrical signal is filtered with a 10 th -order Bessel filter with a bandwidth of 7 GHz. Either a conventional CDR receiver or MLSE receiver is subsequently used to determine the chromatic dispersion tolerance. 194 9.2. Maximum likelihood sequence estimation Figure 9.18a shows that for the CDR receiver the chromatic dispersion tolerance improves from 1140 ps/nm to 1890 ps/nm when the bit-delay is decreased from 1.0 T 0 to 0.5 T 0 (2-dB OSNR penalty). It further shows that there is a trade-off between chromatic dispersion tolerance and back-to-back OSNR requirement, which increases by 1.7 dB when a 0.5-bit delay MZDI is used. Figure 9.18b depicts the chromatic dispersion tolerance when we apply an MLSE receiver to the output of the balanced photo-diode. The chromatic dispersion tolerance is now increased from 1140 ps/nm to 3750 ps/nm when the bit-delay is decreased from 1.0 T 0 to 0.5 T 0 , again for a 2- dB OSNR penalty. The back-to-back OSNR requirement is somewhat higher with 2.6 dB, which indicates that MLSE causes a slight OSNR penalty for partial DPSK. For a 0.5-bit-delay, the use of MLSE results in a nearly identical OSNR requirement for chromatic dispersion ranging from 0 ps/nm to in excess of 3000 ps/nm. Figure 9.18b shows that the chromatic dispersion tolerance is optimum for a bit-delay of 0.5 or 0.6. But on the other hand, a shorter bit-delay results in an increased back-to-back OSNR requirement. The choice of the optimum MZDI bit-delay should therefore take both the back-to-back OSNR requirement and chromatic dispersion tolerance into account. Consequently, a slightly higher bit delay (e.g. 0.65-bit delay) is a more optimal choice in order to balance the chromatic dispersion tolerance and back-to-back OSNR requirement. 0 1000 2000 3000 4000 8 10 12 14 16 18 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) BER = 10 -4 0.5-bit delay 1.0-bit delay (a) 0 1000 2000 3000 4000 8 10 12 14 16 18 Chromatic dispersion (ps/nm) 1.0 bit-delay 0.5 bit-delay BER = 10 -4 (b) R e q u i r e d O S N R ( d B / 0 . 1 n m ) Figure 9.18: Simulated chromatic dispersion tolerance of 10.7-Gb/s NRZ-DPSK with different MZDI bit- delay (a) conventional CDR receiver and (b) MLSE receiver; 1.0-bit delay, 0.9-bit delay, 0.8-bit delay, 0.7-bit delay, 0.6-bit delay, 0.5-bit delay. We now use the experimental setup depicted in Figure 9.16 to verify the chromatic dispersion tolerance of partial DPSK combined with MLSE. Two different MZDIs are employed; one with a 1-bit delay, the other with a 0.5-bit delay, followed by a balanced photodiode. Subsequently, the output of the balanced photodiode is used as the input signal for (1) a real-time MLSE receiver [19], (2) a software based MLSE receiver for off-line processing and (3) a conventional CDR re- ceiver. The measured chromatic dispersion tolerance for both the CDR and real-time MLSE with a 0.5 and 1.0-bit delay MZDI is depicted in Figure 9.19a. A comparison between the CDR and MLSE receiver for a 1-bit delay MZDI confirms the inefficiency of an MLSE for DPSK mod- ulation. On the other hand, when a 0.5-bit delay MZDI is used a considerable improvement in chromatic dispersion tolerance is evident. For partial DPSK combined with MLSE no significant increase in OSNR requirement is measured for a chromatic dispersion up to 3500 ps/nm, which confirms the improvement observed through simulations. To further point out the improvement obtained with partial DPSK and MLSE, Figure 9.19b compares the chromatic dispersion toler- ance of partial DPSK with duobinary modulation. This shows both a clear OSNR improvement 195 Chapter 9. Digital direct detection receivers (∼2.5 dB) and a slightly higher chromatic dispersion tolerance for the partial DPSK scheme with MLSE. In addition, the back-to-back OSNR requirement of partial DPSK can be improved by optimizing the MZDI bit-delay, which would further increase the difference with duobinary modulation. 0 1000 2000 3000 4000 8 10 12 14 16 18 Chromatic dispersion (ps/nm) 1-bit delay 0.5-bit delay DPSK, BER = 10 -4 R e q u i r e d O S N R ( d B / 0 . 1 n m ) (a) 0 1000 2000 3000 4000 10 12 14 16 18 R e q u i r e d O S N R ( d B / 0 . 1 n m ) Chromatic dispersion (ps/nm) DPSK BER = 10 -4 Duobinary (b) Figure 9.19: Measured chromatic dispersion tolerance of DPSK with CDR and 1.0-bit delay, DPSK with CDR and 0.5-bit delay, DPSK with MLSE and 1.0-bit delay, DPSK with MLSE and 0.5-bit delay, duobinary with CDR, duobinary with MLSE. 0 0.1 0.2 0.3 0.4 0.5 6 8 10 12 14 Sampling phase (T/T 0 ) BER = 10 -4 0.5-bit delay 1-bit delay R e q u i r e d O S N R ( d B / 0 . 1 n m ) Figure 9.20: Sampling instant optimization with MLSE; 1.0-bit delay, 0-ps/nm, 0.5-bit delay, 0-ps/nm, 0.5-bit delay, 3000-ps/nm. 0 1000 2000 3000 4000 8 10 12 14 16 Chromatic dispersion (ps/nm) BER = 10 -4 sampling phase [0,T 0 /2] sampling phase [-T 0 /4, +T 0 /4] R e q u i r e d O S N R ( d B / 0 . 1 n m ) Figure 9.21: Difference between real-time and off-line processing; real-time measured, real-time simulated, off-line measured, off- line simulated. In [266] it is shown that due to the deterministic interference between consecutive symbols in an MZDI with ∆T < T 0 bit-delay, the output signal resembles an inverted RZ signal. For a RZ signal, the choice of the sampling phase is more sensitive in comparison to NRZ. Figure 9.20 shows the OSNR requirement of (partial)-DPSK with different sampling instants. The x-axis depicts the sampling instant t of the first sample along the symbol period, whereas the second sample is taken at t +T 0 /2. When we compare the sample phase sensitivity of a 0.5-bit delay MZDI and a 1-bit delay MZDI, the higher sensitivity of the RZ pulse shape becomes apparent. Conventional DPSK with a 1-bit delay MZDI is insensitive to the sampling phase when a two- fold over-sampled MLSE receiver is used. This is similar to what has been reported in [399] for NRZ-OOK. However, in the case of a 0.5-bit delay MZDI and 0-ps/nm chromatic dispersion, the required OSNR shows a significant dependence on the sampling phase offset. The optimum sampling phase of the two samples is at t = 0 and at t = T 0 /2 as most of the information in RZ can be extracted from the middle of the symbol. On the other hand, the dependence on the sampling phase disappears in the dispersion-limited regime. This can be better understood from 196 9.2. Maximum likelihood sequence estimation the partial DPSK eye diagram demodulated with a 0.5-bit delay MZDI, as shown in Figure 9.22. Comparing the eye diagrams back-to-back and with 1900 ps/nm of chromatic dispersion, shows that the signal loses the RZ shape in the dispersion-limited regime. As a result the impact of the sample phase is significantly reduced. Figure 9.21 now compares the chromatic dispersion tolerance of the off-line processed MLSE with the real-time MLSE. The real-time MLSE shows a slight OSNR penalty for low chromatic dispersion, but this difference disappears in the dispersion-limited regime. This can be attributed to the sub-optimal choice of the sample phase, which is not adapted to the partial DPSK signal but to a NRZ-OOK modulated signal. The real-time MLSE samples the signal therefore at a different part of the symbol period (t = -T 0 /4 and t = +T 0 /4), which results in a higher OSNR requirement. In the chromatic dispersion limited regime, on the other hand, the choice of the sampling instant is less critical. This explains why the OSNR requirement of the real-time and off-line MLSE converges in the dispersion-limited regime. Simulated curves confirm the choice in sampling phase as the source of the difference in OSNR requirement. Note that the real-time MLSE receiver could be easily modified to sample at the optimal sampling point. In addition, it might be beneficial to over-sample more than two-fold with partial DPSK. Sampling at -T 0 /4, 0 and +T 0 /4 could somewhat reduce the ∼1 dB OSNR penalty that occurs when partial DPSK is combined with MLSE. -T 0 /4 Offline-MLSE Real time-MLSE T 0 /4 -T 0 /2 0 1900 ps/nm -T 0 /4 Offline-MLSE Real time-MLSE T 0 /4 0 T 0 /2 Back-to- back Figure 9.22: Measured eye diagrams after phase demodulation with a 0.5-bit delay MZDI and balanced detection (a) back-to-back (b) 1900-ps/nm of chromatic dispersion. 9.2.7 Joint-decision and joint-symbol MLSE combined with DQPSK We now combine MLSE with DQPSK modulation. DQPSK modulation on itself supports al- ready an improved tolerance to chromatic dispersion and PMD, and combined with MLSE the necessity of an optical tunable dispersion compensation for a 43-Gb/s transponder might be alle- viated 2 . As well, the higher PMD tolerance can be beneficial in PMD-limited transmission links. In this section we discuss the combination of 21.4-Gb/s NRZ-DQPSK modulation with MLSE, limited by the sampling rate of the ADCs in the DSO that is used for experimental verification. Figure 9.23 shows the different MLSE receivers for DQPSK modulation. We compare three different MLSE schemes and a conventional CDR receiver. In order to assess MLSE combined 2 The required chromatic dispersion tolerance for a robust 43-Gb/s transponder depends on system design, but as a figure-of-merit we assume here a 1000-ps/nm chromatic dispersion window for a 1-dB OSNR penalty. 197 Chapter 9. Digital direct detection receivers with DQPSK modulation, the DSO has been used to store the in-phase and quadrature tributaries, simultaneously. As DQPSK modulation has a low tolerance to phase mismatches in the MZDI, the random drift of two MZDI poses a significant problem to the experimental assessment (see Section 5.3). This causes some residual penalty in the measurements. ~ ~ ~ 50-GHz CSF VOA SSMF or DCF laser ʌ/2 MZ MZ T T MZDI ǻij= ʌ/4 ǻij= -ʌ/4 PD data u (a) data v ~ ~ MLSE A/D (b) (c) BERT I - (t) I + (t) Q - (t) Q + (t) + - + - CDR BERT BERT ~ ~ ~ ~ + - + - ~ ~ MLSE A/D BERT (d) MLSE ~ ~ A/D ~ ~ A/D BERT MLSE ~ ~ A/D ~ ~ A/D BERT ~ ~ A/D + - + - ~ ~ MLSE A/D BERT (e) I - (t) I + (t) Q - (t) Q + (t) I - (t) I + (t) Q - (t) Q + (t) I - (t) I + (t) Q - (t) Q + (t) I - (t) I + (t) Q - (t) Q + (t) Figure 9.23: (a) Experimental DQPSK setup with (b) conventional CDR receiver, (c) MLSE with bal- anced detection, (d) MLSE with joint-decision estimation and (e) MLSE with joint-symbol estimation. As inputs to an MLSE receiver for DQPSK modulation, we can use the constructive and de- structive components of the in-phase and quadrature tributaries. This gives a total of 4 signals that are detected with either balanced or single-ended photodiodes. The three considered MLSE schemes consists of MLSE with balanced detection (B-MLSE), MLSE with joint-decision esti- mation (JD-MLSE) and MLSE with joint-symbol estimation (JS-MLSE). A 5-bit vertical quan- tization resolution, 2-symbol channel memory and two-fold over-sampling is used in all cases. Both the B-MLSE and JD-MLSE consider the in-phase and quadrature tributaries independent of each other and use a 2 2 = 4-state Viterbi decoder. For JD-MLSE the same approach is used as described for DPSK modulation in Section 9.2.4. The principle of JS-MLSE is the same as discussed for JD-MLSE, with the exception that a qua- ternary alphabet (N =4) is used instead of a binary alphabet (N =2). JS-MLSE uses the samples from the in-phase and quadrature tributaries simultaneously to compute the branch metrics in the Viterbi decoder. The JS-MLSE uses the same parameters as the JD-MLSE, except that due to the quaternary alphabet the Viterbi decoder now has 4 2 = 16 states. Either the histogram method or Gaussian model method is used. The Gaussian model method minimizes the Euclidean distance, 198 9.2. Maximum likelihood sequence estimation which is now defined as, ˆ S = argmin i K ∑ k=1 (I k + j Q k −µ i ) 2 ∀ i = 1, 2, . . . , N. (9.26) Equation 9.26 follows from Equation 9.22, except that the term r k is replaced by I k + j Q k , where I k and Q k are the samples from the in-phase and quadrature tributary, respectively and µ i is a complex number. In [400] it has been shown that the Gaussian model is a valid assumption for the channel statistics of DQPSK modulation with a direct detection receiver. 0 1000 2000 3000 4000 8 10 12 14 16 18 20 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) BER = 10 -3 (a) 0 1000 2000 3000 4000 8 10 12 14 16 18 20 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) (b) BER = 10 -3 Figure 9.24: DQPSK with different MLSE configurations for (a) experimental and (b) simulated results; conventional CDR receiver, MLSE with balanced detection, JD-MLSE, JS-MLSE and histogram method, JS-MLSE and Gaussian model method. Figures 9.24a and 9.24b show the OSNR requirement as a function of the chromatic dispersion for experiments and matching simulations, respectively. The small mismatch between simula- tions and experiments can be attributed to the phase drift in the MZDIs and suboptimal digital clock recovery at high accumulated dispersion. It is evident that B-MLSE provides little or no advantage in comparison to a conventional CDR receiver, which is similar to the results obtained for DPSK modulation. When JD-MLSE is used instead of the CDR receiver, the dispersion tol- erance is increased by ∼50% at an OSNR penalty of 2-dB. But when we compare the impact of JD-MLSE for both DPSK and DQPSK modulation, it is evident that the performance improve- ment is less significant for DQPSK. We conjecture that this difference results fromthe suboptimal phase demodulation in the case of DQPSK modulation. As discussed in Section 5.2, this results in crosstalk between the in-phase and quadrature tributaries and therefore in a higher back-to- back OSNR requirement. In the presence of significant chromatic dispersion this crosstalk can limit the MLSE efficiency. JS-MLSE takes the decision on both tributaries simultaneously, and it can take the crosstalk between the two tributaries into account. Figure 9.24a shows that JS-MLSE provides a significantly higher dispersion tolerance of ∼1500 ps/nm compared to 700 ps/nm for the CDR receiver (at a 2-dB OSNR penalty). When we scale the measured dispersion tolerance of DQPSK with JS-MLSE to a 43-Gb/s bit rate, we obtain a 800 ps/nm window. This might be sufficient to alleviate the need for optical tunable dispersion compensation. As well, improve- ment in the signal processing (e.g. a larger number of states in the MLSE decoder) will further increase this figure and meet the requirement of dispersion tolerance modulation format. 199 Chapter 9. Digital direct detection receivers Table 9.1: ESTIMATED COMPLEXITY OF THE DIFFERENT MLSE SCHEMES APPLIED TO DQPSK MODULATION. B-MLSE JD-MLSE JS-MLSE JS-MLSE histograms histograms histograms Gaussian Number of trellis 2 2 1 1 Trellis states 2 L 2 L 4 L 4 L Dimensions of the PDF 2-D 3-D 3-D N.A. Size of the look-up table 2 Q 2 L+1 4 Q 2 L+1 4 Q 4 L+1 4 L+1 Table 9.2: BACK-TO-BACK OSNR REQUIREMENT OF DQPSK MODULATION FOR A 10 −3 BER AND DIFFERENT MLSE SCHEMES. CDR B-MLSE JD-MLSE JS-MLSE JS-MLSE histograms histograms histograms Gaussian Measured (dB) 10.9 10.8 10.4 10.3 9.9 Simulated (dB) 10.0 9.8 9.3 9.5 9.6 Figure 9.24a further shows that both joint-symbol algorithms to calculate the metrics of the trel- lis’s state transitions (histograms and Gaussian model) have a similar performance. This confirms that the Gaussian channel model is a valid assumption for direct detected DQPSK modulation. The advantage of the Gaussian model method is a significantly reduced complexity to store and compute the branch metric. As only the mean value for each state is stored, the size of the look- up tables is 4 L+1 = 64 and 4 Q 4 L+1 = 65536 for the Gaussian model and histogram method, respectively. In addition, when the Gaussian model method is used only the Euclidean distance has to be computed in the trellis diagram. The complexity of the different MLSE schemes is summarized in Table 9.1. From Figure 9.24 it is evident that both JD-MLSE as well as JS-MLSE have a slightly lower back-to-back OSNR requirement, which is also summarized in Table 9.2. As MLSE creates an improved decision variable based on a number of symbols, in this case equal to the channel memory length, this is similar to the improvement observed for MSPE. The back-to-back OSNR requirement of JS-MLSE is 1.0 dB and 0.4 dB lowered in comparison to the CDR receiver for the measurements and simulation, respectively. We note that the difference between the measurements and simulation probably results from phase offsets in both MZDIs. The limited improvement for MLSE compared to MSPE is due to the smaller number of symbols used to compute the improved decision variable. This suggests that a combination of MSPE and MLSE might be a suitable approach to realize robust DQPSK modulation, which has been confirmed by Zhao et. al. in [401, 402]. In this work the MSPE is implemented in the optical domain using multiple MZDIs with different bit-delays, but similar results could be obtained using a digital signal processing implementation. 200 9.3. Summary & conclusions 9.3 Summary & conclusions In this chapter, signal processing algorithms have been discussed that can increase the robust- ness of D(Q)PSK modulation with a direct detection receiver. Multi-symbol phase estimation (MSPE) generates an improved decision variable using a recursive signal processing algorithm. → MSPE approaches the OSNR requirement of coherent detection. It therefore allows for a 0.5-dB and 1.8-dB improvement in back-to-back OSNR requirement for DPSK and DQPSK modulation, respectively. → In the presence of nonlinear phase noise, the advantage of MSPE over conventional di- rect detection increases. This allows for a 1.5-dB improvement in nonlinear tolerance for 10.7-Gb/s DPSK modulation. For DQPSK modulation, no significant compensation of nonlinear phase noise is observed. → MSPE demodulation has only a modest laser linewidth requirement as it is based on inter- ferometric demodulation with an MZDI. It is more tolerant to laser linewidth than a digital coherent receiver with optimized carrier recovery. For lasers with a ¸1 MHz linewidth, the forgetting factor can be lowered as a trade-off between linewidth requirement and OSNR improvement. Maximum likelihood sequence estimation (MLSE) improves the tolerance with respect to trans- mission impairments by basing the decision variable not only on the most recent symbol, but on a received sequence of symbols. → Using the signal after balanced detection as the input of a conventional MLSE receiver does not significantly improve the tolerance against chromatic dispersion for both DPSK and DQPSK modulation. On the other hand, a conventional MLSE receiver does improve the DGD tolerance of DPSK modulation. → For DPSK modulation, the use of joint-decision MLSE significantly improves the chro- matic dispersion tolerance. A joint-decision MLSE operates using both the constructive and destructive component as separate inputs to the MLSE receiver. → The combination of partial DPSK with a conventional MLSE provides a significant in- crease in chromatic dispersion tolerance at the cost of somewhat higher back-to-back OSNRrequirement. For 10.7-Gb/s NRZ-DPSK, a 3750-ps/nmdispersion tolerance is mea- sured for a 2-dB OSNR penalty. → For DQPSK modulation, joint-symbol MLSE provides the best chromatic dispersion toler- ance. This makes a simultaneous decision on the in-phase and quadrature tributaries of the demodulated DQPSK signal. It can therefore compensate for the crosstalk between both tributaries, which degrades the performance of a direct detection DQPSK receiver. 201 Chapter 9. Digital direct detection receivers In summary, signal processing in direct detection receivers seems promising to realize more robust optical transmission. The chromatic dispersion tolerance and PMD tolerance of, in par- ticular, 43-Gb/s DQPSK modulation can be increased to the extent that no optical chromatic dispersion or PMD compensation is required. 202 10 Digital coherent receivers In this chapter we discuss digital coherent receivers, also known as digital intra-dyne receivers, for amplitude, polarization and phase-sensitive detection. Such receivers combine coherent de- tection with digital signal processing to compensate for transmission impairments, and therefore are a suitable candidate for robust optical transmission systems. Coherent detection of an optical signal implies that the received signal is mixed with the output signal of a LO laser. The LO is normally a receiver-side semiconductor laser. Coherent detection has initially received significant research interest in the 1980’s. At that time, no pre-amplification was used in front of the receiver, which results in detection mostly limited by the thermal noise of the photo diode and electrical amplifiers. As the LO signal typically has a much higher power than the received signal, it can be used for coherent amplification. Hence for coherent detection, the receiver sensitivity is only limited by optical shot noise. This can potentially increase the receiver sensitivity with up to 20 dB in comparison to optically unamplified direct detection [403]. However, after the development of the EDFA as an optical pre-amplifier, the interest in coherent detection declined. With EDFA pre-amplification and direct detection, nearly the same receiver sensitivity can be obtained without many of the drawbacks of coherent detection, such as active polarization and phase control. Although the receiver sensitivity of direct detection is close to the theoretical optimum, a small difference remains. As discussed in Chapter 4, the phase demodulation with an MZDI results in an OSNR penalty of 1.1 dB (DPSK) or 2.4 dB (DQPSK) when compared to coherent detection. For state-of-the-art transmission systems, this difference in receiver sensitivity can potentially improve the OSNR requirement and increase the feasible transmission distance. In addition, differential detection provides relatively poor performance with respect to digital equalization as 1 The results described in this chapter are published in c4, c6, c21-c22, c25-c26 203 Chapter 10. Digital coherent receivers discussed in Chapter 9. Using coherent detection not only the amplitude, but the full (base-band) optical field, i.e. the amplitude, phase and polarization information from the received signal is transferred into the electrical domain. This opens up the possibility of distortion compensation and polarization de-multiplexing in the electrical domain and has recently revived the interest in coherent detection. This chapter is organized as follows. The principle of coherent detection is briefly treated in Section 10.1. In more detail, the implementation of a digital coherent receiver is discussed in Section 10.2 and the required signal processing algorithms are reviewed in Section 10.3. In Sec- tions 10.4 and 10.5 the compensation of linear impairments is discussed for 43-Gb/s POLMUX- NRZ-DQPSK and 111-Gb/s POLMUX-RZ-DQPSK, respectively 1 . Subsequently, Section 10.6 discusses the performance of digital equalization in long-haul transmission experiments. Finally, Section 10.7 analyzes the possibilities of baud-rate distortion compensation. 10.1 Analog coherent receivers Figure 10.1 shows the basic layout of a coherent receiver. The received signal is mixed with the output of the LO in an optical hybrid. There are a number of different technologies that allow the construction of an optical hybrid [404]. The most straightforward realization is a 2x2 coupler, which simply produces an interference between the received signal and the LO at the output. data Rx LO PC LO frequency, phase and polarization control Optical hybrid PD Frequency control feedback Polarization control feedback Signal processing + - Figure 10.1: Principle of a coherent receiver. In order to analyze coherent detection, we define the received signal and LO signal at the input of the optical hybrid as, r s (t) = √ P s exp( j[ω s t +ϕ s ]) r LO (t) = √ P LO exp( j[ω LO t +ϕ LO ]). (10.1) 1 A coherent receiver does not necessarily require differential detection, and POLMUX-QPSK would therefore be the correct acronym of the modulation format. However, in the work described in this chapter, electrical differential decoding is used (see Section 10.3.4) and hence the modulation format is still referred to as POLMUX-DQPSK. 204 10.1. Analog coherent receivers Where the LO and transmitter laser are assumed to have different frequency and phase. After mixing, the optical signal at the input of the two photodiodes is then equal to, 1 √ 2 _ r s (t) + j r LO (t) j r s (t) +r LO (t) _ . (10.2) The current after the photodiode is given by i(t) = R [y(t)y ∗ (t)[ +η sh (t). R is the responsivity of the photodiode and η sh (t) the photocurrent shot noise. Thermal noise has been neglected The coherent mixing term after detection with the photodiode is subsequently defined by the photocurrent, i = R 2 _ P s +P LO +2 √ P s P LO sin[(ω s −ω LO )t +ϕ s −ϕ LO ] P s +P LO −2 √ P s P LO sin[(ω s −ω LO )t +ϕ s −ϕ LO ] _ +η sh (t). (10.3) The information is contained in the term ±2 √ P s P LO sin[ω s −ω LO t +ϕ s −ϕ LO ]. This shows directly the advantage of coherent detection in a system without pre-amplification. As P LO ¸P s , the magnitude of the coherent detected term becomes much larger with respect to the photocur- rent shot noise η sh (t) as can be the case for direct detection. The direct detection terms P s and P LO can be filtered out through balanced detection. Whereas for single-ended detection, only ¸P s ) and ¸P LO ) can be removed through D.C. blocking. This leaves a direct detection contribu- tion from the modulation in P s as well as amplitude noise contributions in P LO , better known as relative intensity noise (RIN). When balanced detection is used the RIN of the LO is canceled out [405]. Coherent detection can be realized using a homodyne, heterodyne or intra-dyne receiver. The difference between the three receiver types is the required frequency difference between LO and transmitter laser. In a homodyne receiver the LO and transmitter laser have the same frequency and the phase difference should be zero (or a multiple of 2π). The LO and received signal are mixed in the 180 o hybrid (for example a 2x2 coupler), which generates the desired coherent mixing products. Homodyne detection is the ideal coherent detection scheme in the sense that it allows for the optimal receiver sensitivity. When detection is quantum noise limited it requires 9 photon/bit for BPSK modulation to obtain a 10 −9 BER [403]. However, active control of the fre- quency and phase of the LO is required in a homodyne receiver as the phase difference between the LO and the transmitter laser should be zero. Optical transmission using homodyne detection with a phase-locked-loop was first shown by Malyon in 1984 [406]. The phase-locked-loop oper- ation puts however stringent requirements on the laser linewidth for both the LO and transmitter laser, which makes homodyne detection difficult to realize using semiconductor lasers. In heterodyne detection the difference between the LO and transmitter laser frequency is non- zero and equals a fixed intermediate frequency (IF), i.e. ω s −ω LO = ω IF . Such a receiver has a reduced sensitivity of >3 dB in comparison to homodyne detection, as the signal energy with homodyne detection is twice the signal energy of a heterodyned signal [407, 408]. The linewidth requirements are however about an order of magnitude less stringent in comparison to homodyne detection, which makes such a receiver easier to realize. The main drawback of heterodyne de- tection is that it requires a receiver bandwidth of at least twice the bit rate [409]. A heterodyne receiver therefore needs broadband photodiodes and electrical amplifiers, which makes it chal- lenging to realize high-speed transmission. Recently, bit rates up to 10-Gb/s have been shown for 205 Chapter 10. Digital coherent receivers heterodyne detection [410], but non-ideal electrical components in the receiver make it difficult to match the performance of direct detection with an optical preamplifier. Intra-dyne detection is similar to homodyne detection, with the exception that the frequency difference between the LO and transmitter laser is not exactly zero, but approximately zero. The frequency difference between LO and transmitter laser than can be tolerated by an intra-dyne receiver depends on the signal processing. Intra-dyne detection relies on detection of both the in-phase and quadrature component of the received signal, and is therefore also referred to as a phase-diversity receiver. In order to detect both the in-phase as well as the quadrature component, a 90 o hybrid is required [404]. The phase-diversity reception makes the receiver robust against phase offsets between the LO and transmitter laser. When the signal in one of the arms fades to zero the other signal is still present, and the summation of both signals (for BPSK) will be independent of the phase difference. As the signal has to be split in two components, intra-dyne detection has a 3-dB sensitivity penalty in comparison to homodyne detection for shot noise limited reception. Intra-dyne coherent detection at 680-Mbit/s was first shown by Davis et. al. in 1986 [411]. Similar to heterodyne detection, an intra-dyne receiver that uses single-ended detection is vulnerable to RIN from the LO. This can be solved through balanced detection, which requires a total of 4 photo-diodes and an optical hybrid with 4 outputs, each shifted by 90 o degrees. As an intra-dyne coherent receiver converts both the in-phase and quadrature component into the electrical domain, it can as well be used for QPSK detection. In comparison to a BPSK intra-dyne receiver demodulation, only the electrical baseband processing has to be modified [412, 413]. This is similar for heterodyne demodulation, which can separate both components through electrical baseband processing. For homodyne QPSK demodulation, on the contrary, a second receiver is required which results in a 3-dB sensitivity penalty. Hence, there is no sensi- tivity difference between homodyne, heterodyne or intra-dyne QPSK demodulation. The main disadvantage of coherent QPSK demodulation is that the laser linewidth tolerance is strongly re- duced in comparison to PSK demodulation, as discussed in Section 9.1.4. This makes it difficult to demodulate QPSK with an optical phase-locked loop. The optical phase-locked-loop can be avoided by analog-digital conversion after the photodiode and subsequent phase drift compensa- tion through digital signal processing, as first shown by Derr in 1991 [412, 414]. Frequency control feedback data Rx Y X LO PD PBS TEQTM + - + - Signal processing Signal processing LO frequency and phase control Figure 10.2: Principle of a polarization-diversity coherent receiver. Coherent optical transmission systems require, in addition to active phase control, that the po- larization of the received signal and the LO are matched. This can be achieved either through 206 10.2. Digital coherent receivers active polarization control, as discussed in Chapter 7 for POLMUX with direct detection, or po- larization diversity [415]. A polarization-diversity receiver was first demonstrated by Okoshi et. al. in 1983 [416]. In this scheme two IF signals (heterodyne demodulation) obtained from or- thogonal polarizations are combined after phase adjustment, and the combined IF signal is then demodulated. A more practical approach is to separately demodulate the two polarization com- ponents, as it does not require phase adjustment at an IF frequency [417]. Such a polarization- diversity scheme results only in a 0.4 dB receiver sensitivity penalty with respect to an ideal single-polarization receiver [418]. Figure 10.2 shows the basic layout of a polarization-diversity coherent receiver. Note that the polarization rotation TM↔TE is shown here explicitly, but is normally integrated into a PBS. The combination of an intra-dyne receiver with polarization diversity, results in a coherent re- ceiver that translates all properties of the optical signal into the electrical domain, as first demon- strated by Okoshi et. al. in 1987 [419]. Together with digital signal processing this allows for a receiver implementation that is robust against the most significant transmission impairments. 10.2 Digital coherent receivers As discussed in Chapter 9 the development of high-speed digital electronics allows for the use of powerful digital signal processing algorithms for distortion compensation. A digital coher- ent receiver enables the compensation of linear transmission impairments and polarization de- multiplexing in the electrical domain. This provides in particular a high tolerance towards PMD and chromatic dispersion. The high tolerance against transmission impairments of a digital co- herent receiver enables the upgrade of existing, 10-Gb/s optimized, infrastructure to 43-Gb/s and 111-Gb/s bit rates. 10.2.1 The optical front-end The digital coherent receiver discussed here uses polarization-diversity intra-dyne detection to convert the full optical field (i.e. amplitude, phase and polarization information) to the electrical domain. This requires the detection of both the in-phase and quadrature components for two arbitrary, but orthogonal, polarization states - a total of four signals. Because the full (base- band) optical field is transferred to the electrical domain, a digital coherent receiver can operate with any kind of optical modulation format. The most advantageous modulation format to use is POLMUX-(D)QPSK [355, 420, 421, 422]. As POLMUX-DQPSK encodes 4 bits per symbol, the coherent receiver only has to operate at 10.75 Gbaud to achieve a 43-Gb/s bit rate. This allows the use of optical and electrical components with a ∼10-GHz bandwidth. The typical setup of a digital coherent receiver using POLMUX-RZ-DQPSK modulation is shown in Figure 10.3. The transmitter laser is either a DFB laser or an ECL. The allowable product of linewidth times symbol period for a digital coherent receiver is approximately 1.3 10 −4 [382]. This translates for a 10.75-Gbaud symbol rate into a ∼1.4-MHz beat linewidth, which is difficult to achieve with 207 Chapter 10. Digital coherent receivers Automatic gain control ^ ^ ^ Frequency control feedback 90° Y X 90° hyb X0° 0° 90° hyb 90° 0° X90° Y0° Y90° LO PD PBS C l o c k R e c o v e r y E q u a l i z a t i o n C a r r i e r r e c o v e r y Digital coherent ASIC D i f f . d e c o d i n g Control Receiver data Rx data HI data HQ ʌ/2 MZ MZ data VI data VQ clock ʌ/2 MZ MZ MZM laser H PBS V Transmitter TEQTM TEQTM XI XQ YI YQ ^ optional Figure 10.3: A digital coherent transmitter and receiver using POLMUX-DQPSK modulation. standard DFB lasers. An ECL, with a typical linewidth of several hundred Kilohertz, provides therefore the optimum performance. In addition, the requirements on the LO laser might be somewhat higher than on the transmitter laser as it should have both a narrow linewidth as well as a low RIN. Typically, ECLs will therefore be used as LO in coherent transponders. In the off-line measurements 2 described in this chapter a ∼1 dB OSNR tolerance degradation has been observed when using a DFB laser at the transmitter. We therefore use ECL lasers for both the LO and transmitter laser in the results discussed in this chapter. The POLMUX-RZ-DQPSK modulator chain starts with a MZM for RZ pulse carving. After the RZ pulse carver the signal is split up in two components using a power splitter. Each of the components is then fed to an integrated QPSK modulator. After DQPSK modulation, both polarization components are recombined using a PBS, which results in POLMUX-RZ-DQPSK modulation. For a 43-Gb/s bit rate it might be desirable to use NRZ instead of RZ pulse carving as this removes the need for the additional pulse carver. For a 111-Gb/s bit rate, on the other hand, it can be more attractive to use RZ pulse carving as it reduces (nonlinear) transmission impairments as well as residual chirp in the transmitted optical signal. Moreover, when NRZ coding is used, the required electro-optical bandwidth of the integrated QPSK modulator is higher, which might be difficult to achieve at a 111-Gb/s bit rate. A too low modulator bandwidth results in increased transmission impairments due to the broad amplitude level of the transmitted signal. 2 A real-time digital coherent receiver requires implementation of the digital signal processing into integrated circuits. The measurements discussed here are therefore ’off-line’. In the off-line measurements, a set of data is sampled and stored using a DSO and afterwards processed on a personal computer 208 10.2. Digital coherent receivers The digital coherent receiver structure is shown in Figure 10.3. First, a PBS splits up the signal into two arbitrary, but orthogonal, polarization components X and Y. The polarization compo- nents X and Y are therefore an arbitrary rotation of the two polarization components at the transmitter (H and V). The polarization rotation TM↔TE is once more shown explicitly, but is normally integrated into the PBS. Each of the polarization components is then fed into a 90 o hybrid and mixed with the output of a LO laser. The LO is free-running and should be aligned with the transmitter laser within an approximate frequency range of several hundred megahertz. The allowable frequency range depends on the signal processing algorithms that are used for carrier phase estimation, which is discussed in Section 10.3.3. The LO can be fixed within this frequency range using a slow feedback signal generated through signal processing, as shown in [423]. The mixing of the received signal and LO in the 90 o hybrids gives the in-phase and quadrature components, which are then fed to single-ended Pin/TIA photodiodes. Balanced pho- todiodes are not used in order to test a cost-efficient and lower complexity receiver architecture. The distortions from direct detected signal components are minimized using a high LO-signal power ratio of approximately 18 dB. In the electrical signal, the direct detected LO component can be removed using a D.C. block. Afterwards the four signals are digitalized using an ADCs. 10.2.2 Analog-to-digital converters After the photodiodes, the four signals are quantized using ADCs, which are typically sampling at 2 samples/symbol. A 43-Gb/s transponder therefore requires ∼25-Gsample/s ADCs, whereas a 111-Gb/s transponder would use ∼60-Gsample/s ADCs. A ∼25-Gbaud ADC implementation has been shown in different semiconductor technologies [17, 424, 18]. Particulary BiCMOS technology allows for the realization of high speed ADCs. The most promising architecture is a full-flash topology where 2 Q −1 parallel comparators are used to convert the signal with a reso- lution of Q bits in a single step [17, 425]. ADCs can also be made with CMOS technology, but this requires the use of a number of slower converters which are then time interleaved to achieve a high total sampling rate [424, 18]. Realizing the ADCs in CMOS technology has the important advantage that they can be combined on a single chip with the subsequent digital signal process- ing. And as the digital signal processing has an inherently parallel architecture this fits well with the parallel ADC architecture required for CMOS implementation. At the time of writing, a 50- Gsample/s ADC design has only been realized for digital storage oscilloscopes [426], where the power dissipation requirements are less strict than for a transponder. The required vertical reso- lution of the ADCs to have a negligible penalty resulting from quantization distortions is 5-6 bits [427]. In order to use available vertical resolution as effectively as possible the dynamic range of the ADC should be fully used. This requires an automatic gain control in front of the ADCs to adapt to changes in the received optical power, for example resulting from optical transients or component aging. Finally, also the electrical bandwidth of the ADCs is an important design parameter. Generally, an electrical 3-dB bandwidth of 0.5 times the baudrate is sufficient [428]. However, the required bandwidth depends strongly on the roll-off with frequency and specifying only the 3-dB ADC bandwidth can be somewhat misleading. 209 Chapter 10. Digital coherent receivers Signal after A/D Signal after A/D conversion conversion Clock recovery: Clock recovery: digital filtering and square timing recovery Equalization: Equalization: 4 complex FIR filer banks, optimized with LMS Carrier recovery: Carrier recovery: Viterbi-and-Viterbi 4 th power phase estimation Binary decision & Binary decision & differential decoding differential decoding Re{E} Im{E} Re{E} Im{E} Re{E} Im{E} Re{E} Im{E} Re{E} Im{E} Re{E} Im{E} Ø Ø Ø Ø 2 sample /symbol Re{E} Im{E} Re{E} Im{E} ~1.8 sample /symbol Polarization X Polarization Y Figure 10.4: Overview of the signal processing steps in a digital coherent receiver, signal constellations exemplify the signals obtained after each processing step. 10.3 Digital equalization algorithms In this section, the digital signal processing algorithms that enables the electronic distortion compensation are discussed in detail. Figure 10.4 shows the different steps used in the digital coherent receiver as discussed in this thesis. After detection and quantization, first of all, clock recovery is applied. Afterwards the linear distortions in the signal are equalized using finite impulse response (FIR) filters, this step also realizes the polarization de-multiplexing. Subse- quently, carrier phase estimation (CPE) is applied to cancel out the phase and frequency offset between the LO and transmitter laser. In the final step a digital decision is taken and differential decoding is applied to prevent cycle slips between the LO and transmitter laser. We note that the digital signal processing algorithms would normally process the data in blocks in order to parallelize the processing and reduce the required clock rate of the hardware. This requires an overlap between consecutive blocks, such that the full impulse response of every symbol within the block is taken into account. The block-wise processing results therefore in an overhead to the processing and memory requirements, which scales linearly with the number of equalizer taps and inversely with the block length. The overlap between consecutive blocks can be implemented using, for example, the overlap-and-add method [429]. 210 10.3. Digital equalization algorithms 10.3.1 Clock recovery and re-timing For the transmission experiment discussed in this chapter, a DSO is used to convert the analog signal to the digital domain and subsequently store the received signal for later off-line pro- cessing. The DSO samples at 20 Gbaud (for the 10.75-Gbaud experiments) or at 50 Gsample/s (for the 27.75-Gsample/s experiments). This translates in both cases to ∼1.8 sample/symbol, and hence the sequence must be re-timed to obtain an integer number of samples per symbol (either 1 or 2). In the first step the signal is approximately re-sampled to ∼2 sample/symbol. |x| 2 1 LN _ 1 arg(...) 2t Cubic Interpolator Approx. resample x ~1.8 sample /symbol 2 sample /symbol ( ) r k 2 s j f t e t ÷ ( ) p k 4 sample/symbol Figure 10.5: Clock recovery and re-sampling. This is achieved by increasing the sampling rate from ∼1.8 sample/symbol to 4 sample/symbol through up-sampling, based on knowledge of the symbol rate and oscilloscope sampling rate. This typically leaves some residual timing offset caused by timing error and jitter that must be compensated using a clock-recovery scheme. In order to exactly re-sample to 2 sample/symbol the digital filter and square timing recovery algorithm is used as described by Oeder and Meyer in [430]. In this scheme the timing function is derived from the power envelope of the received signal by block-wise computing the complex Fourier coefficient at the symbol rate χ m . χ m = (m+1)LN−1 ∑ k=mLN p(k)e −j2πk/L , (10.4) where m is the block index for blocks of length N, L is the over-sampling factor. The power envelope p(k) is calculated from the square of the four received signal components (X 2 0 o +X 2 90 o + Y 2 0 o +Y 2 90 o ). Note that the fraction k/L corresponds to the sample period f s t. The normalized phase ˆ ε of the Fourier coefficient χ m is then a measure of the sampling phase error for block m and can be used to re-sample the data using a cubic interpolator, ˆ ε = 1 2π arg(χ m ). (10.5) Re-timing the signal with the ”filter and square timing recovery” algorithm becomes very critical in the presence of large signal distortions. In a digital coherent receiver specifically designed for a 10.75/27.75-Gbaud symbol rate, the ADCs would therefore sample at an exact multiple of the baud rate, and no re-timing of the signal is required. In addition this also saves the implementa- tion complexity of the re-timing algorithm. 211 Chapter 10. Digital coherent receivers 10.3.2 Distortion compensation & polarization de-multiplexing In the next step, the electronic equalization implements both polarization de-multiplexing as well as the compensation of (linear) transmission impairments. The electronic equalization, as depicted in Figure 10.6a, is implemented by a bank of 4 FIR filters with complex tap weights (h xx , h yx , h xy and h yy ). The FIR filters are arranged in a butterfly structure to enable polariza- tion de-multiplexing, this structure is also known as a cross polarization interference canceler (XPIC) [431, 432]. Note that the polarization de-multiplexing can, in principle, be implemented with a single tap structure and that longer FIR filters are necessary to compensate for chromatic dispersion and PMD. The output signal of the equalization stage can be described as _ ˆ X ˆ Y _ . ¸¸ . equalized signal = _ ˆ h −1 xx ( f ) ˆ h −1 yx ( f ) ˆ h −1 xy ( f ) ˆ h −1 yy ( f ) _ . ¸¸ . equalizer _ X Y _ . ¸¸ . detected signal , (10.6) where in principle the matrix ˆ h −1 is an approximation of the inverse of the channel matrix h which is defined as, _ X Y _ . ¸¸ . detected signal = _ h xx ( f ) h yx ( f ) h xy ( f ) h yy ( f ) _ . ¸¸ . channel _ H V _ . ¸¸ . transmitted signal , (10.7) H and V are the polarization tributaries of the transmitted signal, X and Y are the detected polari- zation components and ˆ X and ˆ X are the recovered polarization tributaries after signal processing. Figure 10.6b shows the FIR filter bank in more detail. Each bank consists of a number of taps, which are either baud-rate (T 0 -spaced, 1 sample/symbol) or fractionally-spaced (T 0 /2-spaced, 2 sample/symbol). Fractionally-spaced equalizers generally provide better performance than baud-rate equalizers since they serve as both matched filter and equalizer. Fractionally-spaced equalizers can however have difficulty converging because the neighboring tap signals are highly correlated [433]. Figure 10.6c shows the complex multiplication required for each filter tap. Adapting the filter tap as a single complex filter tap is only possible when the signal is perfectly symmetrical, i.e. when the real and imaginary components have the same magnitude, which is normally not the case. The single complex-valued tap is therefore structured as four real-valued filter taps, which are optimized independently. The filter taps can be optimized using least mean squares (LMS) algorithms such as the constant modulus algorithm (CMA) [434, 435] or the decision-directed least mean squares (DD-LMS) algorithm [436]. CMA exploits the property of PSK modulation (e.g. BPSK, QPSK) that all points in the signal constellation are located on a circle, as shown in Figure 10.7. It therefore tries to choose the tap coefficients in such a way that the variance between the samples and the circle is minimized, which translates into minimizing an error function, ε x = R 2 −[ ˆ x[ 2 ε y = R 2 −[ ˆ y[ 2 , (10.8) 212 10.3. Digital equalization algorithms ^ ^ Data on Xpol. t t t t E h 0 h 1 h 2 h 3 h 4 h yx h xy X Y h yy h xx h xx (a) Butterfly structure (b) FIR filter bank structure = Re{h 0 } Im{h 0 } Re{h 0 } Im{h 0 } Re{X} Im{X} Re{h 0 X} Im{h 0 X} + - + + h 0 = (c) Filter tap structure X Y Figure 10.6: Digital Equalization using linear FIR filters (a) butterfly structure for polarization de- multiplexing; (b) linear FIR filter structure and (c) filter tap structure. The tap delay τ is equal to T 0 for a baud-rate equalizer or T 0 /2 for fractionally-spaced equalizers. R İ Figure 10.7: Principle of CMA. where R is the radius of the constellation points, which can be easily computed from the average optical power. Because of the squaring in the error function, CMA is not influenced by a phase rotation between consecutive symbols. CMA is therefore robust against a large frequency offset between the LO and transmitter laser. Using the error function, the tap coefficients are now updated until the algorithm converges and the error function becomes small enough. The update of the tap coefficients follows according to, ˆ h −1 xx = ˆ h −1 xx +µε x ˆ x x ∗ ˆ h −1 xy = ˆ h −1 xy +µε x ˆ x y ∗ ˆ h −1 yx = ˆ h −1 yx +µε y ˆ y x ∗ ˆ h −1 yy = ˆ h −1 yy +µε y ˆ y y ∗ , (10.9) where µ is a convergence parameter and x ∗ is the complex conjugate of x. Note that for N taps, each tap n of the FIR filter is updated separately, ˆ h −1 n = ˆ h −1 n +µε x ˆ x n x ∗ n . (10.10) The tapweights ˆ h −1 n therefore increase or decrease with µε. The speed of convergence depends on the magnitude of µ, where a larger value results in faster convergence but also increases the 213 Chapter 10. Digital coherent receivers residual error as well as the possibility that the algorithm does not converge to a solution. The more severe the channel distortions are, the smaller µ generally should be chosen. The second algorithm that can be used for equalization is DD-LMS. This is a decision-directed algorithm, which implies that the algorithm makes a decision on the data in order to estimate the error function. However, DD-LMS is still a blind equalization algorithm, and it can be used either before or after the carrier phase estimation. Equation 10.11 gives the DD-LMS error function. ε x = R csgn( ˆ x)/ √ 2− ˆ x ε y = R csgn( ˆ y)/ √ 2− ˆ y , (10.11) where csgn(x) and csgn(y) are the complex sign functions defined by, csgn(x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 1+ j [Re¦x¦ > 0, Im¦x¦ > 0] 1− j [Re¦x¦ > 0, Im¦x¦ < 0] −1+ j [Re¦x¦ < 0, Im¦x¦ > 0] −1− j [Re¦x¦ < 0, Im¦x¦ < 0] . (10.12) The tap coefficients are then updated according to, ˆ h −1 xx = ˆ h −1 xx +µε x x ∗ ˆ h −1 xy = ˆ h −1 xy +µε x y ∗ ˆ h −1 yx = ˆ h −1 yx +µε y x ∗ ˆ h −1 yy = ˆ h −1 yy +µε y y ∗ , (10.13) As there is no squaring in the DD-LMS algorithm, it is sensitive to phase distortions. In the presence of significant phase distortion the convergence parameter µ should therefore be suitably small. Note that it is also possible to combine the DD-LMS algorithm with CPE, which should make it more robust to a larger frequency offset between transmitter and LO laser [435]. A further possibility is to use DD-LMS with training sequences instead of the blind equalization [437]. In this case the error function is computed by comparison of the output sequence with a known training sequence. Ideally, both CMA and DD-LMS converge to the same solution. However, in practice CMA is more robust to channel distortions and especially phase rotations. The DD-LMS algorithm, on the other hand, is less robust to channel distortions and phase offset but is more likely to converge to the optimum solution. When only the DD-LMS algorithm is used for channel equalization, the convergence parameter µ should be smaller and the optimization process will require more iterations. For the off-line measurements described in the remainder of this chapter this results in slow processing as each new measurement starts by assuming an ideal channel model. In a realtime equalizer, each processed block can start with the channel model of the previous block and update this using a limited number of iterations. Under such conditions, the DD-LMS optimization algorithm is more practical. Alternatively, first CMA can be applied to the data to roughly equalize the majority of the channel distortions. In a second step this is then followed by the DD-LMS algorithm, which can be preceded or combined with the carrier recovery, to equalize the remaining distortions [435]. Figure 10.8 shows an example of the resulting equalizer taps after optimization with the CMA algorithm. A further consideration for the digital coherent receiver is the required number of taps to com- pensate for channel distortions. The described equalization scheme can compensate for linear 214 10.3. Digital equalization algorithms 0.4 0.2 0 -0.2 -0.4 0 2 4 6 8 10 12 14 16 18 20 22 Taps X-X 0.4 0.2 0 -0.2 -0.4 0 2 4 6 8 10 12 14 16 18 20 22 Taps X-Y 0.4 0.2 0 -0.2 -0.4 0 2 4 6 8 10 12 14 16 18 20 22 Taps Y-X 0.4 0.2 0 -0.2 -0.4 0 2 4 6 8 10 12 14 16 18 20 22 Taps Y-Y h n , x x h n , y y h n , y x h n , x y tap number tap number real imaginary Figure 10.8: Resulting tap coefficients for a 21 tap FIR filter with 111-Gb/s POLMUX-RZ-DQPSK mod- ulation, 2000-ps/nm and a 30 o polarization offset. The lines depict the real and imaginary part part of the tap vector. distortions as long as the impulse response length of the equalizer is at least equal to the impulse response length of the channel distortion. The chromatic dispersion and PMD that can be com- pensated increases therefore linearly with the number of FIR filter taps. For certain applications it can be desirable that a digital coherent receiver can compensate for the full chromatic disper- sion in a long-haul transmission link [422, 435, 438]. Assuming, for example, transmission over 3000-km of SSMF this requires the compensation of ∼50,000 ps/nm of chromatic dispersion. At a 10.75-Gbaud symbol rate, the impulse response of such a channel broadens an impulse over ∼100 symbol periods. This would require a FIR filter bank with >100 taps, which would be difficult,if not impossible, to realize in a real-time implementation. As well, it is questionable if the optimization algorithms would always converge properly for a FIR filter bank with such large tap counts. For a larger number of taps (>16), it is therefore more efficient to implement a fixed FIR filter by converting the signal to the frequency domain using a fast-Fourier transform (FFT). An arbitrary amount of chromatic dispersion can then be compensated by a single multiplication with the desired frequency response. Afterwards the signal is converted back to the time domain with an inverse FFT. The polarization tracking and compensation, as well as the compensation of any residual chromatic dispersion is implemented afterwards with shorter (typically 5 taps) FIR filter banks. This uses again the above mentioned butterfly structure and is optimized with either the CMA or the DD-LMS algorithm. The drawback of such a scheme is that it is not based on blind estimation, i.e. the amount of chromatic dispersion that should be compensated has to be roughly known. This implementation has the further advantage that the carrier phase be ap- proximately estimated before equalization, as discussed in the next section and shown in [435], which makes the subsequent equalization stage more efficient. The digital equalization steps in such a receiver architecture are shown in Figure 10.9. A further advantage of digital coherent receivers is that the FIR tap values can be used to estimate the transmission impairments for optical performance monitoring [439, 440]. When we assume a linear transmission channel with only chromatic dispersion and DGD the channel matrix can 215 Chapter 10. Digital coherent receivers ^ ^ ^ ^ ^ ^ X0° X90° Y0° Y90° C l o c k R e c o v e r y C a r r i e r r e c o v e r y XI XQ YI YQ D i f f . d e c o d i n g h yx h xy X Y h yy h xx Y X FFT FFT Approx. equalization & carrier recovery Figure 10.9: Digital Equalization using a combination of FFT and linear FIR filters . be written as, H( f ) = _ h xx ( f ) h yx ( f ) h xy ( f ) h yy ( f ) _ = _ u( f ) d( f ) v( f ) d( f ) −v ∗ ( f ) d( f ) u ∗ ( f ) d( f ) _ , (10.14) where _ u( f ) v( f ) −v ∗ ( f ) u ∗ ( f ) _ , (10.15) is a unitary matrix which denotes the transfer function of the DGD. d( f ) is the chromatic disper- sion transfer function, which is equal to d( f ) = exp( j f 2 β 2 L 2 ). (10.16) A property of a unitary matrix is, that the absolute value of its determinant is equal to one, [u( f ) u ∗ ( f ) −v( f ) −v ∗ ( f )[ d( f ) 2 = d( f ) 2 = exp( j f 2 β 2 L), (10.17) where β 2 L/2 is the accumulated dispersion. The absolute value of u( f ) or v( f ) can subsequently be used to estimate the DGD, which is shown in [439]. The accumulated PDL in the received signal can as well be estimated using signal processing in digital coherent receiver, which is discussed in [440]. 10.3.3 Carrier phase estimation After the electronic equalization a CPE stage is used to correct for the frequency and phase offset between transmitter and LO laser as described by Viterbi and Viterbi in [441]. For analog coher- ent receivers the frequency deviations between the transmitter and LO laser is one of the most critical design parameters. For a digital coherent receiver, the signal processing enables a much larger tolerance towards frequency deviations. Depending on the signal processing algorithms a frequency de-tuning range of several hundred Megahertz [353] to several Gigahertz [435] is possible. However, a feedback from the signal processing to LO, as shown in Figure 10.3, is still desirable to tune the LO approximately to the center of this frequency range. The principle behind CPE is shown in more detail in Figure 10.10. As a first step the frequency can be corrected approximately. This is for example possible by integrating the phase change 216 10.3. Digital equalization algorithms j slicer DQPSK decoder X j slicer DQPSK decoder Y (b) Delay ( ) r k 1 ( ) arg(...) 4 k u = ( ) j k e u ÷ 4 ( ) ( ) s k r k = ( ) k N i i k N a s i + = ÷ _ (a) Approx. Frequency corr. Figure 10.10: (a) Carrier phase estimation and (b) slicer followed by a DQPSK decoder. over a large number of symbols or by estimating the shift in the frequency domain after FFT, as shown by Savory et. al. in [435]. Note that the CPE algorithm works also when it is not preceded by approximate frequency correction, but this will generally result in smaller frequency offset window and/or a performance penalty. The CPE algorithm first takes the 4 th power of the symbols in order to remove the phase modulation from the QPSK modulated signal, s(k) = r(k) 4 , (10.18) where r(k) is either the x / or y / vector obtained from the equalization stage. Subsequently a running average is used over a predefined number of symbols of the complex vectors s(k), k+N ∑ i=k−N a i s i . (10.19) For an 2N +1 symbol CPE the N pre-cursor and N post-cursor symbols are considered. The parameter a i can implement a windowing function, such as for example a Wiener filter [383]. The argument then gives the phase correction factor θ(k) that is used to apply a correction to the original symbols. The number of symbols over which the CPE averages can have a critical influence on the perfor- mance of the digital coherent receiver. When ASE is the dominant impairment a larger number of symbols for CPE is more optimal as this will average out the (zero mean) Gaussian noise and obtain a better phase estimate. On the other hand, in the presence of significant phase noise a smaller number of symbols will be preferable as this allows better tracking of the fast change in phase offset. The most likely sources of phase noise are a LO or transmitter laser with a broad 217 Chapter 10. Digital coherent receivers laser linewidth (∼MHz) or XPM-induced phase noise from neighboring WDM channels. The impact of XPM is especially severe when the adjacent channels are 10.7-Gb/s NRZ modulated. For 43-Gb/s POLMUX-NRZ-QPSK the optimum CPE length is found to be averaging over 17 symbols. When DFB lasers are used for the transmission and/or LO laser, a shorter CPE length will result in better performance, as for example shown in [442] where a CPE length of 9 is found to be optimum. Note that using 2 symbols for CPE is similar to differential detection in a direct detection receiver. 10.3.4 Differential decoding & error counting In the final stage of the electronic signal processing, a digital decision on each symbol is made on the symbols using a slicer. In the experiments discussed in this chapter we use digital differential decoding. The digital differential decoding is used to avoid the possibility of cycle slips. A cycle slip result in loss of synchronization, for example because of a sudden jump in phase difference between LO and transmitter laser. The possibility of cycle slips is effectively avoided through differential detection. However, the differential decoding doubles the BER which results in a ∼0.5-dB OSNR penalty [10]. However, there are other algorithms that can be used to detect and correct for cycle slips. This might be desirable as it lowers the OSNR requirement by 0.5 dB. 10.4 Distortion compensation at 43-Gb/s Section 10.3 discussed the algorithms that are used for the distortion compensation with a digital coherent receiver. In this section we discuss the compensation of different impairments using experimental results obtained with a coherent receiver for 43-Gb/s POLMUX-NRZ-DQPSK. The digital coherent receiver setup discussed in Section 10.2 is for simplicity somewhat modified in the experiments, as shown in Figure 10.11a. The output signal of an ECL at a wavelength of 1550.12 nm is modulated using an integrated DQPSK modulator. A 10.75-Gb/s PRBS with a length of 2 15 −1 and a relative delay of 9 bits for de-correlation is split and fed to both inputs (data I and Q) of the DQPSK modulator. Afterwards, a POLMUX signal is generated by dividing the signal into two tributaries (H and V) and recombining those with orthogonal polarizations and a 106 symbol delay between the tributaries for de-correlation. This results in 43-Gb/s POLMUX- NRZ-DQPSK modulation. Figures 10.11b and 10.11c show the directly detected eye diagrams for NRZ-DQPSK with (43 Gb/s) and without (21.5 Gb/s) POLMUX signaling, respectively. At the receiver the OSNR is set using a VOA followed by an EDFA and a 37-GHz CSF. The signal is then fed into the coherent receiver, with an input power of approximately -9 dBm. The PBS splits the signal into two arbitrary, but orthogonal, polarization components X and Y. Each of the polarization components is then fed into a fiber based 90 o hybrids where it is mixed with the output of the LO laser. The LO is a tunable ECL with 100-kHz linewidth, manually aligned to within 400 MHz of the transmitter laser. The output power of the LO is 9 dBm. The 90 o hybrids 218 10.4. Distortion compensation at 43-Gb/s PBS delay V H VOA 10.75G data A 10.75G data B ʌ/2 MZ MZ 90° Y X 90° hyb X0° 0° 90° hyb 90° 0° X90° Y0° Y90° LO PD PBS O f f - l i n e s i g n a l p r o c e s s i n g laser PC PC 2 0 G s / s S t o r a g e O s c i l l o s c o p e ~ ~ ~ 37GHz CSF VOA Set OSNR Arbitrary state of polarization DGD CD SOPMD TEQTM P o w e r ( a . u ) 93 ps P o w e r ( a . u ) 93 ps (b) (c) (a) Figure 10.11: (a) Experimental setup for the 43-Gb/s POLMUX-NRZ-DQPSK transmitter and coherent receiver; eye diagrams for (b) 21.5-Gb/s NRZ-DQPSK and (c) 43-Gb/s POLMUX-NRZ-DQPSK. consist of asymmetric 3x3 fiber couplers with a 20%:40%:40% coupling ratio [420]. Mixing of LO and signal components in the hybrids leads to orthogonal signals on the 20% and one of the 40% outputs. This is discussed in more detail in Appendix C. The polarization controllers (PC) between the LO and the 90 o hybrids are required because the latter are not polarization- maintaining. The in-phase and quadrature components of both polarizations are detected using four single-ended pin/TIA photodiodes. The absolute power on the photodiodes (dominated by the LO) is between -2 and +1 dBm, where the power variation results from the use of an asymmetric 2:2:1 coupler. Using a Tektronix TDS6154 digital storage oscilloscope, each of the four signals is then sampled with 20-Gbaud ADCs to obtain four data sets of 524,184 bits each (in total ∼ 2 10 6 bits). The four data sets are subsequently off-line post-processed with the digital equalization algorithms described in Section 10.3. After processing the differentially decoded sequence is compared to the transmitted PRBS, taking into account the differential decoding. For back-to-back measurements, the BER is measured at a number of different OSNR values, and the OSNR required for a BER of 10 −4 is interpolated. 10.4.1 Back-to-back OSNR requirement Figure 10.12a depicts the required OSNR for single polarization 21.5-Gb/s NRZ-DQPSK and 43-Gb/s POLMUX-NRZ-DQPSK with the digital coherent receiver. This shows the expected 3-dB difference in OSNR tolerance with the doubling of the bit rate. This indicates that a dig- ital coherent receiver is capable of electrical polarization de-multiplexing without a noticeable performance penalty. Note that, unlike the results described in Chapter 7, the receiver is polari- zation sensitive for both cases and the OSNR difference is therefore exactly 3 dB. With 43-Gb/s POLMUX-NRZ-DQPSK, the required OSNR is 11.2 dB and 13.1 dB for a 10 −3 and 10 −4 BER, respectively. 219 Chapter 10. Digital coherent receivers 6 8 10 12 14 16 18 -7 -6 -5 -4 -3 -2 OSNR (dB/0.1nm) l o g ( B E R ) 14 13 12 11 10 9 8 Q ( d B ) 43-Gb/s POLMUX- NRZ-DQPSK 21.5-Gb/s NRZ-DQPSK FEC limit (a) 16 18 20 22 24 10 11 12 13 14 15 16 LO-sig power ratio (dB) R e q u i r e d O S N R ( d B / 0 . 1 n m ) BER = 10 -4 (b) Figure 10.12: (a) Back-to-back sensitivity for 43-Gb/s POLMUX-NRZ-DQPSK with the OSNR require- ment for 21.5-Gb/s NRZ-DQPSK as a reference; (b) Required OSNR versus LO-signal ratio. The required OSNR as a function of the LO-signal power ratio is shown in Figure 10.12b. A high LO-signal power ratio is beneficial as it reduces the impairments resulting from direct detection components. However, the measured results shows that the OSNR penalty is minimal for a relatively broad range of LO-signal power ratios. The optimum LO-signal power ratio is between 18 dB and 20 dB, and 18 dB is used in the remainder of the experiments. A too high LO-signal power ratio results here in a higher OSNR requirement as the signal power becomes too small (the LO power is kept constant). 10.4.2 Differential group delay Probably the most significant impairment that can be compensated with a digital coherent re- ceiver is PMD, as there is no easy optical compensation approach. Since a digital coherent receiver detects the linear optical field for both polarization states and DGD is a linear distortion in the optical field, the inverse channel constructed by the FIR filters can effectively cancel out the distortion induced through DGD. As a first step, only the DGD is considered using a DGD emulator. The input SOP into the DGD emulator is set to a 45 o offset with respect to the transmitted polarization tributaries, which results in a worst-case alignment. Figure 10.13a shows the DGD tolerance for different numbers of FIR taps. For 13 taps no significant penalty is measured for a DGD up to 200 ps. This corresponds to an mean DGD of about 60 ps for a 10 −5 outage probability, which is approximately the DGD tolerance of a direct detection 2.5-Gb/s NRZ-OOK receiver. When the number of FIR taps is reduced to 5, a 1-dB OSNR penalty is evident for 60 ps of DGD. It can also be observed that the OSNR requirement is slightly reduced at 0-ps DGD when the number of filter taps increases. We conjecture that this results from the equalization of transmitter and receiver imperfections. 220 10.4. Distortion compensation at 43-Gb/s 10.4.3 Polarization dependent loss Figure 10.13b shows the influence of PDL on the digital coherent receiver. PDL is more detri- mental for POLMUX signaling in comparison to polarization insensitive modulation as it results in a performance difference between the polarization channels. Here, PDL is added to the signal as a power imbalance by attenuating one of the polarization tributaries in the transmitter, which equals the case shown in Figure 7.11b. As a result, both tributaries will also have a different OSNR at the receiver. In Figure 10.13b the worst-case tributary is depicted for 2 dB and 5 dB of PDL, respectively. The lower signal power in the worst-case tributary reduces the OSNR by 1.1 dB and 3.2 dB compared to the average OSNR, respectively. This indicates that even with a severe power imbalance between both channels, coherent equalization can still recover the po- larization tributaries. When the PDL is combined with up to 120 ps of DGD, slightly higher penalties are evident. This is most likely the result of the attenuated tributary having insufficient signal power to use the full dynamic range of the ADCs. Note that PDL induced depolarization is not considered here, but as shown in Section 7.3.4 the difference in penalty between both cases is marginal for a direct detection receiver. Hence, for this case we also expect to observe similar penalties with a digital coherent receiver. The combined impact of PMD and PDL might have a more significant impact, but is not considered here. 0 50 100 150 200 12 14 16 18 Differential group delay (ps) R e q u i r e d O S N R ( d B / 0 . 1 n m ) 5 taps 7 taps 13 taps BER = 10 -4 (a) -20 0 20 40 60 80 100 120 140 10 12 14 16 18 20 Differential group delay (ps) R e q u i r e d O S N R ( d B / 0 . 1 n m ) 13 taps, BER = 10 -4 5 dB PDL 2 dB PDL no PDL (b) Figure 10.13: (a) required OSNR versus DGD for various tap lengths and (b) DGD tolerance without PDL and in the presence of 2-dB and 5-dB of PDL. 10.4.4 Higher-order polarization-mode dispersion Higher-order PMD can have a severe impact for POLMUX signaling as the polarization de- multiplexing becomes wavelength dependent, which results in depolarization [326]. The experi- mental setup that is used here to evaluate the combined effect of DGD and SOPMD is depicted in Figure 10.14a. The signal passes first through a polarization scrambler to randomize the state of polarization, followed by a DGD emulator. Subsequently, SOPMD is added to the signal using a NewRidge NRT-40133A emulator preceded by a second polarization scrambler. The SOPMD 221 Chapter 10. Digital coherent receivers 60 ps PBS PBS RX scrambler scrambler SOPMD emulator (d) TX (a) (c) (b) 8 10 12 14 16 18 -6 -5 -4 -3 -2 OSNR (dB) l o g ( B E R ) 8 10 12 14 16 18 -6 -5 -4 -3 -2 OSNR (dB) l o g ( B E R ) 8 10 12 14 16 18 -6 -5 -4 -3 -2 OSNR (dB) l o g ( B E R ) 20-ps + 120-ps DGD 20-ps + 60-ps DGD 20-ps DGD Figure 10.14: (a) Experimental setup used for higher order PMD evaluation, (b-d) 270-ps 2 SOPMD combined with different amounts of DGD, the line indicates back-to-back performance and a 13 tap FIR filter is used. 16:10 16:30 16:50 17:10 17:30 17:50 18:11 18:31 18:51 19:11 -7 -6 -5 -4 -3 -2 Measurement timestamp l o g ( B E R ) 14 13 12 11 10 9 8 Q ( d B ) Worst-case tributary Best-case tributary Figure 10.15: Stability test over three hours with 2-dB PDL, 80-ps + 20-ps DGD, 270-ps 2 SOPMD and a 13 tap FIR filter, both best-case and worst-case polarization tributaries are depicted. emulator is set to add the maximum amount of 20 ps of DGD and 270 ps 2 of SOPMD to the signal. For this configuration (Figure 10.14b, 40 measurements for each setting/OSNR) no rel- evant penalty is observed. The measured points below the back-to-back OSNR requirement are due to measurement uncertainty. Note that for a 10-Gbaud symbol rate, 270 ps 2 of SOPMD will normally not result in a significant penalty due to the small spectral width of the signal. In Fig- ure 10.14d the amount of DGD is increased to 120 ps + 20 ps of DGD and 270 ps 2 of SOPMD and still the worst-case OSNR penalty is below ∼2 dB for a 10 −4 BER. This indicates that co- herent equalization is not overly sensitive to SOPMD and meets the requirements of a 43-Gb/s transponder. Further statistical measurements are required to understand the fundamental limits of coherent equalization with respect to higher order PMD impairments. In Figure 10.15, measurements are depicted over a time period of three hours to show system stability. The measurement are taken with a 2 minutes interval. To illustrate the successful 222 10.4. Distortion compensation at 43-Gb/s compensation of PMD related impairments, PDL, DGD and SOPMD are added to the signal. The 2-dB of PDL is once again added by attenuating one of the tributaries at the transmitter. DGD and SOPMD are added in the same way as previously described for the results depicted in Figure 10.14b-d. The results show that despite the presence of severe PMD impairments, only a small BER variation (∼1 dB) is evident over time. -4000 -2000 0 2000 4000 12 14 16 18 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) 7 taps 5 taps 13 taps BER = 10 -4 (a) -4000 -2000 0 2000 4000 12 14 16 18 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) 7 taps 5 taps 13 taps 60-ps DGD, BER = 10 -4 (b) Figure 10.16: Required OSNR versus chromatic dispersion for various tap lengths; (a) only chromatic dispersion and (b) chromatic dispersion plus 60 ps of DGD. 10.4.5 Chromatic dispersion The channel impulse response of chromatic dispersion is typically longer than the impulse re- sponse of DGD, and the impulse energy is therefore spread out over multiple symbol periods. However, when the length of the FIR filters is sufficient to accurately synthesize the inverse trans- fer function of the channel impulse response, an arbitrary amount of chromatic dispersion can be compensated. To verify the feasibility of chromatic dispersion compensation, the tolerance is measured using a combination of DCF/SSMF spools and a fiber-based TDC. The resulting chro- matic dispersion tolerance for different numbers of FIR taps is depicted in Figure 10.16. With 13-tap T 0 -spaced FIR filters in the equalizer, only a small penalty is measured and the tolerance is in excess of ±3000 ps/nm. When the number of taps is reduced to 7, the dispersion tolerance for a 1 dB penalty is about ±2000 ps/nm. The combined compensation of chromatic dispersion and DGD impairments is shown by adding 60 ps of DGD together with different amounts of chromatic dispersion (see Figure 10.16b). Even for 60 ps of DGD and 4,000 ps/nm of chromatic dispersion the OSNR penalty is only in the order of 1 dB for a 13-tap equalizer. For a reduced number of taps the chromatic dispersion tolerance decreases accordingly. The chromatic dispersion and DGD tolerance measured with the digital coherent receiver, con- firms the expectation that for such a receiver the chromatic dispersion and DGD tolerance is only limited by the number of FIR taps in the equalizer. This indicates that a digital coherent receiver does not require tunable optical chromatic dispersion or PMD compensation at the receiver. 223 Chapter 10. Digital coherent receivers 10.5 Distortion compensation at 111-Gb/s Besides 43-Gb/s transmission, the possible application of digital coherent receivers to 111-Gb/s transmission is also of major interest. As chromatic dispersion scale quadratically with the bit rate, the need for either optical or electrical adaptive distortion compensation becomes increas- ingly more important for higher bit rates. And as a digital coherent receiver combines an ex- cellent OSNR tolerance with the compensation of linear transmission impairments it is an at- tractive solution to realize robust 111-Gb/s long-haul transmission. Similar to the 43-Gb/s bit rate, POLMUX-DQPSK is also the modulation format of choice for 111-Gb/s to combine with a digital coherent receiver. The use of POLMUX-DQPSK modulation is particulary important at a 111-Gb/s bit rate, because the 27.75-Gbaud symbol rate is low enough to enable conversion to the digital domain using state-of-the-art ADCs. Figure 10.18 shows NRZ and RZ eye diagrams for both DQPSK and POLMUX-DQPSK at a 27.75-Gbaud symbol rate. ì2 ì10 A W G RZ-DQPSK Tx – even channels RZ-DQPSK Tx – odd channels I N T PBS delay V H VOA Arbitrary state of polarization DGD CD ~ ~ ~ 62GHz CSF VOA Set OSNR 27.75G data A 27.75G data B clock ʌ/2 MZ MZ MZM 90° 90° hyb X0° 0° 90° hyb 90° 0° X90° Y0° Y90° LO PD O f f - l i n e s i g n a l p r o c e s s i n g PC PC 5 0 G s / s S t o r a g e O s c i l l o s c o p e Y X PBS TEQTM Figure 10.17: Experimental setup for the 111-Gb/s POLMUX-RZ-DQPSK transmitter and receiver. (c) 36 ps (d) 36 ps (b) 36 ps (a) P o w e r ( a . u ) 36 ps Figure 10.18: Eye diagrams for (a) 55.5-Gb/s NRZ-DQPSK, (b) 55.5-Gb/s RZ-DQPSK, (c) 111-Gb/s POLMUX-NRZ-DQPSK and (d) 111-Gb/s POLMUX-RZ-DQPSK modulation In order to verify the electronic distortion compensation at a 111-Gb/s bit rate, the transmitter and receiver structure shown in Figure 10.17 are used. The output of 10 ECL between 1548.5 nm and 1552.2 nm centered on a 50-GHz ITU grid are fed to two modulator chains for separate 224 10.5. Distortion compensation at 111-Gb/s modulation of the odd and even WDM channels. Because of the somewhat limited electro-optic bandwidth of the modulators, a RZ pulse carver is included to generate RZ-DQPSK. The elec- trical drive signals consist of a 2 16 PRBS that is split and fed to both inputs of the integrated DQPSK modulators with a 8 bit de-correlation, which results in a 4 8 PRQS. After DQPSK mod- ulation a 50-GHz interleaver with a 45-GHz 3-dB bandwidth is used to combine the even and odd WDM channels. Note that the optical spectrum of 55.5-Gb/s RZ-DQPSK is significantly broader than 45-GHz, and the interleaver is therefore bandlimiting the signal. For the back-to-back mea- surement the nearest neighbor channels are turned off to allow OSNR measurements. Finally, a POLMUX signal is generated by dividing the signal in two tributaries and recombining those with orthogonal polarizations and a 353 symbol delay between the tributaries for de-correlation. The digital coherent receiver is identical to the one described in Section 10.4 with the exception that photodiodes with a ∼30-GHz bandwidth are used. After detection, the signals are sampled with 50-Gsample/s photodiodes using a Tektronix DSA72004 DSO. 10 12 14 16 18 20 22 24 -7 -6 -5 -4 -3 -2 OSNR (dB/0.1 nm) l o g ( B E R ) 14 13 12 11 10 9 8 Q ( d B ) 111-Gb/s POLMUX- RZ-DQPSK 55-Gb/s RZ-DQPSK FEC limit Figure 10.19: Back-to-back sensitivity for 111- Gb/s POLMUX-RZ-DQPSK with a coherent re- ceiver, the OSNR requirement of 55.5-Gb/s RZ- DQPSK is shown as a reference. 20 30 40 50 60 70 80 90 100 16 18 20 22 24 3-dB filter bandwidth (GHz) R e q u i r e d O S N R ( d B / 0 . 1 n m ) Figure 10.20: Required OSNR for a 10 −4 BER versus 3-dB optical filter bandwidth, 111-Gb/s POLMUX-RZ-DQPSK with coherent detection; 55-Gb/s RZ-DQPSK with direct detection. 10.5.1 Back-to-back OSNR requirement For a 111-Gb/s bit rate, the OSNR requirement of the modulation format is particulary significant as it is much higher than for a 10.7-Gb/s and 43-Gb/s bit rate. For a 10.7-Gb/s bit rate, NRZ- OOK is conventionally used as the modulation format for terrestrial long-haul systems. 10.7- Gb/s NRZ-OOK requires a ∼10 dB of OSNR for a 0 −3 BER. When we simply scale the bit rate, the required OSNR scales with 6 dB when increased from 10.7 Gb/s to 43 Gb/s. But this difference can be effectively reduced by using advanced modulation formats. For example, DPSK requires only a ∼12 dB of OSNR. And the use of POLMUX-NRZ-DQPSK with coherent detection would further reduce this to ∼11 dB. However, when upgrading from a 43-Gb/s to a 111-Gb/s line rate, the OSNR requirement cannot be further reduced. This will result in a significant reduction in feasible transmission distance for 111-Gb/s in comparison to 43-Gb/s 225 Chapter 10. Digital coherent receivers transmission. It is therefore advantageous to keep the OSNR requirement as low as possible for 111-Gb/s transmission by using POLMUX-RZ-DQPSK modulation with coherent detection. The back-to-back OSNR requirement of both 55.5-Gb/s RZ-DQPSK and 111-Gb/s POLMUX- RZ-DQPSK is depicted in Figure 10.19. As expected, the doubling of the channel capacity results in a 3-dB OSNR penalty. For 111-Gb/s POLMUX-RZ-DQPSK, a 15.8-dB and 17.8 dB OSNR is required to obtain a BER of 10 −3 and 10 −4 , respectively. This compares favorably with previously reported 100-Gb/s OSNR requirements as it is a 2.3-dB improvement over 107-Gb/s RZ-DQPSK [14] and a >4-dB improvement over 107-Gb/s NRZ-OOK (with an optical equal- izer) [12]. The lower OSNR requirement of POLMUX-DQPSK modulation combined with a digital coherent receiver can therefore be instrumental in realizing long-haul transmission sys- tems with a 111-Gb/s bit rate per wavelength channel 1549.5 1550 1550.5 1551 -40 -30 -20 -10 0 10 Wavelength (nm) R e l a t i v e P o w e r ( d B ) 1549.5 1550 1550.5 1551 -40 -30 -20 -10 0 10 Wavelength (nm) R e l a t i v e P o w e r ( d B ) 1549.5 1550 1550.5 1551 -40 -30 -20 -10 0 10 Wavelength (nm) R e l a t i v e P o w e r ( d B ) 111-Gb/s POLMUX-NRZ-DQPSK 111-Gb/s POLMUX-RZ-DQPSK 111-Gb/s POLMUX-RZ-DQPSK (a) (b) (c) Figure 10.21: Measured optical spectra (0.01nm/res); (a) 111-Gb/s POLMUX-NRZ-DQPSK with filter curves, (b) 111-Gb/s POLMUX-RZ-DQPSK with filter curves and (c) 111-Gb/s POLMUX-RZ-DQPSK after filtering; Interleaver with 44-GHz 3-dB bandwidth; CSF with 40-GHz 3-dB bandwidth. 10.5.2 Narrowband optical filtering The lower symbol rate of POLMUX-RZ-DQPSK in comparison to binary modulation formats is a significant advantage in term of achievable spectral efficiency. It supports a 111-Gb/s bit rate on a 50-GHz WDM grid, which realizes a spectral efficiency of 2.0-b/s/Hz. The tolerance of 111-Gb/s POLMUX-RZ-DQPSK with respect to narrowband optical filtering is shown in Fig- ure 10.20. The optical filter used to assess the tolerance is a NetTest X-Tract filter with a nearly rectangular pass-band. This clearly shows the absence of a noticeable filtering penalty until the 3-dB optical filtering drops below 30 GHz. Note that a nearly similar narrowband filtering tol- erance is obtained when a direct detection receiver is used, as evident from Figure 10.20. This indicates that the narrowband filtering tolerance is not significantly improved by the coherent receiver, but results mainly from the choice in modulation format. The sound tolerance toward narrowband optical filtering enables transmission through a large number of cascaded 50-GHz OADMs for 111-Gb/s POLMUX-RZ-DQPSK. Figure 10.21 depicts the measured optical spectra for 111-Gb/s POLMUX-(N)RZ-DQPSK with the filter curves of a 44-GHz interleaver and 40-GHz CSF superimposed. This shows that both filters result in strong spectral narrowing in the case of RZ pulse carving. Figure 10.21c depicts 226 10.5. Distortion compensation at 111-Gb/s the spectra obtained after filtering for 111-Gb/s POLMUX-RZ-DQPSK. The RZ spectra after passing through the 40-GHz CSF shows a very similar shape as the NRZ spectra without filter- ing. This indicates that the narrowband filtering results in a quasi-NRZ eye shape. Because the symbol rate is lowered by a factor of two, 111-Gb/s POLMUX-RZ-DQPSK requires only half the optical bandwidth of 111-Gb/s (direct-detection) RZ-DQPSK. Whereas 111-Gb/s POLMUX- RZ-DQPSK can be used on a 50-GHz WDM grid, 111-Gb/s RZ-DQPSK is normally limited to a 100-GHz WDM grid. -2500 -1500 -500 500 1500 2500 16 18 20 22 24 26 Chromatic dispersion (ps/nm) R e q u i r e d O S N R ( d B / 0 . 1 n m ) 21 taps 13 taps 31 taps BER = 10 -4 (a) 0 20 40 60 80 100 12 16 18 20 22 24 26 Differential Group Delay (ps) R e q u i r e d O S N R ( d B / 0 . 1 n m ) 3 taps 5 taps 9 taps BER = 10 -4 (b) Figure 10.22: Required OSNR for various tap lengths (a) chromatic dispersion and (b) DGD, both in comparison to direct detection (CDR receiver), 111-Gb/s POLMUX-RZ-DQPSK with coherent detection; 55-Gb/s RZ-DQPSK with direct detection; 111-Gb/s POLMUX-RZ-DQPSK with direct detection (simulated). 10.5.3 Chromatic dispersion & differential group delay The OSNR requirement for a 10 −4 BER as a function of the chromatic dispersion is shown in Figure 10.22. The OSNR penalty is depicted for different numbers of filter taps in the FIR equalizer. For 31 taps, no significant penalty is evident for a dispersion window ranging from - 2000 ps/nmto +2000 ps/nm. And even for 13 taps the measured chromatic dispersion tolerance is in excess of 750 ps/nm. When one compares this tolerance to the ∼8-ps/nm chromatic dispersion tolerance of 107-Gb/s NRZ-OOK [14], or ∼25 ps/nm using 55.5-Gbaud RZ-DQPSK [13], the increased robustness is nearly two orders of magnitude. Although this improvement is in part due to the 27.75-Gbaud symbol rate of POLMUX-RZ-DQPSK, the most significant contribution results from the coherent detection of the optical field and the subsequent distortion equalization. The DGD tolerance for various FIR filter tap lengths is shown in Figure 10.22. It can be observed that a 3-tap FIR filter is effective for a DGD up to 30 ps, while a 9-tap FIR filter shows no penalty for a DGD in excess of 100 ps. When we takes into account that 100 ps of DGD equals 2.8 symbol periods for a 27.75-Gsymbol/s baud rate, this clearly demonstrates the flexibility of a digital coherent receiver. This compares favorably with a ∼3-ps DGD tolerance using 107-Gb/s NRZ-OOK and ∼6 ps using 107-Gb/s RZ-DQPSK. 227 Chapter 10. Digital coherent receivers 10.6 Long-haul transmission The results discussed in Sections 10.4 and 10.5 show that the combination of POLMUX-DQPSK modulation coupled with a digital coherent receiver has excellent tolerance against linear trans- mission impairments. Nonlinear transmission impairments are however a different challenge as a digital coherent receiver has limited capability to compensate for such impairments. In this section we discuss the transmission performance of POLMUX-DQPSK coupled with a digital coherent receiver for both a 43-Gb/s and 111-Gb/s bit rate. 5x 95km SSMF Post- compensation Pre- Compensation DCM DCM TX EDFA EDFA WSS ~ ~ ~ 37-GHz CSF RX Tx switch Loop switch LSPS 2-5x TDC NRZ-DQPSK NRZ-DQPSK NRZ-DQPSK POLMUX 43-Gb/s NRZ-DQPSK only Tx POLMUX 10.7Gb/s NRZ 10.7Gb/s NRZ 21.5Gb/s NRZ-DQPSK Mixed 43-Gb/s + 10.7-Gb/s NRZ Tx POLMUX Ȝ = 1550.12 nm Ȝ = 1550.12 nm I N T I N T I N T I N T (a) (c) (b) Figure 10.23: (a) Experimental transmission link; (b) transmitter with only 43-Gb/s POLMUX-NRZ- DQPSK modulated channels and (c) transmitter with a single 43-Gb/s POLMUX-NRZ-DQPSK channel surrounded with 10.7-Gb/s NRZ-OOK modulated channels. 10.6.1 43-Gb/s POLMUX-NRZ-DQPSK transmission In order to evaluate the performance of 43-Gb/s POLMUX-NRZ-DQPSK modulation in a long- haul WDM transmission system, 9 co-propagating channels between 1548.5 nm and 1552.2 nm are added to the channel under test on a 50-GHz WDM grid. The output of the 9 additional ECLs are modulated using two DQPSK modulators for separate modulation of the even and odd channels, as depicted in Figure 10.23b. The re-circulating loop (Figure 10.23a) consists of five 95-km spans of SSMF with an average span loss of 18.5 dB. The signal is pre-dispersed with DCF having -1360 ps/nm of chromatic dispersion and the in-line under compensation is ∼85 ps/nm/span. Double-stage EDFA-only amplification is used and the input power per channel into the DCF is 6 dB reduced with respect to the SSMF. Loop-induced polarization effects are reduced using a LSPS and power equalization of the WDM channels is provided by a channel- based WSS. At the receiver the channel at 1550.12 nm is selected with a 37-GHz CSF. Using 228 10.6. Long-haul transmission post-compensation and a TDC, the chromatic dispersion at the receiver is either set close to zero, or offset from zero to measure the chromatic dispersion tolerance of the receiver. Afterwards the signal is fed into the coherent receiver. To obtain sufficient measurement accuracy, each measurement is repeated on 10 separate time instants, to obtain a total of 2 10 7 bits for error detection. First of all, the transmission distance and input power per channel are both varied to obtain an estimate for the transmission reach. Figure 10.24a shows the feasible transmission distance for the optimum input power per channel, which is found to be -3 dBm. Note that the optimum input power of -5 dBm per channel after 900 km is likely due to measurement uncertainty. When com- pared to 10.7-Gb/s NRZ, the nonlinear tolerance of 43-Gb/s POLMUX-NRZ-DQPSK is reduced by 4-5 dB. The nonlinear tolerance of 43-Gb/s POLMUX-DQPSK is mainly limited by SPM, which is similar to 43-Gb/s DQPSK modulation. On the other hand, the POLMUX signaling will also somewhat reduce the nonlinear tolerance due to XPM induced nonlinear polarization modulation, as discussed in Chapter 7. 1000 1500 2000 2500 3000 -7 -6 -5 -4 -3 -2 Transmission distance (km) l o g ( B E R ) 2 3 4 5 6 Number of loops 14 13 12 11 10 9 8 Q ( d B ) FEC limit Optimum input power (dBm/ch) -5 -3 -3 -3 -3 (a) 1548 1549 1550 1551 1552 -7 -6 -5 -4 -3 -2 Wavelength (nm) l o g ( B E R ) 14 13 12 11 10 9 8 Q ( d B ) 2375 km FEC limit (b) Figure 10.24: Long-haul transmission results with 43-Gb/s POLMUX-NRZ-DQPSK; (a) BER versus transmission distance and (b) BER for all WDM channels. Figure 10.24a shows that the feasible transmission distance of 43-Gb/s POLMUX-NRZ-DQPSK with EDFA-only amplification is approximately ∼3000 km. Figure 10.24b further depicts the BER for the 10 co-propagating WDM channels after 2375-km (5 loops) transmission. There is a slight variance between the even and odd WDM channels, which results from a slight perfor- mance difference between both DQPSK modulators. This results from a drift in bias voltages of the modulator. 229 Chapter 10. Digital coherent receivers 10.6.2 Co-propagating 10.7-Gb/s NRZ-OOK channels Section 10.6.1 discussed the nonlinear tolerance under the assumption that all co-propagating channels are 43-Gb/s POLMUX-NRZ-DQPSK modulated. However, the currently installed base of WDM links carries predominantly 10.7-Gb/s NRZ-OOK modulated channels. Such links are likely to be upgraded in the near future to a 43-Gb/s bit rate. We therefore consider the case that the neighboring channels of a 43-Gb/s POLMUX-NRZ-DQPSK modulated channel are 10.7- Gb/s NRZ-OOK modulated. The transmitter is modified such that only the center channel is modulated with 43-Gb/s POLMUX-NRZ-DQPSK and that the 9 surrounding channels are 10.7- Gb/s NRZ-OOK modulated (as depicted in Figure 10.23c) (a) -6 -5 -4 -3 -2 -1 0 1 2 -7 -6 -5 -4 -3 -2 -1 Input power (dBm/ch) l o g ( B E R ) 950 km 1425 km 1900 km 2375 km 2850 km 14 12 10 8 6 Q ( d B ) 10ch x 43-Gb/s POLMUX-NRZ-DQPSK (b) -6 -5 -4 -3 -2 -1 -7 -6 -5 -4 -3 -2 -1 Input power (dBm/ch) l o g ( B E R ) 950 km 1425 km 1900 km 2375 km 2850 km 14 12 10 8 6 Q ( d B ) 9ch x 10.7-Gb/s NRZ, center channel 43-Gb/s POLMUX-NRZ-DQPSK Figure 10.25: BER of the center channel versus input power per channel for (a) all channels 43-Gb/s POLMUX-NRZ-DQPSK modulated and (b) 43-Gb/s POLMUX-NRZ-DQPSK center channel with 9 co- propagating 10.7-Gb/s NRZ-OOK channels As shown in Section 5.4, co-propagating NRZ-OOK channels can result in significant XPM impairments for DQPSK modulated signals. However, whereas in a direct detection receiver the impact of XPM is reduced through differential detection, this is not the case for a digital coherent receiver. In this case the transmission penalty can be even more severe as the XPM induced phase noise can potentially impair the CPE in the digital signal processing. In addi- tion, POLMUX signaling can result in XPolM-induced polarization modulation, as discussed in Chapter 7. The XPM tolerance of 43-Gb/s POLMUX-NRZ-DQPSK is therefore a key parameter to determine its suitability for overlay on an existing 10-Gb/s infrastructure. Figure 10.25 com- pares the nonlinear tolerance for 43-Gb/s POLMUX-NRZ-DQPSK with and without 10.7-Gb/s NRZ-OOK neighbors, respectively. For all measurements the CPE averages over 17 symbols. In this case the co-propagating 10.7-Gb/s NRZ-OOK modulated channels clearly reduce the trans- mission performance. The optimum input power is lowered from -4 dBm to below -6 dBm. As a result the feasible transmission distance for 43-Gb/s POLMUX-NRZ-DQPSK modulation is reduced from ∼3000 km to ∼1800 km. This confirms that XPM-induced phase noise from co-propagating 0.7-Gb/s NRZ-OOK neighbors is an important design consideration for 43-Gb/s POLMUX-NRZ-DQPSK. The impact of XPolM is illustrated using the Poincar´ e spheres in Fig- ure 10.26. This shows simulated results for transmission over 20x100-km of SSMF with a - 2 dBm input power per WDM channel. When only a single channel is transmitted, the spread in 230 10.6. Long-haul transmission -100 -50 0 50 100 -40 -30 -20 -10 0 Frequency (GHz) P S D ( d B ) -100 -50 0 50 100 Frequency (GHz) -100 -50 0 50 100 Frequency (GHz) (a) (b) (c) Figure 10.26: Simulated spectra and Poincar´ e spheres showing 43-Gb/s POLMUX-NRZ-DQPSK modu- lation after 2000-km transmission; (a) single-channel, (b)43-Gb/s POLMUX-NRZ-DQPSK neighbors and (c) 10.7-Gb/s NRZ-OOK neighbors. the constellation points is minimal, and no evidence of severe nonlinear impairments is observed. When we add co-propagating WDM transmission on a 50-GHz channel grid, the spread of the constellation point is marginally increased as long as the co-propagating channels are 43-Gb/s POLMUX-NRZ-DQPSK modulated (Figure 10.26b). However, when the neighboring channels are 10.7-Gb/s NRZ-OOK modulated the spread of the constellation points increases dramatically (Figure 10.26c). This directly results from the increased XPM and XPolM impairments gener- ated through the co-propagating NRZ-OOK channels. We now obtain similar depolarization penalties as observed for transmission with POLMUX-NRZ-OOK modulation in Chapter 7. The increased impact of XpolM can be partially alleviated by optimizing the number of symbols used for CPE. As discussed in Section 10.3.3, the XPM induced phase noise depends on the bit sequence of the neighboring channels and therefore does not average out when more symbols are taken into account. Figure 10.27a shows, for transmission over 1900 km, the impact of re- ducing the averaging in CPE. For high input powers XPM induced phase noise is the dominant impairment and CPE with a smaller number of symbols gives better performance. For low input powers, XPM induced impairments are less dominant and the performance is more OSNR lim- ited. In this case a longer CPE length is beneficial, this is evident from the smaller difference between the measured CPE lengths. We find that the optimum input power per channel and CPE lengths are respectively -5 dBm and a 5 symbol CPE length. Figure 10.27b now depicts the feasible transmission distances for 43-Gb/s POLMUX-NRZ-DQPSK with 10.75-Gb/s neighbors when the CPE length is optimized. The shorter CPE (∼5 symbols) improves the reach from ∼1800 km to ∼2800 km. With an optimized CPE length there is still a penalty evident when 231 Chapter 10. Digital coherent receivers -6 -5 -4 -3 -2 -4 -3 -2 -1 Input power (dBm/ch) l o g ( B E R ) 3 symbol 5 symbol 7 symbol 9 symbol 17 symbol 10 8 6 4 Q ( d B ) 17 symbol CPE 3 symbol CPE (a) 1000 1500 2000 2500 3000 -7 -6 -5 -4 -3 -2 Transmission distance (km) l o g ( B E R ) 2 3 4 5 6 Number of loops 14 13 12 11 10 9 8 7 Q ( d B ) FEC limit (b) Figure 10.27: (a) BER versus input power per channel after 1.900 km for 43-Gb/s POLMUX-NRZ- DQPSK with 10.7-Gb/s NRZ neighbors transmission; (b) BER versus transmission distance for, all 43-Gb/s POLMUX-NRZ-DQPSK neighbors; 10.7-Gb/s NRZ neighbors and a 17 symbol CPE length; 10.7-Gb/s NRZ neighbors and an optimized CPE length. compared to transmission with 43-Gb/s POLMUX-NRZ-DQPSK modulated neighbors, but this penalty is relatively small. This indicates that 43-Gb/s POLMUX-NRZ-DQPSK modulation can be used to upgrade transmission systems that carry legacy 10.7-Gb/s NRZ-OOK channels. How- ever, the residual penalty due to XPolM might make it beneficial to increase the wavelength spacing between the 43-Gb/s and 10.7-Gb/s modulated channels to ≥100 GHz. 5x 95km SSMF Post- compensation Pre- Compensation DCM DCM TX EDFA WSS ~ ~ ~ 40-GHz CSF RX Tx switch Loop switch LSPS 2-6x TDC Raman DCM Figure 10.28: Experimental transmission setup. 10.6.3 111-Gb/s POLMUX-RZ-DQPSK transmission In this section we discuss the transmission performance of 111-Gb/s POLMUX-RZ-DQPSK modulation when combined with a digital coherent receiver. The combination of 111-Gb/s POLMUX-RZ-DQPSK modulation with a 50-GHz WDM grid enables long-haul transmission with a 2.0-b/s/Hz spectral efficiency. The same transmitter and receiver structure with 10 WDM 232 10.6. Long-haul transmission channels is used as depicted in Figure 10.17. The re-circulating loop setup used for the 111-Gb/s transmission experiment is shown in Figure 10.28. The re-circulating loop consisting of 5x95 km of SSMF and uses hybrid EDFA-Raman ampli- fiers. The dispersion map is similar as discussed in Section 10.6.1 for 43-Gb/s POLMUX-NRZ- DQPSK, with -1530 ps/nm of pre-compensation and 85 ps/nm of inline under-compensation per span. The ON/OFF Raman gain in the SSMF provided by the backwards pumped Raman amplifiers is ∼14 dB. Note that the same Raman pump powers are used here as previously de- scribed in this thesis. The higher Raman gain results from the use of ”water free” SSMF, which has a lower attenuation around 1450 nm, which is approximately the wavelength range of the Raman pumps. A WSS with a 3-dB channel bandwidth of 43-GHz equalizes the power spec- trum for each re-circulation and emulates strong optical filtering as it would occur in cascaded OADMs. Because of the broad optical spectrum of 111-Gb/s POLMUX-RZ-DQPSK, the signal is severely bandlimited through the 43-GHz filtering. After 5 re-circulations, the received spec- tra of the signal has a bandwidth of 32 GHz and 36.5 GHz (3 dB and 10 dB point respectively). However, as shown in Section 10.5.2 this does not result in a significant penalty for 111-Gb/s POLMUX-RZ-DQPSK modulation. In the receiver the 40-GHz CSF selects the desired chan- nel, and the chromatic dispersion is set to the desired value (either zero or a preselected offset). Subsequently, the signal is fed into the digital coherent receiver. 1000 1500 2000 2500 3000 -7 -6 -5 -4 -3 -2 Transmission distance (km) l o g ( B E R ) 2 3 4 5 6 Number of loops 14 13 12 11 10 9 8 Q ( d B ) -6 -5 -5 -5 -4 FEC limit Optimum input power (dBm/ch) Figure 10.29: 111-Gb/s POLMUX-RZ-DQPSK; BER versus transmission distance for the optimum input power per channel. X Y (a) (b) Figure 10.30: Measured signal constellation for (a) back-to-back with 25-dB OSNR and (b) after 2375-km transmission (BER 2x10 −4 ). First of all, the performance of 111-Gb/s POLMUX-RZ-DQPSK is determined by measuring the BER of the center channel at 1550.1 nm as a function of both input power per channel and transmission distance (see Figure 10.29a). The optimum input power per channel is found to be -4 dBm after 950 km and decreases to -6 dBm after 2850 km of transmission. Note that Figure 10.29 plots the BER for each of the 10 separate measurements, which gives a good in- dication of the loop induced BER variation. The BER variance also increases for higher input powers as nonlinear impairments become more dominant. However, the BER variation is mini- mal for the optimum input power of -4 to -6 dBm. Figure 10.30 shows a comparison of the signal 233 Chapter 10. Digital coherent receivers constellations measured back-to-back and after 2375-km transmission. In the presence of strong nonlinear phase noise, the constellation point would normally become asymmetric, as discussed in Section 2.4.7. The symmetry of the constellation points therefore indicates that the impact of nonlinear phase noise is small. Figure 10.32 shows the measured performance for all 10 wavelength channels after 1900 km and 2375 km. All channels show a similar BER between 1 10 −4 and 5 10 −4 after 2375 km of trans- mission. Hence, all measured channels have a margin with respect to the FEC limit of ∼1.5 dB. By varying the post-compensation and the TDC at the receiver, the chromatic dispersion tol- erance is measured after 2375 km (see Figure 10.32). Using a 13-tap FIR filter, a dispersion tolerance window of ∼1500 ps/nm is measured without a significant penalty. This is equal to the tolerance observed in the back-to-back measurement. 1548 1549 1550 1551 1552 -7 -6 -5 -4 -3 -2 Wavelength (nm) l o g ( B E R ) 14 13 12 11 10 9 8 Q ( d B ) FEC limit 2375 km 1900 km Figure 10.31: BER for all 111-Gb/s POLMUX- RZ-DQPSK WDM channels after 1,900-km and 2,375-km transmission. -1500 -1000 -500 0 500 1000 1500 -6 -5 -4 -3 -2 Chromatic dispersion (ps/nm) l o g ( B E R ) 13 12 11 10 9 8 Q ( d B ) FEC limit after 2375 km transmission Figure 10.32: Chromatic dispersion tolerance with a 13-tap equalizer after 2375-km transmis- sion 10.7 Distortion compensation using baud-rate equalizers Although the current state-of-the-art ADCs allows for sampling rate as high as 50-Gsample/s in DSOs, the power consumption makes it unrealistic to integrate such ADCs in a commercial transponder. In addition, the ADCs in DSO are usually based on BiCMOS or SiGe technology, whereas integration in CMOS technology would be desirable for a single-chip solution. It might therefore takes some time before ∼60-Gsample/s ADCs can be integrated into optical transpon- ders. A further concern besides the raw sample rate itself, is the total signal processing required in a 111-Gb/s digital coherent receiver. Assuming that a digital coherent receiver requires 5-6 bits of vertical resolution, over-sampling with 55.5 Gsample/s on 4 input channels requires the processing of 1100-1300 Gb/s. There is no doubt that given the exponential increase in capability of CMOS integrated circuits [16] this will be realizable in the long-term. In the short-term, sam- pling with only 1 sample/symbol would allow a receiver implementation with a lower complexity and less digital signal processing. On the other hand, sampling with 1 sample/symbol requires the 234 10.7. Distortion compensation using baud-rate equalizers use of a baud-rate (T 0 -spaced) equalizer for the polarization de-multiplexing and distortion com- pensation. A T 0 -spaced equalizer is normally not capable of compensating an arbitrary amount of chromatic dispersion and DGD, and the tolerance will therefore reduce accordingly. 4 8 12 16 20 16 17 18 19 20 21 22 3-dB Filter bandwidth (GHz) R e q u i r e d O S N R ( d B / 0 . 1 n m ) 4 8 12 16 20 16 17 18 19 20 21 22 BER = 10 -3 BER = 10 -3 (a) (b) Figure 10.33: Required OSNR versus Bessel fil- tering bandwidth for (a) T 0 /2-spaced and (b) T 0 - spaced equalization; 0 ps/nm, -250 ps/nm and -500 ps/nm chromatic dispersion. -1500 -1000 -500 0 500 1000 1500 -5 -4 -3 -2 Chromatic dispersion (ps/nm) l o g ( B E R ) 12 11 10 9 8 Q ( d B ) after 2375 km transmission FEC limit Figure 10.34: (c) BER versus chromatic dis- persion after 2375-km transmission and with 13- tap equalizers T 0 /2-spaced, no filtering T 0 /2- spaced, 7-GHz filter T 0 -spaced, 7-GHz filter. The lower performance of a T 0 -spaced equalizer can be somewhat alleviated with strong elec- trical filtering in the receiver [443]. Low-pass electrical filtering increases the ISI and spreads therefore the energy of the received signal to the T 0 -spaced sampling points. In addition it re- moves the aliasing induced through baud-rate sampling. The equalizer must in turn compensate for both the additional ISI resulting from the low-pass filtering, as well as the channel distortions. To illustrate the feasibility of a T 0 -spaced equalizer, we determine the OSNR requirement as a function of low-pass filter bandwidth in the presence of chromatic dispersion. This is achieved by low-pass filtering the input samples with an electrical 5 th order Bessel filter. Afterwards, the samples are re-quantized using 5 bit resolution to ensure that subsequent signal processing using floating point arithmetic does not reverse the low-pass filtering. Subsequently, the digital signal algorithms as described in Section 10.3 are applied, but with the difference that now T 0 -spaced FIR filters are used. Note that the sampling time instant has a large impact when using only 1 sample/symbol. This implies that for such a digital coherent receiver the clock recovery im- plementation is much more critical. Here, the sample time instant is optimized to give the lowest mean-square error at the output of the equalizer. Figures 10.33a and 10.33b shows the required OSNR with 0, -250 and -500 ps/nm of chromatic dispersion for T 0 /2-spaced and T 0 -spaced signal processing, respectively, where a 13-tap FIR is used in all measurements. It is evident that for 2 sample/symbol signal processing, the chro- matic dispersion tolerance is independent of the electrical low-pass filtering bandwidth. The required OSNR increases only when the filtering 3-dB bandwidth is below 10 GHz as the low- pass filtering starts to incurs a significant penalty. For 1 sample/symbol signal processing, on the other hand, the chromatic dispersion tolerance improves significantly as the electrical low-pass filtering bandwidth is reduced. For a 7-GHz low-pass filtering bandwidth, there is a ∼0.7 dB 235 Chapter 10. Digital coherent receivers back-to-back penalty from the low-pass filtering. For -500 ps/nm of chromatic dispersion, the additional OSNR penalty is less than 1 dB. For a low-pass filtering bandwidth below 6 GHz, the performance is limited by the filtering, both back-to-back and with chromatic dispersion. 0 5 10 15 20 -20 -15 -10 -5 0 Frequency (GHz) T r a n s m i t t a n c e ( d B ) 5 th -order Gauss f 3dB = 13 GHz 5 th -order Bessel f 3dB = 7 GHz Figure 10.35: Transmittance spectrum of a 7-GHz Bessel and 13-GHz Gauss filter. The measured optical filter tolerance (as depicted in Figure 10.20) shows a 1-dB OSNR penalty for a ∼27 GHz filtering bandwidth, which is a factor of four difference with the 7-GHz optimal electrical filter bandwidth. In theory, there should be equivalence between the optical and elec- trical filtering after coherent detection. A factor of two is accounted for by noting that the optical filter is defined as a band-pass, double-sided, bandwidth. On the other hand, the electrical filter bandwidth is defined as a low-pass, single-sided, bandwidth. The other factor of two results from the Bessel filter shape, as the narrowband filtering tolerance is not only defined through the 3-dB bandwidth but strongly dependent on the exact filter curve. A Bessel filter has a very flat roll-off, whereas a Gauss-shaped filter has a steeper roll-off with frequency. When a Gauss-shaped elec- trical filter is used in the receiver, the filter bandwidth for a 1-dB penalty increases to 13-GHz, a factor of two difference with the (Gauss-shaped) optical filter bandwidth of 27-GHz. This is illustrated in Figure 10.35, which depicts the filters curves of a 5 th order Bessel and Gauss filter, with a 7-GHz and 13-GHz 3-dB bandwidth, respectively Next, the T 0 -spaced equalizer with 7-GHz 5 th order Bessel filtering is used to process the data ob- tained after long-haul transmission. For both T 0 - and T 0 /2-spaced FIR filters, this results in ∼0.5- dB penalty. When using a T 0 -spaced FIR filter, a chromatic dispersion window of ∼1000 ps/nm is obtained without a significant penalty, as shown in Figure 10.34. Hence, we can conclude that a 111-Gb/s digital coherent receiver can be realized using only 27.75-Gbaud ADCs. The tolerance towards chromatic dispersion is sufficient to enable the use of 111-Gb/s transponders on network infrastructure that has been designed for 10-Gb/s systems, without the use of tunable dispersion. The compensation of PMD using T 0 -spaced equalizers is not determined here, but in [351, 444] it is shown that it is not possible to compensate for an arbitrarily high PMD. An alter- native might be to sample at a slightly higher sample rate, for example with 1.5 sample/symbol, and re-time the samples through signal processing. In [444], Ip and Kahn show that this allows for the compensation of arbitrarily high DGD. In addition, this shows that a 111-Gb/s digital co- herent receiver can be realized using an electrical component with a ∼15 GHz bandwidth, which significantly reduces the cost and complexity of the transmitter and receiver. 236 10.8. Summary & conclusions 10.8 Summary & conclusions The digital coherent receiver architecture discussed in this chapter clearly shows the potential of signal processing in optical communication systems. It allows for high bit-rate transmission systems where the system design complexity is shifted more to the electrical domain instead of the optical domain, as is the case for convention transmission systems. The main benefits of a digital coherent receiver can be summarized as: → A digital coherent detection translated the full optical field into the digital domain. This enables efficient signal processing that can theoretically compensate for any (linear) dis- tortion accumulated along the transmission link. → The optical front-end of a digital coherent receiver consists of a LO, PBS and two 90 o hy- brids, it is therefore much simpler in comparison to a direct detection POLMUX-DQPSK receiver. The four signal components (in-phase & quadrature on both polarizations) are detected with single-ended photodiodes. The resulting direct detection impairments are reduced through a high ∼18-dB LO to signal ratio. → For both 43-Gb/s an 111-Gb/s POLMUX-DQPSK modulation we have shown the effective compensation of linear transmission impairments, i.e. chromatic dispersion, DGD and SOPMD. This confirms that as long as a large enough number of FIR filter taps is used, any linear signal distortion can be compensated. → The impact of PDL results in a penalty for a digital coherent receiver, either due to a OSNR difference between the tributaries or a loss of orthogonality. However, 3 dB of PDL can be tolerated with less than a 2-dB OSNR penalty. We further analyzed the transmission performance of 43-Gb/s and 111-Gb/s POLMUX-DQPSK modulation when combined with a digital coherent receiver: → For 43-Gb/s POLMUX-NRZ-DQPSK, a 2375 km reach is feasible using EDFA-only am- plification and an optimal input power of -3 dBm per channel. → A significant drawback for POLMUX-DQPSK modulation is the severe XPM and XPolM penalty incurred through co-propagating NRZ-OOK channels, which reduces the feasible transmission reach. This penalty can be reduced by optimizing the number of symbols used for CPE. However, it remains desirable to increase the channel spacing to ≥100 GHz between 43-Gb/s and 10.7-Gb/s modulated channels. → For 111-Gb/s POLMUX-RZ-DQPSK, a transmission reach of 2375 km is measured using hybrid EDFA/Raman amplification. The optimum input power per channel is approxi- mately -5 dBm. → With 111-Gb/s POLMUX-RZ-DQPSK modulation, a spectral efficiency of 2.0-b/s/Hz is feasible while maintaining a sound tolerance towards narrowband filtering. In a long-haul 237 Chapter 10. Digital coherent receivers transmission experiment, 5 add/drop nodes on a 50-GHz grid are passed. This results in a 32-GHz spectral width after transmission, which does not incur a noticeable penalty. → The higher sampling rate of the ADCs in a 111-Gb/s transponder can be reduced through 1-sample/symbol quantization and subsequent T-spaced signal processing. This requires electrical low-pass filtering with a 7-GHz Bessel filter to spread the energy to the T-spaced sampling points. A >1000-ps/nm chromatic dispersion tolerance with only 0.7-dB OSNR penalty is obtained using a T-spaced 13-tap equalizer. On the basis of these results we can concludes that long-haul transmission with a 43-Gb/s and 111-Gb/s bit rate can be realized using POLMUX-DQPSK modulation and digital coherent re- ceivers. The feasibility of upgrading an existing transmission systems that already carries 10.7- Gb/s NRZ-OOK modulation remains a question for further research. The results discussed in this chapter are all based on off-line processing, and the step to real- time processing is a critical one to determine the feasibility of such transmission systems. For example, in [428], Sun et. al. reported the first real-time ASIC implementation of a digital coherent receiver at 43-Gb/s. The described ASIC requires 20 million transistors and has a power dissipation of 21 Watts, which underlines the state-of-the-art nature of this technology. However, the advantages of digital coherent detection are such that it is likely that this technology will be broadly adapted in the upcoming years. 238 11 Outlook & recommendations In upcoming years, the steady growth in Internet bandwidth will fuel the need to develop and deploy 40-Gb/s and 100-Gb/s optical transmission systems. In this section we aim to compare the various options that can be considered for such transmission systems based on the results described in the thesis. Table 11.1 shows a summary of the advantages and disadvantages of the different modulation formats. It should also be stressed here that technology changes constantly. In the little over three years that have been covered by the work in this thesis, DQPSK modulation went from the first experi- mental demonstration at 43-Gb/s to commercial products [309]. And whereas 100-Gb/s DQPSK was not even on the horizon three years ago, a field trail has now already demonstrated its feasi- bility in a deployed network [310]. This is even more true for POLMUXsignaling. Until recently, many people in the fiber-optic industry considered it only suitable for transmission experiments and never stable enough for commercial deployment. But when digital coherent detection pro- vided a practical alternative to optical polarization de-multiplexing, this technology went in the course of less than two years from the first lab demonstrations to commercial deployment [428]. The comparison in this section is therefore based on the current state-of-the-art and bound to be soon outdated. 11.1 Robust optical modulation formats The choice of the optical modulation format is a trade-off between a number of different require- ments: (1) spectral efficiency and optical filter tolerance, (2) OSNR requirement, (3) nonlinear tolerance, (4) chromatic dispersion tolerance, (5) PMD tolerance and (6) transponder complexity. 239 Chapter 11. Outlook & recommendations The importance of each of these requirements differs depending on the optical transmission sys- tem. It is therefore unlikely that a ’standard’ modulation format will be the best choice for a wide range of transmission systems. More likely, the optimal choice of the modulation format will depend on such factors as the bit rate, fiber type, transmission distance and network architecture. We first consider the modulation formats of interest in the absence of electronic equalization. This makes it difficult to use POLMUX signaling as the interaction between PMD-related im- pairments and other transmission impairments complicates system design too much. Hence, the choice is reduced to duobinary, (partial-)DPSK or DQPSK modulation 1 . When we consider the OSNR requirement and nonlinear tolerance, which determine the transmission reach, the dif- ferences are significant and particulary poor for duobinary modulation. Duobinary is currently (beginning of 2008) the most widely deployed modulation format for 40-Gb/s transmission. But it is likely that, at least for long-haul transmission, it will be replaced by other options as soon as they become available. However, due to its low transponder complexity 40-Gb/s duobinary might be the best choice for regional networks (300 km - 800 km). DPSK and DQPSK both have a significantly lower OSNR requirement, with only a 1-dB ad- vantage for DPSK. However, this 1-dB advantage combined with a 2-3 dB advantage in non- linear tolerance makes DPSK the more suitable choice for long-haul transmission (1,000 km - 1,500 km). In comparison, the feasible transmission distance of 40-Gb/s DQPSK modulation is not likely to exceed 1,000 km. The poor filter tolerance of 40-Gb/s DPSK when used on a 50-GHz wavelength grid is its most significant drawback, in particular when a transmission link contains multiple OADM/PXC. In this case, either partial DPSK or DQPSK modulation is a bet- ter choice because of their higher narrowband filtering tolerance. A further concern for DPSK modulation is the smaller chromatic dispersion and PMD tolerance. It therefore requires both tunable dispersion compensation as well as PMD compensation for transmission over high-PMD fiber. DQPSK modulation has a better chromatic dispersion tolerance, but it is insufficient to negate the need for tunable dispersion compensation (generally 500 ps/nm for a 1-dB OSNR penalty). However, the higher PMD tolerance is a definite advantage of DQPSK modulation, which might be useful for PMD-limited transmission links. DQPSK modulation seems therefore the better choice for PMD-limited transmission links and/or systems with multiple OAMD/PXC nodes. However, the higher transponder complexity of a DQPSK transponder in comparison to DPSK might negate these advantages. For 100-Gb/s transponders, both duobinary and DPSK are difficult to realize due the high sym- bol rate. This puts stringent requirements on the bandwidth of the electrical components in the transponder. But more importantly, binary modulation formats do not provide a (significant) increase in spectral efficiency when the bit rate is increased from 40-Gb/s to 100-Gb/s. At the same time, the higher OSNR requirement will limit the feasible transmission distance. This com- bination of a limited spectral efficiency and feasible transmission distance, is likely to stall the deployment of such formats. DQPSK modulation, on the other hand, is a much more attractive option as it allows for a 1.0-b/s/Hz spectral efficiency as well as a reduction in the electrical 1 We assume here EDFA-only amplification, SSMF fiber with a 21-dB span loss, multiple cascaded OADM/PXC in the link and a 3-dB margin with respect to the FEC limit. Only those options are discussed that are likely to have a spectral efficiency of >0.8-b/s/Hz and a reach in excess of 500-km. 240 11.2. Robust electronic equalization bandwidth of the transponder components. But, similar as observed for 40-Gb/s transmission, the limited nonlinear tolerance and high OSNR requirement will restrict the feasible transmis- sion distance. For 100-Gb/s DQPSK, it is not likely to exceed ∼600 km in commercial systems. In addition, 100-Gb/s DQPSK modulation is not directly compatible with the 50-GHz channel spacing of most deployed long-haul transmission systems. 11.2 Robust electronic equalization We now consider the impact of electronic equalization on the choice of the modulation format. The main difference with the previously discussed modulation formats is that electronic equal- ization makes it feasible to use POLMUX signaling. On the other hand, the limited speed of state-of-the-art ADCs restrict the symbol rate to <30-Gbaud. This disqualifies the use of bi- nary modulation formats for electronic equalization at either 40-Gb/s or 100-Gb/s bit rates. We therefore consider the following options: direct detection DQPSK modulation combined with MSPE/MLSE and POLMUX-BPSK or POLMUX-QPSK modulation combined with a digital coherent receiver. The OSNR requirement is close to optimum in all three cases with a slight exception for DQPSK, as differential detection is required. For all three formats, the nonlinear tolerance can be im- proved through digital signal processing. However, (POLMUX-)DQPSK modulation is more vulnerable to phase perturbations as it has a more dense signal constellation. POLMUX-BPSK is therefore likely to have the highest nonlinear tolerance, which makes it the most suitable choice with respect to transmission reach. The improvement in chromatic dispersion and PMD tolerance is one of the main benefits of electronic equalization. For a digital coherent receiver, the chromatic dispersion and PMD tolerance depend only on the signal processing and can there- fore be nearly arbitrarily high. With a direct detection receiver, on the other hand, the chro- matic dispersion compensation is somewhat limited as the signal processing cannot compensate for arbitrary large distortions without penalty. The same is true for the PMD tolerance as no polarization-diversity receiver is used. However, both the chromatic dispersion and PMD toler- ance can be sufficiently high such that no tunable optical compensation is required in the receiver. The main drawback of all three formats is the high transponder complexity, which results from both multi-level modulation as well as the required electronic signal processing. For 40-Gb/s transponders all three modulation formats seem to be a suitable choice. POLMUX- QPSK has the advantage of a lower symbol rate, which reduces the requirements on the ADCs. On the other hand, it requires the most complex transmitter structure of all three modulation formats. When the difference in symbol rate is less significant, POLMUX-BPSK might be the best choice for long-haul transmission as the higher nonlinear tolerance improves transmission reach. DQPSK plus MSPE/MLSE can be an option in transmission links where it is desirable to have a polarization-insensitive receiver, for example in the presence of co-propagating 10-Gb/s NRZ-OOK channels. For a 100-Gb/s transponders, only POLMUX-QPSK seems to be a viable option as the symbol rate of both DQPSK and POLMUX-BPSK is too high to combine with digital signal processing. A transmission reach of ∼1000 km seems feasible with POLMUX- 241 Chapter 11. Outlook & recommendations Table 11.1: COMPARISON OF MODULATION FORMATS 2 . Spectral OSNR Nonlinear CD PMD Transponder Efficiency requirement tolerance 3 tolerance tolerance Complexity 4 OOK 88 8 88 8 - 9 duobinary 9 88 88 9 8 9 RZ-DPSK 8 9 99 8 - 8 partial DPSK - - - - - - DQPSK 99 - 8 9 9 88 DQPSK, 99 9 9 99 99 88 MSPE/MLSE POLMUX-BPSK, 99 99 99 999 999 88 coherent POLMUX-QPSK, 999 99 9 999 999 888 coherent QPSK modulation and a digital coherent receiver. This in turn indicates that for a 100-Gb/s data rate per wavelength, it becomes challenging to realize long-haul transmission even when the best possible solution is considered. A further improvement in transmission reach is only possible through an improvement in nonlinear tolerance. It is therefore likely that the compensation of nonlinear transmission impairments will become one of the most significant fields of research in the upcoming years. This can either be realized through nonlinear signal processing, in the transmitter and receiver, or through optical compensation along the link, for example with optical phase conjugation. In summary, the combination of multi-level modulation formats and digital signal processing has very advantageous properties to realize robust high-capacity transmission. However, this combination comes also at the cost of a higher transponder complexity. This could be alleviated through a higher level of optical integration, for example using InP photonic integrated circuits. We therefore conclude that the combination of multi-level modulation, digital signal processing and photonic integration, can enable robust and cost-effective optical transmission systems with the capacity to transport the data required for tomorrow’s Internet applications. 2 Partial DPSK is the state-of-the-art binary modulation format for 40-Gb/s transmission, and is therefore used here as the reference. 3 The nonlinear tolerance depends strongly on the bit rate and dispersion map, the denoted comparison is an estimation at a 40-Gb/s bit rate. 4 The transponder complexity denoted in the table does not include either optical dispersion or PMD compensa- tion, as this is different for each transmission link and not strictly determined by the choice in modulation format. 242 A List of symbols & abbreviations A.1 List of symbols ¸) Ensemble average var() Ensemble variance ∇ Vector differential operator α Fiber attenuation β n Group velocity of the n th order γ Fiber nonlinearly ˆ γ Path-averaged fiber nonlinearly ∆τ mean DGD ε 0 Permittivity of vacuum θ Optical polarization angle λ Optical wavelength λ 0 Zero-dispersion wavelength µ Statistical mean µ 0 Permeability of vacuum ¸ρ) Nonlinear phase noise σ Statistical variance τ PMD vector φ Optical phase φ SPM SPM-induced phase shift χ (n) Susceptibility of the n th order ψ Optical polarization phase 243 Appendix A. List of symbols & abbreviations ω Angular frequency ω 0 Optical carrier frequency A e f f Effective area of a fibers core B 0 Signal bandwidth (B 0 = 1/T 0 ) c Speed of light (c = 2.99792 10 8 m/s) D Dispersion parameter D local Local dispersion E(z, t) Optical field as a function of time and distance f Optical frequency f 0 Optical carrier frequency F Noise figure (optical amplifier) g R Raman gain coefficient G Gain (optical amplifier) h Planck’s constant (h = 6.626068 10 −34 m 2 kg/s) I In-phase tributary n Refractive index n 0 Linear refractive index n 2 Nonlinear refractive index n sp Spontaneous emission factor N 0 Noise power spectral density N span Number of spans in the transmission link P Optical power P 0 Optical input power PDλ Polarization dependent wavelength shift L Fiber length L D Normalized dispersion length L e f f Effective fiber length L span Fiber span length L W Walk-off length Q Quadrature tributary S Dispersion slope parameter t, T Time T 0 Symbol time v p Phase velocity V π Characteristic voltage of a modulator V pp Peak-to-peak voltage z Transmission distance 244 A.2. List of abbreviations A.2 List of abbreviations ADC Analog-to-digital converter AGC Automatic gain control Al 2 O 3 Aluminium Oxide AM Amplitude modulation APol Alternating polarization modulation ASE Amplitude spontaneous emission ASIC Application specific integrated circuit AWG Arrayed waveguide grating BER Bit-error-rate BERT Bit-error-rate tester BPF Band pass filter BSF Band selection filter BPSK Binary phase shift keying CDR Clock and data recovery CMA Constant modulus algorithm CPE Carrier phase estimation CR Clock recovery CRZ Chirped return-to-zero CSF Channel selection filter CSRZ Carrier-suppressed return-to-zero CW Continuous wave DD Decision-directed DCF Dispersion compensated fiber DCM Dispersion compensation unit DFB Distributed feedback DFF Data flip-flop DFG Difference frequency generation DGD Differential Group Delay DGE Dynamic gain equalizer DML Directly modulated laser DPSK Differential phase shift keying DOP Degree of polarization DQPSK Differential quadrature phase shift keying DSF Dispersion shifted fiber DSL Digital subscriber line DSO Digital Storage Oscilloscope EAM Electro-absorption modulator ECL External cavity laser EDFA Erbium doped fiber amplifier EO Eye opening EOP Eye opening penalty 245 Appendix A. List of symbols & abbreviations Er 3+ Erbium FBG Fiber Bragg grating FEC Forward error correction FIR Finite impulse response FFT Fast Fourier transform FWM Four wave mixing GaAs Gallium Arsenide GDR Group delay ripple GeO 2 Germanium Oxide GVD Group velocity dispersion IFWM Intra-channel four wave mixing InP Indium Phosphite INT Interleaver ISI Inter symbol interference ITU International telecommunication union IXPM Intra-channel cross polarization modulation JD Joint decision LiNbO 3 Lithium Niobate LMS Least mean square LSPS Loop-synchronous polarization scrambler MEMS Micro electro-mechanical system MLSE Maximum likelihood sequence estimation MSPE Multi-symbol phase estimation MZM Mach-zehnder modulator MZDI Mach-Zehnder delay interferometer NRZ Non-return-to-zero NZDSF Non-zero dispersion shifted fiber OADM Optical add-drop multiplexer OH − Hydroxyl OPC Optical phase conjugation OOK On-off keying OSNR Optical signal-to-noise ratio OTN Optical transport network PBF Pump block filter PBS Polarization beam splitter PC Polarization controller PCD Polarization chromatic dispersion PDF Probability density function PDL Polarization dependent loss PDM Polarization division multiplexing PM Phase modulator PMD Polarization mode dispersion POLMUX Polarization multiplexing POLSK Polarization shift keying 246 A.2. List of abbreviations PPLN Periodically-poled lithium Niobate PRBS Pseudo random bit sequence PRQS Pseudo random quaternary sequence PSBT Phase shaped binary transmission PSD Power spectral density PSK Phase shift keying PSP Principle state of polarization PXC Photonic cross connect QPM Quasi phase matching QPSK Quadrature phase shift keying RIN Relative intensity noise RX Receiver RZ Return-to-zero SBS Stimulated Brillouin scattering SHG Second harmonic generation SiO 2 Silicon Oxide SOP State of polarization SOPMD Second order polarization mode dispersion SPM Self phase modulation SRS Stimulated Raman scattering SSMF Standard single mode fiber TDC Tunable dispersion compensator TX Transmitter VOA Variable optical attenuator WDM Wavelength division multiplexing WSS Wavelength selective switch XPIC Cross polarization interference canceler XPM Cross phase modulation XPolM Cross Polarization modulation 247 Appendix A. List of symbols & abbreviations 248 B Definition of the Q-factor and eye open- ing penalty The experimental results discussed in this thesis use the bit-error-ratio (BER) to quantify trans- mission impairments and pulse degradations. The BER quantifies the fraction of errors that occurred in a given time interval ∆T, according to, BER = k(∆T) K(∆T) , (B.1) where k(∆T) are the bit errors counted during the time interval ∆T and K(∆T) is the total number of received bits during this interval. The BER is normally measured as a function of the OSNR, in order to define the required OSNR for a certain BER. The impact of isolated transmission impairments, such as chromatic dispersion or DGD, can then be quantified as a function of the required OSNR for a chosen BER. The impact of isolated transmission impairments in a long-haul WDM transmission system is more difficult to quantify. The OSNR is normally determined by dividing signal and ASE power, where the ASE power is measured at a wavelength close to the signal. The more accurate mea- surement is to take the average of the noise power at a slightly higher and lower wavelengths, as this corrects for a (linear) tilt in the spectrum. However, with co-propagating WDM channels it is difficult to quantify the noise level. As a result, the OSNR cannot easily be measured with high accuracy using this method. We therefore use the BER/Q-factor to quantify the performance in the long-haul WDM transmission experiments. 249 Appendix B. Definition of the Q-factor and eye opening penalty B.1 Q-factor The Q-factor is related to the signal-to-noise ratio at the decision circuit expressed in terms of the photocurrent [445]. It is defined as the distance from the decision threshold to the mean photocurrent divided through the standard deviation, e.g. Q 0 = µ 0 −I σ 0 (B.2) Q 1 = µ 1 −I σ 1 where µ 0 and µ 1 are the mean photocurrents of the marks (’1’s) and spaces (’0’s) level, respec- tively, and σ 0 / σ 1 is the standard deviation. This is valid independently of the specific distribution of the noise probability density functions. When a hard-decision threshold receiver takes a binary decision on a signal degraded by ASE, the optimum decision threshold I D is defined as, I D = σ 0 µ 1 +σ 1 µ 0 σ 0 +σ 1 , (B.3) which is visualized in Figure B.1a. The Q-factor can then be defined as, Q = µ 1 −I D σ 1 = I D −µ 0 σ 0 . (B.4) This can be written independently of the optimum threshold I D by combining Equations B.3 and B.4, Q = µ 1 −µ 0 σ 0 +σ 1 . (B.5) The photocurrent of an ideal photodiode has a Chi-square distribution when the amplitude of the ASE noise is Gaussian distributed. This is a result of the quadratic relation between photocurrent and incident optical power. However, for a direct detected OOK modulated signal the Chi-square distribution can be approximated with a Gaussian distribution. This approximation is valid under certain conditions, such as a high enough OSNR (>10 dB) and low ISI. The Q-factor can then be used to approximate the BER, as shown by Bergano et. al. in [445]. BER ≡ 1 2 er f c( Q √ 2 ) ≈ 1 √ 2πQ exp(− Q 2 2 ), (B.6) where er f c() is the complementary error function and the approximation is valid for a BER lower than 10 −2 . For direct detected phase modulated formats, Bosco and Poggiolini showed in [446] that a Gaus- sian approximation of the Chi-square distributed photocurrent is not accurate. This results from 250 B.2. Eye opening penalty the phase demodulation with an MZDI and subsequent balanced detection, which affects the probability density distribution of the noise. We note that the Q-factor can still be defined for phase modulated formats, but it is not accurate to compute the BER using Equation B.6. Al- ternatively, BER estimation for phase modulated formats is possible through the Eigenfunction Expansion Method [288] or using the Karhunen–Lo´ eve approximation [299]. Both BER estima- tion approaches have been used in the analytical simulations of this thesis. The Q-factor is often defined in logarithmic units, Q(dB) = 20 log 10 (Q). (B.7) Using Q(dB) as an indication of transmission performance has the advantage that it is propor- tional to the OSNR. Hence, a 1 dB increase in OSNR will result in a ∼1 dB increase in Q(dB). This property is used to express the system margin in long-haul transmission systems. When a transmission operates at a 3 dB margin with respect to the FEC limit, this implies that either the Q(dB) or OSNR can be lowered by 3 dB before the FEC limit is reached. Figure B.1b visual- izes the relation between log(BER) and Q(dB). We note that Equation B.6 is still valid for phase modulated formats, and can be used to compute the Q-factor based on a known BER. This is used in this thesis to compute Q(dB) for D(Q)PSK modulation, which gives an indication of the system margin. I 0 I 1 I D ‘0’s ‘1’s Photocurrent (mA) P r o b a b i l i t y (a) -12 -10 -8 -7 -6 -5 -4 -3 -2 6 8 10 12 14 16 18 log(BER) Q ( d B ) (b) Figure B.1: (a) Definition of the optimum decision threshold and (b) relation between Q and BER. B.2 Eye opening penalty In the analytical simulations, the eye opening penalty (EOP) is used as a measure besides the BER to qualify signal impairments. The EOP is not dependent on the OSNR but it is computed only from the shape of the eye diagram. It has therefore the advantage that it can be computed 251 Appendix B. Definition of the Q-factor and eye opening penalty with relatively low computational effort. Several definitions of the EOP exist in literature, but in this thesis we defined it as, EOP = 2 mean EO , (B.8) where mean defines the average value of all lines in the eye diagram and EO is the eye opening. The definition of the eye opening is the largest square box with a width equal to 20% of the symbol period that fits into the eye diagram. The 20% eye opening width is used here to account for signal jitter. Figure B.1 graphically depicts the definition of the EOP, where T 0 is the bit interval. The EOP is not always a good approximation of the OSNR penalty. In particular in the presence of ISI, such as chromatic dispersion or PMD, it can be a factor of 2-3 smaller than the OSNR penalty [330]. The EOP is usually defined in logarithmic units as, EOP(dB) = 10 log 10 (EOP). (B.9) The EOP(dB) is zero for an ideal NRZ-OOK eye diagram, but it can be lower than zero for other modulation formats. In particular RZ pulse carving lowers the EOP below zero. In the comparison between modulation formats, such as for example in Chapter 8, the EOP is therefore normalized with respect to the EOP in the absence of transmission impairments We note that the EOP can be computed either from the optical eye diagram (before the photo- diode) or the electrical eye diagram. The EOP based on the electrical eye diagram is a more realistic definition as it includes the impact of narrowband electrical filtering. For phase mod- ulated formats, the necessity to include balanced detection limits the EOP computation to the electrical eye diagram. Time (ps) S i g n a l a m p l i t u d e ( m A ) mean 0.2T 0 T 0 Eye opening (EO) Figure B.2: Definition of the EOP and its relation to the shape of the (electrical) eye diagram. 252 C Asymmetric 3 x 3 coupler for coherent detection As discussed in Chapter 10, a coherent receiver requires a 90 o hybrid for detection of the in-phase and quadrature components. In this thesis this has been realized using an asymmetric 3x3 fiber coupler. In this appendix we will give the proof that an asymmetric 3x3 fiber coupler can be used as a 90 o Hybrid. The configuration of a coherent receiver using an asymmetric fiber coupler is depicted, for a single polarization, in C.1. The two inputs signals of the fiber coupler consist of the received optical signal and the LO laser. LO ( ) x t 2 ( ) i t 1 ( ) y t 1 ( ) i t 1:2:2 coupler 2 ( ) y t PD Figure C.1: Coherent receiver using an asymmetric 3x3 coupler with 2:2:1 output ratio The input vector x can thus be defined as, x(t) = _ √ P s exp( j[ω 0 t +ϕ(t)]) √ P LO exp( j[ω 0 t +ϕ LO ]) _ , (C.1) where we assume that the information is carried in the optical phase ϕ(t) and both the received signal and local oscillator have the same carrier frequency ω 0 . The output vector y of the asym- 253 Appendix C. Asymmetric 3 x 3 coupler for coherent detection metric 3x3 coupler is now defined by multiplication of the input vector with a 3x3 scattering matrix S. The elements of S can be written as, S ik = s ik e jφ ik , (C.2) where i and k are the matrix indexes. The scattering matrix derivation for a generalized 3x3 coupler has been analyzed by Pietzsch in [447]. We now follow this derivation to compute the scattering matrix of an asymmetric coupler with a 1 : 2 : 2 output ratio. For simplicity, we assume the coupler to be lossless. In this case the dissipated power is zero and the scattering matrix has to be unitary, i.e., 3 ∑ k=1 s 2 ik = 3 ∑ i=1 s 2 ik = 1. (C.3) The amplitude coefficients of S are therefore directly defined by the output ratio. For a 1 : 2 : 2 output ratio we then find, s 2 = ⎛ ⎝ 0.2 0.4 0.4 0.4 0.2 0.4 0.4 0.4 0.2 ⎞ ⎠ . (C.4) By variation of the optical path lengths in and out of the fiber coupler it can be shown that five of the nine angle coefficients can be chosen arbitrarily (see for example also [448]). Using the normalization of the scattering matrix given in [447], this results in, φ 12 = φ 21 , φ 23 = φ 32 , φ 11 = φ 22 = φ 33 = 0 . (C.5) The remaining amplitude coefficients of S can be computed directly out of the amplitude coeffi- cients, cos(φ ik −φ il −φ jk +φ jl ) = s 2 ml s 2 mk −s 2 jl s 2 jk −s 2 il s 2 ik 2s il s ik s jl s jk , (C.6) where i ,= j ,= m and l ,= k. Solving this set of equations for a 1 : 2 : 2 output ratio results in the following scattering matrix S, S = 1 √ 5 ⎛ ⎜ ⎜ ⎝ 1 √ 2exp( j π 4 ) √ 2exp( j π 2 ) √ 2exp( j π 4 ) 1 √ 2 − √ 2 √ 2 1 ⎞ ⎟ ⎟ ⎠ . (C.7) The output vector y(t) follows now out of y(t) = Sx(t), y(t) = 1 √ 5 ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ √ P s exp( j[ω 0 (t) +ϕ(t)]) + √ 2P LO exp( j[ω 0 (t) +ϕ LO + π 4 ]) √ 2P s exp( j[ω 0 (t) +ϕ(t) + π 4 ]) + √ P LO exp( j([ω 0 (t) +ϕ LO ]) √ 2P s exp( j[ω 0 (t) +ϕ(t) +π]) + √ 2P LO exp( j[(ω 0 (t) +ϕ LO ]) ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ . (C.8) 254 The third fiber output of the coupler can be detected with a third photodiode and used to cancel out the DC term √ P s . But in the work described in this thesis the third output is not used and the DC term √ P s is canceled out using a high LO to signal ratio P LO /P s . The current after an ideal photodiode is then given by i(t) =[y(t)y ∗ (t)[, i(t) = 1 5 _ P s +2P LO + √ 2P LO P s [exp( j[ϕ(t) −ϕ LO − π 4 ]) +exp(−j[ϕ(t) −ϕ LO − π 4 ])] 2P s +P LO + √ 2P LO P s [exp( j[ϕ(t) −ϕ LO + π 4 ]) +exp(−j[ϕ(t) −ϕ LO + π 4 ])] _ , where we neglect all high-frequency terms at the carrier frequency. 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(ECOC), Cannes, France, Sep. 2006, paper Mo4.2.4. 280 List of publications Invited contributions c1. D. van den Borne, S. L. Jansen, E. Gottwald, E. D. Schmidt, G. D. Khoe, and H. de Waardt, ”DQPSK Modulation for Robust Optical Transmission”, in Proc. Optical Fiber Commun. Conf. (OFC), San Diego, USA, Feb. 2008, paper OMQ1. c2. S. L. Jansen, I. Morita, T. C. W. Schenk, D. van den Borne, and H. Tanaka, ”Optical OFDM - A Candidate for Future Long-Haul Optical Transmission Systems”, in Proc. Optical Fiber Commun. Conf. (OFC), San Diego, USA, Feb. 2008, paper OMU3. c3. M. S. Alfiad, D. van den Borne, A. Napoli, F. N. Hauske, A. M. J. Koonen, and H. de Waardt, ”A 10.7-Gb/s DPSK Receiver with 4000-ps/nm Dispersion Tolerance Using a Shortened MZDI and 4-State MLSE”, in Proc. Optical Fiber Commun. Conf. (OFC), San Diego, USA, Feb. 2008, paper OWT3. c4. C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. D. Schmidt, T. Wuth, J. Geyer, E. de Man, G. D. Khoe, and H. de Waardt, ”Coherent Equalisation and POLMUX-RZDQPSK for Robust 100GE Trans- mission”, Accepted for invited publication in J. Lightwave Technol., Jan. 2008. c5. S. L. Jansen, D. van den Borne, P. M. Krummrich, S. H. Spaelter, H. Suche, W. Sohler, G. D. Khoe, H. de Waardt, I. Morita, and H. Tanaka, ”Overview of important results concerning the application of optical phase conjugation to increase system robustness”, in Proc. Asia-Pacific Optical Commun. Conf. (APOC), Wuhan, China, Nov. 2007, paper 6783-37. c6. D. van den Borne, T. Duthel, C. R. S. Fludger, E-D. Schmidt, T. Wuth, C. Schulien, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Electrical PMD Compensation in 43-Gb/s POLMUX-NRZ-DQPSK enabled by Coherent Detection and Equalization”, in Proc. Eur. Conf. Optical Commun. (ECOC), Berlin, Germany, Sep. 2007, paper We8.3.1. c7. D. van den Borne, S. L. Jansen, E. Gottwald, P.M. Krummrich, G. D. Khoe, and H. de Waardt, ”1.6-b/s/Hz Spectrally Efficient Transmission Over 1,700 km of SSMF Using 40 x 85.6-Gbit/s POLMUX-RZ-DQPSK”, J. Lightwave Technol., Vol. 25, No 1, pp. 222-232, Jan. 2007. c8. S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Sp¨ alter, H. Suche, W. Sohler, G. D. Khoe, and H. de Waardt, ”Phase Conjugation for Increased System Robustness”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Feb. 2006, paper OtuK3. c9. S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabr` o, H. Suche, P. M. Krummrich, W. Sohler, G. D. Khoe, and H. de Waardt, ”Optical Phase Conjugation for Ultra Long-haul Phase Shift Keyed Transmission”, J. Lightwave Technol., Vol. 24, No 1, pp. 54-64, Jan. 2006. c10. S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Sp¨ alter, G. D. Khoe, and H. de Waardt, ”Long- Haul DWDM Transmission Systems Employing Optical Phase Conjugation”, IEEE J. Sel. Topics Quantum Electron., Vol. 12, No. 4, pp. 505-520, Jul.-Aug. 2006. 281 Appendix C. List of publications Journal Papers c11. D. van den Borne, V. Veljanovski, U. Gaubatz, C. Paquet, Y. Painchaud, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Bit Pattern Dependence in Optical DQPSK Modulation”, Electron. Lett., Vol. 43, No. 22, pp. 1223-1225, Oct. 2007. c12. D. van den Borne, V. Veljanovski, U. Gaubatz, C. Paquet, Y. Painchaud, E. Gottwald, G. D. Khoe, and H. de Waardt, ”42.8-Gb/s RZ-DQPSK Transmission with FBG-based in-line Dispersion Compensation”, IEEE Photon. Technol. Lett., Vol. 19, No. 14, pp. 1069-1071, Jul. 2007. c13. D. van den Borne, N. E. Hecker-Denschlag, G. D. Khoe, and H. de Waardt, ”PMD induced transmission penalties in polarization multiplexed transmission”, J. Lightwave Technol., Vol. 23, No. 12, pp. 4004-4015, Dec. 2005. c14. S. L. Jansen, H. Chayet, E. Granot, S. Ben Ezra, D. van den Borne, P. M. Krummrich, D. Chen, G. D. Khoe, and H. de Waardt, ”Wavelength conversion of a 40Gbit/s NRZ signal across the entire C band by an asymmetric Sagnac loop”, IEEE Photon. Technol. Lett., Vol. 17, No. 10, pp. 2137-2139, Oct. 2005. c15. S. L. Jansen, D. van den Borne, C. Climent, S. Sp¨ alter, P. M. Krummrich, G. D. Khoe, and H. de Waardt, ”Reduction of Gordon-Mollenauer phase noise by mid-link spectral inversion”, IEEE Photon. Technol. Lett., Vol. 17, No. 4, pp. 923-925, Apr. 2005. c16. D. van den Borne, S. L. Jansen, N. E. Hecker-Denschlag, G. D. Khoe, and H. de Waardt, ”Reduction of Nonlinear Penalties Through Polarization Interleaving in 2x10 Gb/s Polarization-Multiplexed Transmission”, IEEE Photon. Technol. Lett., Vol. 17, No. 6, pp. 1337-1339, Jun. 2005. c17. D. van den Borne, S. L. Jansen, G. D. Khoe, H. de Waardt, S. Calabr` o, P. M. Krummrich, W. Schairer, and C.- J. Weiske, ”Inter-channel nonlinear transmission penalties in polarization-multiplexed 2x10Gbit/s DPSK transmission”, Opt. Lett., Vol. 30, No. 12, pp. 1443-1445, Jun. 2005. c18. D. van den Borne, N. E. Hecker-Denschlag, G. D. Khoe, and H. de Waardt, ”PMD and nonlinearity induced penalties on polarization multiplexed transmission”, IEEE Photon. Technol. Lett., Vol. 16, No. 9, pp. 2174-2176, Sep. 2004. International Peer-reviewed Conferences c19. M. S. Alfiad, D. van den Borne, F. Hauske, A. Napoli, B. Lankl, T. Koonen, and H. de Waardt, ”Disper- sion Tolerant 21.4-Gb/s DQPSK Using Simplified Gaussian Joint-Symbol MLSE”, in Proc. Optical Fiber Commun. Conf. (OFC), San Diego, USA, Feb. 2008, paper OThO3. c20. F. N. Hauske, J. C. Geyer, M. Kuschnerov, K. Piyawanno, T. Duthel, C. R. S. Fludger, D. van den Borne, E.-D. Schmidt, B. Spinnler, H. de Waardt, and B. Lankl, ”Optical Performance Monitoring from FIR Filter Coefficients in Coherent Receivers”, in Proc. Optical Fiber Commun. Conf. (OFC), San Diego, USA, Feb. 2008, paper OThW2. c21. D. van den Borne, C. R. S. Fludger, T. Duthel, T. Wuth, E-D. Schmidt, C. Schulien, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Carrier phase estimation for coherent equalization of 43-Gb/s POLMUX-NRZ-DQPSK transmission with 10.7 Gb/s NRZ neighbors”, in Proc. Eur. Conf. Optical Commun. (ECOC), Berlin, Germany, Sep. 2007, paper We8.3.1. c22. T. Duthel, C. R. S. Fludger, D. van den Borne, C. Schulien, E-D. Schmidt, T. Wuth, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Impairment tolerance of 111Gbit/s POLMUX-RZ-DQPSK using a reduced complexity coherent receiver with a T-spaced equaliser”, in Proc. Eur. Conf. Optical Commun. (ECOC), Berlin, Germany, Sep. 2007, paper Mo1.3.2. 282 c23. M. S. Alfiad, D. van den Borne, F. N. Hauske, A. Napoli, A. M. J. Koonen, and H. de Waardt, ”Robust Detection of 10.7-Gb/s DPSK Using Joint Decision Maximum Likelihood Sequence Estimation”, in Proc. Eur. Conf. Optical Commun. (ECOC), Berlin, Germany, Sep. 2007, paper Th9.1.2. c24. D. van den Borne, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Pseudo-Random Sequences for Modeling of Quaternary Modulation Formats”, in Proc. Optoelectronics Commun. Conf. (OECC), Jul. 2007, paper 13P-10. c25. D. van den Borne, T. Duthel, C. R. S. Fludger, E-D. Schmidt, T. Wuth, C. Schulien, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Coherent Equalization versus Direct Detection for 111 Gb/s Ethernet Transport”, in Proc. LEOS Summer Topicals, Jul. 2007, paper MA2.4. c26. C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E-D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, ”10 x 111 Gbit/s, 50 GHz spaced, POLMUX-RZ-DQPSK transmission over 2375 km employing coherent equalization”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Mar. 2007, Post-Deadline paper PDP22. c27. D. van den Borne, V. Veljanovski, E. de Man, U. Gaubatz, C. Zuccaro, C. Paquet, Y. Painchaud, S. L. Jansen, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Cost-effective 10.7 Gbit/s Long-Haul Transmission using Fiber Bragg Gratings for In-line Dispersion Compensation”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Mar. 2007, paper OThS5. c28. S. L. Jansen, R. H. Derksen , C. Schubert, X. Zhou, M. Birk, C. J. Weiske, M. Bohn, D. van den Borne, P. M. Krummrich, M. M¨ oller, F. Horst, B. J. Offrein, H. de Waardt, G. D. Khoe, and A. Kirst¨ adter, ”107-Gb/s full-ETDM transmission over field installed fiber using vestigial sideband modulation”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Mar. 2007, paper OWE3. c29. S. L. Jansen, I. Morita, D. van den Borne, G. D. Khoe, H. de Waardt, and P. M. Krummrich, ”Experimental study of XPM in 10-Gbit/s NRZ pre-compensated transmission systems”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Mar. 2007, paper OThS6. c30. S. C. J. Lee, F. Breyer, S. Randel, B. Spinnler, I. L. Lobato Polo, D. van den Borne, J. Zeng, E. de Man, H. P. A. van den Boom, and A. M. J. Koonen, ”10.7 Gbit/s Transmission over 220 m Polymer Optical Fiber using Maximum Likelihood Sequence Estimation”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Mar. 2007, paper OMR2. c31. V. Veljanovski, D. van den Borne, W. Schairer, and N. Hanik, ”Equalisation of Fibre Bragg Gratings’ Group Delay Ripple by means of Maximum Likelihood Sequence Estimation”, in Proc. IEEE/LEOS Annual Meet- ing, Montreal, Quebec, Canada, Nov. 2006, paper ThH4. c32. D. van den Borne, S. L. Jansen, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Lumped Dispersion Manage- ment in Long-Haul 42.8-Gbit/s RZ-DQPSK Transmission”, in Proc. Eur. Conf. Optical Commun. (ECOC), Cannes, France, Sep. 2006, paper Mo3.2.2. c33. S. L. Jansen, D. van den Borne, P. M. Krummrich, H. Suche, W. Sohler, G. D. Khoe, and H. de Waardt, ”Transmission of 42.8-Gbit/s RZ-DQPSK over 42x94.5-km SSMF Spans using Optical Phase Conjugation and EDFA only Amplification”, in Proc. Eur. Conf. Optical Commun. (ECOC), Cannes, France, Sep. 2006, paper Mo3.2.3. c34. I. L. Lobato Polo, D. van den Borne, E. Gottwald, H. de Waardt, and E. Brinkmeyer, ”Comparison of Maximum Likelihood Sequence Estimation equalizer performance with OOK and DPSK at 10.7 Gb/s”, in Proc. Eur. Conf. Optical Commun. (ECOC), Cannes, France, Sep. 2006, paper We2.5.3. c35. D. van den Borne, S. L. Jansen, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Optical Filtering tolerances of 42.8-Gbit/s RZ-DQPSK Modulation”, in Proc. Optoelectronics Commun. Conf. (OECC), Kaohsiung, Taiwan, Jul. 2006, paper 5F3-5. c36. D. van den Borne, S. L. Jansen, E. Gottwald, P. M. Krummrich, G. D. Khoe, and H. de Waardt, ”1.6-b/s/Hz Spectrally Efficient 40 x 85.6-Gb/s Transmission Over 1,700 km of SSMF Using POLMUX-RZ-DQPSK”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Feb. 2006, Post-Deadline paper PDP34. 283 Appendix C. List of publications c37. D. van den Borne, S. L. Jansen, E. Gottwald, G. D. Khoe, and H. de Waardt, ”A Comparison between Multi-level Modulation Formats: 21-4Gbit/s RZ-DQPSK and POLMUX-RZ-DPSK”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Feb. 2006, paper OThR2. c38. D. van den Borne, S. L. Jansen, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Line Optimization in Long- Haul Transmission Systems with 42.8-Gbit/s RZ-DQPSK modulation”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Feb. 2006, paper OFD2. c39. D. van den Borne, S. Calabr` o, S. L. Jansen, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Differential Quadra- ture Phase Shift Keying with close to Homodyne Performance based on Multi-Symbol Phase Estimation”, in Proc. IEE seminar on electrical signal processing in optical communications, London, United Kingdom, Dec. 2006, paper 12. c40. S. L. Jansen, D. van den Borne, A. Sch¨ opflin, E. Gottwald, P. M. Krummrich, G. D. Khoe, and H. de Waardt, ”26x42.8-Gbit/s DQPSK Transmission with 0.8-bit/s/Hz Spectral Efficiency over 4,500-km SSMF using Optical Phase Conjugation”, in Proc. Eur. Conf. Optical Commun. (ECOC), Glasgow, United Kingdom, Sep. 2005, Post-Deadline paper Th4.1.5. c41. S. L. Jansen, D. van den Borne, P. M. Krummrich, G. D. Khoe, and H. de Waardt, ”Experimental Comparison of Optical Phase Conjugation and DCF Aided DWDM 2x10.7Gbit/s DQPSK Transmission”, in Proc. Eur. Conf. Optical Commun. (ECOC), Glasgow, United Kingdom, Sep. 2005, paper Th2.2.3. c42. M. Serbay, C. Wree, A. Sch¨ opflin, C.-J. Weiske, D. van den Borne, S. L. Jansen, G. D. Khoe, P. M. Krumm- rich, P. Leisching, and W. Rosenkranz, ”Coding Gain of FEC encoded 21.42Gb/s RZ-D(Q)PSK Using an Electrical Differential Quaternary Precoder”, in Proc. Eur. Conf. Optical Commun. (ECOC), Glasgow, United Kingdom, Sep. 2005, paper We4.P.10. c43. S. Calabr` o, D. van den Borne, S. L. Jansen, G. D. Khoe, and H. de Waardt, ”Improved detection of differ- ential phase shift keyed transmission through multi-symbol phase estimation”, in Proc. Eur. Conf. Optical Commun. (ECOC), Glasgow, United Kingdom, Sep. 2005, paper We4.P.118. c44. S. L. Jansen, D. van den Borne, P. M. Krummrich, G. D. Khoe, and H. de Waardt, ”Nonlinear phase noise degradation in ultra-long haul 2x10Gbit/s DQPSK transmission”, in Proc. Optoelectronics Commun. Conf. (OECC), Seoul, South Korea, Jul. 2005, Post-Deadline paper PDP04. c45. S. L. Jansen, S. Calabr` o, B. Spinnler, D. van den Borne, P. M. Krummrich, G. D. Khoe, and H. de Waardt, ”Nonlinear Phase Noise Reduction in DPSK Transmission by Optical Phase Conjugation”, in Proc. Opto- electronics Commun. Conf. (OECC), Seoul, South Korea, Jul. 2005, paper 6B1-3. c46. S. L. Jansen, D. van den Borne, C. Climent, M. Serbay, C.-J. Weiske, H. Suche, P. M. Krummrich, S. Sp¨ alter, S. Calabr´ o, N. E. Hecker-Denschlag, P. Leisching, W. Rosenkranz, W. Sohler, G. D. Khoe, T. Koonen, and H. de Waardt, ”10,200km 22x2x10Gbit/s RZ-DQPSK Dense WDM Transmission without Inline Disper- sion Compensation through Optical Phase Conjugation”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Feb. 2005, Post-Deadline paper PDP28. c47. S. L. Jansen, D. van den Borne, C. Climent, S. Sp¨ alter, P. M. Krummrich, G. D. Khoe, and H. de Waardt, ”Reduction of nonlinear phase noise by mid-link spectral inversion in a DPSK based transmission system”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Feb. 2005, paper OThO5. c48. D. van den Borne, S. L. Jansen, G. D. Khoe, H. de Waardt, S. Calabr´ o, and N. E. Hecker-Denschlag, ”Po- larization interleaving to reduce inter-channel nonlinear penalties in polarization multiplexed transmission”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Feb. 2005, paper JWA41. c49. D. van den Borne, N. E. Hecker-Denschlag, G. D. Khoe, and H. de Waardt, ”Cross phase modulation induced depolarization penalties in 2x10Gbit/s polarization-multiplexed transmission”, in Proc. Eur. Conf. Optical Commun. (ECOC), Stockholm, Sweden, Sep. 2004, paper Mo4.5.5. c50. B. Spinnler, N. Hecker-Denschlag, S. Calabro, M. Herz, C.J. Weiske, E. D. Schmidt, D. van den Borne, G. D. Khoe, and H. de Waardt, R. Griffen, S. Wadsworth, ”Nonlinear Tolerance of differential phase shift keying modulated signals reduced by XPM”, in Proc. Optical Fiber Commun. Conf. (OFC), Anaheim, USA, Feb. 2004, paper TuF3. 284 Local Conferences c51. D. van den Borne, V. Veljanovski, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Fiber Bragg Gratings for In line Dispersion Compensation in Cost effective 10.7 Gbit/s Long-Haul Transmission”, in Proc. IEEE/LEOS BENELUX Annual Symposium, Eindhoven, pp. 17-20, Dec. 2006. c52. S. C. J. Lee, F. Breyer, S. Randel, B. Spinnler, I. L. Lobato Polo, D. van den Borne, J. Zeng, E. de Man, H. P. A. van den Boom, and A. M. J. Koonen, ”Performance of Maximum Likelihood Sequence Estimation in 10 Gb/s Transmission Systems with Polymer Optical Fiber”, In Proc. IEEE/LEOS BENELUX Annual Symposium, Eindhoven, pp. 177-180, Dec. 2006. c53. D. van den Borne, S. L. Jansen, E. Gottwald, P. M. Krummrich, P. Leisching, G. D. Khoe, and H. de Waardt, ”A robust modulation format for 42.8-Gbit/s long-haul transmission: RZ-DPSK or RZ-DQPSK?”, in ITG Fachbericht 193, 7th ITG-fachtagung on Photonic Networks, pp. 113-120, Leipzig, Germany, Apr. 2006. c54. S. L. Jansen, D. van den Borne, P. M. Krummrich, G. D. Khoe, and H. de Waardt, ”Compensation of nonlin- ear phase noise impairments through optical phase conjugation in long-haul transmission systems”, In Proc. IEEE/LEOS BENELUX Annual Symposium, pp. 129-132, Mons, Belgium, Dec. 2005. c55. D. van den Borne, S. L. Jansen, E. Gottwald, G. D. Khoe, and H. de Waardt, ”Inter-channel Depolarization Impairments in 21.4-Gbit/s POLMUX OOK and DPSK Transmission”, In Proc. IEEE/LEOS BENELUX Annual Symposium, pp. 133-136, Mons, Belgium, Dec. 2005. 285 Appendix C. List of publications 286 Samenvatting Sinds de introductie van de eerste glasvezelcommunicatiesystemen is de transmissiecapaciteit voortdurend toegenomen en zijn de kosten per verzonden bit continue verlaagd. De kern van het wereldwijde telecommunicatienetwerk bestaat tegenwoordig uit golflengte gestapelde (wave- length division multiplexed, WDM) optische langeafstandstransmissiesystemen. WDM is een aantrekkelijke technologie omdat het een hoge spectrale effici¨ entie mogelijk maakt, i.e. de ef- fici¨ entie waarmee de beschikbare bandbreedte van een fiber wordt benut. Commerci¨ ele WDM transmissiesystemen gebruiken tegenwoordig maximaal 80 kanalen met een 50-GHz kanaalaf- stand en 10-Gb/s of soms 40-Gb/s per golflengte kanaal. Dit vertaalt zich in een spectrale ef- fici¨ entie van 0.2 tot 0.8-b/s/Hz. Echter, op basis van de voorspelde toename van het dataverkeer zal het binnen niet al te lange tijd nodig zijn om een volgende generatie van transmissiesystemen te ontwikkelen. Deze systemen zullen naar verwachting 40 Gb/s of 100 Gb/s per kanaal trans- porteren met een spectrale effici¨ entie tussen 0.8 tot 2.0-b/s/Hz. Daarnaast is het een vereiste dat de tolerantie ten opzichte van signaalverstoringen vergelijkbaar is met de huidige generatie van transmissiesystemen. Van oudsher maken optische transmissiesystemen gebruik van intensiteit gemoduleerde signalen. Voor de volgende generatie van transmissiesystemen is intensiteitsmodulatie echter ongeschikt. Het vereist doorgaans een te grote kanaalafstand, heeft een hoge signaal-ruis verhouding (optical signal-to-noise ratio, OSNR) nodig en genereert sterke niet-lineaire verstoringen op de trans- missielijn. De transmissiesystemen die momenteel worden ontwikkeld, maken daarom meestal gebruik van differenti¨ ele fasemodulatie (differential phase-shift keying, DPSK). Vergeleken met intensiteitsmodulatie, genereert DPSK minder niet-lineaire verstoringen en voldoet een lagere OSNR in de ontvanger. Maar door de hoge symboolsnelheid (e.g. 40 Gbaud) is de robuus- theid ten opzichte van de belangrijkste lineaire verstoringen, namelijk chromatische dispersie en polarisatiemode dispersie (polarization mode dispersion, PMD), nog steeds beperkt. Het eerste gedeelte van deze dissertatie behandelt modulatieformaten die het mogelijk maken om de capaciteit en transmissieafstand van optische transmissiesystemen verder te verbeteren. Zo kunnen niet-binaire modulatieformaten met meer dan twee signaalniveaus worden gebruikt. Deze formaten zijn dispersie bestendig en gaan daarnaast zuinig om met optische bandbreedte (en maken daardoor een hogere spectrale effici¨ entie mogelijk). In het bijzonder 40-Gb/s dif- ferenti¨ ele kwadratuur fasemodulatie (differential quadrature phase shift keying, DQPSK) wordt uitgebreid besproken in deze dissertatie. 40-Gb/s DQPSK moduleert 2 bits per symbool en ben- 287 Appendix C. Samenvatting odigd daardoor slechts een symboolsnelheid van 20-Gbaud. Niet-binaire modulatie heeft echter zowel voor- als nadelen. Het verbetert de tolerantie ten opzichte van chromatische dispersie en PMD, maar resulteert ook in een meer complexe zender en ontvanger structuur, een verhoging van de benodigde OSNR en een lagere tolerantie ten opzichte van niet-lineaire verstoringen. We bespreken de mogelijkheid om langeafstandstransmissie te realiseren met 40-Gb/s DQPSK modulatie en laten zien dat een maximale afstand van 2,800-km kan worden overbrugd met 0.8-b/s/Hz spectrale effici¨ entie. Gecombineerd met optische fase omkering (optical phase conju- gation) kan dit verder worden verbeterd en is het mogelijk om een transmissieafstand van 4,500- km te overbruggen. We beschrijven daarnaast de combinatie van 40-Gb/s DQPSK modulatie met verschillende dispersie compensatie technieken, zoals de concentratie van dispersie compensatie op slechte enkele punten langs de transmissielijn en dispersie compenserende fiber-Bragg grat- ings. In het tweede deel van deze dissertatie komen polarisatie gestapelde (POLMUX) signalen aan de orde. Deze techniek moduleert de beide orthogonale polarisaties in een fiber onafhankelijk van elkaar. Hierdoor kan de spectrale effici¨ entie worden verdubbeld en de symboolsnelheid worden gehalveerd in vergelijking tot niet-polarisatie gestapelde signalen. Om de spectrale effici¨ entie verder te verhogen, kan POLMUX signalering worden gecombineerd met DQPSK, waardoor modulatie met 4 bits per symbool wordt gerealiseerd. We bespreken een transmissie experiment met 80-Gb/s POLMUX-RZ-DQPSK over een transmissie afstand van 1,700 km en een spectrale effici¨ entie van 1.6-b/s/Hz. Echter, de wisselwerking tussen PMD en andere signaalverstoringen maakt het problematisch om deze techniek toe te passen zonder de compensatie van PMD. In het derde deel van deze dissertatie behandelen we elektrische compensatie methoden. Deze kunnen worden ingezet om de nadelige eigenschappen van DQPSK modulatie en POLMUX sig- nalen te verminderen. Voor incoherente ontvangers kan multi-symbol phase estimation (MSPE) worden gebruikt om zowel de OSNR als de niet-lineaire tolerantie van D(Q)PSK modulatie te verbeteren. Daarnaast kan Maximum likelihood sequence estimation (MLSE) worden gebruikt om de chromatische dispersie en PMD tolerantie te verhogen. Elektrische compensatie is echter bijzonder effectief wanneer het wordt gecombineerd met een coherente ontvanger. In een co- herente ontvanger wordt niet alleen de amplitude, maar het volledige optische basisband veld (amplitude, fase en polarisatie) overgezet naar het elektrische domein. Daardoor kunnen bijna onbeperkt hoge chromatische dispersie en PMD waardes worden gecompenseerd en tegelijker- tijd kan een polarisatie gestapeld signaal worden opgesplitst in de beide polarisatiecomponenten. We bespreken de benodigde systeemarchitectuur voor een digitale coherente ontvanger en be- handelen daarnaast een 100-Gb/s POLMUX-DQPSK transmissie experiment over 2,375 km met 2.0-b/s/Hz spectrale effici¨ entie. Op basis van de resultaten in dit proefschrift kunnen we concluderen dat met behulp van niet- binaire modulatieformaten het mogelijk is om langeafstandstransmissie te realiseren met zowel 40-Gb/s als 100-Gb/s per golflengte kanaal en een 50-GHz kanaalafstand. Elektronische com- pensatie versimpelt daarnaast het systeemontwerp en maakt deze modulatieformaten robuust tegen signaalverstoringen. 288 Acknowledgement ”A dwarf standing on the shoulders of a giant may see farther than the giant himself.” (Didacus Stella) The end of a Ph.D. project is a very suitable moment in time to look back and reflect on the years past. Doing so, I can wholeheartedly conclude that the past three and a half years have been an exciting time, both professionally as well as in private life. This would not have been possible without the support of many, to whom I would like to express my sincere gratitude here. I am very grateful to Prof. Djan Khoe for his support during these years. He offered me a chance to pursue research in fiber-optic transmission by arranging for me to go to Munich for my grad- uation project. His continuing support throughout my Ph.D. project as well as his flexibility in the cooperation with Nokia Siemens Networks (previously Siemens Communications) have been of great value to me. I also would like to thank Dr. Nancy Hecker-Denschlag, for supervising my graduation project within Siemens and, later on, for offering me the possibility to pursue my Ph.D. there. In a time when engineering positions where hard to come by this provided me with the best possible choice I could have made. I am also greatly indebted to Dr. Huug de Waardt for being my supervisor during all these years. Despite the challenge posed by the distance be- tween Eindhoven and Munich, he was always only a phone call away when I need advice or a trusted opinion. It is an interesting observation, that together we discussed all aspects of a Ph.D. on fiber-optic transmission systems while using exactly such systems. As well, I would like to thank Dr. Stefano Calabr` o and Dr. Erich Gottwald, for supervising my Ph.D. project within Nokia Siemens Networks and for all the stimulating technical discussions we had over the years. I would further like to express my thanks to Prof. Palle Jeppesen, Prof. Peter Krummrich, Prof. Ton Koonen, Dr. Robert Killey and Dr. Jos van der Tol for the time they invested in read- ing this thesis and providing me with feedback. I am as well indebted to Dr. Antonio Napoli, Vladimir Veljanovski and Mohammad Alfiad for reading parts of this thesis and helping me to improve this work through their comments. The most intensive and rewarding cooperation during my Ph.D. has without doubt been with Dr. Sander Jansen. The research project we pursued together have redefined my definition of teamwork. His ”let’s get this working” mentality was instrumental in building up the highly complicated transmission experiments of which some are described in this thesis. As well, I will fondly remember the many parties, in all corners of the world, that we celebrated together during these years. I also received support from many other co-workers and students within Nokia Siemens Net- works throughout the Ph.D. project. In particular, I would like to thank Claus-J¨ org Weiske, 289 Appendix C. Acknowledgement Andreas Sch¨ opflin and Erik de Man. Without their help on all things electrical, it would not have been possible to build up many of the optical transmission experiments covered in this thesis. I also very much enjoyed working together with Ernst-Dieter Schmidt, and I’m grateful for the effort he put into organizing the various cooperations. As well, although he never convinced me of his theory on group velocity dispersion, I’m grateful to Dr. Ulrich Gaubatz for the helpful advice he has given over the years. I further would like to thank Vladimir Veljanovski for his ev- erlasting good mood and our after-work parties in ’Dilingers’. Dr. Sebastian Randel is gratefully acknowledged for his work on the DPSK receiver software and our many technical discussions. Furthermore, I want to express my thanks to, without the intention to forget someone, Dr. Got- tfried Lehmann, Dr. Lutz Rapp, Dr. Bernhard Spinnler, Dr. Patrick Leisching, Dr. Uwe Feiste, Dr. Torsten Wuth, Dr. Hans-Joerg Thiele, Dr. Arne Striegler, Dr. Cornelius Cremer, Dr. Achim Autenrieth, David Stahl, Wolfgang Schairer, Dr. Alessandro Bianciotto, Dr. Dario Setti, Dr. Juraj Slovak, Christian Sanabria von Walter, Christian Palm and Carlos Climent. Finally, I would like to thank Dr. Stefan Sp¨ alter for the effort he put into keeping me at Nokia Siemens Networks after finishing my Ph.D. From Eindhoven University of Technology I would further like to thank, without the intention to forget someone, Jeffrey Lee, Bas Huiszoon, Johan van Zantvoort, Maria Garc´ıa Larrod´ e, Prof. Harm Dorren, Dr. Eduard Tangdiongga and Dr. Nicola Calabretta. As well, I am indebted to the secretaries of the department, Susan de Leeuw, Els Gerittsen and Jos´ e Hakkens for their great help with the administrative work. A word of encouragement and thanks here also to Mohammad Alfiad, for his excellent master thesis work, which covers most of the results in Section 9.2. I hope that your Ph.D. project at Nokia Siemens Networks will be as successful as your master thesis. During my Ph.D. project, I have been in the privileged position to cooperate with many people from other universities and companies. I particulary would like to thank Murat Serbay from the University of Kiel for his work during our first long-haul RZ-DQPSK transmission experiment, Fabian Hauske of the Federal Armed Forces University Munich for his work on MLSE receivers, Maxim Kuschnerov of the Federal Armed Forces University Munich for our fruitful discus- sions on signal processing algorithms, Dr. Chris Fludger, Dr. Thomas Duthel and Dr. Christoph Schulien of CoreOptics for our cooperation on the transmission experiments with a digital coher- ent receiver, Carl Paquet and Yves Painchaud of Teraxion for supplying me with FBG samples to measure the impact of phase ripple on DQPSK modulation, Dr. Bernt Satorius and Carsten Bornholdt from the Heinrich-Herz Institute for our cooperation on DPSK regeneration and the Enterprise Services group from T-Systems for their support during our DQPSK field-trail. I am very grateful to my parents Walter and Antoinette, my sister Marieke, her husband Dolf and my brother Gijs for supporting me throughout these years. As well, the many trips to D¨ usseldorf airport when I was coming from or going to Munich are very much appreciated. I also would like to thank my mother for correcting the Dutch summary in this thesis. And finally, I would like to thank Iveth for her support, encouragement, patience, as well as for reading and correcting large parts of this thesis. But most of all I would like to thank her, to finish with the words of Moliere, because to live without loving is not really to live. 290 Curriculum Vitae Dirk van den Borne was born in Bladel, The Netherlands, on October 7, 1979. After completing the VWO (secondary school) at the PIUS-X college in Bladel in 1998, he started studying elec- trical engineering at the Eindhoven University of Technology. In 2002-2003 he spend 4 months, as part of the M.Sc. programm, at the Fujitsu laboratories Ltd. in Kawasaki, Japan, working on super-continuum generation and pulse compression. Later on, he performed his Master’s thesis work at Siemens AG in Munich, Germany, working on polarization-mode dispersion related im- pairments in polarization-multiplexed transmission. He received his M.Sc. degree, cum laude, in 2004. In June 2004, he started working towards the Ph.D. degree in electrical engineering at the Eind- hoven University of Technology. The research was carried out in the long-haul optical trans- mission R&D department of Nokia Siemens Networks (previously Siemens AG) in Munich, Germany. His Ph.D. work focused on improvements in long-haul optical transmission systems using robust modulation formats, alternative dispersion compensation schemes and electronic impairment mitigation. During his Ph.D. studies, he has authored and co-authored more than 50 peer-reviewed journal papers and conference contributions, of which 10 were invited contributions. In addition, he wrote 5 patents related to fiber-optic communications. In 2007 he received the telecommuni- cation award from the Royal Institution of Engineers in the Netherlands (KIVI-NIRIA) and the IEEE Laser & Electro-Optics Society (LEOS) graduate student fellowship. Since March 2008, Dirk is with Nokia Siemens Networks in Munich, Germany. 291 Appendix C. Curriculum Vitae 292 Index AGC, 39 AMI, 77 amplification EDFA, 41 hybrid EDFA/Raman, 44 Raman, 44 analog-to-digital converters, 7, 209, 234 ASE, 43 C-band, 14 coherent receivers, 203 analog, 204 digital, 207 hetrodyne, 205 homodyne, 205 intra-dyne, 206 polarization diversity, 207 CRZ, 69 CSRZ, 38, 69 CWDM, 14 cycle slips, 218 DCF, 49 attenuation, 49 index profile, 49 system penalty, 49 differential group delay, 19 digital coherent receiver, 207 baud-rate equalizers, 234 chromatic dispersion, 223, 227 DGD, 220, 227 long-haul transmission, 228 OSNR requirement, 219, 225 polarization dependent loss, 221 digital signal processing, 7, 210 baud-rate, 234 carrier recovery, 216 clock recovery, 211 CMA, 212 coherent, 207 differential decoding, 218 direct detection, 173 equalization, 212 FFT, 215 LMS, 214 MLSE, 184 MSPE, 175 performance monitoring, 215 polarization de-multiplexing, 212 dispersion compensation, 48 DCF, 49 FBG, 55, 113 in-line, 48 OPC, 62, 121 tunable, 51 dispersion maps, 25, 51 accumulated dispersion, 50 inline under-compensation, 52 lumped, 54, 111 optimization of, 106, 109 post-compensation, 52 pre-compensation, 52 dispersion slope, 15 DPSK, 74 balanced detection, 77 chromatic dispersion, 82 demodulation, 76 DGD, 82 OSNR requirement, 79 partial, 83 single-ended detection, 77 293 Index DQPSK, 87 chromatic dispersion, 97 demodulation, 89 DGD, 97 long-haul transmission, 106 narrowband filtering, 94 nonlinear tolerance, 99 OSNR requirement, 92 precoder, 89 PRQS, 101 DSF, 16 duobinary, 69, 76 chromatic dispersion, 73 DGD, 73 electrical, 71 optical, 72 OSNR requirement, 71 polybinary, 73 PSBT, 69 EDFA, 41 amplifier structure, 43 ASE, 47 noise figure, 47 stimulated emission, 42 FBG, 55 cascading of, 117 DQPSK, 113 GDR, 56 phase ripple, 57 tunable, 57 wavelenght de-tuning, 116 FEC, 40 group velocity, 15 group velocity dispersion, 15 Kerr effect, 23 L-band, 14, 30 laser linewidth, 180 long-haul transmission, 1 Mach-Zehnder modulator, 36 meshed networks, 5, 58 MLSE, 184 DPSK, 189 Gaussian model method, 187 histogram method, 186 joint-symbol, 191, 197 OOK, 188 partial DPSK, 194 trellis decoding, 186 modulation, 36 direct, 36 DPSK, 75 DQPSK, 88 duobinary, 70 electro-absorption, 36 Mach-Zehnder, 36 OOK, 67 POLMUX, 134 POLMUX-DQPSK, 158 MSPE, 175 laser linewidth, 180 nonlinear phase noise, 182 OSNR requirement, 178 priciple of, 176 multi-level modulation, 87 MZDI, 76 amplitude imbalance, 81 colorless, 77 constructive port, 76 destructive port, 76 differential delay, 83, 93 phase offset, 82, 93 polarization dependence, 77, 138 NLSE, 23 nonlinear impairments, 22 FWM, 29 IFWM, 30 IXPM, 30 nonlinear phase noise, 31 SPM, 25, 145 SRS, 33 XPM, 27, 150 XPolM, 28, 150, 230 nonlinear phase noise, 31 compensation, 63, 182 294 Index nonlinear Schr¨ odinger equation, 23 NRZ-OOK, 67 NZDSF, 16 OADM, 5, 58 OOK, 67 optical fiber, 11 birefringence, 18 chromatic dispersion, 14 effective length, 25 insertion loss, 12 manufacturing, 12 nonlinear coefficient, 23 nonlinearity, 22 polarization, 16 optical phase conjugation, 59 conversion efficiency, 121 dispersion compensation, 62 DQPSK, 121 nonlinear phase noise, 63 polarization dependence, 61 PPLN, 60 partial DPSK, 83, 194 photodiode, 38 polarization degree of, 18 dependent loss, 22, 143, 221 interleaving, 28 Jones vector, 17 Poincar´ e sphere, 18 principle states of, 19 state of, 16 Stokes parameters, 17 polarization diversity, 207 polarization interleaving, 164 polarization mode dispersion, 20 depolarization, 21 distribution, 20 optical compensation, 57 outage, 20 POLMUX, 138 second order, 21 polarization multiplexing, 131 POLMUX, 131 depolarization, 150 dispersion tolerance, 142 nonlinear tolerance, 145 OSNR requirement, 137 PMD tolerance, 138 polarization dependent loss, 143 polarization interleaving, 152 principle, 132 XPolM, 150 POLMUX-DQPSK, 157 coherent detection, 207 direct detection, 159 long-haul transmission, 162, 228 narrowband filtering, 162, 226 nonlinear tolerance, 166 OSNR requirement, 160 PMD, 165 power map, 25 PRQS, 101 pulse carving, 37 Raman amplification, 44 all-Raman, 45 amplifier structure, 46 backward pumping, 44 effective noise figure, 45 forward pumping, 45 safety, 46 re-circulating loop, 106 robustness, 4 spectral efficiency, 4, 169 SSMF, 12 transponder, 4 WDM, 3 WSS, 58 295 Robust Optical Transmission Systems Modulation and Equalization PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op woensdag 19 maart 2008 om 16.00 uur door Dirk van den Borne geboren te Bladel en Netersel Dit proefschrift is goedgekeurd door de promotoren: prof.ir. G.D. Khoe en prof.ir. A.M.J. Koonen Copromotor: dr.ir. H. de Waardt CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN Borne, Dirk van den Robust optical transmission systems : modulation and equalization / by Dirk van den Borne. Eindhoven : Technische Universiteit Eindhoven, 2008. Proefschrift. - ISBN 978-90-386-1794-7 NUR 959 Trefw.: optische telecommunicatie / modulatie / signaalverwerking / optische polarisatie. Subject headings: optical fibre communication / electro-optical modulation / signal processing / optical fibre polarisation. Copyright c 2008 by Dirk van den Borne All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without the prior written consent of the author. A Typeset using L TEX, printed in The Netherlands ”The only constant in technology is change.” Samenstelling van de promotiecommissie: prof.dr.ir. A.C.P.M Backx, Technische Universiteit Eindhoven, voorzitter prof.ir. G.D. Khoe, Technische Universiteit Eindhoven, eerste promotor prof.ir. A.M.J. Koonen, Technische Universiteit Eindhoven, tweede promotor dr.ir. H. de Waardt, Technische Universiteit Eindhoven, copromotor prof.dr.tech. P. Jeppesen, Danmarks Tekniske Universitet prof.dr.-ing. P.M. Krummrich, Technische Universit¨ t Dortmund a dr. R.I. Killey, University College London dr. J.J.G.M. van der Tol, Technische Universiteit Eindhoven The work leading to this thesis was part of a cooperation between Nokia Siemens Networks (previously Siemens Communications) in Munich, Germany and the Electro-Optical Communications group, department of Electrical Engineering of the Eindhoven University of Technology, The Netherlands. The studies presented in this thesis were performed within the long-haul optical transmission R&D department of Nokia Siemens Networks. iv Summary Robust optical transmission systems Modulation and Equalization Since the introduction of the first optical transmission systems, capacities have steadily increased and the cost per transmitted bit has gradually decreased. The core of the global telecommunication network consists today of wavelength division multiplexed (WDM) optical transmission systems. WDM is for these systems the technology of choice as it allows for a high spectral efficiency, i.e. the transmitted capacity per unit bandwidth. Commercial WDM systems generally use up to 80 wavelength channels with a 50-GHz channel spacing and a bit rate of 10-Gb/s or sometimes 40-Gb/s per wavelength channel. This translates into a spectral efficiency between 0.2 and 0.8-b/s/Hz. However, to cope with the forecasted increase in data traffic it will be necessary to develop next-generation transmission systems with even higher capacities. These transmission systems are expected to have a 40-Gb/s or 100-Gb/s bit rate per wavelength channel, with a spectral efficiency of between 0.8 and 2.0-b/s/Hz. At the same time, such systems should be robust, i.e. provide a tolerance towards transmission impairments similar to currently deployed systems. Traditionally, optical transmission systems have used amplitude modulation. However, for the next generation of transmission systems this is not a suitable choice. They normally require a too large channel spacing, have a high optical-signal-to-noise ratio (OSNR) requirement and generate significant nonlinear impairments. Current state-of-the-art transmission systems therefore often use differential phase shift keying (DPSK). Compared to amplitude modulation, DPSK generates less nonlinear impairments and has a lower OSNR requirement. However, due to the high symbol rate (e.g. 40-Gbaud) the robustness against the most significant linear transmission impairments, i.e. chromatic dispersion and polarization-mode dispersion (PMD) is still small. Tunable optical dispersion compensators can be used to improve the chromatic dispersion tolerance and PMD impairments are generally avoided through fiber selection. But optical compensation and fiber selection are generally not suitable for cost-sensitive applications. The first part of this thesis focuses on modulation formats that can further increase the capacity and robustness of long-haul WDM transmission links. In particular 40-Gb/s differential v However.6-b/s/Hz spectral efficiency.500-km transmission distance. phase and state of polarization). The second part of this thesis discusses polarization-multiplexed (POLMUX) signaling. In the third part of this thesis we review electronic equalization techniques. the interaction between PMD and other transmission impairments makes it challenging to realize transmission systems employing POLMUX signaling without the compensation of PMD-related impairments. not only the amplitude of the optical signal. simplifies system design and allows these formats to be used on the existing infrastructure of systems optimized for 10-Gb/s transmission. This enables the equalization of nearly arbitrarily high amounts of chromatic dispersion and PMD.8-b/s/Hz spectral efficiency. Electronic equalization improves the transmission tolerances. In addition. Maximum likelihood sequence estimation (MLSE) can be used to increase the chromatic dispersion and PMD tolerance.375 km and with a 2.700 km) with a 1. For direct detection receivers.quadrature phase shift keying (DQPSK) modulation is discussed extensively in this thesis. as well as electronic polarization de-multiplexing in the case of POLMUX signaling. In a coherent receiver. vi . Electronic equalization is particulary attractive when combined with coherent detection.0-b/s/Hz spectral efficiency. but the full baseband optical field is transferred to the electronic domain (amplitude. We further verify the feasibility of long-haul 40-Gb/s DQPSK transmission and show that a transmission reach of 2. As a quaternary modulation format. This can be used to mitigate some of the drawbacks of DQPSK modulation and POLMUX signaling. it modulates 2 bits per symbol and therefore requires only a 20-Gbaud symbol rate. which improves the nonlinear tolerance and enables a 4. such as lumped dispersion compensation and fiber-Bragg gratings. has a higher OSNR requirement and reduces the nonlinear tolerance. As well. we show that multi-symbol phase estimation (MSPE) can be used to improve the OSNR requirement and nonlinear tolerance of D(Q)PSK modulation. the narrow optical spectrum allows for a high spectral efficiency. To further increase the spectral efficiency. we discuss the combination of 40-Gb/s DQPSK modulation with different chromatic dispersion compensation technologies. The work discussed in this thesis shows that multi-level modulation formats enable long-haul transmission systems with a bit rate of 40-Gb/s or 100-Gb/s per WDM channel and a 50-GHz channel spacing.800-km is viable with a 0. POLMUX signaling and DQPSK modulation can be combined to realize optical modulation with 4 bits per symbol. DQPSK also requires a more complex transmitter and receiver structure. This is an attractive transmission format as it modulates independent data onto each of the two orthogonal polarizations of an optical fiber. On the other hand. We discuss the required system architecture for a digital coherent receiver and demonstrate its feasibility through a 100-Gb/s POLMUX-DQPSK transmission experiment over 2. In order to realize ultra long-haul transmission we combine DQPSK modulation with optical phase conjugation. The lower symbol rate improves the tolerance towards both chromatic dispersion and PMD. We discuss a transmission experiment with 80-Gb/s POLMUX-RZ-DQPSK and verify the feasibility of long-haul transmission (1. In addition. This can double the spectral efficiency and halve the symbol rate in comparison to single-polarization modulation. . . . . . . . . . . . . . . . . . . .2 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 vii . . . . . . . . . . . . . . .4 3. . . . . .1 2. . . . . . . . . . . . . . . . . . . . . Framework & objectives . . . . . . . . . . . . . . . . . 41 Chromatic dispersion compensation . . . . . . . . . . . . . . . . . . . . . . 1 1 3 8 8 2 The fiber-optic transmission channel 2. . . . . . . 48 PMD compensation . . . . . . . . . . 35 Fiber loss compensation .Contents 1 Introduction 1. . . .3 2. . . .3 3.2 3. . . . . . . . . . . . . . . . .5 3. . . Motivation . . . . . . . . . . . . .1 3. . . . . . . . . . . 58 Optical phase conjugation . . . . . . . . .4 The global telecommunication hierarchy . . . . . . . . . .4 11 Fiber attenuation . . . 57 Narrowband-optical filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 1. . . . . . . . . . 16 Nonlinear transmission impairments . . . . . . . . . . . . . . . . . . . . . . . . . . . . Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 1. . . . . . . . . . . . . . . . . . . . . . . 14 Polarization of light . . . . .3 1. . . . . . . . . . . . . . . . . . . .6 35 Transmitter & receiver structure . . . 22 3 Long-haul optical transmission systems 3. . . . . . . . . . . . 12 Chromatic dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Comparison of DQPSK transmission experiments . . . . . . 113 OPC-supported long-haul transmission . . . . 134 Transmitter & receiver properties . .Contents 4 Binary modulation formats 4. . . . . . . . . . . . . . . . . . . 88 Back-to-back OSNR requirement . . . . . . . . . . . . . . . . . . . . .8-Gb/s RZ-DQPSK transmission . . . . . . . . . . . . . . . . . . . .3 7. . . . . . . . . . . . . . . . . 67 Duobinary . . . . . . . . . . . . 74 Partial DPSK . . . . . . . . . . . . . 92 Transmitter & receiver properties . . . . . . . . . . . . . . . .6 Transmitter & receiver structure . . . . . . . . 83 87 Differential quadrature phase shift keying 5. . . . . . . .4 Principle of polarization-multiplexing . . . .1 5. . . . . . 106 42. . . . . . . . . 126 Summary & conclusions . . . . . . . . . . . . . . . 104 105 6 Long-haul DQPSK transmission 6. . .1 6. . . . . . . . . 128 131 7 Polarization-multiplexing 7. . . . . . . . . . . . . . . . . . . . . .5 6. . . .7 21. . . . . 137 Nonlinear tolerance . . . . . . . . . . . . . . . . . . .2 4. . . . . . . . . . . . . . . .3 5. . . . . . . . . . . . . . . . . . . . . . . . 69 Differential phase shift keying . . . . . . . . . . . . . . . . . .2 6. . . . . . . . . . . . . .4 5. . . . . . . . . . . . . . . . . . . . . . . . . . 99 Pseudo random quaternary sequences . . . . . 101 Summary & conclusions . . . . . . . . . . . . . .1 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 5. . . . . . . . . . . .3 4. . . . . . . . 108 Lumped dispersion compensation . 93 Nonlinear tolerance . . . 111 Chirped-FBGs based dispersion compensation . . . . . . . . 132 Transmitter & receiver structure . . . . . . . . .4 5 67 On-off-keying . . . . .4-Gb/s RZ-DQPSK transmission . . . . . . . . . . . . . . . . .3 6. . . . . . . . . . . . . .1 7. .2 7. . . . . . . . . 145 viii . . . . . .6 6. . . . . . . . . . . . . . . . . . . . .5 5. . . . . . . . . .4 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 203 10 Digital coherent receivers 10. . . . . . . . . .2 Digital coherent receivers . . . . . . . . . . . . . .3 Digital equalization algorithms . . 207 10. . . . . . . . . . . . . . . . . . . . . . . . 241 A List of symbols & abbreviations 243 A. . . . . . . . . . . .5 8 Summary & conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 Analog coherent receivers . . . . . . . . . . . . . . . 155 157 Polarization-multiplexed DQPSK 8. . . . . 239 11. . . . . . . . . . . . . . . . . . . . 204 10. . . . . . . . . . .3 8. . . . . . . . . . . . . . . . . . .4 Distortion compensation at 43-Gb/s . . . . . . . . . . . . . . . .1 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 10. . . . . . . . .1 Robust optical modulation formats . . . . . . . .3 Multi-symbol phase estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 173 9 Digital direct detection receivers 9. . . . . . . . . . . . . . . . . . . . . .8 Summary & conclusions . . . . . .6 Long-haul transmission . . . . . . . . . . . . . .1 List of symbols . 218 10. . . . . . . . . . . . . . . . . . . 243 ix . . . .2 8. . . . . . . . . . . . . . . . . . . . . . . . 169 Summary & conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 162 Transmission with a high spectral efficiency . . . . . . . . . . . . . . . . . . 224 10. . . . . . . . . . . . . . . . . . . . . .Contents 7. . . . . .1 8. 228 10. . . . . . . . . . . . . . . . . . .5 Distortion compensation at 111-Gb/s . . .7 Distortion compensation using baud-rate equalizers . . . . . . . . . . . .2 Robust electronic equalization . . . . . . . . . . . . . . 175 Maximum likelihood sequence estimation .4 Transmitter & receiver structure .2 9. . . . . . . 184 Summary & conclusions . 237 11 Outlook & recommendations 239 11. . . . . . . . . . . . . . . . . . . . . . . . 158 Long-haul transmission . 234 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 B. . . . 251 C Asymmetric 3 x 3 coupler for coherent detection References List of publications Samenvatting Acknowledgement Curriculum Vitae Index 253 257 281 287 289 291 293 x . . . . .Contents A. . . . . . . . . . . . . . . . . . . . . . .1 Q-factor . . . . . . 245 B Definition of the Q-factor and eye opening penalty 249 B. . . . . . . . . . . . . . . . . . . . .2 List of abbreviations . . . . . . . . .2 Eye opening penalty . . . . . . . . . . . . . . Internet services such as Skype [1]. Figure 1. This is best described through the telecommunication network hierarchy. In the core network. data traffic has been increasing exponentially. Table 1. anytime. Ever since the first developments that led to today’s Internet and. to the invention of the World Wide Web. which in turn made it possible to offer services that relied on even higher bandwidth requirements. transport technologies are required that enable a long regenerator-free transmission distance at the lowest cost. Although many people are not aware of it. transcontinental and transoceanic communication.1 depicts the typical distances covered by transmission links in such networks.1 shows a simplified model of this network hierarchy. Fiber-optic transmission is ideally suited for this purpose as it allows for both high throughput and long transmission distance. fiber-optic transmission plays a key role in global transport of telecommunications services.1 Introduction 1. dividing it up into a long-haul core network. In addition. Today. 1 . later on. anywhere. This exponential bandwidth growth has spurred the development of new technologies.1 The global telecommunication hierarchy Today’s society has been shaped in all its aspects by the progress in telecommunication technology. YouTube [2] or Google earth [3] depend on a backbone of high-speed ‘data pipes’ so that they can be accessed by people around the world. The core of the global telecommunication network is used for transnational. and the physical limits of optical fiber as a transmission medium has a significant impact on their design. A transmission link in this (ultra) long-haul core network therefore transports the largest amount of data over the longest distances (>1000 km). regional networks and ’last-mile’ access networks. Such systems are engineered to transmit a large capacity over a long-haul transmission distances. and interlinked to the core network. Between 2004 and 2006 traffic has grown over 200%. However. Such networks provide data transport within a smaller geographical region. i. When we extrapolate the current annual growth in data traffic over a 10 year period with a conservative 30% per year. Long-haul core network. are smaller regional and metropolitan networks. is much larger. The amount of traffic carried on a typical metropolitan network is much smaller than on a link in the core network.5 Tb/s to 1. the points where data originates from or is destined to. Moving down in the telecommunication hierarchy.1: Optical network hierarchy. Consequently. we arrive at a figure of 22 Tb/s for the Trans-Atlantic IP traffic in 2016.Chapter 1. the required capacity per fiber will still be in the range of 2 to 3 Tb/s.6 Tb/s [4]. When we take into consideration that the aggregated traffic is carried over multiple transmission links. for example a metropolitan area (<300 km) or a small country (<1000 km). each consisting of a number of fibers. and serves therefore well as an example. this presents a significant engineering challenge. This increase in required capacity is largely fueled by new internet video-on-demand services. To exemplify the capacity increase in long-haul data transport we look more closely at the TransAtlantic Internet protocol (IP) traffic.e. Considering the vast distances that have to be spanned for a Trans-oceanic link. A metropolitan network connects again a number of access or ’last-mile’ networks together. Introduction Long-haul core network Regional / Metropolitan networks Internet ‘last-mile’ access networks residential mobile storage enterprise Figure 1. Such networks facilitate the connection of the end-user to the global telecommunication hierar2 . This connection is one of the better documented transmission links in the core network. the number of exchange points. from 0. regional/metropolitan and ’last-mile’ access network. the challenge for such systems is predominantly the cost-effective realization of a complex network switching architecture. 3. such networks are predominantly engineered to provide a lowest-cost solution [5]. We focus here in particular on terrestrial long-haul transmission systems. To cope with the expected bandwidth demand in the near future. As a result. depending on their regenerator-free transmission distance.000 .000 >3. In an optical transmitter (Tx). as shown in Table 1. The optical transmission links in the backbone of the telecommunication network can be classified. AFTER [7]. and ’fiber-tothe-home’ or ’fiber-to-the-curb’ technology is already deployed on a significant scale. for example an arrayed waveguide 3 . spanning from residential internet access to business and storage area networks. it allows for a tremendous decrease in the cost of the transmitted bandwidth. Many different kinds of end-user applications are possible. the cost per transmitted bit. maybe even more importantly.1. The use of WDM therefore allows for a manifold increase in the capacity of longhaul optical transmission systems.000 1. System Access Metro Regional Long-haul Ultra long-haul Distance (km) <100 <300 300 . The preferred transmission format to increase bit rates over this infrastructure is digital subscriber line (DSL) technology. developed and subsequently deployed in long-haul transmission systems. Figure 1.1.3 depicts an example of an optical spectrum for a high-capacity WDM system. Optical fibers has a significant advantage over copper networks due to its much higher bandwidth-distance product.e.1. An overview of fiber-based technologies for ’last-mile’ access can be found in [6].2. i. However. The separate wavelength channels are then multiplexed together using a wavelength multiplexer. especially when the distance between the local exchange point and the end-user is longer than a few kilometers.2 shows the typical layout of a long-haul optical transmission system and Figure 1. Table 1. Fiber-optic solutions are therefore also gaining momentum in ’last-mile’ networks. Or.2 Motivation The backbone of the global telecommunication hierarchy consists of long-haul wavelengthdivision-multiplexed (WDM) transmission links.000 1. new technologies have to be researched.1: C LASSIFICATION OF OPTICAL TRANSMISSION SYSTEMS . a data sequence is modulated onto an optical carrier. Legacy last-mile networks are still largely based on copper networks. either co-axial or twisted pair. A WDM transmission link transports large amount of data traffic by multiplexing a number of lower capacity wavelength channels onto a single fiber. a large variety in access network technologies exists. even with DSL technology the bandwidth of copper networks is limited. which enables high-speed connections over longer distances. each with their own requirements and specific end-users. Motivation chy. As the infrastructure of an access network is generally not shared by a large number of customers. generated by a laser. As not all transmission impairments can be compensated along the transmission link. For example. At bit rates of 10-Gb/s. which typically has a 100-GHz channel spacing. Deployed transmission systems with 80 WDM channels are currently state-of-the-art. which is referred to as a transponder. in the transmission experiments or simulations that use a Monte-Carlo approach. An important aspect of the optical transmission systems that we consider in this thesis is their robustness. which converts the signal back to the electrical domain. such as chromatic dispersion or DGD. The aggregate capacity of such systems would then increase to 3 to 8-Tb/s over a single fiber.0-b/s/Hz.7-Gb/s for 10-Gb/s transmission and 42. Such transmission links rely nowadays on bit rates of 10-Gb/s and sometimes 40-Gb/s per wavelength channel to realize a 1 to 3-Tb/s aggregate capacity1 . Introduction grating (AWG). However.8-Gb/s for 40-Gb/s transmission. which is the transmitted capacity per unit bandwidth. transmission impairments such as chromatic dispersion and polarization-mode dispersion (PMD) have to be precisely dealt with. This allows long-haul transmission while maintaining a sufficiently high optical signal-to-noise ratio (OSNR) at the output of the fiber link. The optical amplifiers amplify the weak input signal from the previous span and launch it again into the next span. As most optical transmission systems are bi-directional (on separate fibers) the optical transmitter and receiver are usually combined in a single module. The density of the WDM channels can be further increased through channel interleaving with an optical interleaver (INT). from a 10-Gb/s to a 40-Gb/s actual transmitted bit rate includes an overhead for forward error correction (FEC). 2 The OSNR margin is dependent on the required bit-error-ratio (BER). At the receiver side of the transmission link. The bit rate used in this thesis is therefore 10. the WDM channels are de-multiplexed using a combination of de-interleaver and de-multiplexers. a BER of 10−3 or 10−4 is used to improve the accuracy of the estimation.g. The tolerance of a transmission system against isolated transmission impairments. When an optical transmission system is upgraded. the receiver should be able to recover the transmitted data sequence in their presence. but in long-haul transmission experiments up to 200 channels are sometimes multiplexed onto a single fiber. And as such impairments accumulate in a long-haul optical transmission link.8 and 2. this can severely limit the feasible transmission distance. which is typically 7%. Each of the de-multiplexed channels is then fed into an optical receiver (Rx). as required for Ethernet transport. e. Nextgeneration transmission links will use bit rates of 40-Gb/s or 100-Gb/s per wavelength channel. Other signal impairments are more difficult to compensate as they fluctuate over time. For 100-Gb/s transmission an additional 4% overhead is normally taken into account for 64B/66B coding. Some transmission impairments are deterministic and therefore straightforward to compensate with proper link design. This results in WDM systems with a 50-GHz channel spacing and a total number of 80 WDM channels that are multiplexed on a single optical fiber. The bit rate and wavelength spacing of a transmission system is often expressed in terms of the spectral efficiency. The transmission link itself consists of cascaded fiber spans with optical amplifiers in-between. which results in a spectral efficiency between 0.2 and 0. 1 The 4 .8-b/s/Hz. For currently deployed systems the spectral efficiency is between 0. which increases the bit rate to 111-Gb/s. and in particular 40-Gb/s or 100-Gb/s. is often expressed in terms of the required OSNR margin2 .Chapter 1. the accumulated chromatic dispersion is normally compensated using a dispersion compensation module (DCM) placed in-between two fiber spans. In this thesis we used a BER of 10−5 to quantify the required OSNR in the analytical simulation as this matches a transmission system that operates with a 3-dB margin with respect to the FEC limit. This is discussed in more detail in Appendix B. such as PMD. 2. This requires optical modulation formats that are tolerant to the narrowband optical filtering that occurs when multiple OADMs are cascaded along a transmission link.1. In this thesis we define a 40-Gb/s or 100-Gb/s transmission format to be robust when its transmission tolerances are sufficiently high to allow deployment on links optimized for transmission with 10-Gb/s bit rate. when the symbol rate of the optical signal is doubled or quadrupled. A second important consideration for optical transmission systems. optical compensation or electronic equalization can be used. At such OADM nodes traffic is routed to other links. Motivation bit rate per wavelength channel. the spectral width scales accordingly. the width of the optical spectrum is not a significant concern for 10-Gb/s systems and WDM channels can be switched transparently through an optical network. no modifications are made in the transmission link. the spectral width of the optical signal can become a key concern [8.2: Typical layout of a WDM optical transmission link. This requires the flexibility to pass multiple optical add-drop multiplexer (OADM) nodes along the transmission link. either sophisticated modulation formats. First of all. At such a channel spacing. However. is that they are rapidly evolving from point-to-point links to meshed optical networks. most deployed long-haul transmission systems have a 50-GHz spacing between the WDM channels. This would require a 40-Gb/s transponder that has a similar tolerance to transmission impairments as the deployed 10-Gb/s transponders. TX TX TX TX laser A W G Optical amplifier I N T Up to 80 channels Fiber DCM Optical Add/Drop DCM A W G I N T A W G A W G RX RX RX RX Photo diode Figure 1. To counter the lower transmission tolerances at a higher bit rate. 9]. PSD (dB) 0 -10 -20 -30 1530 1535 1540 1545 1550 1555 1560 1565 Wavelength (nm) Figure 1.3: Measured WDM spectrum with 89 channels and a 85. ideally.6-Gb/s bit rate per channel. However. thereby creating a meshed network. when transmission systems that are designed for a 10-Gb/s bit rate are upgraded to a 40-Gb/s or 100-Gb/s bit rate per WDM channel. this is not straightforward as the tolerance against most transmission impairments scales linearly or even quadratically with the symbol rate. we discuss the use of robust multi-level optical modulation formats. Today. Hence. Such modulation formats often have favorable transmission properties that can be used to either 5 . In this thesis we focus predominantly on two technologies that can enable more robust optical transmission. crosstalk from neighboring channels is assumed to be unknown and hence treated as a noise source.6-b/s/Hz. This has largely prevented the use of more complex modulation formats and NRZ-OOK is still used nearly exclusively in deployed 10-Gb/s terrestrial long-haul transmission systems. i. Another potential candidate to reduce the symbol rate is polarization multiplexing (POLMUX). This doubles the number of bits per symbol by transmitting independent information in each of the two orthogonal polarizations of an optical fiber. Multi-level modulation with 2 bits per symbol. for 40-Gb/s or 100-Gb/s bit rates the spectral efficiency is an important consideration. This is particulary true for 40-Gb/s or 100-Gb/s bit rates. Binary modulation restricts the achievable spectral efficiency to 1-b/s/Hz [10]. But in particular phase modulation. And in practical systems. Combined with DQPSK modulation. using differential phase shift keying (DPSK). can increase this to ∼1. such as return-to-zero differential quadrature phase shift keying (RZ-DQPSK) modulation. where the transmission tolerances of NRZ-OOK modulation are too small to realize robust longhaul transmission systems with a 50-GHz channel spacing. the realizable spectral efficiency is significantly lower than 1-b/s/Hz because WDM is considered to be transparent. wavelength drift in the transmitter laser and (de-)multiplexing filters as well as the limited filter order of optical filters and interleavers. Modulation formats such as duobinary or DPSK are more tolerant to narrowband optical filtering and allow a spectral efficiency of up to 0. Until recently. Only recently the growing interest in more robust optical transmission technologies has opened up the possibility for commercial deployment of different modulation formats.e. 1. And other system design aspects that further reduce the spectral efficiency have to be taken into account.Chapter 1. In addition it is more tolerant to many linear transmission impairments as well as narrowband optical filtering. which can be used to improve the tolerance against chromatic dispersion and narrowband optical filtering. such as the 7% overhead usually required for forward error correction (FEC). the optical modulation format of choice for nearly all optical transmission systems has been non-return-to-zero on-off keying (NRZ-OOK). Combined. POLMUX signaling enables modulation with 4 bits per symbol. NRZ-OOK combines a cost-effective transmitter and receiver structure with a transmission performance sufficient to realize long-haul 10-Gb/s transmission systems. Secondly. Introduction increase the capacity of an optical transmission link or increase its robustness against transmission impairments. the required margins restrict the feasible spectral efficiency to approximately <0.8-b/s/Hz. 6 .7-b/s/Hz when using NRZOOK modulation. Currently deployed 40-Gb/s transmission systems use modulation formats that are more robust against transmission impairments than NRZ-OOK.1 Robust optical modulation formats The modulation format defines the characteristics of the optical signal that is transmitted over the transmission link. we focus on electronic equalization that can be combined with robust modulation formats to further improve the performance of the transmission link.2. This includes duobinary. is currently the most widely used state-of-the-art modulation format. In addition. 2.2. combined with multi-level modulation such as POLMUX-DQPSK. we look more closely at the potential impact of DQPSK modulation and POLMUX signaling in long-haul transmission systems. In particular.0-b/s/Hz. the sample rate requirements for a 100-Gb/s transponder are lowered to ∼50-Gbaud. The combination of multi-level modulation formats and digital signal processing is a particularly interesting approach to realize high spectrally efficient transmission. POLMUX-RZ-DQPSK modulation enables 100-Gb/s transmission with only a ∼25-Gbaud symbol rate. For efficient digital signal processing. 1. 14. Taking this approach a step further. Motivation Multi-level modulation is particulary beneficial for 100-Gb/s transmission. In particular. This increases the tolerance to chromatic dispersion and PMD and will enable next-generation optical transmission systems with a spectral efficiency of 2. This thesis focuses on multi-level modulation formats that can enable robust 40-Gb/s and 100Gb/s modulation per wavelength channel. multi-symbol phase estimation (MSPE) or related approaches 7 . 20]. pre-distortion. Current state-of-the-art ADCs in commercial products have a sample rate of ∼25-Gbaud [17. For 100-Gb/s modulation the main advantage of DQPSK is that it reduces the bandwidth requirement of the electrical components in the transponder as it operates at a 50-Gbaud symbol rate. respectively. 12] the use of such a modulation format would pose considerable challenges in deployed transmission systems due its high OSNR requirement and low chromatic dispersion and PMD tolerance. This implies that for binary modulation formats a sample rate of 80-Gbaud and 200-Gbaud is required for 40-Gb/s and 100-Gb/s transponders. DQPSK is therefore a more likely candidate for long-haul 100-Gb/s transmission and a number of long-haul transmission experiments have demonstrated its feasibility [13. The conversion of the optical signal to the digital domains enables the use of powerful digital signal processing algorithms. A figure that seems to be feasible in the foreseeable future.2 Robust electronic equalization Digital signal processing speeds have increased exponentially over the years [16] and have now started to catch up with bit rates common in optical transmission systems. the signal has to be sampled at twice the symbol rate. Digital signal processing can further be used to lower the required OSNR through the use of improved decision variables as well as an increase in nonlinear tolerance.1. Although 100-Gb/s NRZ-OOK has been demonstrated using ultra-high frequency electronics [11. highspeed analog-to-digital converters (ADC) have become available to convert the analog signal in an optical receiver to the digital domain for subsequent digital signal processing. It reduces the need for precise optical compensation of chromatic dispersion and it negates the need for fiber selection to reduce the PMD on an optical transmission link [19. However. 18] and sample rates up to ∼50-Gbaud have shown to be feasible in research and development as well as measurement equipment. maximum likelihood sequence estimation (MLSE). These figures are well beyond the sample rates that seem to be feasible in the foreseeable future. Digital signal processing increases the robustness of the transponder and can help to simplify transmission link design. 15]. The electronic equalization schemes that have attracted the most significant interest in recent years include feed-forward and decision-feedback equalizers. which discuss the fiber-optic transmission channel and long-haul 8 . in cooperation with the Electro-Optical Communications group. 1. the use of sophisticated optical modulation formats and electronic equalization can enable more robust 40-Gb/s and 100-Gb/s optical transmission systems. in the electrical domain. But after the telecom bust in 2001. such as chromatic dispersion and PMD. it has u been carried out in close cooperation with the work of Jansen [21]. This has spurred a significant research and development effort by the optical systems industry into developing these technologies for their next-generation products. The research discussed in this thesis focuses on a number of next-generation transmission technologies that might significantly impact the design of long-haul transmission systems in the foreseeable future. Ideally. Introduction and digital coherent receivers. 1. The first part of the thesis consists of the Chapters 2 and 3. This thesis describes in particular the most promising modulation and equalization technologies and demonstrates their feasibility using long-haul optical transmission experiments. which focuses on optical phase conjugation in long-haul transmission systems. the optical systems industry has become more cost-oriented and moved away from performanceoriented system design that was common during the telecom boom. the combination of digital coherent detection and multi-level modulation formats such as POLMUX-DQPSK seems to be one of the most suitable choices for the next generation of high-capacity optical transmission systems. Hence. department of Electrical Engineering of the Eindhoven University of Technology.Chapter 1. The first generation of transmission systems with a 40-Gb/s bit rate per wavelength channel could therefore not compete on a cost basis with deployed systems that operated with 10-Gb/s bit rates. these technologies will allow for 40-Gb/s and 100-Gb/s transmission systems that can be cost-effective in comparison to existing 10-Gb/s systems. Germany. In addition.3 Framework & objectives Long-haul WDM optical transmission systems with a 10-Gb/s bit rate per wavelength channel have been deployed on a significant scale over the last decade.4 Outline of this thesis In this section we give a general overview of the thesis structure. The work described in this thesis has been carried out at Nokia-Siemens networks (previously Siemens Communications) in Munich. The Netherlands. This work has been part of the ’MultiTeraNet’ and ’Eibone’ projects from the German Bundesministerium f¨ r Bildung und Forschung (BMBF). However. In addition. This has prevented commercial deployment of such systems and limited their use to transmission experiments and field-trails. it can potentially recover polarization multiplexed data and correct for linear distortions. In particular the combination of coherent receivers with digital signal processing has proven to be useful together with multi-level modulation formats. Polarization multiplexing is then combined with DQPSK modulation in Chapter 8 to realize high spectrally efficient long-haul transmission. And in Chapter 10 the use of digital coherent receivers is treated. in particular the specific transmission impairments that occur when two orthogonal polarizations are used to transmit information. Chapter 7 discusses POLMUX signaling. 9 . digital signal processing combined with direct detection receivers is discussed in more detail. respectively. In addition. DQPSK modulation. Chapter 4 discusses in detail the binary modulation formats which are currently deployed in state-of-the-art 40-Gb/s transmission systems. Outline of this thesis transmission systems. Next. Finally. In Chapter 9. the third part of the thesis focuses on electronic equalization and digital signal processing. we discuss in detail the relevant technologies for amplification and distortion compensation in a state-of-the-art transmission systems.0-b/s/Hz spectral efficiency. These technologies are used in the transmission experiments described in the remainder of this thesis.1. Subsequently. In addition. Chapter 5 introduces the properties of DQPSK modulation. whereas Chapter 6 discusses in detail a number of long-haul transmission experiments that make use of DQPSK modulation.4. which deal with the relevant optical modulation formats for long-haul transmission systems. The second part of the thesis consists of the Chapters 4 to 8. The aim of these two chapters is to provide a physical framework of the optical fiber as the transmission medium in long-haul telecommunication systems. Chapters 5 and 6 focus on the most significant multi-level modulation format described in this thesis. long-haul transmission experiments are described that use digital coherent detection together with multi-level modulation formats to realize robust long-haul transmission with a 2. Introduction 10 .Chapter 1. 48 (at 1550 nm) and is higher by ∼0.5 % coating cladding core core radius (a) (b) Figure 2.1a shows a cross-section of an optical fiber. This can be achieved either by doping the core with Germanium-Oxide (GeO2 ). Note that the majority. Made from silica glass. progress in material technology and fiber manufacturing [23] has resulted in the widespread availability of optical fiber with near optimal properties.5% than the refractive index of the cladding [24].1: (a) Cross-section of an optical fiber and (b) refractive index profile of standard single-mode fiber. The fiber cladding confines the light to the fiber core through total internal reflection and the low refractive index difference of the core-cladding boundary reduces the scattering loss.2 The fiber-optic transmission channel Single-mode optical fibers are circular dielectric waveguides that weakly guide a single transverse mode in two orthogonal polarizations. Figure 2. In the center of the fiber is the core. Since then. For silica fibers the refractive index of the core is n ≈ 1. 11 . which raises the refractive index. or doping the cladding with fluoride (F). single-mode fibers have very advantageous properties for the transmission of guided waves over long-distances. The use of glass fiber for communication at optical frequencies was first proposed by Kao and Hockham in 1966 [22]. n cladding core nsilica 0 n 0. which lowers the refractive index. which is surrounded by the fiber cladding. After a transmission distance z in [km]. The core of a SSMF is normally doped with GeO2 .1). When heated close to the melting point in a furnace.2).Chapter 2. This chapter discusses the physical properties of an optical fiber that are the most relevant to long-haul fiber-optic transmission systems. optical fiber has an intrinsic power loss when a signal propagates along it. it is preferable to dope the cladding with fluoride for low-attenuation fibers [26]. the preform is pulled into a thin fiber [23]. (2. Finally.652 fiber [25].2. The preform contains a part with an increased refractive index along its axis. the fiber attenuation coefficient in [dB/km] will be used unless noted otherwise.4). but it is still widely used in optical transmission systems. which after fiber drawing becomes the fiber core. A preform is a glass rod which has a diameter of a few centimeters and is roughly a meter in length.1b. following Equation 2. αdB = 10log10 (exp(αN p )) = 10log10 (e) · αN p = 4. 2. It was the first single-mode fiber type to be developed. The fiber-optic transmission channel but not all of the optical wave propagates through the core.343 · αN p . which is the lowest wavelength that allows for single-mode operation. which is sometimes referred to as G.2) In the remainder of the thesis. 12 . This is characterized by the cut-off wavelength. Such fibers are referred to as pure-silica core fibers and are used in Trans-oceanic optical transmission systems. P(z) = P0 · exp(−αz). polarization properties (Section 2. Most optical fibers are fabricated (drawn) from a preform in a fiber drawing tower.3) and fiber nonlinearities (Section 2. chromatic dispersion (Section 2.1) where P0 is the power coupled into the optical fiber in [W ] and α is the attenuation coefficient in Neper per kilometer [N p/km]. the signal power can be denoted by. The signal power P(z) in [W ] decreases exponentially with the fiber length. SSMF has a step refractive index profile. The most widely used fiber type in optical transmission systems is standard single-mode fiber (SSMF).1 Fiber attenuation As any physical medium besides vacuum. but it is more convenient to define the fiber attenuation in decibel per kilometer (base 10 logarithmic). a coating of the optical fiber is necessary for protection of the fiber. The core size is upper-bounded by the need for single-mode propagation in the wavelength range of interest. The fiber core has a typical diameter of 9 µm and the cutoff wavelength is < 1260 nm so that it provides single-mode operation in the entire low-loss wavelength range of the optical fiber. as depicted in Figure 2. The remainder of the preform becomes the cladding of the optical fiber. The Neper is a logarithmic unit that uses base e. This includes fiber attenuation (Section 2. (2. As doping with GeO2 slightly raises the fiber attenuation. which is referred to a fiber attenuation. A too large core diameter with respect to the signal wavelength can result in multi-mode propagation. this entire wavelength band can be used for optical communication purposes. This wavelength range is divided into 6 wave13 2 a bs 1675 1715 . In principle. It is proportional to the inverse fourth power of wavelength. bending losses and SiO2 absorption [29]. The remaining contributions to the fiber attenuation in low-loss optical fibers comes from several sources of which the most dominant are: Rayleigh scattering. In comparison.4 dB/km. For even longer wavelength (> 1700 nm). However.2. allowing for un-repeated transmission links up to 500 km [28]. OH − absorption. and therefore attenuates shorter wavelength more than longer wavelength [30].3 0. this absorption peak can be nearly eliminated by reducing the concentration of hydroxyl (OH − ) ions in the core of the optical fiber [32. 9979·108 m/s. For long-haul transmission links.1.5 µm and 1. 26]. which increases the scattering losses.2 catt erin g 0. The wavelength (λ ) and the optical frequency ( f ) of a spectral component are related according to λ = c/ f .1 1200 1260 1360 1460 1530 1565 1625 SiO OH.4 µm [31]. which span from 1260 nm to 1625 nm. Frequency (THz) 250 0. The wavelength range is lower bounded by the fiber cut-off wavelength and upperbounded by bending and SiO2 absorption losses.6 0. Rayleigh scattering results from microscopic fluctuations in the material density much smaller than the wavelength of the light. The wavelength bands of interest for optical fiber communication are defined by the International Telecommunication Union Standardization (ITU-T) in [33].2. Bending losses are more dominant for longer wavelength because the bending radius relative to the wavelength becomes too small.148 dB/km [27].652C/D fibers [25]. the attenuation of conventional (window) glass is approximately 1000 dB/km. Such fibers have a ∼ 60-THz low-loss bandwidth with an attenuation below 0.4 Bending losses orp tio n 0. SiO2 absorption becomes the dominant loss mechanism. Apart from the higher fiber attenuation at lower and higher wavelengths. The minimum fiber loss occurs between 1. where c is the speed of light in vacuum which is equal to c = 2. ∼ 100 km spans with re-amplification after each span is widely used. there is often an OH − absorption peak around 1.5 240 230 220 210 200 190 180 Attenuation (dB/km) 0.-absorption Ray le igh s Wavelength (nm) O E S C L U Figure 2.2: Fiber loss as a function of wavelength and frequency. This extremely small attenuation in single-mode silica fiber. Optical fibers with a negligible OH − absorption peak are commonly referred to as water-free or G.6 µm and can be as low as 0. This results from the harmonic vibrations in the bonds of the silica molecules that make up the glass. For longer wavelength (> 1600 nm) the dominant sources of fiber attenuation are bending losses and SiO2 absorption. Fiber attenuation The fiber loss as a function of wavelength and frequency is depicted in Figure 2. Such a channel spacing allows the use of uncooled lasers.. i. The fiber-optic transmission channel length bands: O. The other wavelength bands are only sporadically used in denseWDM optical transmission systems due to the higher fiber loss and lack of optical amplifiers with a high efficiency. and it results for optical transmission systems in inter-symbol interference (ISI).5) . the speed of light in an optical fiber is lower than in vacuum.4) The wavelength dependency of β (ω) can be approximated with a polynomial using a Taylor series expansion. L and U. This mismatch in refractive index causes waveguide dispersion.77 nm and 1610.5. n is the refractive index of the guiding material and ω is the angular frequency in [rad/s]. 37]. c v p (ω) = . The dependency of the refractive index on the angular frequency is known as material dispersion. This restricts the dispersion limited reach. and is known as coarse-WDM (CWDM) [36. v p (ω) c (2. 6.49 nm. which spans the wavelength range between 1528.. S. This results in Equation 2. the main dispersion effects are material and waveguide dispersion. 35]. [5. c 2 6 (2. β (ω) = [n + n(ω)] 14 ω 1 1 ≈ β0 + β1 (ω − ω0 ) + β2 (ω − ω0 )2 + β3 (ω − ω0 )3 + .e. In single-mode optical fibers. For long-haul optical transmission systems the C-band is generally used. C.2 Chromatic dispersion Chromatic dispersion in a single-mode fiber refers to the pulse broadening induced through the wavelength dependence of the fiber’s refractive index. both bands allow a total of approximately 160 wavelength channels on a 50-GHz WDM grid [34]. In this section the background of chromatic dispersion and the impact on optical transmission links is explained. The impact of material dispersion on a modulated signal can be described by the mode-propagation constant β β (ω) = ω ω = [n + n(ω)] . as cost-effective vertical cavity emitting lasers are available for this wavelength band. A part of the optical field propagates therefore in the cladding. as depicted in Figure 2. 2. E. The speed at which the phase of any one frequency component of a wave travels along an optical fiber is equal to. Waveguide dispersion is related to the optical field being not totally confined to the core of the fiber.3) n + n(ω) where v p is the phase velocity of a spectral component.Chapter 2. In addition.2. The O-band is used extensively for optical communication in metropolitan networks. to increase the transmission capacity the L-band is sometimes used in commercial long-haul systems. All wavelength bands combined are also used in metropolitan networks to enable WDM transmission with a large 20 nm channel spacing.77 nm and 1568. Combined.36 nm. the feasible transmission distance without the need for regeneration or dispersion compensation. (2. which has a different refractive index. which spans the wavelength range between 1568. As the refractive index n is larger than 1. this nomenclature is also adopted in this thesis. 25 Dispersion (ps / nm / km) 20 15 10 5 0 -5 -10 1250 1300 1350 1400 1450 1500 Wavelength (nm) 1550 1600 1650 Oband Cband Lband Standard Single Mode Fiber (SSMF) G. which defines the change in GVD and GVD slope with respect to a reference wavelength λ . ∂ ωn (2. In fiber-optic communication it is common to use the dispersion (D) and dispersion slope (S). ∂λ λ λ (2. which is known as the group velocity dispersion (GVD) in [ps2 /km].652 Non-zero Dispersion Shifted Fibers (NZDSF) G. respectively. However. the term β0 in [1/km] represents a constant phase shift and β1 in [ps/km] corresponds to the speed at which the envelope of the pulse propagates.2. But the fiber dispersion is related to the group-velocity dispersion and not to the groupvelocity of the spectral components. This is in principle not correct as chromatic dispersion implies that different spectral components travel at different velocities. it is also the wavelength where waveguide and material dispersion have the same magnitude (but opposite signs). as it is common terminology in the literature to refer the fiber dispersion as chromatic dispersion. The wavelength for which D equals zero is referred to as the zero-dispersion wavelength (λ0 ). Figure 2. Chromatic dispersion where βn is defined as the nth derivative of β with respect to the angular frequency.655 Dispersion Shifted Fiber (DSF) G.7) Where D is expressed in [ps/nm/km] and S is expressed in [ps2 /nm/km]. The second order term β2 defines the acceleration of the spectral components in the pulse. The third order derivative correspond to β3 in [ps3 /km] and is known as the GVD slope.653 Figure 2. The group-velocity of the pulse is then defined by β1 = 1/vg . βn = ∂ nβ |ω=ω0 .2. The term chromatic dispersion is commonly used to refer to the fiber dispersion. as it significantly increases 15 .3 shows the dispersion as a function of wavelength for the most common optical fiber types in optical fiber communication.3: Dispersion as a function of wavelength for the most common fiber types in optical communication. This is widely exploited in access and metropolitan networks.6) In the context of pulse propagation inside an optical fiber. They are related to β2 and β3 as D= 2πc ∂ β1 = − 2 β2 ∂λ λ S= ∂ D 4πc πc = 3 (β2 + β3 ). The zero-dispersion wavelength of SSMF is near 1310 nm [38]. depending on the exact fiber type. There is no common definition for NZDSF. The transverse plane is again orthogonal to the direction of propagation z. DSF have been developed to extend the dispersion limited reach of optical transmission systems employing the C-band. Such fibers can compensate for the chromatic dispersion of transmission fibers and are therefore referred to as dispersion compensating fiber (DCF).5 ps/nm/km around 1528 nm and D = 17. Alcatel TeraLight. By changing the core-cladding refractive index profile of the fiber. The state of polarization (SOP) is then defined as the pattern traced out by the electric field in the 16 . e. As T0 is inverse proportional to the symbol rate. The pulsewidth T0 is the width of a chirp-free transform limited pulse. which is discussed in Section 3. Note that we do not define a frame of reference for the x and y component. both the material and waveguide dispersion can be modified. In the C-band. The zerodispersion wavelength of NZDSF fiber is around ∼ 1460 nm and the chromatic dispersion in the C-band between 3-8 ps/nm/km. and their orientation is therefore arbitrary. A third class of optical fibers that are frequently used in longhaul fiber-optic transmission systems are non-zero dispersion-shifted fibers (NZDSF) or G.3 Polarization of light The polarization of light is the property of electromagnetic waves that describes the direction of the transverse electric field.8) The normalized dispersion length defines the propagation distance over which the pulse broadens √ with approximately a factor 2. It is also possible to lower the dispersion slope and create a fiber with a nearly flat dispersion profile [39]. For example. The fiber-optic transmission channel the dispersion limited reach [35]. T02 LD = |β2 | (2.3. In the transverse plane.4) which makes such fiber unsuitable for WDM transmission systems. but different manufactures have their own proprietary solutions. the electric field vector can be divided into two orthogonal components x and y. 2. the chromatic dispersion tolerance scales quadratically with the symbol rate.Chapter 2. The magnetic field vector is normally ignored as it is orthogonal to the electric field vector. by increasing the waveguide dispersion the zero-dispersion wavelength shifts to higher wavelengths. The ISI induced through chromatic dispersion in a fiber-optic transmission link can be quantized by using a normalized dispersion length LD .8 [42]. By modifying the refractive index profile it is also possible to create fibers that have a both a negative chromatic dispersion and dispersion slope.653 fibers [40].g. Corning LEAF and Lucent TrueWave. Dispersion-shifted fibers (DSF) have a zero-dispersion wavelength in the C-band around 1550 nm and are also known as G. All electromagnetic waves propagating in vacuum or in a waveguide have electric and magnetic fields that are orthogonal to each other in a transverse plane.8 ps/nm/km around 1568 nm.655 fiber [41]. The dispersion slope for SSMF is approximately S = 0. as defined in Equation 2.057 ps2 /nm/km. A low chromatic dispersion coefficient however increases inter-channel nonlinear impairments (see Section 2. the chromatic dispersion of SSMF is typically between D = 15. which is more straightforward to measure. The Stokes vector consists of four stokes 17 . the light is right-circular polarized or left-circular polarized for a −90o phase difference (Figure 2. An alternative representation to describe the SOP of an optical signal are the Stokes parameters. The angle of the linear polarized light depends on the amplitude in the x component with respect to the amplitude in the y component. (b) right circular and (c) left elliptical. which is also known as the Jones vector.3.10) = Px + Py exp( jφx ) Py exp( jϕy ) exp( j|φx − φy |) sin ψ √ where ψ is defined such that tanψ = Px / Py . Ex Ey √ = Px exp( j[ω0t + ϕx (t)]) Py exp( j[ω0t + ϕy (t)]) . it is still possible to model un-polarized light as polarized light by assuming a random change in SOP for each fraction of time. The normalized Jones vector with unity amplitude is widely used to characterize the SOP of an optical signal. √ Px exp( jϕx ) cos ψ . When there is no phase difference between the x and y components.9) The SOP of an optical signal can be described using the vector notation of the complex envelope.4: Example of different SOP of an electro-magnetic wave. For horizontally polarized light the pulse travel completely in the x component. x y x y x y (a) (b) (c) Figure 2. (2. (a) 45o linear. which can also describe partially or unpolarized light [43]. The SOP is then defined by relative amplitude and phase of the orthogonal polarization components x and y. In [43]. the light is linear polarized. In the special case both components contain an equal amplitude and have a +90o phase difference.4c). In an optical fiber. whereas for vertically polarized light the pulse travels in the y component. (2. is that they express the SOP in term of optical powers instead of the electric field. The polarization of an optical signal can be described in a vector notation by separately describing the electric field vector of the x and y component. for example sunlight is un-polarized light. Polarization of light transverse plane as a function of time.4b). the two orthogonal components in the transverse plane can be interpret as the fiber supporting two orthogonal polarizations. An additional advantage of using Stokes parameters. the mathematical background of the polarization of light is discussed in detail.2. However. as shown in Figure 2.4. Note that not all light is polarized. When there is a phase difference between the x and y component the light is elliptically polarized (Figure 2. 11) ⎪ ⎪ S2 = Ex E ∗ + Ey E ∗ = 2Ex Ey cos(|ϕx − ϕy |) ⎪ y x ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ∗ ∗ S3 = iEx Ey − iEy Ex = 2Ex Ey sin(|ϕx − ϕy |) The Stokes parameters are often normalized with respect to the total optical power S0 .5. Hence. DOP = 2 2 2 S1 + S2 + S3 S0 .1 First-order polarization mode dispersion In an ideal optical fiber with no imperfections and circular symmetry. S = [S0 S1 S2 S3 ]T . ⎧ ∗ ∗ 2 2 ⎪ S0 = Ex Ex + Ey Ey = Ex + Ey ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ∗ ∗ 2 2 ⎪ S1 = Ex Ex − Ey Ey = Ex − Ey ⎨ (2. e parameters. The fiber-optic transmission channel +90o circular polarized S3 +45o linear polarized Vertically polarized S2 -45o linear polarized S1 Horizontally polarized -90o circular polarized Figure 2. (2.Chapter 2. whereas partially or unpolarized e light is described by a point within the sphere. Expressed in term of the Stokes parameters the DOP is equal to. the signal will not couple into the orthogonal 18 . The degree of polarization (DOP) defines the distance from S to the center of the Poincar´ sphere and it is therefore an important parameter to e quantify depolarization. Fully polarized light can be described by a point on the Poincar´ sphere.12) 2. which can be defined in terms of the electrical field vectors using. both orthogonal polarizations have an identical group delay. The Poincar´ sphere is a graphical representation of the SOP which uses the normalized Stokes pae rameters as the axis of a 3-dimensional coordinate system.3.5: The Poincar´ sphere. as shown in Figure 2. the SOP is constant along the fiber. the birefringence results 19 . After an optical signal propagated over a distance L.x − β1. An example of a fiber type with constant birefringence are polarization-maintaining fibers. outside pressure due to mechanical stress. In the fibers used for optical transmission links. is then called e the slow axis. Figure 2. c (2. which is on the opposite side of the Poincar´ sphere. Consequently.7: Possible causes of random birefringence in non-ideal optical fibers.3. which results in fiber birefringence ∆n and a difference in the group delay ∆β1 between the two orthogonal polarizations. an oval core shape. the core of the optical fiber is in practice not completely symmetric and the material has imperfections. From left to right. the principle states of polarization (PSP). ∆β1 = |β1. wind or temperature. because a signal traveling along this axis has a higher group velocity. the signal coupled into the slow axis travels slower than the signal coupled into the fast axis. birefringence is random. which are fabricated by artificially enhancing the stress induced birefringence in the fiber core [44]. Polarization of light polarization and the received SOP is identical to the SOP launched into the fiber. In a fiber with constant birefringence. On the Poincar´ sphere the constant birefrine gence results in a periodic rotation of the output SOP around two orthogonal polarization axes. The PSP with the lower refractive index is referred to as the fast axis. Figure 2. the differential group delay (DGD) is equal to ∆τ = ∆β1 · L. The random coupling can be the result of both imperfections introduced in the manufacturing process or external influences as depicted in Figure 2. Rashleigh and Ulrich were in 1978 the first to note that this random coupling between both orthogonal polarizations could result in signal impairments [45]. However.2. When the signal is coupled into one of the PSP.13) fast axis Transmission link slow axis DGD Figure 2. Following a similar argument the orthogonal PSP.7.6: Differential group delay in an optical fiber. both orthogonal polarizations periodically exchange power with a periodicity equal to the beat length 2π/∆β1 in [km] when the signal is coupled into the fiber in between both orthogonal polarizations.6 illustrates DGD in an optical transmission link.y | = ω |nx − ny |. fiber bending and fiber twisting. and changes both along the optical fiber and over time. the probability density function of the magnitude of the PMD vector is Maxwellian distributed [50]. The unit [ps/ km] shows that the maximum allowable PMD decreases with approximately a factor of two when the symbol rate is doubled. 53]. A widely accepted value for the system outage probability is 30 minutes per year or a probability of 5. PMD =< ∆τ > (2. and with a magnitude equal to the DGD. the mean DGD (< ∆τ >) does not increase linearly with propagation distance. For optical fiber with random birefringence this implies that the normalized stokes parameters S1. that the PMD limited transmission distance scales quadratically with the symbol rate. When there are points along the fiber with a high local birefringence. For older √ installed optical fibers the typical PMD coefficient can be as high as 1 ps/ km. one therefore defines a system outage probability. For random coupling. The PMD properties of an optical fiber can be characterized through the PMD vector τ [49]. When the normalized stokes parameters S1.16) The Maxwellian distribution of Pr{∆τ} is only correct when the differential group delay is equally distributed over all (infinitely small) fiber sections. The DGD variance var(< ∆τ >) can be denoted through a square relation with the average DGD [47].3 are Gaussian distributed.3 are Gaussian distributed. independent of the specific distribution of the variables [48].Chapter 2. τ is a vector in normalized Stokes space.7 · 10−5 . The lower 20 . The PMD coefficient√ the PMD (mean DGD) is √ √ divided by the square root of the propagation length ( L) in [ps/ km]. This is equal to an average PMD of between 10% and 15% percent of the symbol rate. pointing in the direction of the slow PSP.15) We assume now that the fiber consists of an infinitely large number of infinitely small fiber section. which is defined as the statistical average of the DGD. in the order of 0. This is also known as the Hinge model [52. the distribution will begin to resemble the square root of a non-central Chi-square distribution with three degrees of freedom [51]. Due to the statistical nature of PMD there is a finite probability that an arbitrarily high DGD will occur. but with its root-mean-square [29].. This is known as polarization mode dispersion (PMD) in [ps]. The random birefringence in a fiber also implies that the DGD is a statistic distribution. which implies that the DGD can not exceed a certain value during more than a specific fraction of the time. var(< ∆τ >) = 3 π/8 < ∆τ >2 (2. which all rotate the SOP according to the random walk theorem.. however. But modern √ optical fibers can have a much lower PMD value. Note.14) where < ∆τ > is the mean DGD and denotes an ensemble average. Then the central limit theorem states that the distribution of the sum of a large number of independent but identically distributed variables is approximately Gaussian distributed.05 ps/ km [54]. 32∆τ 2 4∆τ 2 Pr{∆τ} = 2 exp(− ) π < ∆τ >3 π < ∆τ >2 (2. A high local birefringence can result from tight bends in the fiber or points of alleviated mechanical vibrations such a roads or railroad tracks. The fiber-optic transmission channel in a random change of the SOP that is analog to the random walk theorem [46]. Usually. < ∆τω >≈ 0. which refers to all orders of PMD excluding first-order PMD (DGD). such as fiber spinning during the drawing stage of fiber manufacturing [55]. When the PMD vector is aligned with the PSP’s there is no rotation on the Poincar´ sphere. 192 (2. Polarization of light PMD results mainly from improvements in the manufacturing process. Similar to the DGD variance. which is the most important contribution to higher-order PMD for WDM transmission systems. (2. where the magnitude of the DGD determines the rate of rotation. The first term of the SOPMD expression denotes the change of the DGD with wavelength (∆τω ).20) 21 .18) dω where the subscript ω denotes differentiation with respect to frequency. On the other hand. Sω = The magnitude and the orientation of the PMD vector change with wavelength and Equation 2. for example. The variance of the statistical distribution of both PCD and the depolarization component of the SOPMD in [ps4 ] can be described by [47]. (2.3. when S is launched in between the PSP’s the rotation angle is maximized because τ × S has its largest value.17 applies only for a narrow wavelength range. which is known as polarization chromatic dispersion (PCD). Due to the improvements in fiber PMD. due to depolarization. The change of the PMD vector with wavelength can be described by a Taylor expansion of the PMD vector around a carrier frequency ω0 [49]. 64 var(< pω >) = π2 · < ∆τ >4 .3.19) The average SOPMD depolarization component is equal to zero which follows directly from the definition of a vector in normalized stokes space.2. Using the PMD vector the frequency derivative of the Stokes vector S is defined as. The change in the PMD vector with wavelength results in higher-order PMD. Using e Sω it can be shown that with a change in frequency the output PMD vector rotates around the PSP’s. the average PCD in [ps2 ] is related to the square of the average PMD. var(< ∆τω >) = 3π 2 · < ∆τ >4 .5831· < ∆τ >2 . dτ τω = = ∆τω p + ∆τ pˆω . When visualized on the Poincar´ e sphere the PSP’s would trace out a random path with frequency. ˆ (2. ∂S = τ × S. be determined by measuring the change in DGD over either time or frequency and an overview of PMD measurement techniques can be found in [56]. and the PMD consists only e of the DGD. We limit here the description of higher-order PMD to second-order PMD (SOPMD). the PMD-related penalties in state-of-the-art transmission systems are often dominated by PMD in the dispersion compensation and fiber amplifiers.2 Second-order polarization mode dispersion The change in SOP under the influence of fiber birefringence is wavelength dependent. which is then denoted by. The first frequency derivative describes SOPMD. 2. The probability distribution of PMD can. The second term denotes the change of the PSP with frequency ( pˆω ) and describes the depolarization of the signal.17) ∂ω This describes how S rotates over the Poincar´ sphere when the frequency is changed. 4 Nonlinear transmission impairments Optical fibers are essentially a nonlinear guiding medium for electromagnetic waves at deep infrared wavelengths. It results in a change of the optical power in the transmission link. In the remainder of the thesis we assume 3-dB of PDL as a realistic figure for a long-haul transmission link. the noise emitted in the orthogonal polarization can become polarized parallel to the signal. which can cause an increase in DGD and SOPMD related impairments. The influence of ASE orthogonal to the signal is minimal as it does not coherently interfere with the optical signal. SOPMD can be particulary important for higher symbol rates (e. However. The impact of PDL is more significant for modulation formats which use the SOP to transmit information. This results from the high confinement of the propagating electromagnetic waves to the core of a single-mode optical fiber. due to the fourth power dependence between SOPMD variance and average DGD.g. The amount of average PDL that results in a penalty of 1 dB (with probability of 99. it requires unrealistically high values of PDL before a noticeable penalty occurs. The polarization dependent change in optical power causes depolarization.3 Polarization dependent loss Polarization dependent loss (PDL) refers to the polarization dependence of the insertion loss. frequency and along the fiber.9%) due to PDL-induced OSNR fluctuations is approximately 3 dB [58. However. It mainly occurs in in-line optical components.Chapter 2. 59]. in the presence of severe PDL.3. and the worst-case cumulative PDL is normally much lower than the added PDL of all components in the link. This can be of particular importance for optical transmission systems that use PMD compensation.4. which depends on the random evolution of the SOP over time. 40 Gbaud). because of the broader spectral width of the signal. such as isolators and couplers. the influence of SOPMD is normally small for lower symbol rates (e. as both PSP’s are no longer orthogonal to each other. For SSMF. 2.3. or which periodically change the SOP to enhance the nonlinear tolerance. The PDL at the end of the transmission link is therefore statistically distritbuted. 10 Gbaud).g. PDL further impacts the probability distribution of DGD and SOPMD. 22 . But as reported by Shtaif and Rosenberg in [59]. the effective area of the fiber core is typical 85 µm2 and it is even smaller for fiber types such as DCF or NZDSF. 2. and can result in fluctuations in the OSNR. Although silica is only a weakly nonlinear medium. Compared with the impact of DGD. The fiber-optic transmission channel This shows that the SOPMD variance is related to the fourth power of the average DGD. the nonlinear properties of optical fiber are important to consider. The OSNR consists of both ASE polarized parallel to the signal and ASE polarized orthogonally to the signal. This is discussed in more detail in Section 7. which causes an OSNR penalty [57]. the influence of SOPMD can increase considerably for high average PMD. cross phase modulation (XPM. Such nonlinear processes are called non-resonant and can be described as an intensity dependent variation in the refractive index of the silica fiber. This is especially the case for long-haul optical transmission links. In non-elastic processes the optical field transfers a part of its energy to the dielectric medium.t) = − 2 − µ0 . 1 ∂ 2 E(z.3). also known as nonlinear phase noise.4. The third type of nonlinear processes are known as the resonant processes or non-elastic scattering processes.2.5) and intra-channel XPM and FWM (Section 2. The nonlinear Schr¨ dinger equation (NLSE) is related to the Schr¨ dinger equation o o used in quantum mechanics and models the evolution of a (single polarization) optical field E(z.21) dispersion Where E is the complex envelope of the optical field. It can be written as: ∂E = − ∂z α E 2 attenuation − j β2 ∂ 2 E + 2 ∂T2 β3 ∂ 3 E 6 ∂T3 dispersion slope + jγ|E|2 E Kerr nonlinearities (2.4. Section 2. 2. which is proportional to the power of the optical field times the nonlinear coefficient γ. discovered in 1875 by John Kerr. The impact of nonlinear phase noise on optical transmission systems is discussed in Section 2.1 Pulse propagation The Schr¨ dinger equation. The most important nonelastic scatting processes. (2. the light intensities within the fiber’s core are then in the MW /m2 range. which describes the propagation of light through an optical fiber and is denoted by.4.t) ∇ × ∇ × E(z. where nonlinear impairments add up over long propagation distances. The term jγ|E|2 E represents the nonlinear contribution to the NLSE. four-wave mixing (FWM.7. For such intensities.2.t) ∂ 2 P(z.8. The nonlinear coefficient can be derived from the wave equation.t) in an optical fiber [42]. This change in the refractive index of a fiber is known as the Kerr effect. z the propagation distance in [km]. cross-polarization modulation (XPolM. the nonlinear properties of optical fiber become important. Section 2. The second type of nonlinear processes describes the nonlinear interaction between signal and noise.4.4. There are three types of nonlinear processes that are important for optical transmission systems.4).and o o time-dependence of a quantum mechanical system and plays therefore a central role in quantum mechanics. Nonlinear transmission impairments For optical powers in the mW range. Section 2.6).4. The first type are the nonlinear processes where there is no energy transfer between the optical field and the dielectric medium.4. The most important Kerr nonlinear processes are self-phase modulation (SPM) which is discussed in Section 2. T = t − β1 z is the time measured in a retarded frame and α is denoted in [N p/km].4. stimulated raman scattering (SRS) and stimulated Brillouin scattering (SBS) are discussed in Section 2. proposed by Erwin Schr¨ dinger in 1926 describes the space.22) c ∂t 2 ∂t 2 23 .4. . For silica fiber it is approximately n2 = 2.t).. The linear refractive index is related to the first order susceptibility χ (1) by: n0 = 1 + Re{χ (1) }. The fiber-optic transmission channel where ∇ is the vector differential operator. This can 24 . are related to χ (2) . |E|2 ) = n0 (ω) + n2 |E|2 /Ae f f . a tensor of order n +1. the influence of fiber nonlinearities is not evenly divided over the fiber length but the majority of the nonlinear interaction takes place in first part of the fiber. The dependence of the refractive index on the power of the optical field is denoted by.t) the dielectric polarization vector. λ · Ae f f (2. it changes the refractive index of the fiber. n(ω.t) the electrical field vector and P(z. (2. E(z. (2.24) where |E|2 in [W ] is the power of the optical field in the fiber.Chapter 2. Higher order susceptibility are small and can be neglected. When the optical frequency of the signal is far away from the resonance frequency of the medium (in this case silica) the dielectric polarization vector P(z. In highly nonlinear fibers for nonlinear signal processing the nonlinearity can be as high as γ = 21 km−1 W−1 [60] while for a photonic crystal fibers this value can reach γ = 640 km−1 W−1 [61]. The first order susceptibility χ (1) determines the linear behavior of an optical fiber. . 3 (3) Re{χxxxx }. When an intense pulse travels through an optical fiber.6.t) + χ (2) : E 2 (z. For example. The second order susceptibility χ (2) vanishes for optical fibers because SiO2 is a symmetric medium.).25) The nonlinear contribution to the refractive index depends on the third order susceptibility χ (3) and the linear refractive index.t) + χ (3) . (2. γ= 2π · n2 . 3 (z.E (2.26) n2 = 8n0 The nonlinear refractive index is a material parameter which is related to the chemical composition of the optical fiber. n0 the linear refractive index and n2 in [m2 /W ] the nonlinear contribution to the refractive index.t) + . the nonlinear processes that enables optical phase conjugation as discussed in Section 3. P(z.3 km−1 W−1 . but this value is slightly higher for fiber doped with GeO2 [42]. However other materials can have a strong second order susceptibility.27) The nonlinearity coefficient for SSMF and a wavelength around 1.t) can be described as a power series of the electrical field vector E(z.3 · 10−20 m2 /W.23) where ε0 is the vacuum permittivity and χ (n) is the nth order susceptibility.. The nonlinear effects that play a role in optical transmission links are included through the third order susceptibility χ (3) .t) = ε0 (χ (1) · E(z. the nonlinear interaction in an optical fiber depends also on the effective core area Ae f f in [µm2 ]. The nonlinearity coefficient γ in [km−1W −1 ] combines the nonlinear refractive index and the effective core area of the fiber in a single coefficient. As a smaller core area results in stronger confinement of the light. Due to fiber attenuation.5 µm is γ = 1. Ae f f in [m2 ] the effective mode area. T ) · exp(− αz ) · exp( jφSPM (z. which is referred to as self-phase modulation (SPM). which has an asymptotic behavior for increasing fiber length.30) where E(0. When two pulse components with different frequency are overlapping they 25 .21 reduces to ∂E α = − E + jγ|E|2 E .2 Self-phase modulation The nonlinear change in the refractive index causes an intensity dependent nonlinear phase shift. (2.31) α The maximum nonlinear phase shift is obtained after propagation over length L and for a peak power P0 at the center of the pulse (T = 0).31 then reduces to. T )) 2 (2.4. The combined effect of SPM-induced nonlinear chirp and chromatic dispersion results in amplitude distortions. this results in a SPM-induced chirp.2 dB/km and a fiber span of 100 km the effective length is equal to 21.max = γP0 Le f f . In this case Equation 2. For example. φSPM. which results in. This is discussed in more detail in Section 3. where along the fiber the chromatic dispersion is compensated. 2. which causes pulse broadening. The signal power as a function of the transmission distance is also referred to as the power map. T )|2 . E(z. (2. Because nonlinear impairments results from the combined impact of fiber nonlinearities and chromatic dispersion. (2. for a fiber attenuation of 0. T ) = E(0.2. Equation 2. T ) is the complex field amplitude at z = 0 and the SPM induced nonlinear phase shift is defined as 1 − exp(−αz) φSPM (z. i. The SPM-induced nonlinear chirp shift the leading edge of a pulse to lower frequencies (red-shift) and the trailing edge of pulse to higher frequencies (blue-shift). Nonlinear transmission impairments be denoted by the effective length of the fiber. 1 − exp(−αL) Le f f = . T ) = γ|E(0.4. the asymmetric power map in a fiber has a strong impact on the dispersion map.29) ∂z 2 attenuation Kerr nonlinearities This equation can be solved analytically. For long fibers this van be approximated with Le f f ≈ 1/α.5 km.e.32) Equation 2.28) α where α is defined in [N p/km].31 shows that the nonlinear phase shift changes across the pulse because different parts of the pulse have a different intensity. the red-shifted and blue-shifted parts of the pulse travel at a different speed. The impact of SPM can be analytically studied using the NLSE in the absence of chromatic dispersion. In the presence of chromatic dispersion.3. (2.1. 8: Eye diagrams showing the impact of SPM after 100-km SSMF with 15-dBm input power. this would require a loss-less fiber as the fiber attenuation destroys the balance between chromatic dispersion and SPM. al. the nonlinear SPMinduced chirp cannot be compensated as this would require a material with a negative Kerr effect. Soliton propagation has been an extensive field of research throughout the 1990’s [64.3 km−1W −1 . they are commonly referred to as nonlinear impairments. However. The fiber-optic transmission channel interfere. This can be used to reduce the impact of SPM by appropriately choosing the residual chromatic dispersion at the receiver. This is know as soliton propagation and was first demonstrated by Mollenauer et. which is also known as dispersionmanaged soliton transmission [67]. and therefore (partially) cancel each other out. which increased inter-channel impairments in WDM transmission system [66]. Ideally. D = 17 ps/nm/km) with a 15-dBm input power. Figure 2. The balance between chromatic dispersion and SPM induced chirp can also be used to construct transmission links where the signal propagates undistorted by chromatic dispersion or fiber nonlinearity [42]. no residual dispersion and (c) nonlinear transmission. 65] as it allows for error-free transmission over Trans-oceanic distances. soliton propagation is also possible for lossy fiber.Chapter 2. 26 . 600-ps/nm residual dispersion. The combined effect SPM-induced nonlinear chirp and chromatic dispersion can be used to reduce the impact of nonlinear impairments. As these amplitude distortions are dependent on the signal power. which causes amplitude distortions.8c) nearly the same eye opening is obtained as in the absence of nonlinear impairments. Unlike chromatic dispersion. although it requires small amplifier spacings. Figure 2. When the SPM induced phase shift is partially compensated with 600-ps/nm of chromatic dispersion (Figure 2. Figure 2. which is known as post-compensation [62].8 depicts an example of SPM-induced signal distortions. But a drawback of transmission systems using soliton propagation is that they require a low chromatic dispersion coefficient for high bit rates. In WDM transmission systems it is therefore preferable to use in-line dispersion management. (a) linear transmission (b) nonlinear transmission. The eye diagrams show transmission over a 100-km SSMF span (γ = 1.8b shows the impact of SPM through overshoots near the edge of the pulse. in 1980 [63]. For a positive chromatic dispersion coefficient (D > 0) the nonlinear and dispersion-induced chirp have opposite signs. XPM is therefore most detrimental for narrow channels spacing or low dispersion fiber [68.35) LW = |β12 − β11 | |β2 |∆ω where β1k is the group velocity for the kth co-propagating pulse with k = 1. the smaller the difference in nonlinear phase shift will be across the pulse at ω2 .23). The factor 1/3 results from the weaker interaction between two orthogonal polarizations. In the extreme case. |Ek |2 (2. which double for two distinct optical frequencies compared to the single (degenerate) case [42].34) When two pulses at different wavelengths propagate along the fiber perfectly overlapping each other (in the absence of chromatic dispersion) the impact of XPM is similar to SPM. in an optical transmission system with 27 . The nonlinear phase shift interacts with chromatic dispersion along the link. Consider the nonlinear phase shift that a pulse at ω1 imposes on a pulse at ω2 .2 ) = n0 (ω) + n2 (|Ek | + B|E3−k | )/Ae f f . 2 2 n(ω. as is the case in WDM transmission systems. In Equation 2. The faster the two pulses walk-off.4. For example. both pulses walk-off fast enough that the nonlinear phase shift is nearly constant across the pulse and the impact of XPM diminishes. The XPM efficiency is therefore related to the walk-off length LW in [m]. Neglecting chromatic dispersion results in expression 2. φk (z) = γ(|Ek (0)|2 + c|E3−k (0)|2 ) 1 − exp(−αz) . There is only a distinction between SPM and XPM in the case both pulses have a clearly separated spectrum. Nonlinear transmission impairments 2. 69].33) k=1. which converts the phase shifts into amplitude distortions. 2.2. When both channels have the same polarization B is equal to 2 and when they are orthogonally polarized B is equal to 2/3.3 Cross-phase modulation Cross phase modulation (XPM) describes the nonlinear phase change through the Kerr effect that results from the interaction with another optical pulse at a different wavelength. This implies that impact of XPM decreases both for higher chromatic dispersion and a higher symbol rate. T0 T0 ≈ . Chromatic dispersion decreases the XPM induced nonlinear phase shift as both channels have a different group velocity and therefore walk-off from each other.4. where B is a measure for the difference in polarization between the two channels. The walk-off length is further dependent on the symbol period T0 . ∆ω is equal to |ω1 − ω2 | and proportional to the difference in wavelength. The factor two stems from the number of terms of the χ (3) susceptibility that contribute to the nonlinear polarization rotation (Equation 2. The XPM induced nonlinear phase shift is however more detrimental when the two pulses at different wavelengths are partially overlapping in time.33 the refractive index is denoted a function of two co-propagating wavelength channels [42]. (2. One part of the pulse will experience a nonlinear phase shift whereas the other part of the pulse will be unaffected.34 for the total nonlinear phase shift induced through SPM and XPM when two channels are co-propagating. α (2. The impact of XPolM becomes more detrimental for multiple co-propagating WDM channels. polarization interleaving complicates system design as it requires the transmitter to use polarization maintaining components up to the point where the orthogonally polarized WDM channels are multiplexed. In the context of equalization. In the context of optical or electrical equalization of nonlinear impairments there is a further significant difference between SPM and XPM.3. However.4. In the case of SPM. This is evident by computing the magnitude of the nonlinear refractive index for. The reduced XPM efficiency between neighboring WDM channels with an orthogonal SOP is exploited in polarization interleaved transmission systems [71. |Ey |2 )) is independent of the SOP.36 shows that the strength of XPolM between orthogonal polarization components is a factor 2 of the SPM strength when only a the single polarization is considered. |Ex |2 ) + n(ω. which can be considered as a XPM-like effect. The total nonlinear phase shift in a single WDM channel is therefore independent of the SOP.Chapter 2. the source of the impairment are trailing or leading pulses at the same wavelength. However.36) ⎩ 2 ) = n (ω) + n (|E |2 + 2 |E |2 ).1) and shifting or scrambling the relative timing between adjacent WDM channels with optical delay lines [73]. |Ey | y 0 2 3 x Equation 2. both polarization components carry a portion of the same signal and XPolM has therefore a similar impact as SPM [42].4 Cross-polarization modulation Cross-polarization modulation (XPolM) is an extension of SPM when the two orthogonal polarizations in the fiber are considered. n(ω. For XPM. However. the source of the impairment are neighboring WDM channels that are unknown to any (practical) equalizer. we 3 can also observe from Equation 2. respectively. Ex = 1. 72].e. Further techniques to reduce the impact of XPM-induced nonlinear impairments are optimization of the dispersion map (see Section 3. |Ex |2 ) = n0 (ω) + n2 (|Ex |2 + 2 |Ey |2 ) 3 (2.36 that the refractive index of both polarizations components combined (i. 2. n(ω. Nonlinear interaction between both polarization components at the same wavelength results in coherent coupling. As an example we assume that a pulse train propagates at a frequency ω1 with its power equally √ divided over the two orthogonal polarizations Ex = Ey = 1/2 · 2. XPM induced impairments therefore appear as noise. ⎧ ⎨ n(ω. the nonlinear impairment is XPM dominated for a 25-GHz WDM channel spacing [70] and SPM dominated for a 100-GHz WDM channel spacing. 75]. The source of the impairment is thus known to an equalizer with memory. The fiber-optic transmission channel SSMF and a 10-Gb/s symbol rate. which can therefore (partially) compensate for it [74. which reduces the XPM caused by the nearest neighbor channels. The SOP of a second copropagating pulse train at a frequency ω2 is such that all power propagates in one of the polari28 . Ey = 0 and Ex = Ey = √ 1/2 · 2. This is evident by considering the nonlinear contribution to the refractive index ∆nx and ∆ny for a two-polarization model. In this case. 81]. For equally spaced WDM channels (e. The nonlinear phase shift induced on the Ey component of a pulse at ω1 is then smaller by a factor 3 compared to the Ex component. n1 ω1 + n2 ω2 = n3 ω3 + n4 ω4 . XPolM is particulary detrimental when a polarization sensitive receiver is used. Two or three photons are annihilated and new photons are created at difference frequencies such that the net energy and momentum are conserved.37 [79]. such as DSF [80. In the presence of PDL. This results in a change of the relative phase difference between both polarization components Ex and Ey of the pulse. When two WDM channels at ω2 and ω3 are co-propagating this results in FWM products at ω1 = 2ω2 − ω3 and ω4 = 2ω3 − ω2 . (2. hence.5 Four-wave mixing Four-wave mixing (FWM) is a parametric nonlinear process which involves interaction between four optical waves. The second mixing process annihilates two photons and creates two photons. as the FWM products result in crosstalk for other co-propagating channels. Chromatic dispersion decreases the FWM efficiency considerable as the difference in phase velocity causes the phase matching condition to be only satisfied over a short transmission distance. Nonlinear transmission impairments zation components Ex = 1. The frequency (left) and phase matching (right) conditions are denoted in Equation 2. FWM generates two photons at the Stokes and anti-Stokes wavelengths of ω2 . Ey = 0.2. The FWM efficiency depends on the frequency and phase matching among the four optical waves. as the depolarization translates into amplitude distortions when a single polarization is filtered out [77.4. The phase matching condition for this process is hard to satisfy in an optical fiber and is therefore not of significance to optical transmission systems. 2. There are two distinct four wave mixing processes. which in turn changes the SOP. This is illustrated in Figure 2. hence the name four-wave mixing. The phase condition is most easily satisfied in the case ω1 = ω2 .37) Where ω j is the frequency and n j the refractive index of the fiber at this frequency. on a 50-GHz wavelength grid) FWM has the worst impact.4. ω1 + ω2 = ω3 + ω4 . This decreases FWM efficiency considerable and is therefore only the dominating Kerr nonlinear impairment for small WDM channel spacings and low dispersion fiber. the depolarization is converted into amplitude fluctuations. which follows from Equation 2. In particular for polarization-multiplexed transmission (Chapter 7) this results in crosstalk between the two polarization tributaries. in this case different WDM channels. A 29 .9. In the first process three photons are annihilated and a new photon is created at the sum frequency of the three photons (for example third-harmonic generation). which are located at frequencies ω3 and ω4 . it results in a noise-like change of the SOP and. 78]. Because the SOP change depends on the pulse train at ω2 . This depolarization can severely degrade the efficiency of PMD compensation [76].g.33. The Stokes shift ω2 − ω3 = ω4 − ω2 depends on the fiber parameters. depolarization. which is also referred to as degenerate FWM. 4. similar to a linear transmission link. This effect is the most evident for amplitude modulated signals. This transmission regime is known as pseudo-linear because. which results in two FWM products. which describe the interaction between co-propagating WDM channels. which averages out the nonlinear interaction between symbols from the same wavelength channel as well as the interaction between co-propagating WDM channels. When subsequently the accumulated dispersion 30 . Intrachannel XPM (IXPM) and intra-channel FWM (IFWM) are a subdivision of SPM. IFWM results in energy transfer between subsequent time slots [85. 86]. with pure single pulse SPM sometimes referred to as isolated SPM (ISPM).9: Principle of four-wave mixing. The FWM efficiency is also reduced when the polarization of the neighboring WDM channels is orthogonal.28) is significantly larger than the normalized dispersion length (Equation 2.8). IXPM and IFWM are particulary important for transmission at bit rates of 40-Gb/s or above and high dispersive fiber such as SSMF [85. potential solution to reduce the FWM efficiency is the allocation of unequal channel spacings. Pseudo-linear transmission occurs when the normalized nonlinear length (Equation 2. The IFWM induced energy transfer further results in amplitude jitter in the ’1’ symbols. This is illustrated in Figure 2.Chapter 2. Intra-channel XPM and FWM occur mainly in transmission links with high dispersive fiber. 87]. and is therefore referred to as intra-channel XPM and FWM. The fiber-optic transmission channel FWM 2 3 1 2 3 4 Figure 2. but this significantly reduces the number of allowable WDM channels [82. as it creates ghost pulses in the time slots where a ’0’ is transmitted.6 Intra-channel XPM and FWM The nonlinear interaction that occurs between subsequent pulses at the same wavelength is very similar to XPM and FWM. 83].10 where a ’0’ ’1’ ’1’ ’0’ sequence is transmitted over high dispersive fiber. 2. as a single pulse is spread out over multiple time slots. as is the case for polarization interleaved transmission systems [71. For such bit rates. the optimum residual dispersion is close to zero. At the same time the Kerr effect causes both pulses interact with each other. the impact of FWM can generally be neglected. the signal waveforms evolves very fast when propagating along the fiber. For C-band transmission systems using SSMF. 72] or when using the higher dispersion coefficient in the L-band [84]. Along the fiber the signal is dispersed and the pulses are spread out beyond their respective time slots. The XPM and FWM processes explained in the previous section are inter-channel nonlinear effects. 92] 31 . This is.7 Nonlinear phase noise Nonlinear phase noise results from the interaction between the optical signal and ASE induced power fluctuations. is compensated at the receiver. The impact of intra-channel XPM and FWM impairments in high-dispersive transmission links can be reduced through a symmetric transmission link. which is referred to as SPM induced nonlinear phase noise [90]. IXPM generates a frequency shift due to the intensity change of the overlapping pulses. 2. as discussed in Section 3. This results in a different power for each pulse. mid-link optical phase conjugation allows for a symmetrical link design.11 illustrates this origin of nonlinear phase noise through the interaction of ASE with the Kerr effect. Several methods have been demonstrated to reduce or cancel out the impact of nonlinear phase. When ASE from optical amplifiers is added to the signal along the transmission link. The nonlinear phase shift introduced through the Kerr nonlinearity is then the same for each pulse. When the signal propagates further along the link the pulses then experiences a difference in nonlinear phase shift. possible by evenly splitting the chromatic dispersion compensation between the transmitter and receiver [88] In addition. These power fluctuations are transformed into phase noise through interaction with the Kerr effect.2.6. for example. Figure 2. It is only of significant importance for modulation formats that encode the information in the phase of the optical signal.10: Impact of intra-channel FWM (after [85]).4. each pulse interferes constructively or destructively with the ASE. Nonlinear transmission impairments Chromatic dispersion Kerr nonlinearity Chromatic dispersion compensation 0 1 1 0 FWM 0 1 1 0 t E E t E t E Ghost pulses t t t t t Figure 2. Through the interaction with chromatic dispersion this frequency shift is subsequently converted into timing jitter [86]. the two FWM products appear as ghost pulses in the time slots where a ’0’ is originally transmitted.4. a phase modulated signal has a regular pulse shape and each pulse contains an equal amount of optical power. Ideally. Nonlinear phase noise was first described by Gordon and Mollenauer in 1990 and is therefore commonly referred to as the Gordon-Mollenauer effect [89]. including optical phase conjugation [91. The impact of nonlinear phase noise is also strongly dependent on the OSNR along the transmission link. Nonlinear phase noise is therefore mainly the dominating impairment for D(Q)PSK modulation at < 20-Gb/s bit rates or transmission over low dispersion fiber. The nonlinear phase noise strength is dependent on both the fiber chromatic dispersion coefficient as well as the OSNR along the transmission link [95]. the path-averaged OSNR. i. As the OSNR requirement increases for high bit rates. 95] or electronic [96] means. Alternatively. and semiconductor optical amplifier based optical regeneration [93]. In this case the ASE that is added along the transmission link changes the power level of the co-propagating channels. signal processing in the receiver could take the ying-yang shape into account when making a decision on the data [95]. The constellation diagram in Figure 2. This is possible through either optical [94. Nonlinear phase noise can further result from interaction through XPM. For XPM induced nonlinear phase noise. which either enhances or reduces the XPM-induced nonlinear phase shift. For example. there is no correlation between signal power and phase shift in the constellation diagram. the power in a symbol period changes rapidly along the fiber which averages out the nonlinear phase shift contribution. which makes it more difficult to compensate for. This correlation between signal power and nonlinear phase shift can be used to reduce the impact of SPM induced nonlinear phase noise.e. in the receiver a phase shift can be applied to each symbol that is dependent on the intensity of the symbol.Chapter 2. 32 .11: Impact of nonlinear phase noise on optical transmission systems.11 shows the typical nonlinear phase noise induced ying-yang shape. such as DSF. The fiber-optic transmission channel ASE 10-3 Kerr effect Im(E) 10-3 Probability 10-4 10-5 Im(E) 10-4 10-5 BER = 10-4 10-6 n2 Probability Intensity Re(E) 10-6 Re(E) Figure 2. For high dispersive fiber. This reduces the impact of nonlinear phase noise as the ASE power is not large enough to make a significant contribution to the total nonlinear phase shift. The difference in XPM strength in turn translates into nonlinear phase noise. so will the path-averaged OSNR. In WDM transmission.2. The SRS efficiency dependent on the fiber type and the intensity of the incident pulse [97]. Raman scattering can result in stimulated emission when co-propagating WDM channels are present within the Raman bandwidth.2 THz ≈ 100 nm downshifted from the original frequency. which use the fiber as a gain medium by launching a strong pump signal in the fiber. a continuous spectrum is created with a peak value around 13. SRS 1 2 3 4 1 2 3 4 Figure 2. Non-elastic scattering effects depend on the interaction between the optical pulses and the silica molecules of the optical fiber. The optical pulses transfer a part of the photon energy to the dielectric medium. The origin of Raman scattering is related to the imaginary part of the χ (3) susceptibility (see Equation 2. For long-haul optical transmission systems the input power per channel is generally lower than the SRS threshold. In particular when the optical power is above a critical power. Raman scattering transfers a part of the photon energy to the silica molecule which makes a transition to a higher-energy vibrational state. the Stokes band will build up nearly exponentially. this is called the Stokes band. which is not a crystalline material. Time averaged SRS crosstalk results in a gain tilt 33 . Nonlinear transmission impairments 2. SRS is the most effective when both channels have the same polarization and the wavelength difference is close to the 100 nm Raman gain peak. SRS can be exploited to create Raman amplifiers [98]. Raman amplifiers are discussed in more detail in Section 3. The most important non-elastic scatting effects in optical transmission are stimulated raman scattering (SRS) and stimulated Brillouin scattering (SBS).12: Principle of Stimulated Raman Scattering.2. The frequency shift of the generated photon is dependent on the propagating material. For silica.8 Non-elastic scattering effects The second class of nonlinear effects important to optical transmission systems are the nonelastic scattering effects.2. which does not transfer any energy to the silica molecule.4. However. which results in unwanted crosstalk. it normally scatters through elastic Rayleigh scattering. for a small fraction of the photon-molecule collisions (∼ 10−6 ) Raman scattering occurs. hence SRS-induced impairments are normally not significant. SRS can also occur between neighboring channels. the SRS threshold.23. whereas the Kerr nonlinearities have their origin in the real part. When a photon collides with a silica molecule of the fiber. This transfers energy from the high frequency channels to lower frequency channels and can result in bit-dependent [99] and time averaged SRS crosstalk [100]. Bitdependent crosstalk behaves similarly as XPM and its impact is therefore relatively small for fibers with a high dispersion coefficient [99].4. In the process a lower frequency photon is generated. However. for optical transmission systems SBS is not of significant importance as it nearly vanishes for pulses shorter than several nanoseconds. 34 . An optical signal traveling through the fiber generates an acoustic wave. Stimulated Brillouin scattering (SBS) results from the interaction between photons and acoustic waves. The power reflected through SBS increases exponentially when the power is above the SBS threshold. This periodic variation of the refractive index scatters the light of the incident wave through Bragg refraction. The virtual Bragg grating is moving with a certain acoustic velocity. SBS therefore limits the optical power that can be launched into the fiber. This crosstalk can be reduced in optical transmission systems using dynamic gain equalizers (DGE) along the transmission link. However. This generates a backwards propagating wave. Phase modulation of the optical signal is also an effective method to reduce the SBS efficiency.Chapter 2. counter-directional to the optical signal. The fiber-optic transmission channel in the WDM spectrum as depicted in Figure 2.12 [101]. which causes a Doppler shift of ∼10 GHz between the backward reflecting wave and the optical signal [42]. which in turn modulates the refractive index of the optical fiber in a periodic manner. or even quadratically. Section 3. chromatic dispersion. in Section 3.3 then describes the chromatic dispersion compensation in long-haul optical transmission systems and the design of dispersion maps. if possible. with the bit rate.5 describes the impact of optical-add-drop multiplexing in transparent optical networks. After a binary decision.1 the optical transmitter and receiver are discussed. First of all. PMD and nonlinear impairments. ideally.1 Transmitter & receiver structure An optical transmission link can be defined as the physical medium over which an information carrying optical signal propagates between a transmitter and a receiver. to build robust long-haul transmission systems at high bit rates these transmission impairments should be considered and.6. The tolerance with respect to these limitations scales linearly. Subsequently. This chapter deals with the design of long-haul optical transmission systems and the required technologies to compensate for the dominant transmission impairments. At the receiver. This section 35 .2 the periodic amplification of optical signals is explained. generally the output of a laser. compensated. the optical signal is again converted into an electrical signal using one or more photodiodes. in Section 3. optical bandwidth. In the transmitter an optical carrier. the transmitted bit sequence is again obtained. In Section 3. 3. Finally in Section 3. is modulated with a bit sequence. optical phase conjugation is discussed as a potential technology to compensate for nonlinear impairments. Hence.4 the compensation of PMD is briefly treated and Section 3.3 Long-haul optical transmission systems In long-haul WDM transmission systems there are basically five dominant limitations: OSNR. When subsequently a narrowband optical filter is placed after the DML the frequency modulation is converted into intensity modulation with a high extinction ratio [104]. Modulation with an EAM can result in an optical signal with lower chirp than a DML and a high electro-optical bandwidth can be realized [105]. This can be achieved by a variety of modulation technologies. e. In order to realize high-speed modulation an optical modulator should have (1) a high electro-optical bandwidth. The most widely used device for optical modulation is the MZM. first proposed by Ernst Mach [106] and Ludwig Zehnder [107]. An EAM modulates the optical field by controlling the absorption of the device material using the externally applied voltage. and Indium Phosphide (InP) [110]. as show in Figure 3. In addition. High-speed modulation of a DML introduces frequency chirp. EAMs mainly find applications in low-cost 10-Gb/s transmitters but have also been used extensively in (single-channel) OTDM transmission experiments. 3. However. high insertion loss (10 dB typical) and a limited optical input power. up to 2.1. In such an electro-optic crystal the refractive index depends on the applied 36 . external modulators are generally required as they result in a nearly chirp-free signal.1.3 explains the use of forward error correction in optical communication systems. EAMs have a wavelength dependent performance. Although DMLs have been shown to operate at bit rates up to 40 Gb/s [102.1) and receiver structure (Section 3. The frequency chirp broadens the modulated spectrum. which include directly modulated lasers (DML). frequency chirp reduces the chromatic dispersion tolerance.g.1.1 Optical modulation Optical modulation is the conversion of a signal from the electrical into the optical domain. Long-haul optical transmission systems discusses the most common optical modulation principles (Section 3.1. They are today mainly used in low-bit rate applications. but sometimes other materials are used such as Gallium Arsenide (GaAs) [109]. which makes it unattractive to use DML in WDM systems. alongside the desired intensity modulation and reduces the extinction ratio. electro-absorption modulators (EAM) and Mach-Zehnder modulators (MZM). A special application of DMLs that is better suited for high-speed modulation is the use of frequency instead of amplitude modulation. For high-speed modulation.2). A DML is a very cost-efficient modulation technique as it is compact and does not require any further optical components apart from the transmitter laser.1. depending on the electrical drive signal applied to the modulator. 103] their modulation bandwidth is limited. Optical modulation can be most easily realized by direct modulation of the laser drive current. (2) low optical insertion loss. The extinction ratio is defined as the ratio of the energy in the ’0’ compared to the energy in the ’1’s. low extinction ratio (<10 dB typical).5 Gb/s or short-reach 10-Gb/s transmission.Chapter 3. A MZM consists of two 3-dB couplers with two interconnecting waveguides of equal length to create an interferometer. An external modulator switches the incoming continuous-wave laser output ON or OFF. Section 3. (3) not induce undesired frequency chirp in the signal and (4) have a high enough extinction ratio. The MZM waveguides are normally made from a Lithium-Niobate (LiNbO3 ) electro-optic crystal [108]. a residual phase modulation. The MZM can be used to generate several different optical modulation formats. The two waveguides of a MZM can be modulated separately. both waveguides can be coupled together. A dual-drive modulator. on the other hand. This is attractive for high-bit rates as there is a trade-off between the electrooptical bandwidth and the Vπ of the MZM. (a) Electrode Waveguide (b) Optical phase = 0 Optical phase = RZ66 Crest Transmittance Ein z x y (c) 3 Power (mW) Power (mW) 2 1 0 -40 3 2 1 Eout RZ50 Quadrature RZ33 Trough Bias V0 (d) 3 Power (mW) 2 1 (e) -20 0 20 40 0 -40 -20 0 20 40 0 -40 -20 0 20 40 Time (ps) Time (ps) Time (ps) Figure 3. which is known as dual-drive operation and which is used in Z-cut modulators. RZ pulse carving is widely used for different optical modulation formats as it is less sensitive to imperfections in the transmitter. i. the electro-optical bandwidth of the modulator and driver amplifier voltage swing. low insertion loss (4 dB typical) and is (nearly) wavelength-independent. 37 . for example. By choosing the electrical drive voltage level appropriately.1. In high bit rate optical transmitters this can help to reduce the often stringent requirement on. (d) 50% and (e) 66% pulse carving. the interference in the second 3-dB coupler can be either constructive or destructive. Transmitter & receiver structure electric field. (c-e) RZ eye diagrams for (c) 33%. A MZM is particulary suitable for long-haul transmission as it has a high extinction ratio (>20 dB typical). Another application of a MZM is pulse carving. The difference in drive voltage which changes the interference from constructive to destructive is known as the Vπ of the modulator. the conversion of a non-return-to-zero (NRZ) signal into a return-to-zero (RZ) pulsed signal. which in turn changes the velocity of the light propagating through the waveguide. has the drawback that it requires two broadband driver amplifiers to amplify the electrical drive signal to a sufficiently high peak-to-peak voltage.1: (a) Structure of a X-cut MZM. A typical Vπ for a single-drive LiNbO3 MZM modulator is ∼4 V.e. (b) Operation of a MZM for pulse carving. which is described in more detail in Chapter 4. high power and broadband driver amplifiers are therefore required.3. In a dual-drive modulator the peak-to-peak voltage swing of the electrical drive signal is reduced by a factor of two when a differential drive signal is applied to both waveguides. An electrical drive signal can therefore modulate the refractive index of the crystal. which is known as single-drive operation and which is used in X-cut modulators. In order to amplify the electrical drive signal to the required peak-to-peak voltage (Vpp ). Alternatively. Because of the more narrow optical spectrum. RZ modulation with a duty-cycle below 33% is possible by cascading two pulse carvers with a time offset between the two drive signals.2. bias voltage and drive signal voltage swing are summarized in Table 3.1c-e. the broadened optical spectrum reduces the chromatic dispersion tolerance somewhat [112]. This reduces the tolerance against narrowband filtering. but the most common one found in optical receivers is a p-i-n photodiode. which is a significant disadvantage for spectrally efficient optical transmission or optical transmission systems with cascaded optical add-drop filtering. The drive frequency. As a photodiode only detects the power envelope of the optical. RZ pulse carving. 3. RZ pulse carving Modulator Drive signal duty cycle bias voltage voltage swing 33% 50% 66% crest quadrature trough 2 · Vπ Vπ 2 · Vπ Drive frequency 0. Especially for a 40-Gb/s symbol rate. any phase information is discarded from the signal. The narrower the duty-cycle of the RZ pulse. the broader the optical spectrum and the higher the peak-to-average power.2 Optical receivers The most common configuration of an optical receiver is depicted in Figure 3. RZ modulation with a high duty-cycle is often preferred in WDM transmission. improves the PMD tolerance as the ISI between adjacent bits is reduced [112. i. There are several types of high-speed photodiodes. The main drawback of RZ modulation is the more complex transmitter structure as well as broadening of the optical spectrum.1. Note that RZ modulation with a 66% duty-cycle. Both types of optical receiver use a high-speed photodiode to convert the optical signal to the electrical domain. RZ modulation improves the tolerance against nonlinear signal impairments.1.5 · symbol rate The impact of transmission impairments changes significantly when comparing NRZ and RZ modulation. In addition. Both 33% or 66% duty-cycle are realized by driving a MZM with a sinusoidal drive signal at half the symbol rate.Chapter 3. This has been used in high-bite rate OTDM transmission experiments [114]. there is a clear improvement in nonlinear tolerance [111]. in addition to the amplitude modulation. The change in pulse shape is evident from Figure 3. Because of its more regular pulse shape.5 · symbol rate symbol rate 0. transmission limited by intra-channel nonlinear impairments. three different RZ pulse shapes can be generated. RZ pulse carving with a 50% duty-cycle is generated by driving a MZM with a sinusoidal drive signal at a frequency equal to the symbol rate. It is therefore often referred to a carrier-suppressed return-to-zero (CSRZ).e. Using a MZM. 113]. It can be subdivided in the lower speed optical receivers (up to ∼10-Gb/s) and high bit-rate receivers for 40-Gb/s transmission systems. A p-i-n photodiode is a semiconductor device that contains a p − n junction with an 38 . as depicted in Figure 3.1: D RIVE SIGNAL PROPERTIES FOR RZ PULSE CARVING WITH A MZM. also encodes a 180o phase shift between consecutive symbols.1. Long-haul optical transmission systems Table 3. on the other hand. which has typical peakto-peak voltage of 10 mV for 50Ω termination. 40-Gb/s receivers require tunable dispersion compensation (TDC) to optimize the accumulated dispersion. In the clock and data-recovery (CDR). Most p-i-n photodiodes have a responsivity of 50%-70%. a transimpedance amplifier is typically used for automatic gain control (AGC). an optical pre-amplifier is used in the receiver to amplify the signal.5µm . For lower speed optical receivers. The electro-optical 3-dB bandwidth of a photodiode should be in excess of 70% of the symbol rate. and a photodiode therefore low-pass filters the signal. this is discussed in more detail in Section 3. In addition.3. FEC decoding is applied to recover errors that occurred in the received sequence and the transmitted data is extracted from the transport frame (e. and controls the gain such that a constant output voltage is obtained. as the optimum threshold changes under the impact of transmission impairments such as chromatic dispersion and PMD. A variable sampling threshold is normally used for data recovery. the bandwidth and gain of a transimpedance amplifier can be inadequate. For high-speed optical receivers. In this case. The signal is then time de-multiplexed for further processing. DEMUX 39 . This threshold can be optimized using a feedback signal from the forward error correction (FEC) that minimizes the BER. Transmitter & receiver structure undoped (intrinsic) layer between the n (negative) and p (positive) layers. the receiver is synchronized with the signal in order to sample at the correct time instant within the symbol period.1. a photocurrent is generated.2: Optical receiver configuration. Photodiodes for the 1. which defines the efficiency with which the photodiode converts the optical signal into a photocurrent. but high-speed photodiodes often have a somewhat reduced responsivity.6µm wavelengths range are normally made from indium gallium arsenide (InGaAs).g OTN [optical transport network] framing). When incident light is absorbed in the depletion region of the intrinsic layer. The data recovery then takes a digital decision on the signal. The electro-optical conversion in a photodiode cannot detect arbitrary high frequencies. The transimpedance amplifier amplifies the photocurrent. DEMUX PD 10 Gb/s AGC EDFA 40 Gb/s CDR PD FEC & framing TDC CDR control FEC & framing slow PD Figure 3.3. A photodiode is further characterized by its responsivity in [A/W ].1. Afterwards. for example. 40 . When the bit-errors are not Gaussian distributed but come in error-bursts (e. In optical transmission experiments.975 [118]. RS or Boss-ChaudhuriHocquenghem (BCH) codes or a combination of both. which defines the difference in required OSNR for a BER of 10−13 with and without FEC coding.1. the Reed-Solomon(RS) code RS(255.3 Forward-error correction For long-haul transmission systems.988) with 10-fold iterative decoding. but the first application to fiber-optic transmission systems was reported by Grover in 1988 [116]. This code corrects a 2.3 dB. FEC has been used since the 1960s in radio communication. This increases the bit rate. where also more advanced codes using turbo codes and soft-decision decoding are discussed.1 subclause I. The highest BER before FEC that can be corrected to a BER below 10−13 after FEC is typically referred to as the FEC limit. In some long-haul transmission experiments in the literature a more advanced code is used that achieves a coding gain of 8. This code is known as the first-generation FEC and provides a coding gain of up to 5. Long-haul optical transmission systems 3. a coding gain of 8. These codes consist of two interleaved codes. In particular. the use of FEC is normally assumed by taking into account the 7% required overhead and measuring the transmission performance at the FEC limit. the signal quality at the receiver is normally too low to ensure error-free transmission (BER < 10−13 ).1 [119]. For such systems. FEC coding requires that some redundant information is added to the transmitted data. Such codes have a code gain of ∼ 8.1007)/BCH(2047. for example.709 Gb/s. An overview of FEC in optical transmission systems is given in [120].Chapter 3. This code is defined in ITU-T G.4. For the transmission experiments described in this thesis we assume the use of a concatenated RS(1023. PMD-induced) the FEC code might not be able to correct all bit-errors at the FEC limit. although in submarine ultra long-haul transmission a FEC overhead of 25% is normally used. 123]. FEC coding also increases the system robustness against signal impairments such as chromatic dispersion and PMD.8 dB with a 6. The use of FEC results in a coding gain. The first commercial applications of FEC were submarine optical transmission systems in the early 1990’s [117].5 dB and have been standardized in ITU-T G.69% overhead [122. This code is widely used in transmission experiments and deployed long-haul transmission systems [121].239) has been adopted for submarine-transmission systems and has been specified in ITU-T G.9 and consists of interleaved BCH(1020.975. A 4·10−3 BER before FEC is corrected by this code to a 1·10−13 BER after FEC.g. which is referred to as the FEC overhead. from 10 Gb/s to 10.975. where the individual codes can be. Nowadays. FEC enables the correction of bit-errors after transmission by encoding the data appropriately at the transmitter. In optical communication systems the typical FEC overhead is 7%. the most common error correcting codes used in optical transmission are known as second-generation FEC codes.1952) code with 7% overhead as defined in ITU-T G.1 subclause I.23 · 10−3 BER before FEC to a 1 · 10−13 BER after FEC. FEC coding therefore interleaves the data before transmission in order to obtain Gaussian-like error statistics after transmission [115].975.8 dB. The output isolator prevents that that the output light can be reflected back into the amplifier. Fiber loss compensation 3. The input signal and output of the pump lasers is combined using a pump combiner.2 Fiber loss compensation As discussed in Section 2. Either co-directional or counter-directional pumping is also possible when the required output power is not too high. On of the main advantages of optical amplification over optical-electrical-optical conversion is thats it can amplify the optical signal independently of modulation format and bit rate. this 41 . The energy levels (vibrational states) in Figure 3.000 km) periodic amplification is required after each fiber span in order to compensate for fiber loss.000 km . in order to realize long-haul transmission systems (1. defined later) to propagate backwards out of the amplifier input.1. In addition. Depending on fiber quality and splicing losses this translates into a span length between 80 km and 110 km.2. The actual optical amplification takes place in the Erbium-doped fiber with a typical length of ∼ 10 meters. optical amplification is nearly exclusively used to amplify the signal in between fiber spans. which is the most common for optical amplifiers that require a high output power.3a the fiber is bidirectionally (forward and backward direction) pumped by two laser diodes. The gain equalizing filter is necessary to ensure that all WDM channels are amplified uniformly and that a flat output spectrum is obtained. Gain equalization can be realized using a variety of filter technologies. The input isolator prevents light from the counter-directional pump or amplified spontaneous emission (ASE. A detailed overview of EDFA design and technologies can be found in [126]. a single amplifier can amplify the full C-band transmission window. In this section we discuss doped fiber amplifiers and Raman amplification. Early work on EDFAs was pioneered by Mears [124] and Desurvire [125] in 1987. The span length varies strongly in deployed transmission systems.3. which is due to the non-crystalline nature of silica.2.1 Erbium-doped fiber amplifiers In long-haul optical transmission systems. 3. In Figure 3. The most common type of optical amplifiers are Erbium doped fiber amplifiers (EDFA). In between the fiber spans different amplification technologies can be used to compensate for the fiber loss. Each energy level that appears as a discrete spectral line in an isolated Erbium ion is split into a manifold when silica glass is doped with the Erbium ions. However.3c are not discrete levels but rather a manifold.3a. such as thin-film filter [127] or long-periodicity fiber Bragg gratings [128]. which could cause lasing. but a typical design value is a span attenuation of 21 dB. The general structure of an EDFA is shown in Figure 3.3. The wavelength of the pump signal is either around 980 nm or 1480 nm. optical fiber is a low-loss transmission medium that allows for considerable transmission distances without re-amplification of the signal. which is pumped with light from one or more laser diodes. Optical isolators are normally required in optical amplifiers to prevent backreflections. which allows for a low insertion loss. EDFAs are constructed by doping a single mode fiber with Erbium (Er3+ ) ions and pumping the fiber with one or more pump lasers. from where there is a quick (∼ 1µs) non-radiative transfer (relaxation) to the 4 I13/2 manifold.Chapter 3. pump laser (1480 nm. 980 nm) Gain equalizing filter Isolator (a) Isolator Er3+ Pump combiner = 6. The spectral gain profile can be flattened by doping the Erbium-doped fiber with co-dopants such as Aluminium Oxide (Al2 O3 ) [126]. When a photon from the input signal collides with the Erbium ion it falls back to the lower vibrational state and at the same time releases a duplicate photon with the same properties (frequency. In the case of pumping with a 980-nm laser the ions are first exited to the 4 I11/2 manifold. An exception to this are systems that use burst-mode transmission where the burstinterval can be longer than the fluorescence time [129]. The typical gain of an EDFA can therefore be in excess of 40 dB. 42 .6µs 4I 11/2 Relaxation Gain (dB) = 10ms 4I 13/2 Stimulated Spontaneous emission emission 1530 1560 Wavelength (nm) 980 nm pumping 1480 nm pumping 4I 15/2 (b) (c) Figure 3. which is known as the fluorescence time. state of polarization). This is orders of magnitude longer than the bit rates that are normally used in optical communication systems (i. as first described by Einstein in 1917 [130]. from where they can amplify light in the 1500-nm wavelength region via stimulated emission.3b. The principle behind optical amplification is stimulated emission. this process is repeated numerous times which results in an exponential increase in signal power. a photon from the pump signal transfers a part of its energy to the Erbium ion which makes a transition to a higher-energy vibrational state.3: (a) schematic of an EDFA. which is generally sufficient to amplify up to 80 WDM channels in the wavelength band between roughly 1525 nm and 1570 nm. the EDFA generally exhibits a gain peak around 1530 nm. (b) gain spectra of a C-band EDFA and (c) energy level diagram of an erbium-doped silica fiber. As depicted in Figure 3. 2. or through the use of gain flattening filters. The 4 I13/2 manifold is metastable with a half-time of around 10 ms. The output power of an EDFA strongly depends on the number of pump lasers and their respective pump powers. A typical value for the EDFA output power is ∼23 dBm. Pumping with a 1480 nm laser excites the Erbium ions from the ground-state manifold 4 I15/2 into the 4 I13/2 manifold. In stimulated emission. In optical amplification.e. Long-haul optical transmission systems is known as the Stark effect.5-Gb/s to 40-Gb/s). The Stark effect explains why amplification occurs in a wavelength band rather than at a single wavelength. 4 shows the typical EDFA structure used in the long-haul transmission experiments discussed in this thesis.or L-band. 133]. Doping with other rare-earth elements can be used to construct optical amplifiers for wavelengths other than the C. praseodymium.5 such an amplifier is used as pump amplifier for phase conjugation. stimulated emission of the 1480-nm pump wave occurs along the Erbium-doped fiber.2. which are excited to a higher vibrational state. Fiber loss compensation Besides stimulated emission. where a large part of the output signal can consists of ASE. as part of the energy is lost through relaxation when the ion falls back to the 4 I13/2 manifold. but this requires a different optimization of the fiber length (∼ 100 m) and Erbium ion concentration. the small-signal gain as a function of pump power. a longer Erbium doped fiber is required which generally results in a higher noise figure. As the spontaneous emission is in turn also amplified along the optical amplifier. A practical C-band EDFA normally has a noise figure between 4 dB and 6.e. the emitted photon has an arbitrary frequency and state of polarization. In contrast to stimulated emission. The co-doping is often combined with double-clad amplifiers. ytterbium. The received optical signal is first fed into a pre-amplifier stage. In spontaneous emission. an ion in the high energy 4 I13/2 manifold falls back to the ground state. emitting a photon in the process. With a 1480-nm pump wavelength a higher power efficiency can be achieved as no transfer to the 4 I11/2 manifold occurs. Ytterbium doping can further be used to construct Ytterbium-Erbium co-doped double-clad optical amplifiers [132. Optical amplifiers for the L-band also used Erbium-doped fiber. A double-clad amplifier pumps the cladding of the fiber to obtain a more equal distribution of the pump power along the fiber length.3. Pumping the erbium-doped fiber with a 980-nm laser allows the highest gain efficiency and lowest noise figure. which reduces the OSNR. ASE is the most dominant for high gain amplifiers. Figure 3. A pre43 .5 dB. A single erbium-doped fiber can therefore not amplify both wavelength bands. i. also spontaneous emission occurs in an optical fiber amplifier. SSMF VOA DCM next span Pre-amp EDFA Booster EDFA Figure 3. The ASE generated by an optical amplifier is added to the amplified signal. The fraction of Erbium ions in the exited 4 I13/2 manifold is therefore much smaller. or thulium doped fiber amplifiers [131]. In Section 6. Such amplifiers can have output powers as high as 33 dBm. An optical amplifier can therefore be characterized with its noise figure.4: EDFA structure used in the long-haul optical transmission experiments. As a result. As the Ytterbium doping density can be much larger than the Erbium doping density this allows for a higher amplifier gain. The Ytterbium ions subsequently transfer their energy to the Erbium ions. which denotes the difference in OSNR between the input and output of the amplifier. which reduces the gain efficiency. Such a transfer reduces the power efficiency. this causes amplified spontaneous emission (ASE). In such amplifiers the 980-nm pump is absorbed by the Ytterbium ions. The EDFA belongs to a broader family of rare-earth doped fiber amplifiers that also includes neodymium. On the other hand. which results from the effect of SRS (see Section 2.Chapter 3.4 dB.8 µm2 . Backwards pumped Raman amplification is the most common and the power of the pump Pp (z) and signal Ps (z) can be expressed as follows. which is launched counter-propagating to the optical signal from the back-end of the transmission fiber. The VOA is used to dynamically reduce the tilt in the wavelength spectrum. in 1972 [134] and demonstrated by Hegarty et. Note that pump depletion is not included in this equation. In Figure 3.428 · 10−13 m/W for SSMF [98]. ⎧ ⎪ Pp (z) = Pp (L)exp(−α p (L − z)) ⎨ (3. This is known as hybrid EDFA/Raman amplification.1) ⎪ ⎩ Ps (z) = Ps (0)exp(−αs z)exp gR Pp (L) [exp(−α p (L − z)) − exp(−α p L)] Ae f f α p Where gR is the Raman gain coefficient in [m/W ].2.2 dB/km. which can either result from SRS along the fiber or the preamplifier amplification itself. αs = 0. α p = 0. a dispersion compensation module (DCM) is used for chromatic dispersion compensation. The use of SRS to construct a Raman amplifier was proposed by Stolen et. 3.8). The Raman ON/OFF gain can also be denoted through Gon/o f f = exp gR gR Pp (L) Pp (L)Le f f = exp [1 − exp(α p L)] . The attenuation coefficients are normally different for the pump and signal. al. The attenuation coefficients α p and αs in [N p/km] denote the fiber attenuation at the pump and signal wavelengths. The most well known type of Raman amplification is distributed Raman amplification. A Raman amplifier can be forward (co-propagating) pumped. This improves the OSNR compared to EDFA-only amplification as the lowest power that occurs along 44 . as the pump is in the 1445 nm wavelength region where the fiber attenuation is slightly higher. After the preamplifier.2) Raman amplification does not necessarily compensate the full span loss. Ps = 0 dBm. backward (counter-propagating) pumped or a combination of both (bi-directional). which is optimized for high output power. Pp (L) is the Raman pump power in [W ]. Long-haul optical transmission systems amplifier EDFA is optimized for high gain and a low noise figure. This results in Raman ON/OFF gain Gon/o f f of 12. The signal is then fed to the booster EDFA. and the remaining part can be compensated using an EDFA.25 dB/km and Pp = 24. generally. The combination of pre-amplifier and booster stage allows the realization of both a low-noise figure and high output power. which uses the transmission fiber as a gain medium.4. Ps in [W ] is the signal power launched into the transmission fiber.5 dBm.2 Raman amplifiers A Raman amplifier is an optical amplifier based on Raman gain.5a the optical signal power as a function of transmission distance is depicted for backwards pumped Raman amplification with Ae f f = 72. al. Ae f f Ae f f α p (3. The Raman gain coefficient of depolarized light is 0. The pre-amplifier stage can consist of two separate EDFAs with a variable optical attenuator (VOA) in between both amplifiers. in 1985 [135]. 3. The evolution of the signal and pump powers along the transmission fiber is now denoted through. backward and forward-pumped Raman amplification have the same ON/OFF Raman gain. using a 23. using the same parameters as the backward-pumped scheme. which results in increased nonlinear impairments (see Figure 3. (b) Forward-pumped Raman and (c) bi-directional Raman and all-Raman amplification.2.5: Optical signal power as a function of the transmission distance for (a) Backward-pumped Raman. Be45 Gon/off With Raman m an W t ou ith Ra an m W W t ou ith Ra an m t ou ith Ra an m . ⎧ ⎪ Pp (z) = Pp (0)exp(−α p z) ⎨ (3.5-dBm pump power for both co-propagating and counter-propagating directions. For the same pump power. except for all-Raman amplification which uses a total pump power of 26. The noise figure of a hybrid Raman/EDFA amplifier can be characterized with the effective noise figure.5 dBm. Fiber loss compensation Backward-pumped Raman amplification Forward-pumped Raman amplification Bi-directional Raman amplification 5 Al l-R 5 Signal power (dBm) 0 -5 5 Signal power (dBm) 0 Signal power (dBm) 0 -5 -10 -15 -20 W ith am an W ith Ra -5 -10 -15 -20 an m Ra -10 -15 -20 Gon/off Gon/off 0 20 40 60 80 100 Transmission distance (km) 0 20 40 60 80 100 Transmission distance (km) 0 20 40 60 80 100 Transmission distance (km) (a) (b) (c) Figure 3. Finally. Equation 3.5).2 is therefore also valid for forward-pumped Raman amplification when Pp (L) is replaced with Pp (0).3) ⎪ ⎩ Ps (z) = Ps (0)exp(−αs z)exp gR Pp (0) [1 − exp(−α p z)] Ae f f α p Figure 3. in bi-directional Raman amplification. All-Raman amplification is depicted in Figure 3. However. The effective noise figure of a Raman amplifier is defined as the noise figure that EDFA-only amplification would need to have in order to achieve the same OSNR as obtained with Raman amplification The effective noise figure of a hybrid EDFA/Raman amplifier can be as low as -3 dB [136.5b shows an example of the power evolution for the forward-pumped scheme. Raman pumps are both co-propagating as well as counter-propagating with the signal. This can be used for all-Raman amplification. All schemes use a total pump power of 24. the link is now much higher. This scheme is less desirable as it increases the signal power in the first part of the transmission link.5c. intra-band SRS between the Raman pumps increases the noise figure for lower wavelengths and a typical hybrid-EDFA/Raman amplification scheme has therefore an effective noise figure between 0 dB and 1 dB for the worst WDM channel [138]. A further possible amplification scheme is forward-pumped Raman amplification. 137].5 dBm. where the signal and pump are co-propagating along the fiber. A Raman amplifier is very suitable for WDM transmission as the 3-dB bandwidth of the Raman gain spectrum is approximately 55 nm. Figure 3. 46 . To further flatten and broaden the Raman gain spectrum. The SSMF is backward pumped with an average Raman gain between 11 dB and 14 dB. SSMF DCF DCF Raman pumps Pre-amp EDFA Booster EDFA next span Figure 3. which compensate for part of the chromatic dispersion. 142].2. For the transmission experiments in this thesis. discrete Raman amplification is used to investigate the feasibility of lumped chromatic dispersion compensation. Finally. Raman amplification has also some important drawback compared to EDFAs.6. This allows for a Raman amplifier with a flat 100-nm gain spectrum [139].3.6 depicts the typical hybrid Raman/EDFA structure used in the long-haul transmission experiments discussed in this thesis. discrete Raman amplification can be used. Instead DCF or specially designed fiber is used as a Raman gain medium.3).6: Hybrid Raman/EDFA structure used in the long-haul optical transmission experiments. Long-haul optical transmission systems cause of the high required pump powers for all-Raman amplification it is desirable to combine it with fiber types that have a high Raman gain coefficient. The remaining chromatic dispersion is compensated between the pre-amplifier and booster EDFA.Chapter 3. 1453 nm (90 mW) and 1467 nm (150 mW) [140]. The high optical powers can cause injuries to skin and eyes and cause optical connectors to damage easily when there is dirt or dust on the connector [141. the distributed nature of high pump powers in Raman amplification makes handling safety precautions important. A multi-pump Raman amplifier consists often of a single strong pump and several smaller pumps to equalize the gain spectrum [138]. depending on the transmission fiber used in the experiment. Alternatively. the full chromatic dispersion can be compensated with a DCF module placed after the Raman pumps followed by only a pre-amplifier (see Section 10. The pump powers required for Raman amplification are typically significantly higher than the pump powers required in an EDFA. This results in a more expensive amplifier design and the high pump powers can reduce the reliability of the pump lasers [138]. As an alternative. The insertion loss of the DCF is distributed by placing a DCF module after the Raman pumps. multiple Raman pump laser at different wavelengths are often used. The high Germanium doping in the core and the small effective area results in ∼7 times the Raman gain efficiency of SSMF [143]. which is nearly equal to the Stokes shift in SSMF. Hybrid EDFA/Raman amplification is used with four Raman pumps. In discrete Raman amplification the high optical powers are contained within the amplifier subsystem and do not propagate into the transmission fiber. such as NZDSF. In Section 3. A 300-mW polarizationmultiplexed pump at 1423 nm and depolarized pumps at 1436 nm (150 mW). After Nspans .2.3 Optical-signal-to-noise ratio The ASE added by the optical amplifiers in a long-haul transmission link ultimately limits the feasible transmission distance. When we consider a long-haul transmission link with Nspans .3. The factor two results from the two orthogonal polarization dimensions in the fiber. PASE Nspans 2N0 ∆ f0 (3.2. which results from spontaneous–spontaneous beat noise. F = 2nsp (1 − 2nsp (αLspan − 1) + 1 1 1 )+ = .626068 ·10−34 m2 kg/s). The noise power can be expressed as the noise power spectral density per polarization N0 . the ratio between ASE power and signal power is known as the OSNR and is defined as. The amplifier gain G is substituted with the fiber span loss αLspan under the assumption that the gain of each amplifier is equal to the span loss. (αLspan F − 1)h f0 ∆ f0 Nspans Fh f0 ∆ f0 Nspans (3. although the ASE is assumed to be unpolarized. G G αLspan (3. N0 = nsp h f0 (G − 1)Nspans = nsp h f0 (αLspan − 1)Nspans . usually 0.5 and 3. This shows that even a perfect optical amplifier nsp = 1 has a noise figure of 3 dB.6) In the limit of high gain (G = αLspan 10) the noise figure therefore approaches F = 2nsp . which is expressed through the reference bandwidth ∆ f0 in [Hz].4. but there is no signal–spontaneous beat noise as the ASE does not coherently interfere with the signal. The noise power spectral density of an amplifier can be expressed as.1 nm.7) = 47 . The ASE in the orthogonal polarization is added to the signal upon detection with the photodiode.6 gives an expression for the OSNR as a function of the amplifier noise figure and the span loss. For measurement purposes the OSNR is often normalized with respect to a certain optical bandwidth. OSNR = Pout put (αLspan F − 1)h f0 ∆ f0 Nspans αLspan Pinput Pinput ≈ . The noise figure of an EDFA can then be expressed as [144]. This is valid under the assumption that a single amplifier adds a noise power PASE and that all spans have the same insertion loss. (3. Combining Equations 3. 3. Note that. f0 the reference frequency in [Hz] and h is Planck’s constant (6. tot tot the total ASE power PASE in [W ] added by all optical amplifiers along the link equals PASE = PASE Nspans .4) where Pout put defines the signal power at the output of the last amplifier of the transmission link and has unit [W ]. only the ASE that is polarized parallel to the signal results in signal–spontaneous beat noise upon detection with the photodiode. It therefore worsens the OSNR tolerance with only ∼0. Fiber loss compensation 3. OSNR = Pout put Pout put = .5) where nsp is the spontaneous emission factor of a single amplifier.3 dB [10]. 8 107 SSMF (km) 640 40 2.1 nm).1.D B OSNR PENALTY. Chromatic dispersion compensation can generally be subdivided into two categories. OSNR[dB] ≈ 10log10 ( Pinput ) Nspans Fh f0 ∆ f0 (3. which depicts the dispersion-limited transmission reach over SSMF. Long-haul optical transmission systems Denoting Equation 3. The input power is ultimately limited by degradations due to nonlinear impairments.4 THz (1550 nm) and a reference bandwidth ∆ f0 of 12.7 42. In order to increase the OSNR at the receiver.7: Refractive index profile of a DCF.Chapter 3.5 0. i. We can therefore conclude that the OSNR scales linearly with Pout put and inversely with the insertion loss of the fiber span. dispersion managed cables [145].7 10. where −10log10 (h f0 ∆ f0 ) equals 58 dBm for a reference frequency f0 of 193.e. 48 . the dispersion-limited reach.8) = Pinput [dBm] − 10log10 (Nspans ) + 58dBm − F[dB] = Pout put [dBm] − αLspan − 10log10 (Nspans ) + 58dBm − F[dB]. as is often done for ultra long-haul transmission systems that have to bridge transoceanic distances.4 nsilica 0 core radius Figure 3.7 in [dB] gives. chromatic dispersion compensation is required. 3. The normalized dispersion length in Equation 2. or the use of Raman amplification.2: core cladding Symbol rate (Gb/s) 2. Higher-order mode DCF [146]. The bulk of the chromatic dispersion in a long-haul transmission link is normally compensated using in-line dispersion compensation. 3.5 GHz (0. in-line and accumulated dispersion compensation. either the input power into the fiber span (which equals Pout put ) has to be increased or the loss of the fiber span αLspan has to be reduced.LIMITED REACH FOR NRZ-OOK AND A 2.8 shows that there is a quadratic dependence between the dispersion-limited reach and the symbol rate. fiber Bragg gratings and optical phase conjugation. Hence. The span loss can be reduced by spacing the amplifiers closer together.3 Chromatic dispersion compensation Chromatic dispersion accumulates along an optical fiber which causes ISI and limits the feasible transmission distance. This is also evident from Table 3. Several technologies have been developed for in-line chromatic dispersion compensation. n Table D ISPERSION . in order to realize long-haul transmission systems. such as dispersion compensating fiber (DCF). the input power into the DCF is an important design parameter. The relatively high insertion loss of the DCF must be compensated while keeping at the same time the input powers into the DCF low enough to avoid nonlinear impairments. The refractive index of the core is raised through GeO2 doping. ˆ ˆ φNL = φNL.3. DCF has a smaller core effective area (∼20 µm2 ) and different core index profile in comparison to SSMF.DCF = γSSMF P0. ˆ γ =γ z=L exp(−αz)dz. We now consider 100 km of SSMF and matching DCF and use the fiber parameters in Table 3. This is due to the higher insertion loss per kilometer and the higher complexity of cable installation. ∆φNL. Normally.9) where L is the length of the fiber and α is denoted in [N p/km]. al.10) The DCF-induced increase in the total nonlinear phase shift can be denoted as. Figure 3. DCF was first proposed by Lin et. because the impact of the higher DCF nonlinearity is offset through the higher DCF attenuation coefficient. respectively. The path average nonlinearity is independent of the input power. z=0 (3.7 shows the core index profile of DCF.5 dB and 25.SSMF γSSMF · ∆P0 (3. Despite the fact that the DCF consists of several kilometers of fiber. It yields colorless. The triple cladding design also changes the sign of the dispersion slope such that the DCF is slope-matched with the transmission fiber. The small core size and triple-cladding structure forces a larger part of the optical field to propagate in the cladding. The difference between SSMF and DCF is small. It also makes DCF more vulnerable to core ovality than SSMF. which normally has triple-cladding structure. slope-matched dispersion cancelation with negligible cascading impairments. (3. which makes it unattractive to use DCF as part of the transmission fiber. The insertion loss of state-of-the-art DCM is ∼6 dB for a module that can compensate for the chromatic dispersion of 100 km of SSMF (1700 ps/nm). The triple cladding index profile has a narrow high-index core surrounded by a deeply depressed cladding followed by a raised ring.SSMF + φNL. In such a two-stage amplifier.DCF .3. but by multiplying with the input power we obtain an expression for the total nonlinear phase shift.DCF γDCF = 1+ . The high (GeO2 ) doping in the core of the DCF and the fact that a larger part of the optical field propagates in the cladding slightly raises the attenuation of the DCF.3. which increases the significance of waveguide dispersion and results in large negative values of D. it is normally used as dispersion compensation module (DCM) where the fiber is coiled around a spool for discrete dispersion compensation. which is typically close to α = 0.11) 49 .0 dB for the SSMF and DCF. Chromatic dispersion compensation Nowadays.4). [148]. State-of-the-art DCF can therefore accurately compensate the chromatic dispersion of all channels in the C-band.SSMF + γDCF P0. al. ˆ φNL.SSMF + φNL. The path-averaged nonlinearity is then 24. DCF is the standard solution to compensate for the chromatic dispersion accumulated in long-haul optical transmission systems. An extensive overview of dispersion compensation using DCF can be found in [143]. which results in higher module PMD [149] and raises the nonlinear coefficient. a two-stage EDFA structure with mid-stage access for the DCM is used to compensate the insertion loss (see Figure 3.5 dB/km. in 1980 [147] and demonstrated in 1992 by Dugan et. This relative impact ˆ of nonlinear impairments can be quantized using a path-averaged nonlinearity γ.DCF = ˆ φNL. 3.3: SSMF AND DCF FIBER PARAMETERS . For ≤10 Gb/s transmission systems the accumulated dispersion tolerance is generally large enough such that a standard 50 .Chapter 3. The pre-amplifier gain G1 is equal to the SSMF span loss minus ∆P0 . we can conclude that DCFbased chromatic dispersion compensation results in a ∼2 dB penalty due to the combined effect of an increased nonlinear phase shift and higher effective noise figure. The total noise figure of a two-stage amplifier can be calculated using Friis’s formula [126]. a single-stage EDFA with a 5 dB noise figure would in principle be sufficient to amplify the signal and no nonlinear phase shift would be accumulated in the DCF. Figure 3. This simplified analysis does not take the amplifier spectral tilt into account. The noise figure of the pre-amplifier F1 and booster F2 are assumed to be 5.SSMF .0 dB and 7.2 17 1. Hence. which results in a combined penalty of ∼7 dB. which might change the choice of the SSMF and DCF input powers. We note that this penalty is independent of the modulation format. Long-haul optical transmission systems Table 3.5 dB. DCF PARAMETERS ARE TAKEN FROM [143]. The chromatic dispersion at the receiver is referred to as the accumulated dispersion. the chromatic dispersion slope. respectively [143].5 dB. the DCFinduced contribution to the total nonlinear phase shift diminishes. The accumulated chromatic dispersion of a long-haul link is normally only roughly known as not all fiber is measured accurately before deployment. P0. as it is based on the DCF-induced increase in nonlinear phase shift and not the absolute nonlinear tolerance. SSMF DCF unit Insertion loss (α) Dispersion (D) Nonlinearity (γ) 0. Ftot = F1 + αDCF LDCF · F2 + 1 αDCF LDCF · F2 + 1 = F1 + G1 αSSMF LSSMF /∆P0 (3.13) where Ftot is the total noise figure of the amplifier. Combining the total noise figure and the increase in nonlinear phase shift gives a measure of the optimal difference in input power between SSMF and DCF.3 0. ∆P0 = P0. In addition. When dispersion compensation is not required.24 [dB/km] [ps/km/nm] [W −1 km−1 ] where ∆P0 is the difference input power between the SSMF and DCF. different propagation paths in a transparent optical network and temperature dependence [150] also introduce a variation in the accumulated dispersion at the receiver. This shows that a smaller difference in input power leads to an increased nonlinear phase shift but a decrease in total noise figure of the two-stage EDFA.8 depicts the total noise figure and the increase in nonlinear phase shift for a 100 km SSMF span using the fiber parameters of Table 3.5 -170 5.DCF (3. This shows that the optimum power difference is 6.12) This shows that when the input power difference between SSMF and DCF increases. direct detection receiver can compensate for the variations that occur. on the other hand. Depending on the local dispersion along the transmission link. This can be solved by using optical modulation formats that are more tolerant to chromatic dispersion. including Fiber Bragg gratings [151. as extensively discussed in the remainder of this thesis.1 Dispersion map In a long-haul transmission system.8: Effective noise figure and increase in nonlinear phase shift as a function of the input power difference between SSMF and DCF.g.3.9: Degrees of freedom in the design of a dispersion map. For higher symbol rates (e. Digital signal processing such as pre-distortion and digital coherent receivers are an exception to the subdivision of in-line and accumulated dispersion compensation as they can compensate for the full dispersion of the fiber link (see Chapter 10). 3. A number of different technologies have been proposed for tunable dispersion compensation. Pre-compensation Chromatic Dispersion (ps/nm) Postcompensation Total noise figure (dB) Increase in nonlinear phase shift (dB) 0 Inline undercompensation Transmission distance (km) Postcompensation Figure 3. It is therefore important to design the local dispersion evolution along the link. chromatic dispersion interacts with the SPM and XPM induced nonlinear phase shifts. tunable chromatic dispersion compensation can be employed to improve the chromatic dispersion tolerance at the receiver. Alternatively. this can result in severe transmission impairments. 51 . which is known as the dispersion map. the accumulated dispersion tolerance is generally too small to compensate for such variations. Chromatic dispersion compensation 10 8 6 4 2 0 Comb ined penalty (dB) 0 2 4 6 8 10 12 14 Input power SSMF . the solid curve shows both penalties combined.3. 152].3.Input power DCF (dB) Figure 3. thin film etalons [153] and digital signal processing technologies. 40-Gb/s). g. The inline under-compensation is particulary important to reduce the impact of XPM. the pre-compensation refers to a DCM with negative dispersion that is added to prechirp the signal directly after the transmitter [154]. only slightly dependent on the pre-chirp and local dispersion [157]. the post-compensation optimizes the accumulated dispersion at the receiver. Finally. as it is similar to a path-averaged walk-off length. (3. This is illustrated in Figure 3. 156]. [158. on the other hand.[160. First of all.8-Gb/s 0. hence.2.14) When the path-average nonlinearity is close to zero it results in a transmission link where the high-power areas are nearly symmetric with respect to the zero-dispersion point. Long-haul optical transmission systems Figure 3.6 Chromatic Dispersion (ps/nm) Average power per pulse (mW) 42. 0.g. The optimal amount of post-compensation can compensate to a certain degree the SPM-induced nonlinear phase shift as discussed in Section 2. Such a link design is possible through the use of a dispersion map that is symmetric with respect to the middle of the link [88.4 0.10: (a) Dispersion map with indication of high-power area and (b) average standard deviation of the power in a symbol (75% symbol period) for 10. 161]). minimizes the distortions due to SPM-induced nonlinearities [155]. 157.Chapter 3. A lower path-average pulsewidth reduces the overlapping of neighboring pulses and. 52 . which denotes the difference between the chromatic dispersion of each span and the chromatic dispersion of the subsequent DCF module. 159]) and experimental studies (e.2 0 0 High-power area Transmission distance (km) 10. n=Nspans γ n=1 ∑ z=Lspan (n) z=Lspan (n−1) sign[Dlocal (z)]exp(−αz)dz ≈ 0. as the power envelope is slightly different for each of the following high power regions. This averages out the interaction between the nonlinear phase shift and chromatic dispersion. An optimized pre-compensation makes the dispersion map more symmetric with respect to the zero-dispersion point and minimizes the pathaveraged pulsewidth over the high power area of the transmission system.10a which indicates the high-power areas along the transmission link directly after each EDFA. A rule of thumb for the design of the dispersion map is to choose the pre-compensation such that the path-averaged nonlinearity corrected for the sign of the local dispersion is close to zero.4.8-Gb/s NRZ-OOK modulation. The XPM penalty is. The optimization of the dispersion map for WDM transmission systems is reported in many theoretical (e. The inline under-compensation changes the chromatic dispersion in the high power region at the beginning of each subsequent span.7-Gb/s 0 1000 single SSMF span 2000 3000 4000 5000 Chromatic dispersion (ps/nm) (b) (a) Figure 3.7-Gb/s and 42.9 visualizes the degrees of freedom that can be used in the design of a dispersion map. The second degree of freedom is the inline under-compensation. as a function of chromatic dispersion only. This indicates that for higher symbol rates. In order to exclude the pulse transitions. We note that another measure often used to characterize the impact of nonlinearities is the peak power along the transmitted sequence. Depicted in Figure 3. As an example. Figure 3. in-line. The peak power shows a similar trend as the average standard deviation.7-Gb/s NRZ-OOK channel. as the number of interacting pulses is relatively small. only the middle 75% of the time slot is used in the calculations.11a is the nonlinear tolerance for 20x100 km transmission with a single 10. it is more dependent on the length of the transmitted sequence. an input power of -1 dBm per span results in a 2-dB OSNR penalty. For a 42.3. The optimum in-line under-compensation ranges from 51 ps/nm (lower powers) to 68 ps/nm (higher powers).7-Gb/s symbol rate the standard deviation increase up to an accumulated dispersion of ∼2000 ps/nm and then saturates. in-line and accumulated dispersion.and in-line compensation improves the nonlinear tolerance significantly to 6-dBm input power per span. the number of interacting pulses rapidly increases which limits the efficiency of suppressing nonlinear impairments through the choice of the dispersion map. optimized in-line and pre-compensation. but as there is no averaging in computing the peak power. the standard deviation saturates for a ∼150 ps/nm accumulated dispersion.8-Gb/s symbol rate. When no dispersion map is used and the pre-.11 illustrates the impact of dispersion map optimization on the nonlinear and dispersion tolerance in a long-haul transmission system. Chromatic dispersion compensation The choice of the dispersion map is particulary important for a ∼10 Gb/s symbol rate. This indicates that if the dispersion map keeps the local dispersion in high-power area below ∼2000 ps/nn the nonlinear impairments will be lower than when the chromatic dispersion is not periodically compensated. For a 10.7-Gb/s NRZ-OOK after 2000-km transmission with a all optimized dispersion map. When furthermore the accumulated dispersion at 53 . zero accumulated dispersion and zero pre. averaged out over all pulses in the transmitted sequence. (b) accumulated dispersion tolerance for different input powers.3.1nm) 18 16 14 12 10 -10 BER = 10-5 -5 0 5 10 15 22 5 dBm 19 16 13 10 -5 dBm -1 dBm 1 dBm 3 dBm BER = 10-5 1600 2000 0 400 800 1200 Input power (dBm) (a) Chromatic dispersion (ps/nm) (b) Figure 3. 20 25 11 dBm 9 dBm OSNR (dB/0.11: (a) Required OSNR for 10. This is illustrated in Figure 3. The standard deviation of the power increases with the accumulated chromatic dispersion as the overlapping pulses interfere with each other. the optimum pre-compensation is in the range -1190 ps/nm (lower powers) to -680 ps/nm (higher powers). For this link.and accumulated dispersion are all equal to zero.10b which shows the standard deviation of the power in each pulse.1nm) OSNR (dB/0. Optimizing the pre. As shown previously.7-Gb/s NRZ-OOK modulation. The use of a lumped dispersion map can potentially also improve transmission performance. which compensate the chromatic dispersion every several spans or. A practical chromatic dispersion map for such transmission systems is a double-periodic dispersion map [162].3. for 10. less pump lasers are required and the EDFA can have a lower noise figure. This shows that in the nonlinearity-limited transmission region the accumulated dispersion can be as high as 900-ps/nm. In deployed transmission systems.7-Gb/s NRZ-OOK modulation the use of a lumped disper54 . In the long-haul transmission experiments described in this thesis. but once every several spans the accumulated dispersion is reduced through a high inline over-compensation. The optimum accumulated dispersion for different input powers per span is depicted in Figure 3. Figure 3. Furthermore. optimizing the accumulated dispersion also improves the nonlinear tolerance (to ∼ 8 dBm. for WDM transmission the impact of XPM would be particulary strong in this case. the nonlinear tolerance increases to 10 dBm per span. But it also requires complex system engineering to obtain a near optimal dispersion map in deployed transmission systems. For example. Such a dispersion map typically has a high inline under-compensation for each span. 3. An alternative approach is the use of lumped dispersion maps.11b for a dispersion map with -680 ps/nm pre-compensation and 68 ps/nm in-line under-compensation. When the pre. Note that for a zero pre. not shown). A further requirement for opticallyswitched networks is that at each add-drop points the accumulated dispersion is low in order to minimize the required post-compensation. However. which makes lumped dispersion compensation less interesting for ultra long-haul transmission systems or modulation formats that require careful optimization of the dispersion map. this can improve the OSNR with up to 2 dB. the dispersion map is optimized in order to understand its impact on the transmission properties of different modulation formats (see Chapter 6). it has the advantage that simpler EDFAs can be used in between the dispersion compensation nodes.Chapter 3. the optimization of the dispersion map is somewhat restricted because every span has a different length and the DCMs are only available in a certain granularity.2 Lumped dispersion compensation The design of a dispersion map improves the reach in a long-haul transmission system significantly.and in-line compensation are optimized. This allows the replacement of multiple small DCMs with a single ”large-dispersion” DCM. The higher local dispersion can reduce the nonlinear tolerance. the impact of XPM can be reduced. When no mid-stage access are required for the EDFAs. For example. and then independently varying the pre-compensation and in-line under-compensation. the dispersion compensation can be concentrated only at specific points. even for an optimized dispersion map the impact of XPM will considerably limit the nonlinear tolerance.and in-line compensation. do not apply in-line dispersion compensation at all. in the extreme case. The dispersion map is optimized by starting of with an dispersion map as would be optimal for 10. which makes it less relevant. This illustrated that the local dispersion along the link is significantly higher in the case of a lumped dispersion map. However. such as optical add-drop nodes. Long-haul optical transmission systems the receiver is optimized.12 depicts the accumulated dispersion along a transmission link for both a conventional and a lumped dispersion map. as DCF has a high Raman gain coefficient. al. which is sufficient to compensate the chromatic dispersion of 500 km of SSMF. in 1978 [169]. The refractive index variation generates a wavelength specific dielectric mirror that reflects a particular wavelength. To make lumped dispersion compensation practical an important consideration is the large insertion loss of the single centralized DCM.12: Example of a lumped dispersion map. When a FBG is combined with a circulator. 3. It consists of a short segment of fiber with a periodic variation of the refractive index along the fiber core. An efficient amplification scheme to reduce the insertion loss is backwards pumped Raman amplification. This combines a large chromatic dispersion with an insertion loss small enough to be compensated using EDFA-only amplification. first demonstrated by Hill et. A chirped 55 . A further increase in Raman gain can result in double Rayleigh scattering. A FBG is a type of distributed Bragg reflector. A FBG can therefore be used to construct a very narrow optical filter that reflects the desired wavelength and transmits all other wavelengths. which increases the noise figure [165. Chromatic dispersion compensation Accumulated Dispersion (ps/nm) Transmission distance (km) Figure 3. 168]. particulary when phase shift keyed modulation formats are used [164].14. An alternative approach for lumped dispersion compensation would be the use of chirped FBGs. in the order of 25 dB. sion will result in a reduced nonlinear tolerance as this modulation format strongly benefits from an optimized dispersion map [163].3. The signal enters the circulator through port 1 and outputs it again through port 2. This allow for a high ON/OFF Raman gain. But 40-Gb/s transmission has shown to be highly resistant towards a large accumulated dispersion. When hybrid EDFA/Raman amplification is used the total DCF insertion loss can be ∼30 dB. An example of long-haul transmission with a lumped dispersion map is discussed in Section 6. The FBG connected to port 2 then reflects only the desired wavelengths back into the circulator. 166]. the resulting component transmits only the desired wavelength and attenuates all others. which introduces chirp into the signal. Such chirped fiber Bragg gratings can be used for dispersion compensation. which outputs the signal again through port 3.3. The refractive index profile of a FBG can have a linear variation in the grating period.3 Chirped fiber-Bragg gratings Chirped multi-channel fiber-Bragg gratings (FBG) are an alternative to DCF for the compensation of chromatic dispersion in long-haul transmission links [167. as shown in Figure 3.3.3. Different wavelength are then reflected at different positions along the FBG. while using only low power Raman pumps. for example the full C-band. The low-frequency ripples can Dispersion Compensating Fiber Colorless Cascadibility High insertion loss High nonlinear coefficient 0 1000 Chirped Fiber Bragg Gratings Low insertion loss Negligible nonlinearity coefficient Compact size (a) Group delay ripple 45 Group delay ripple (ps) 30 15 0 -15 -30 -45 -30 65 GHz Group delay (ps) Attanuation (dB) -10 500 Peak-to-peak GDR -20 100 GHz 0 -30 -500 -40 -80 -60 -40 -20 0 20 40 60 Normalized frequency (GHz) 80 -1000 -80 -60 -40 -20 0 20 40 60 Normalized frequency (GHz) 80 -20 -10 0 10 20 Normalized frequency (GHz) 30 (b) (c) (d) Figure 3. Scheerer et.Figure 3. Figure 3. 56 . This can be used to construct FBGs with a broad bandwidth. Long-haul optical transmission systems FBG does not reflect a single wavelength.13d shows the obtained GDR circulator when the a linear fit is subtracted from the group delay response. but rather reflects a range of wavelength defined by the variation of the grating period.13: (a) Comparison between FBGs and DCF for chromatic dispersion compensation. al. This shows a very flat insertion loss with a ripple of <0. Low frequency ripples. which can compensate the chromatic dispersion for multiple WDM channels.with circulator. A drawback of chirped FBGs is that they suffer from distortions in their phase reFBG sponse.e.14: FBG tude and period of the GDR in the frequency domain. This pulse broadening is analog to chromatic dispersion and therefore merely changes the residual dispersion of the signal. multiple short gratings can be written on top of each other to reflect multiple WDM channels with a single complex grating.5 dB across a 65-GHz bandwidth and a ∼25 dB insertion loss in between two pass-bands. (c) group delay and (d) group delay ripple of a channelized chirped-FBG. The amplitude response of a chirped FBG with 100-GHz channel spacing is depicted in Figure 3. The GDR is caused 2 3 by imperfections in the gratings fabrication process and limits the num1 ber of FBGs that can be cascaded.Chapter 3.13c. with only a fraction of the ripple period within the signal bandwidth. the phase response of a chirped FBG is depicted. cause pulse broadening. In [172]. showed that the penalty can be calculated from the ampli. (b) amplitude. i. ation is the ripples frequency relative to the symbol rate. The main consider. These satellite pulses interfere with adjacent pulses and therefore cause ISI. better known as the group delay ripple (GDR). ripples with more than one ripple period within the signal bandwidth. High-frequency ripples. In Figure 3. Such a structure enables the manufacturing of full C-band FBGs that can be used on a 100-GHz [170] or 50-GHz grid [171].13b. Alternatively. create satellite pulses in the time domain. An extensive overview of PMD compensation technologies is given by Sunnerud et. as illustrated by Figure 3. several approaches have been proposed that either mitigated or actively compensated the impact of PMD. Optical PMD compensators can either use single-stage [180] or two-stage compensation [181]. The main advantage of FBGs is their lower insertion loss and negligible nonlinearity. and FEC-supported polarization scrambling [177.4. PMD compensation be compensated using tunable dispersion compensation. PSP coupling simply aligns the input SOP with the PSP of the transmission link. but cannot be used to compensate for second-order PMD or in the presence of strong PDL. It also requires a feedback signal from the receiver to the transmitter. As a result. by cascading the FBG and transmission fiber without a mid-stage amplifier. which complicates system design.15: (a) single-stage PMD compensator. A FBG can be made tunable through heating or stretching of the fiber grating. This is a fairly easy method to compensate for DGD. improved fabrication processes have gradually reduced the PR of slope-matched FBGs. the use of optical PMD compensators [180. which enables ultra long-haul transmission using FBGs for dispersion compensation. This potentially allows simpler EDFA design. A single stage PMD compensator consists of a polarization controller followed by either a fixed 57 . 181] and optical [182] or electrical signal processing. which enables dispersion tuning over a range of typically 800 ps/nm [174]. as discussed further in this thesis. Figure 3. (b) two-stage PMD compensator. mainly the high-frequency ripples cause transmission impairments. PMD related penalties are among the most cumbersome for state-of-the-art long-haul optical transmission systems.15.4 PMD compensation As there is no easy compensation solution. in [183]. al. PC DGD RX PC DGD PC DGD RX feedback feedback (a) (b) Figure 3. Note that the best prediction of the penalty associated with cascaded FBGs is generally the phase ripple (PR) weighted by the signal spectrum [173]. which enables the integration of a (tunable) FBGs in the receiver. Another advantage is the compact size. the time delay in a long transmission link makes it impossible to track fast polarization changes.3.7-Gb/s NRZ-OOK and 42. which significantly increases their cascadability [175] A further reduction in PR-related impairments is possible using equalization [176].8-Gb/s RZ-DQPSK modulation. However. Passive PMD mitigation technologies include the use of robust modulation formats. However. Active PMD compensation techniques include PSP coupling [179]. 178]. 3. In Section 6.4 the impact of PR-induced impairments are discussed for a long-haul WDM transmission experiment using 10. The main disadvantage of FBGs is the PR-related impairments.13a lists the most significant differences between DCF and FBGs for dispersion compensation. In addition. This section discusses the impact of optical narrowband filtering. temperature changes. whereas a WSS is generally realized using micro-electro mechanical system (MEMS) technology [190]. This can either be achieved with a wavelength blocker or a wavelength selective switch (WSS). for example. In order to track these polarization changes with e a (θ < 10o ) accuracy. The feedback required for optical polarization controllers makes it difficult to obtain such response times. with N and M being the number of input and output ports. The combined requirement of a short response time and control algorithms that do not suffer from local suboptima has stalled the deployment of optical PMD compensators in recent years.15b) has normally 4 degrees of freedom. This requires both a sophisticated control algorithm as well as a suitable choice of the feedback signal. 187]. Most two-stage PMD compensators schemes are known to have the tendency of getting trapped in suboptima [183]. A wavelength blocker can be realized using planar lightwave circuits or liquid crystal technology [189]. respectively. An OADM compromises different optical sub-systems to realize wavelength switching. for 43-Gb/s transmission a two-stage PMD compensator is desirable. Such a PMD compensator has either two (fixed) or three (tunable) degrees of freedom. vibrations. With a fixed single birefringent section. 58 . The degrees of freedom of a PMD compensator is a good figure of merit for the complexity of the control algorithm. human handling or wind in the case of aerial fibers. Common types are a 1x4 or 1x9 WSS. An optical meshed network requires that signals routed through the network have the flexibility to pass multiple optical add-drop multiplexer (OADM) and photonic cross connects (PXC) nodes along the transmission link [188]. Note that a singlestage PMD compensator can only compensate for a limited amount of second-order PMD [184]. the response time of the automatic polarization control should be in the order of 1 ms. with the difference being that a wavelength blocker has a 1x1 structure whereas a WSS can be a NxM switch. 3. Hence. Long-haul optical transmission systems or tunable birefringent section. Polarization changes in an optical fiber are normally on the scale of a few degrees per second. 186.Chapter 3. However under the influence of.5 Narrowband-optical filtering The previous three sections discussed the compensation of transmission impairments that occur in a long-haul optical transmission link. the amount of birefringence should match the average PMD of the link and a penalty is introduced when the compensator DGD is larger than the DGD of the transmission link. A two-stage PMD compensator (Figure 3. the WDM spectrum is de-multiplexed in order to block certain WDM channels and let other WDM channels pass through. The combination of a wavelength blocker with fiber-optic couplers at the input and output makes it possible to add/drop WDM channels. a transmission impairment that typically occurs in an optical transmission network. An important design aspect for PMD compensators is the speed of compensation. Generally. the polarization changes can reach a speed of ∼50 revolutions per second on the Poincar´ sphere [185. 3. Optical phase conjugation Relative transmittance (dB) 0 Table 3. the filter transmittance of the cascaded OADM/PXC is likely to be slightly shifted in wavelength. This implies a 0. as depicted in Figure 3. the 3-dB bandwidth is reduced significantly.8-b/s/Hz spectral efficiency for 40-Gb/s transmission. Today. 3. In the remainder of the thesis. This mainly results from the lack of a technology that can inverse the nonlinear impairment. It uses the transmission fiber itself to compensate for transmission 59 .g. This indicates that on a 50-GHz ITU grid. The more narrow optical spectrum of multi-level modulation formats is therefore one of the more decisive advantages over binary modulation formats. Figure 3. due to temperature differences or slight variations in the device specifications. Optical phase conjugation (OPC) is one of the technologies that can (partially) compensate for nonlinear transmission impairments. the available 3-dB bandwidth is approximately 35-GHz when a realistic number of 3-4 OADM/PXC is passed along the transmission link. e.16: Transmittance of a 50-GHz WSS. For binary formats this is close to the theoretical limit which makes it difficult to cascade multiple OADM with an acceptable OSNR penalty. When the measured transmittance is cascaded multiple times to simulate cascaded filtering.6 Optical phase conjugation Nonlinear transmission impairments are clearly the most difficult transmission impairments to compensate in a long-haul transmission link. This bandwidth is therefore a suitable figure-of-merit to determine if a modulation format can be used with a 50-GHz channel spacing. state-of-the-art transmission systems have a 50-GHz WDM channel spacing. In deployed optical networks. The wavelength de-multiplexing that occurs in an OADM/PXC results in spectral filtering of the WDM channels. Particulary when multiple OADM/PXC are cascaded this filtering can limit the optical bandwidth to a fraction of the channel spacing. -10 -20 -30 -40 -50 5 2 10 cascaded 3-dB 20-dB filters bandwidth bandwidth (GHz) (GHz) 1 2 5 10 43 39 35 32 59 52 45 40 -30 -10 10 30 50 Normalized frequency (GHz) Figure 3. a material with a negative Kerr effect.16. a WSS is included in the optical transmission experiments to emulate the strong optical filtering as it occurs in a transparent optical network. for example.4: 1 O PTICAL FILTER BAND WIDTH OF A CASCADED 50-GH Z WSS. which has a (single-pass) 3-dB bandwidth of 43-GHz on a 50-GHz ITU grid.6.16 shows the measured transmittance of a state-of-the-art WSS. Note that we here assume that all optical filters have exactly the same transmittance as a function of wavelength. 195] and nonlinear phase noise [91]. but it is one of the most promising technologies to increase the robustness against nonlinear transmission impairments. Several other techniques have been proposed to phase conjugate an optical signal and have been used in earlier experiments. IXPM/IFWM [194. which implies that OPC with a PPLN waveguide is transparent to bit rate and modulation format [203] and has a high conversion efficiency [204]. This section briefly discusses the theory behind optical phase conjugation.Chapter 3. OPC is currently not used in deployed optical transmission systems. Simultaneously DFG occurs where the second harmonic 2 · ω pump interacts with the input signal ωinput . The frequency of the output signal is therefore ωcon jugate = 2 · ω pump − ωinput .1 Periodically-poled lithium-niobate The most promising technology to realize OPC is parametric difference frequency generation (DFG) in a periodically-poled lithium-niobate (PPLN) waveguide. It is also possible to phase conjugate the signal using only DFG. And as OPC compensates the chromatic dispersion along a transmission link. in effect. Yariv et. silicon waveguides [198] and AlGaAs waveguides [199].6. An in-depth description of optical phase conjugation in long-haul transmission systems can be found in [21]. in [202] conversion is 60 . The DFG generates a phase conjugated output signal that mirrors the input signal ωinput with respect to the pump signal ω pump . The principle of the cascaded SHG and DFG process in a PPLN waveguide is illustrated in Figure 3. the impairments that occurred before conjugation can be canceled out by impairments that occur after phase conjugation. semiconductor amplifiers and silicon waveguides are all media with a high χ 3 and therefore use FWM to conjugate the optical signal. Phase conjugation with a PPLN waveguide is realized by second harmonic generation (SHG) and DFG [200. 193]. al. As a result. the phase conjugated signal is degenerated through SPM and XPM that occur simultaneously with the FWM in a χ 3 nonlinear media. A PPLN waveguide has a high second order susceptibility χ 2 but negligible third order susceptibility χ 3 . With OPC. The broad range of transmission impairments that can be compensated using OPC makes it a very powerful technology to extend the reach of long-haul transmission systems. 201]. in that case the pump signal should have a frequency 2 · ωsignal + ∆ω [202]. it also allows for simpler EDFA design.17. 3. invert the sign of the Kerr effect in the second half of the transmission link. Long-haul optical transmission systems impairments and. where ∆ω is the frequency difference between the input and phase conjugated output signal. The DFG and SHG processes can conjugate signals over a broad wavelength range. The cascaded SHG/DFG process is instantaneous and phase sensitive in its response. For example. the pump at frequency ω pump is up-converted to the frequency 2 · ω pump . OPC can also be used to compensate for other (deterministic) linear and nonlinear transmission impairments. But apart from the compensation of chromatic dispersion. a semiconductor optical amplifiers [197]. Nonlinear interaction resulting from the third-order susceptibility (i. XPM and FWM) can therefore be neglected. Highly nonlinear fibers. SPM. This includes the compensation of SPM [192. Section 6. This includes highly nonlinear fiber [196].5 discusses long-haul transmission experiments using OPC for the compensation of transmission impairments. Through SHG.e. proposed in 1979 the use of chromatic dispersion compensation by means of OPC [191]. the phase matching period of the periodic poling is ∼16. SHG and DFG have a very low efficiency because of the phase mismatch caused by the dispersion of the lithium-niobate. magnesiumoxide doped PPLN waveguide are more practical for use as an optical subsystem. this phase mismatch needs to be compensated. However. Note that the phase matching period fixes the wavelength of the pump signal. This lowers the operating temperature to between 50o and 90o Celsius [194. Because of the high operating temperature. which is possible through quasi-phase matching (QPM).3. showed the simultaneous conversion of 103 WDM channels using a single PPLN waveguide. Typically.6. slight tuning of the operating wavelength can be realized by changing the operating temperature of the PPLN waveguide. hence a PPLN waveguide has to be designed for a specific pump wavelength. In the parallel polarization-diversity scheme. In an ordinary LiNbO3 waveguide. Yamawaku et. The counter-directional polarization-diversity scheme. on the 61 .31µm and 1. al. a PPLN waveguide is operated at 180o to 200o Celsius. pigtail fibers cannot be glued to the waveguide and free-space optics have to be used to couple the light in and out of the PPLN waveguide. Figure 3.5µm. the input signal is split up into two orthogonal polarization components that are separately phase conjugated by two PPLN waveguide. which complicates sub-system design.17: Second harmonic generation (SHG) and difference frequency generation (DFG) in a PPLN. SHG power 2 pump pump circ input conjugate PBS TE 2 input 1 3 TE TM TM PPLN pump output wavelength DFG Figure 3. which is a significant drawback for in-line OPC in a long-haul transmission system. A concern of OPC using a PPLN waveguide is that it suffers from the presence of the photorefractive effect [206]..5µm band. The input signal can be a single wavelength channel or multiple WDM signals. two polarization diversity schemes can be used to make the PPLN structure polarization independent. A PPLN waveguide is intrinsically polarization dependent. This can be mitigated by heating the PPLN waveguide. Optical phase conjugation shown between the 1. Another approach to mitigate the photorefractive effect is doping the LiNbO3 slightly with magnesium-oxide [207]. which allows gluing the fibers to the waveguide. Either using a parallel [208] or a counter-directional [209] approach. First order QPM can be realized by reversing the sign of the nonlinear susceptibility (periodically poling) with every phase matching period. Typically. In [205]. Hence. For efficient SHG and DFG. However. 195].18: Counter directional polarization independent OPC subsystem. Chapter 3. Long-haul optical transmission systems other hand, uses a single PPLN waveguide. In the transmission experiments described in Section 6.5 a counter-directional polarization-diversity structure is used, as depicted in Figure 3.17. A polarization beam splitter (PBS) splits the incoming signal with arbitrary polarization into the two orthogonal polarization modes (TM and TE). Counterclockwise rotating, the signal on the TM mode is then phase conjugated in the TM aligned PPLN waveguide, and subsequently converted to the TE mode with a TE ↔ TM fusion splice. Clockwise rotating, the TE mode is first converted to the TM mode and and afterwards phase conjugated. Both counter propagating modes are again recombined with the same PBS. The pump signal ω pump is combined with the input signal ωinput before the polarization-diversity structure. In order to obtain the same conversion efficiency for both the clockwise and counter-clockwise direction, the pump has to be launched at 45o with respect to the principal axes of the PBS such that the pump power is split with a 50% − 50% ratio. As both the TE and TM mode travel through the same components for the counter-direction polarization-diversity scheme, the structure has an inherently low DGD. And as long as the pump power is high enough that the DFG and SHG processes are not saturated, the PDL is also inherently low. The main disadvantage is the vulnerability to multiple path interference resulting from reflections and the finite extinction ratio of the PBS. 3.6.2 Compensation of transmission impairments As discussed in Section 2.4, the propagation of an optical signal can be expressed by the Nonlinear Schr¨ dinger equation assuming a slowly varying envelope approximation. The complex o conjugate of the Nonlinear Schr¨ dinger equation can be denoted as, o ∂ E∗ α ∗ β2 ∂ 2 E ∗ β3 ∂ 3 E ∗ = − E + j + − ∂z 2 2 ∂T2 6 ∂T3 attenuation dispersion dispersion slope jγ|E ∗ |2 E ∗ , Kerr nonlinearities (3.15) where E ∗ denotes the complex conjugate of the optical field. Comparing Equations 2.21 and 3.15 shows that the contributions of the chromatic dispersion and the Kerr effect have an inverted sign. We now assume that the signal is phase conjugated in the middle of a perfectly symmetrical transmission link. In this case, impairments due to chromatic dispersion and the Kerr effect that occurred along the first part of the link are perfectly canceled out in the second part of the link. The sign of the attenuation and the dispersion slope remains unchanged and are not compensated. An important consideration for OPC-aided transmission links is that, ideally, compensation of chromatic dispersion and the Kerr effect can only be realized in a transmission link that is perfectly symmetric with respect to the OPC unit. However, due to the attenuation of the optical fiber, the power envelope decreases exponentially with propagation distance along a single span. As a result, the transmission link will not be fully symmetric with respect to the OPC unit. The asymmetry can be reduced by using all-Raman amplification, as discussed in Section 3.2.2 [208]. However, Chowdhury et. al. showed that also with hybrid EDFA/Raman amplification, where the power profile along the link is not fully symmetric with respect to the OPC unit, significant nonlinearity compensation can be achieved [194, 195]. And in [210], Jansen et. al. showed that also with EDFA-only amplification a significant gain in nonlinear tolerance can be achieved. 62 3.6. Optical phase conjugation Compensation of the dispersion slope can be achieved by optimizing the post-compensation on a per-channel basis after transmission [211, 208, 203]. Alternatively, the third order dispersion can be compensated using a slope compensator [212]. In a long-haul transmission link, the power envelope evolution is a periodic function of the transmission distance. This produces a periodic variation of the fiber refractive index through the Kerr effect. This causes the transmission link to act as a very long FBG with a grating period equal to the amplifier spacing. Such a virtual grating induces a parametric gain which causes exponential growth of the signals spectral sidebands [213]. This parametric gain is known as sideband instability and can be interpreted in the frequency domain as a FWM process which is quasi phase-matched through the virtual grating. The growth of the spectral sidebands in not symmetric with respect to the middle of the transmission link and can therefore not be fully compensate with OPC [193, 214]. Modulation instability can be mitigated with a periodic dispersion map [215], hence it is insignificant in transmission system using periodic dispersion compensation. The lumped dispersion map in OPC-aided transmission systems does not suppress modulation instability, which can therefore result in signal impairments. However, in deployed transmission links not every span will have the same length and power profile, and this significantly reduces the effectiveness of the parametric gain. In the long-haul transmission experiments described in this thesis no modulation instability impairments have been observed, which probably also results from (slight) differences in span length [203, 216]. When hybrid EDFA/Raman amplification is used in a transmission link, the noise figure of the amplifiers can vary across the C-band. This is a result of pump-to-pump interaction between the Raman pumps, which reduces the OSNR of the lower wavelength [138]. This in turn causes a wavelength-dependent performance, where the higher wavelength channels generally have a better performance than the lower wavelength channels. In an OPC-aided transmission link, wavelength conversion occurs in the middle of the transmission link. As a result, all wavelength channels propagate both in the higher and the lower wavelength band for part of the transmission distance. This can ease the design of transmission links somewhat as the wavelength dependent performance among the WDM channels is averaged out. The most significant drawback of OPC in a long-haul transmission link is its incompatibility with OADM. As an example we assume that an OPC unit is placed in the middle of a transmission link which also contains an OADM, offset from the middle of the transmission link. This implies that the dispersion of the add/drop channels will not be fully compensated by the OPC. OPCbased dispersion compensation in a transmission link with OADMs therefore requires phase conjugating the signal at multiple points in the link. Alternatively, the OPC can be only used for the compensation of nonlinear impairments and the chromatic dispersion is compensated by other means [194, 195]. 3.6.3 Nonlinear phase noise compensation The impact of nonlinear phase noise is, due to its statistical nature, one of the most difficult transmission impairments to take into account in the design of a transmission system. OPC can 63 Chapter 3. Long-haul optical transmission systems partially compensate for nonlinear phase noise impairments, as originally proposed by Lorattanasane and Kikuchi [193]. Figure 3.19 depicts a transmission link of 6 spans with and without mid-link OPC for nonlinear phase noise compensation. We assumes the every EDFA has the same output power and introduces the same amount of ASE onto the signal. The ASE generated by an EDFA adds amplitude noise to the signal. When the signal plus amplitude noise subsequently propagates over the another fiber span, it introduces a nonlinear phase shift to the signal that is dependent on the total power level (i.e. signal plus noise). The total nonlinear phase shift is defined by the number of spans that the ASE propagates along the link and therefore accumulates with ρtot,N = ρtot,N−1 + N · ρ , where ρ is the nonlinear phase shift added in the first span and N is the nth span of the transmission link. It can be shown that this is equal to, ρtot,N = ρ · n=N n=1 ∑ n= ρ · N (1 + N). 2 (3.16) A TX B C D E F G RX (a) < > < tot> 0 0 +1 1 +2 3 +3 6 OPC +4 10 +5 15 +6 21 +7 28 RX + TX (b) < > 0 +1 +2 +3 -3 0 +1 -2 +1 +2 5 -1 +2 +3 9 0 +3 +4 16 phase conjugated terms + < tot> 0 1 3 6 4 Figure 3.19: Nonlinear phase noise compensation using optical phase conjugation (after [193]). When mid-link OPC is used in the transmission link, the nonlinear phase noise can be partly compensated. This is depicted in Figure 3.19b, which shows how the nonlinear phase noise adds up along the transmission link. As an example, we now take the amplitude noise generated by amplifier B. After amplifier B, the signal plus noise propagates over two spans before reaching the OPC unit (between amplifiers B and D), generating a nonlinear phase shift equal to 2 ρ . The OPC unit conjugates this signal, which reverses the sign of the nonlinear phase shift but keeps the power of the signal plus noise unchanged. After the OPC unit, transmission over the two more spans (between amplifiers D and F) generates again the same nonlinear phase shift equal to 2 ρ . However, the contribution to the nonlinear phase shift before and after the OPC have an opposite sign and therefore add up to zero. In the last two spans (between amplifier F and Rx) another nonlinear phase shift equal to 2 ρ is generated, which is not compensated anymore. The total nonlinear phase shift generated by the noise of amplifier B, reduces therefore from 6 ρ to 2 ρ . Computing this for all amplifiers shows that the total nonlinear phase shift is reduced from 64 3.6. Optical phase conjugation 28 ρ to 16 ρ ). Note that it is beneficial to place the OPC unit at 66% of the transmission link. For example, when in the example in Figure 3.19 the OPC unit is placed after then 5th span, the total nonlinear phase shift is reduced to 7 ρ . The nonlinear phase noise penalty is related to the nonlinear phase noise variance, rather than the average and scales with ρ 2 N 3 [193]. McKinstrie et. al. showed in [217] that with mid-link OPC the accumulated nonlinear phase noise variance becomes proportional to (2 ρ 2 )(N/2)3 = ρ 2 (N 3 /4), resulting in about 6 dB phase noise suppression. When the OPC unit is placed at 66% of the transmission link, the phase noise reduction can be increased to 9.5 dB. However, the OPC can then not fully compensate for the chromatic dispersion of the link. When not every amplifier adds the same amount of noise to the signal, the optimum placement of the OPC unit changes. For example, amplitude distortions in the transmitted signal can be modeled as an amplifier with a high noise factor. The optimum placement of the OPC unit to compensate for transmitter-induced impairments is at 50% of the transmission link. This will shift the optimal position of the OPC unit more towards the middle of the link. /wo OPC 10-3 /w OPC 50% 10-3 /w OPC 66% 10-3 Probability Im(E) Im(E) 10-4 10-5 10-6 10-4 10-5 10-6 Im(E) 10-4 10-5 10-6 Re(E) (a) Re(E) (b) Re(E) (c) Figure 3.20: Simulated constellation diagrams of DPSK modulation, (a) without OPC, (b) with OPC at 50% of the transmission link and (c) with OPC at 66% of the transmission link. Figure 3.20 illustrates the compensation of nonlinear phase noise through OPC in a long-haul transmission link. Simulated is single channel DPSK transmission (see Section 4.3) over 30 x 90-km spans with a 3-dBm input power per span and the ASE added along the transmission line. The fiber attenuation is α = 0.25 dB/km, fiber nonlinearity γ = 1.3 W−1 km−1 and chromatic dispersion is neglected. Without OPC, a constellation plot is obtained that illustrates the typical ying-yang shape of a nonlinear phase noise distorted signal. This shape disappears partly or completely when OPC is used to reduce the impact of nonlinear phase noise. In particular when the OPC unit is placed at 66%, the impact of nonlinear phase noise is almost fully compensated. 65 Chapter 3. Long-haul optical transmission systems 66 4 Binary modulation formats Many different modulation formats exist that use either amplitude, phase, frequency or polarization modulation to either transmit information or enhance the transmission tolerance. We focus here on the most significant binary modulation formats that are deployed in long-haul transmission systems. As a reference format we use NRZ-OOK modulation, as this currently still the most widely deployed modulation format for terrestrial long-haul transmission systems. The other modulation formats are evaluated in comparison to OOK. First of all, Section 4.1 introduces briefly the advantages and disadvantages of OOK modulation. Subsequently, Section 4.2 described duobinary modulation, which is currently the most widely used modulation format for 40-Gb/s transmission. We then focus on phase shift keyed modulation formats, which is likely to replace duobinary modulation for long-haul 40-Gb/s transmission. Differential phase shift keying (DPSK) is discussed in Section 4.3. Finally, in Section 4.4 we describe a narrowband filtering tolerant DPSK format, known as partial DPSK. 4.1 On-off-keying From the first application of fiber optics in the middle of the 1970’s until only recently, NRZOOK has been the modulation format of choice for most commercial applications. NRZ-OOK is an amplitude modulation format, as it encodes the information in the amplitude of the optical field. The transmitter and receiver structure of NRZ-OOK modulation is depicted in Figure 4.1. At the transmitter, NRZ-OOK is realized by switching the output of a laser ON or OFF, depending on the information to be transmitted. Direct modulation can be used for NRZ-OOK 67 respectively. typically a distributed feedback laser (DFB).u) Quadrature Trough Bias V0 Time 93 ps (c) Power (a. which results in a chirp-free signal with high extinction ratio. (b) 10. For long-haul transmission systems. NRZ-OOK has a strong component at the carrier frequency.1 and 4. The MZM modulates the output of a laser.1: NRZ-OOK transmitter and receiver structure and simulated optical spectrum for 42.2: (a) Operation of the MZM for OOK modulation and eye diagrams showing. The electrical drive signal requires therefore a peakto-peak amplitude of Vπ .7-Gb/s RZ-OOK modulation.Chapter 4. external modulation with a MZM is normally preferred to reduce the residual chirp in the modulated signal. The spectrum further shows clock tones that are spaced at multiples of the symbol rate.u) Electrical drive signal Time V 93 ps Figure 4.7-Gb/s NRZ-OOK and (c) 10. Note that due to the nonlinear transmission function of the MZM. Binary modulation formats 0 clock MZM data Tx PD MZM 0 1 1 0 1 0 data Rx PSD (dB) -10 -20 -30 -40 -100 laser optional -50 0 50 100 Frequency (GHz) Figure 4. This shows the power spectral density (PSD) as function of optical frequency.8-Gb/s NRZ-OOK. as well as external modulators.2a.2b. (a) Optical phase = 0 Optical phase = Crest Transmittance (b) Power (a. The optical spectrum of a NRZ-OOK modulated signal is depicted in Figures 4. The bandwidth of the optical spectrum is approximately twice the symbol rate. The operation of a MZM for NRZ-OOK modulation is depicted in Figure 4. The MZM is biased in the quadrature point and is driven from minimum to maximum transmittance. respectively. overshoots and ripples on the electrical drive signal can be suppressed during modulation. which contains half the optical power and is referred to as the carrier. 68 . but which are strongly reduced compared to the carrier component. modulation. 220]. CRZ modulation can be generated by modulating the phase of the RZ-OOK signal using a phase modulator (PM). a specific amount of phase modulation is imposed on the RZOOK signal [219.1. Chirped RZ-OOK has an increased nonlinear tolerance in comparison to RZ-OOK modulation.4. Because of this alternating phase change. Duobinary has originally been introduced in the 1960’s by Lender as a suitable technique to transmit binary data into an electrical cable with a high-frequency cutoff characteristic [223. It can either be generated as a 3-level amplitude signal (’0’. This implies there is a trade-off between spectral efficiency and nonlinear tolerance for CRZ. and the optimum phase modulation index therefore depends on the system properties. The zero-mean optical field also improves the nonlinear tolerance in the pseudo-linear regime where there is strong pulse overlapping. This results in a zero-mean optical field envelope. pulse carving and phase modulation. ’0. Note that CRZ thus requires three modulators in cascade. Similar to OOK. also known as CRZ. which results in a more compact spectrum. The most suitable RZ-OOK modulation format for WDM transmission is CSRZ. Duobinary The simple transmitter and receiver structure of OOK modulation comes at the cost of suboptimal transmission properties. in [221]. for data coding.2 Duobinary Duobinary modulation is the best known example of a class of coding formats known as partial response codes. 224]. which is often abbreviated to NRZ. ’0’. such modulation formats transmit the information in the amplitude domain and rely on straightforward direct detection at the receiver. there is predefined phase relation between consecutive bits that can be used to improve the optical filtering tolerance as well as the chromatic dispersion tolerance. 4. the RZ pulse caring results in a 180o phase change between consecutive symbols for CSRZ.1. Without RZ pulse carving. However. But unlike OOK. 218]. Duobinary is sometimes also referred to as pseudo binary transmission (PSBT) [222].2. In CRZ.5’. ’1’). As discussed in Section 3. or alternatively known as phase engineering or phase coding formats. whereas the other half has a negative sign. the optical field has a positive sign for half the ’1’ symbols. which is referred to as AM-PSK modulation [224]. Because of its higher nonlinear tolerance. al. Another approach to improve the nonlinear tolerance is the use of chirped RZ-OOK modulation. The first optical duobinary experiment using 3-level amplitude modulation was reported at 280 Mb/s by O’Mahony in 1980 [225]. respectively. but at the same time the signal chirp results in spectral broadening. This either requires careful synchronization of the three drive signals or an integrated CRZ modulator such as reported by Griffin et. The main characteristic of duobinary modulation is a strong correlation between consecutive bits. which suppresses the carrier component. duobinary generation through 3-level amplitude modulation results in a lower receiver 69 . CRZ is used in ultra long-haul (transoceanic) transmission systems. OOK is referred to as NRZ-OOK. ’1’) or as a 3-level signal that combines phase and amplitude signaling (’-1’. which results in RZ-OOK modulation [111. In particular the nonlinear tolerance is low due to the strong optical carrier in OOK modulation. The nonlinear tolerance can be improved through RZ pulse carving. To realize duobinary 70 .8-Gb/s optical transmission systems where the chromatic dispersion tolerance is a key design parameter. Prior to encoding. Note that the encoder operation converts a binary signal into a 3-level amplitude signal. This has made duobinary modulation a useful modulation format to increase the robustness of 10.Chapter 4. the logical signal is first pre-coded.1) where d(k) represents bit k of the input sequence. such that at the receiver the transmitted sequence is again recovered. Analogous to OOK modulation. Note that pre-coding is not required in transmission experiments that uses a PRBS to evaluate the performance. Precoded data Tx B/4 MZM data Rx PSD (dB) ~ ~ encoder decoder 0 -10 -20 -30 -40 -100 1 1 1 0 0 0 -1 0 0 -1 0 1 1 1 0 0 PD laser -50 0 50 100 Frequency (GHz) Figure 4. modulation and decoder combined. A duobinary pre-coder can be implemented through the operation. The transmitter and receiver structure of duobinary modulation is shown in Figure 4.8-Gb/s duobinary. (4. c(k) = b(k) + b(k − 1). The use of AM-PSK duobinary generation is advantageous in optical communication as it has ideally the same or an even better OSNR requirement than OOK modulation [228].3. the transmitter consists of a standard MZM. which is difficult to realize with high-speed electronics.7-Gb/s and 42. 228]. The duobinary signal constellation in Figure 4. The phase coding in duobinary modulation is exemplified in Figure 4. The pre-coder therefore implements the inverse transfer function of the encoder. Optical transmission experiments using AM-PSK modulation for duobinary generation have therefore gained interest in the mid-90’s [227. the electrical signal is encoded before modulation to realize the required correlation between consecutive bits that characterizes duobinary modulation. In addition. The pre-coder implementation is therefore a recursive operation.2) where c(k) is the output sequence of the encoder that is used for modulation. Duobinary encoding can be realized through a delay-and-add.3: Duobinary transmitter and receiver structure and optical spectrum of 42.4 depicts the three constellation points and the binary logical symbols that they represent. b(k) = d(k) ⊕ b(k − 1). as the duobinary encoding then merely results in a cyclic shift of the input sequence. At the same time the narrower optical spectrum and strong correlation between consecutive bits result in an increased dispersion tolerance [227]. (4. Consecutive logical 1 s have a 1800 phase shift when they are separated by an odd number of logical 0 s. b(k) is the sequence after pre-coding and ⊕ is a logic exclusive OR operation. Binary modulation formats sensitivity as the symbol distance is reduced by a factor of two [226]. A logical 0 is coded as a zero whereas a logical 1 is coded as either − 1 or 1 .4. followed by a toggle flip-flop (T-FF) [229]. An alternative non-recursive implementation consists of an AND operation of the input sequence and clock signal. 0 → 0 and 1 → 1. The delay-and-add operation can be replaced by low-pass filtering the signal with a B0 /4 bandwidth. i. Due to its simplicity this transmitter structure has become the standard duobinary implementation.4: Duobinary signal and signal constellation.7-Gb/s duobinary modulation. This results in a 2-3 dB back-to-back OSNR penalty compared to NRZ-OOK modulation. But duobinary encoding does not allow a logical sequence ’1 0 1’ to occur. Duobinary modulation with a MZM preceded by electrical low-pass filtering is depicted in Figure 4.al. Hence a 42. where the bandwidth B0 is twice the inverse of the symbol period (B0 = 1/T0 ). However. low-pass filtering with a B0 /2 bandwidth results in severe eye closing. Kim et. instead coding it to ’-1 0 1’ or ’1 0 -1’. −1 → 1. which is evident from comparing the optical spectrum of duobinary modulation (Figure 4.e. As a result.1).5b shows the eye diagram for 10. Duobinary modulation therefore uses the same direct detection receiver as NRZ-OOK modulation. Duobinary Re{E} [sqrt(mW)] Im{E} 1 0 -1 0 100 200 300 400 500 600 0 0 -1 0 0 0 1 0 -1 0 0 -1 0 1 0 -1 0 0 -1-1-1-1 0 1 1 1 1 0 -1 0 2ES 1 Re{E} Time (ps) Logical ‘1’ Logical ‘0’ Figure 4. This effectively maps: 0 → exp( j · π) = -1 1 → 0 = 0 . 231]. For ’standard’ binary coding. The energy from the surrounding ’-1’ and ’1’ that leaks into the middle ’0’ through narrowband filtering now destructively interferes. 2 → exp( j · 0) = 1 which is equal to the duobinary partial response code.2. which have a 180o phase difference.4. The MZM then switches between two crest points. The duobinary eye diagram in Figure 4.8-Gb/s duobinary transmitter can be realized using a ∼10-Gb/s modulator. modulation with a MZM. The low electrical bandwidth allows for a further simplification as the MZM modulator used in duobinary transmitter only requires a B0 /4 electro-optical bandwidth [230. This is best exemplified with a ’1 0 1’ logical sequence. and Figure 4. Low-pass filtering results in energy leakage from the surrounding ’1’ into the middle ’0’ which closes the eye. on itself the duobinary partial response code does not result in an improved chromatic dispersion tolerance.3) and OOK modulation (Figure 4. strong low-pass filtering does not impact the signal too severely. the electrical driving voltage should have a peak-to-peak voltage of 2Vπ and the MZM has to be biased in the trough point. The optimal op71 .5a. which limits the eye closing. The narrowband electrical filtering results in a compact optical spectrum. At the receiver.5b shows a triangular shape with residual energy in the 0 s. To improve the dispersion tolerance the spectral width has to be reduced by electrically low-pass filtering the signal with a B0 /2 bandwidth. showed that the OSNR requirement of duobinary can be significantly improved through narrowband optical filtering at either the transmitter or receiver [232]. the decoding of duobinary modulation results directly from the square-law detection |E|2 of the photodiode. which can be generated using an additional pulse carver at the transmitter.6a compares the back-to-back OSNR tolerance of duobinary. Figure 4.5c. After narrowband optical filtering the duobinary signal becomes more NRZ-like. which becomes similar to RZ-OOK modulation. The OSNR tolerance of duobinary is also improved through the use of RZ-duobinary instead of NRZ-duobinary. In a commercial transponder penalties often arise from variations in the electrical component bandwidth. narrowband filtered duobinary and NRZ-OOK. Because of the narrower optical bandwidth the OSNR tolerance for filtered duobinary is approximately 1 dB better than NRZ-OOK [235]. but for a 10-Gb/s receiver this requires a very narrow optical filter with a ∼8-GHz bandwidth. However. Optical filters with a 32-GHz bandwidth are readily available. tical filter bandwidth is approximately 0.u) ~ ~ . the broader optical bandwidth of RZ-duobinary cancels out the improved chromatic dispersion tolerance that characterizes duobinary. RZ-duobinary is therefore only sporadically used in optical transmission experiments and not in deployed transmission sys72 Power (a. as evident from Figure 4.5: (a) Operation of the MZM for duobinary modulation and (b-c) measured eye diagram shows 10. Although the chromatic dispersion tolerance can be recovered through narrowband optical filtering at the receiver this again reduces the OSNR tolerance [237]. the theoretically obtainable performance of duobinary modulation is hard to achieve in practice. Narrowband optical filtering at the receiver is particularly interesting as it filters out more noise than a broad de-multiplexing filter. optical filtering is more practical as the required filter bandwidth scales inversely with the symbol rate. Binary modulation formats (a) Optical phase = 0 Optical phase = Crest Transmittance Optical Filter After narrowband optical filtering Quadrature 3B0/4 Trough Bias ~ ~ ~ V0 Time Electrical drive signal after low pass filtering Electrical filter (b) Time (c) B0/4 Electrical drive signal 93 ps 93 ps 2V Figure 4. which results in a ∼4 dB OSNR improvement [234]. However.Chapter 4. The quantum limit for a theoretically optimal duobinary modulation is therefore also ∼1 dB below the quantum limit of NRZ-OOK modulation [236]. This can be improved through the integration of a narrowband optical filter. For a 40-Gb/s receiver. with a 2nd order Gaussian shape [233].8 · B0 .7-Gb/s duobinary (b) without and (c) with additional narrowband optical filtering. the narrow optical spectrum reduces the PSP depolarization and the large chromatic dispersion tolerance reduces the impact of PCD [238].7Gb/s [239] and 42. We note that the narrowband optical filtering strongly reduces the chromatic dispersion tolerance for a 2-dB OSNR penalty. a w shape is obtained in the dispersion curve. 42. 241]. Figure 4.8-Gb/s NRZ-OOK.1nm) (a) Chromatic dispersion (ps/nm) (b) Figure 4.8-Gb/s duobinary. this is not due to a reduction in the absolute dispersion tolerance but rather a side-effect of the improved back-to-back OSNR requirement.8-Gb/s [240. -2 -3 Required OSNR (dB/0. which further raises the residual energy in ’0’s and results in an OSNR penalty. Duobinary modulation has been used extensively in long-haul transmission experiments at 10.8-Gb/s transmission with a 50-GHz channel spacing. The residual energy in the 0 s that cause the ’w’ shape in the dispersion tolerance also reduces the DGD tolerance of duobinary modulation. enabling a 0. The narrower spectral width of duobinary makes it a good candidate for DWDM transmission with narrow channel spacing [243]. they cannot further reduce the total spectral width in comparison to a duobinary signal [245]. The optical filter bandwidths are 90-GHz 3rd order Gaussian for duobinary and OOK. We note though that the SOPMD tolerance of duobinary is more beneficial.8-Gb/s filtered duobinary 42. Higher-level partial response (polybinary) codes generally do not offer a further improvement in the dispersion tolerance. which improves the back-to-back OSNR requirement. 73 .1nm) 26 24 22 20 18 16 -300 log(BER) -4 -5 -7 -9 -11 10 12 14 16 18 20 22 24 BER = 10 -200 -100 0 100 200 -5 300 OSNR (dB/0. Hence.2. Duobinary tems.4. But the simplicity of duobinary encoding through electrical low-pass filtering has made it the most widely used partial response format. A different application of RZ-duobinary is the reduction of intra-channel impairments. Besides duobinary modulation there are a large number of other partial response codes that offer similar properties [244]. 241. Although such formats concentrate the power closer to the carrier. 242] bit rates. However.6b shows the chromatic dispersion tolerance of duobinary. This is typical for duobinary modulation. and 34-GHz 2nd order Gaussian for filtered duobinary.6: Simulated comparison of (a) back-to-back OSNR tolerance and (b) chromatic dispersion tolerance for 42. In the absence of narrowband optical filtering. duobinary modulation can be used to realize 42. In the presence of DGD the pulses spread out. in which it obtains a similar performance as CSRZ [111]. The w shape disappears when the duobinary signal is narrowband optical filtered.8-b/s/Hz spectral efficiency [240. In optical transmission systems a low-complexity self-homodyne (interferometric) demodulation scheme is therefore often used [10. encodes the information in the signal’s phase. 246]. Various schemes are capable of demodulating BPSK signals. Binary phase shift keying (BPSK). phase shift keying requires demodulation at the receiver before it can be detected. as visualized in Figure 4. the information is encoded in the differential phase of the optical signal. Hence. or DPSK.3 Differential phase shift keying Both OOK and duobinary modulation encode the information in the amplitude of the optical signal. The main benefit of DPSK modulation is the lower OSNR requirement when compared to OOK. (c) constructive component. With self-homodyne demodulation. Binary modulation formats 4. In the case of OOK modulation.7. on the contrary. (b) before phase demodulation. the difference 74 . The transmitter and receiver structure of DPSK modulation is shown in Figure 4.u) 23 ps 23 ps 23 ps 23 ps (b) (c) (d) (e) Figure 4.8.7: (a) Transmitter and receiver structure of RZ-DPSK and (b-e) measured eye diagrams for 42.Chapter 4. Homodyne demodulation provides the best performance but is complex to realize. DPSK modulation has a number of advantages over OOK modulation that makes it a suitable modulation format for robust long-haul transmission systems.8: Signal constellations for binary OOK and binary DPSK modulation. both signal constellations have the same average optical power. (a) clock MZM precoded data Tx (b) MZM Balanced detection MZDI T -1 -1 1 -1 -1 1 (d) (c) PD + (e) laser - data Rx optional Power (a. OOK: Im{E} DPSK: Im{E} 0 1 ES Re{E} -1 1 2ES Re{E} Figure 4. (d) destructive component and (e) after balanced detection. This can be understood directly from the signal constellation. the name differential BPSK.8Gb/s RZ-DPSK. Because a photodiode is only sensitive to the incident optical power. which results in constant amplitude.7-Gb/s NRZ-DPSK and (c) 10. similar to OOK modulation. The width of the intensity dips in the NRZ-DPSK signal depends on the electro-optical bandwidth of the MZM and/or the bandwidth of the electrical drive signal. an infinite extinction ratio and an average optical power 1/2 · 0 + 1/2 · |Es |2 = 1/2 · |Es |2 . as the electrooptical bandwidth of a practical phase modulators is limited. based on a MZM. The more practical DPSK transmitter design is. ideally.7-Gb/s RZ-DPSK modulation. 1/2 · |1/ 2Es |2 + 1/2 · |1/ 2Es |2 = 1/2 · |Es |2 . (a) Optical phase = 0 Optical phase = Crest Transmittance (b) Power (a. respectively.9. However. In the presence of chromatic dispersion and/or nonlinear impairments. For DPSK. The MZM is biased in the trough of the modulator curve and the electrical driving voltage has a peak-to-peak voltage of.u) Quadrature Trough Bias V0 93 ps Time (c) Power (a. the 180o phase transition is not instantaneous. 2Vπ .3.e. Differential phase shift keying between the two constellation points equals the signal energy Es . The MZM therefore switches between two crest points. this chirp limits transmission tolerances. √ However. 4. DPSK modulation with a MZM is depicted in Figure 4. i. we obtain a ∼ 3-dB advantage in OSNR tolerance.9: (a) Operation of the MZM for DPSK modulation and eye diagrams before phase demodulation showing.3. assuming NRZ pulse coding.4. both constellation points have the same signal energy but a differential phase√ either ∆φ = 0 of or ∆φ = π.1 Transmitter structure As DPSK modulation carries the information in the optical phase. which encodes the 180o phase jumps. This is visible in the NRZ-DPSK output signal. (b) 10. An (ideal) phase modulator changes only the phase of the optical signal. which shows characteristic intensity dips when the MZM switches from − 1 to 1 or vice-versa. which introduces chirp between symbol transitions. as the symbol distance is increased with a factor 2 in comparison to OOK modulation. the most straightforward modulator configuration is based on a phase modulator. The electro-optical bandwidth of a MZM is similar to what can be 75 . When the difference between the two constellation points equals 2Es the average √ √ power of DPSK is the same as for OOK.u) Electrical drive signal Time 2V 93 ps Figure 4. Both signal components have a different optical spectra and signal structure but carry the same (but inverted) information. for partial DPSK). destructive interference occurs at one of the outputs and constructive interference at the other output. In the optical spectrum of the destructive output signal the carrier frequency is suppressed. delays one copy over a single bit period ∆T in [s] and recombines both arms to create optical interference.9c show typical eye diagrams for 10.10 depicts in more detail the phase demodulation with an MZDI.2. which implements the differential decoding of DPSK modulation. not realized at the transmitter but through the phase demodulation at the receiver. An MZDI demodulates the differential phase between each data bit and its successor.7-Gb/s NRZ-DPSK and RZ-DPSK. similar as discussed for OOK modulation. the constructive and destructive output ports exhibits a periodic notch response with a 3-dB bandwidth of 1/(2∆T ) and a free spectral range (FSR) of 1/∆T .2 Receiver structure In a DPSK receiver. The pre-coder for DPSK is similar to the pre-coder required for duobinary modulation (Section 4. Figure 4. it does not suffer from modulator induced chirp. But as a MZM has exact 180o phase changes.10a). Note that the ’encoding’ of the signal is.9b and 4. 2B0 = 2/T0 . Note that ∆T is not necessarily equal to the symbol period T0 (e. pulse carving with a 66% duty-cycle does not result in alternating phase coding but merely inverts the encoded information in the DPSK signal. The center spectral lobe of the NRZ-DPSK optical spectrum has a width equal to twice the signal bandwidth.10c. although the abbreviation is often used in the literature. It is therefore not fully correct to refer to CSRZ-DPSK.Chapter 4. which results in duobinary modulation [247. As DPSK modulation is based on differential detection.3) where u± (t) is the constructive and destructive component. The MZDI splits up the signal in two copies.g. This can be understood by noting that for this phase shift and an unmodulated input signal. The optical spectrum of the constructive output port has a central lobe with a spectral width of B0 = 1/T0 . respectively. it requires pre-coding of the transmitted sequence. When the DPSK modulator is followed by an additional pulse carver the NRZ pulse shape is converted to a RZ shape. u± (t) = r(t) ± exp( j∆φ )r(t − ∆T ). respectively. the differential phase modulation is normally converted into amplitude modulation using a Mach-Zehnder delay-line interferometer (MZDI). When ∆T is the delay in the interferometer arm. which results in an alternating mark 76 . respectively. For DPSK. respectively. Binary modulation formats realized for a phase modulator. r(t) is the input signal and ∆φ the phase difference between both interferometer arms.10b and 4. Figure 4. The phase difference is ideally ∆φ = 0 ± π. the output ports of the MZDI are referred to as the constructive and destructive port. 4. The optical input signal before demodulation is NRZ-DPSK modulated and has an average optical power of 1 mW (Figure 4. in contrast to duobinary modulation. The transfer function of the MZDI is defined through.[239]). 248]. (4. The constructive and destructive components obtained after demodulation are depicted in Figures 4. Hence.3. When both arms of the MZDI have a polarization dependent propagation coefficient. which would degrade signal quality without an active control. the periodic notch response of the MZDI is dependent on the SOP of the incoming light. Both the constructive and destructive output port of an MZDI carry the full information of the DPSK signal. The transfer function of a DPSK receiver. Figure 4.4) 1 1 1 1 = | r(t) + exp( j∆φ ) r(t − ∆T )|2 − | r(t) − exp( j∆φ ) r(t − ∆T )|2 . The penalty that results from a PDλ can be avoided through polarization tracking. which gives the characteristic RZ shape of the AMI signal. This is depicted in Figure 4. separately. When the MZDI should be colorless. There is a high probability this will occur. the drawback of an MZDI design without active control is that the phase difference between the two interfering arms cannot be adjusted to the center frequency of the received signal. but more difficult to avoid. But in order to obtain the ∼3-dB OSNR improvement of DPSK over OOK modulation. we assume that the phase offset in the MZDI is minimized for a certain input SOP. Hence.3. This is known as single-ended detection.7 depicts measured eye diagrams for 42.e. i. such an MZDI must be matched to a predefined wavelength (usually the ITU grid). as even slight changes in temperature result in a change in the differential delay of a fraction of an optical cycle. 2 2 2 2 where u(t) is the output after balanced detection. Minimizing the PDλ is therefore one of the more important criteria in the design of an MZDI. An MZDI based on fiberoptic couplers requires active phase stabilization. The worst penalty then occurs when the input SOP changes to the orthogonal SOP on a time scale faster than the phase offset control loop. This is known as balanced detection. An MZDI based on free-space technology is athermal and therefore does not require active phase stabilization. 77 . detecting either only the constructive or destructive output is sufficient. instead of 43-GHz FSR as would be optimal for a 43-Gb/s bit rate. when it can be used for any WDM channel.10d.4. since polarization changes are generally much faster than a thermal control. which shows that the peak-to-peak amplitude of the balanced output is twice that of the constructive and destructive signal. The path-length difference changes the interference between the two signals. i. for example with fiber-optic couplers [249]. Closely related to the phase stabilization of an MZDI. An AMI signal has a 180o phase jump between each consecutive ’1’. but this is impractical as it significantly raises the receiver complexity.8-Gb/s RZ-DPSK before demodulation and the constructive. An MZDI can be realized with different technologies. u(t) = |u+ (t)|2 − |u− (t)|2 (4.e. However. Therefore. which uses two photodiodes followed by a differential amplifier. Differential phase shift keying inversion (AMI) signal. As an example. both MZDI output ports have to be detected simultaneously. is the polarization dependent wavelength shift (PDλ ). destructive and balanced signals after demodulation. the MZDI plus balanced detection is now defined through. a fiber-Bragg grating [250] or free space technology [251]. this implies a fixed 50-GHz FSR. 5 0 -40 Amplitude [sqrt(mW) ] 1 0 -1 -20 0 20 40 (4) Output differential amplifiers Re{u(t)} [mA] Time (ps) Re{u(t)} [mA] 1 0 -1 -40 -20 0 20 40 1 0 -1 0 100 200 300 400 500 600 700 800 1 -1 -1 1 1 1 1 1 -1 1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 -1 1 1 1 1 -1 1 Time (ps) Time (ps) Figure 4. Binary modulation formats Optical input 10 0 Constructive (a) 10 0 -10 -20 Destructive (b) 10 0 -10 -20 (c) PSD (dB) -10 -20 -30 -40 -100 -50 2B0 0 50 100 -30 -40 -100 -50 B0 0 50 100 -30 -40 -100 -50 2B0 0 50 100 Frequency (GHz) Frequency (GHz) Frequency (GHz) r(t) (1) T MZDI (2) u+(t) u-(t) (3) + (4) u(t) 1 (1) Optical input signal |r(t)| [sqrt(mW)] 0.5 0 Re{u+{t)} [sqrt(mW)] (2) Duobinary 1 0 -1 0 100 200 300 400 500 600 700 800 0 -40 -20 0 20 40 Time (ps) |u+(t)|2 [mW] 1 0 0 1 1 1 1 1 0 -1 0 1 1 1 1 0 0 0 0 1 1 1 0 -1-1-1-1 0 1 0 0.8-Gb/s NRZ-DPSK showing the input signal before demodulation.Chapter 4.10: Phase demodulation of 42. The phase difference between the MZDI arms is equal to ∆φ = π in the example.5 1 -1 1 1 1 1 1 1 -1 -1 1 1 1 1 1 -1 1 -1 1 1 1 1 -1-1-1-1-1 1 1 |r(t)|2 [mW] 1 0.5 0 -40 -20 0 20 40 (3) Alternating mark inversion (AMI) Re{u-{t)} [sqrt(mW)] Time (ps) |u-(t)|2 [mW] 1 1 0 -1 0 100 200 300 400 500 600 700 800 1 -1 0 0 0 0 0 1 0 -1 0 0 0 0 1 -1 1 -1 0 0 0 1 0 0 0 0 -1 0 1 0. destructive and balanced outputs of the MZDI. 78 . as well as the spectra of the constructive. Figure 4. This can be achieved using a DPSK transmitter followed by an MZDI to demodulate either the constructive or destructive component. The total difference in OSNR requirement between 10.7 Gb/s. the transmitter is more complicated as it requires an MZDI and higher bandwidth optical and electrical components (drive amplifiers. respectively. Hence the theoretical sensitivity difference between OOK and DPSK modulation is 2. Especially the generation of optical duobinary via this method has some practical applications. the sensitivity penalty is therefore a product of the phase error in both symbols. When one assumes an ideal transmitter and LO laser in 79 .7-Gb/s BPSK with coherent detection and DPSK with direct detection is therefore 1. Experimental verification has shown receiver sensitivities for direct detection DPSK of 30 photons/bit [254] and 38 photons/bit [255.3. direct detection with an MZDI. Differential detection is not required in a coherent receiver and this can improve the OSNR requirement with a further 0. for OOK with direct detection the quantum limit is 38 photons/bit. In comparison. coherent detection without differential decoding. The difference is slightly dependent on the BER and it can be shown that the theoretical receiver sensitivity or ’quantum limit’ at a BER of 10−9 is 18 photons/bit for coherent BPSK and 20 photons/bit [253] for direct detection DPSK. Differential phase shift keying A special application of DPSK demodulation is the optical generation of either duobinary or AMI modulation.7-Gb/s DPSK with coherent and direct detection is 0. optical modulator).2. coherent detection can have further advantages over interferometric detection in the nonlinear transmission regime. Besides the lower OSNR requirement. The difference in OSNR requirement between 10.55 dB. This can be especially interesting in transmission links where strong narrowband filtering occurs [252].7-Gb/s DPSK modulation coherent detection with differential decoding. 112] at a bit rate of 10 Gb/s and 42. -2 log(BER) -3 -4 -6 -8 -10 2 FEC limit 8 10 12 14 3 4 5 6 7 8 OSNR (dB/0.4.11: Theoretical performance of 10.11 compares the theoretical performance of the different detection schemes for 10.3 Back-to-back OSNR requirement The use of interferometric detection in DPSK allows for a lower-complexity receiver but requires a high OSNR to obtain the same performance as homodyne (coherent) detection. On the other hand.7-Gb/s DPSK.3. The optical duobinary signal has similar properties as the (electrical) duobinary described in Section 4. Interferometric detection compares the phase difference between two consecutive symbols.8 dB at low BER.1 dB for a 10−3 BER. 4.1nm) 9 16 10 Q (dB) Figure 4.6 dB for a 10−3 BER. 2 OSNR (dB/0. 80 .8 dB. the transfer function of the MZDI narrowband filters the signal which reduces the spontaneousspontaneous beat noise in the signal. The >3-dB penalty is a result of the broad 90-GHz optical filter bandwidth used in the simulations. constructive. For OOK. This is a consequence of the RZ pulse shape of the destructive (AMI) components in comparison to the NRZ-pulse shape of constructive (duobinary) component. The difference between NRZ-DPSK and the constructive/destructive component is 2.8-Gb/s NRZ-DPSK.1 11. In all cases a 90-GHz optical filter bandwidth is used Figure 4. a 90-GHz filter bandwidth is a reasonable assumption for transmission systems with a 100-GHz channel spacing. which is discussed in Chapter 10.8Gb/s NRZ-OOK. balanced NRZ-DPSK.5 dB and 1. For the simulations depicted in Figure 4. Hence. the OSNR requirement is higher as the spontaneous-spontaneous beat noise is not filtered out.8-Gb/s NRZ-DPSK. NRZ-DPSK.1nm) 42. self-homodyne demodulation is therefore the preferable choice for deployed transmission systems.7 dB in OSNR requirement.4 dB.8 14. constr. for a 10−3 BER but increases for lower BER. 42.e.Chapter 4. 42.12: Simulated OSNR requirement for The difference in OSNR requirement between DPSK and OOK modulation depends on pulse shape and receiver parameters. balanced. a 0. destructive.3 13. NRZ-OOK 12 14 16 18 20 22 log(BER) -4 -5 -6 -8 -10 -12 10 required OSNR (dB) for 10−3 BER 11. coherent detection theoretically reduces the impact of nonlinear phase noise by a factor of two in comparison to interferometric detection [256]. A practical approach for homodyne demodulation that is currently under consideration is a coherent intra-dyne receiver. balanced. For the same reasons.6 15. on the other hand. the difference in required OSNR between NRZ-DPSK and NRZ-OOK is 3. no phase noise) the penalty only dependent on the phase error in the received symbol itself. The main drawback of homodyne demodulation is the higher complexity of a coherent receiver as it requires the detection of the full optical field. For DPSK modulation.12. Binary modulation formats coherent detection (i. We note that with narrowband optical filtering the comparison changes as each of the signal has a different optimal filter bandwidth. 42. -2 -3 Modulation format RZ-DPSK. In this section we further discuss the properties of DPSK modulation using a direct detection receiver.7 dB difference in OSNR is observed between NRZ-DPSK and RZ-DPSK. balanced NRZ-DPSK. including the state of polarization. destr.8-Gb/s NRZ-DPSK. It is further observed that the constructive and destructive components of the NRZ-DPSK signal differ by 0. 42. However. Because of its relative simplicity. respectively.8-Gb/s RZDPSK. For NRZ-DPSK. Furthermore. an amplitude or time imbalance between the constructive and destructive outputs. |u+ |2 + |u− |2 (4.6 dB 14 13 -1 BER = 10 -0. and is therefore discussed extensively in the next section.13a shows the amplitude imbalance between the constructive and destructive component. The simulated penalty is with 2. 42.3. The bit-delay in the MZDI is an important aspect for partial DPSK.13: Simulated DPSK receiver imperfections.6 dB slightly lower than the 2. We note that although the simulated results are for a 42. 258]. which results from the difference in OSNR requirement between the constructive component (dominant for α < 0) and destructive component (dominant for α > 0). The amplitude imbalance is defined as [257]. The amplitude imbalance results in a shift of the optimum threshold whereas the time imbalance offsets the constructive and destructive components.1 nm) 17 20 19 18 17 16 15 14 13 -60 -40 -20 0 20 40 -5 16 15 2. Figure 4. Differential phase shift keying 4.4 Receiver imperfections Imperfection in the phase demodulation have a significant impact on the optical performance characteristics of a DPSK receiver [257. An α = 0.8-Gb/s NRZ-DPSK. The amplitude imbalance varies between α = ±1 and is in the extremes equal to singleended detection of either the constructive or destructive component.8-Gb/s RZ-DPSK.) (a) Figure 4. For RZ-DPSK.5 -5 BER = 10 MZDI phase mismatch (degrees) (b) 1 60 Balanced detector amplitude imbalance (a. the phase differences and bit-delay between the signal and its delayed copy upon interfere within the MZDI are important to consider. (a) amplitude imbalance and (b) phase mismatch. 42. An amplitude imbalance results from a difference in the pigtail or connector loss in one of the two arms. resulting in a skewed eye diagram.8-dB penalty that one would expect from theory. or a difference in conversion efficiency between the two photodiodes. Required OSNR (dB/0.5 0 0.8-Gb/s symbol rate.5) where |u− |2 and |u+ |2 are the averaged output powers of both photodiodes before balanced detection. α= |u+ |2 − |u− |2 . the curve is slightly asymmetric.4. for example.2 81 .1nm) Required OSNR (dB/0. most of the receiver imperfections are bit rate independent.u.3. A direct detection DPSK receiver can be impaired through. which is caused by the higher BER (10−5 ) used in the simulations. the difference is negligible as both components have a similar OSNR requirement. 6) where ∆ f is the laser frequency drift in [Hz]. To counter a temperature or laser wavelength drift. ∆φ = 360 · ∆ f ∆T. 42. |u+ |2 ≈ −|u− |2 . which equals approximately a 1. a phase offset in the MZDI lowers the RF power obtained after balanced detection and maximizing the RF power will minimize the phase offset in the MZDI.5o (see Figure 4.5 dB difference between the two outputs of the MZDI.14a. destructive component. The phase offset in degrees is related to the laser wavelength through. 60-GHz filter 42.Chapter 4.3. (2) temperature drift of the MZDI and (3) polarization-dependent wavelength shift of the MZDI [259].8-Gb/s RZ-DPSK.8-Gb/s NRZ and RZ-DPSK. The phase offset penalty results from a phase difference upon interference between the two arms of the MZDI. A (slow) thermal control can therefore be used to change the phase difference between the two arms and as a control signal. (4.13b). the required tracking speed is generally slow and in the seconds range.5-dB penalty. 40-GHz filter. Figure 4. the RF power after balanced detection can be measured [260]. constructive component.8Gb/s NRZ-DPSK.8-Gb/s NRZ-DPSK. This shows that the dispersion tolerance differs between the destructive and constructive component of DPSK.e.1 nm) Required OSNR (dB/0. 90-GHz filter 42. A phase offset in the MZDI can be induced through (1) wavelength drift of the transmitter laser. the constructive and destructive component are not anymore fully orthogonal to each other.5 Chromatic dispersion & DGD tolerance The chromatic dispersion tolerance of DPSK modulation is depicted in Figure 4. as ∆φ = 0 is optimal.1nm) 22 20 18 16 14 0 5 10 -5 22 20 18 16 14 -200 -100 0 -5 BER = 10 100 BER = 10 15 200 20 Chromatic dispersion (ps/nm) (a) Differential group delay (ps) (b) 42. For an OSNR penalty of 1 dB.8Gb/s NRZ-DPSK. This difference can be explained by the line coding in both components. after balanced detection. Note that the penalty is independent of the pulse coding (RZ or NRZ). The substraction of the constructive and destructive component through balanced detection then result in a lower RF power. When a phase offset is present in the MZDI. Hence. the allowable phase offset is about 20. 90-GHz filter. 4. Binary modulation formats results in a 0. Due to its 82 .14: (a) chromatic dispersion and (b) DGD tolerance for 42. Required OSNR (dB/0. i. Note that the optical filter bandwidth for both the constructive and destructive component is different and has been optimized. For the destructive component. and was first demonstrated in 2003 by Yoshikane et. This improves the dispersion tolerance. respectively. Partial DPSK duobinary coding. The use of a shortened MZDI in the DPSK receiver. there is less ISI for small amounts of DGD because the pulses spread out but not yet interfere with the neighboring pulses. [261]. However. a significant reduction is evident. and the optical bandwidth can be reduced to ∼35 GHz. For larger amounts of DGD the tolerance of both RZ and NRZ is similar. 4.15a and 4. as the DGD tolerance is mainly determined by the symbol rate. In addition. improves the narrowband filtering tolerance.15b depicts the concept of partial DPSK and the OSNR requirement as a function of the bit-delay. But when OADM/PXCs are passed along the transmission link this result in severe narrowband optical filter. For a RZ pulse shape. together with narrowband filtering (not shown) the dispersion tolerance becomes similar to the tolerance of the constructive component.4 Partial DPSK Ideally. the constructive component has a duobinary line coding which significantly improves its tolerance to narrowband filtering. which has a ∆T < T0 bit-delay between both arms. which results in deterministic interference at the beginning and end of the symbol 83 .14b shows the DGD tolerance for 42.4. which limits the number of add-drop nodes that can be passed When a NRZ-DPSK signal is narrowband filtered. Figures 4. there is no significant difference between the constructive and destructive component for RZ-DPSK.8-Gb/s NRZ-DPSK there is a strong asymmetry with respect to the 1bit delay. For ∆T < T0 .8-Gb/s NRZ-DPSK and RZ-DPSK. Hence. on the other hand. Figure 4. For 42. which broadens the optical spectrum. although the tolerance is somewhat lower compared to conventional duobinary. This is known as partial DPSK. 42.8-Gb/s modulated signals can be deployed in transmission systems with a 50-GHz channel spacing. the signal and its delayed copy are only partially overlapping upon interference.8-Gb/s NRZ-DPSK modulation this result in high OSNR penalties. The destructive component. the constructive component remains nearly unaffected because most of the energy is close to the carrier. al. the signal after balanced detection is asymmetric and the optimum threshold shift towards the constructive component. we find a 9 ps and 10 ps DGD tolerance (1-dB OSNR penalty) for NRZ-DPSK and RZ-DPSK. has a reduced dispersion tolerance. on the other hand. As a result. This results from the broader optical spectrum of the RZ signal. which becomes distorted.4. most of the energy is relatively far away from the carrier. This shows that for 42. the constructive component has similar properties as duobinary modulation. The chromatic dispersion tolerance after balanced detection is determined by both components. This results from the RZ-shape of the signal. respectively. In addition. When we furthermore compare the dispersion tolerance of RZ-DPSK with NRZ-DPSK. Narrowband filtering therefore reduces the power in the destructive component. 8-Gb/s NRZ-DPSK. This is evident from Figure 4. For ∆T > T0 . Depicted is the penalty for 42. For ∆T T0 . The impact of a shortened bit-delay on the narrowband filtering tolerance is show in Figure 4.8-Gb/s NRZ-DPSK. apart from a negative offset.34-bit delay 10 0 0.bit delay (a) MZDI bit-delay ( T/T0) (b) Figure 4.65 x T0 0.1-nm res.15b. similar to a duobinary signal. 84 .65 .6 0. constr.2 1. which shows simulated eye diagrams of the balanced output for several MZDI bit-delays. PSD (dB) -10 -20 -30 -40 -100 -50 0 50 100 -100 -50 0 50 100 -100 -50 0 50 100 -100 -50 0 50 100 Frequency (GHz) 1 0 -1 -40 -20 0 20 40 -40 Frequency (GHz) Frequency (GHz) Frequency (GHz) Re{E} (mA) -20 0 20 40 -40 -20 0 20 40 -40 -20 0 20 40 Time (ps) Time (ps) Time (ps) Time (ps) Figure 4.5-bit delay 0. 42. 90-GHz filter bandwidth period. This is explained by the observation that the constructive and destructive components are not fully orthogonal anymore. The shortened bit-delay in the MZDI results in a somewhat higher OSNR requirement.4 input signal -1 -1 1 1 -1 -1 1 1 1 1 signal delayed over 0.0-bit delay destr.8 1 1. 35-GHz filter bandwidth.2 0.) of the constructive and destructive output port. The penalty reduces for ∆T T0 and is close to zero for ∆T ∼ 2T0 as the symbol transitions are again aligned with each other [262]. The upper row show the optical spectra (0.16. Binary modulation formats delay mismatch Required OSNR (dB/0.65-bit delay 1.8-Gb/s RZ-DPSK.1 nm) 20 18 16 14 BER = 10-5 0 0. (b) OSNR penalty for different MZDI bit-delays 42. The lower row show the electrical signal after balanced detection. the symbol transition of the delayed copy occurs in the middle of the symbol period which results in crosstalk.4 0.Chapter 4.15: (a) phase demodulation with < 1-bit delay. 3rd order Gauss filter as a 0.8-Gb/s NRZ-DPSK with a 35-GHz. which results in a lower signal power after balanced detection. After balanced detection the electrical signal appears. 90-GHz filter bandwidth 42.16: Impact of < 1-bit MZDI delay. the destructive component fades out and the penalty is solely determined by the constructive component. The optical narrowband filtering mainly affects the destructive component. a larger part of the signals energy passes through the constructive port.9-dB OSNR penalty. When the bit-delay is decreased. as shown in Figure 4. The contour plots show the required OSNR for a 10−5 BER. on the other hand. which is attenuated anyway through the demodulation with a shortened MZDI.2 1.4. The constructive component (with the duobinary line coding) becomes the dominant signal compo- Chromatic dispersion (ps/nm) Optical filter bandwidth (GHz) 200 17 15 15 14 16 15 17 17 16 14 15 16 17 90 17 80 70 60 17 16 14 15 14 15 17 100 17 16 0 16 16 15 15 16 17 16 14 14 17 50 40 30 20 0. as no performance variation has to be accounted for.4 0. In this case the DPSK signal is demodulated through narrowband optical filtering [263]. Note that for a 0. the narrowband filtering penalty reduces accordingly.6 0.d) tolerance for NRZ-DPSK (a. with a minimum penalty for a 0. a 16.d) as a function of MZDI differential delay.2 1. This is particulary interesting from a system design point of view.0-dB OSNR is required.8 1 1. Partial DPSK function of the MZDI bit-delay.2 1. the 3-dB bandwidth of the MZDIs periodic notch response broadens.2 1. is attenuated and fades out for shorter bit-delays.6 0.65 bit-delay there is a negligible difference in OSNR requirement between NRZ-DPSK with (35 GHz) and without (90 GHz) optical filtering.4 0.6 0.4 -100 -200 0.4 0. a 1. the bit-delay can be reduced to zero with only a minor penalty.8 1 1.8 1 1.65 bit-delay. The improved narrowband filtering tolerance for a shortened bit-delay is best explained with the optical spectra of the constructive and destructive component. As a result. 85 .4 MZDI bit-delay ( T/T0) (c) MZDI bit-delay ( T/T0) (d) Figure 4.c) and optical filter bandwidth (b.b) and RZ-DPSK (c. When the bit-delay is reduced.6 0.4 MZDI bit-delay ( T/T0) (b) 16 17 14 14 15 100 15 14 14 0 16 15 15 16 16 17 14 15 15 16 17 -100 15 17 16 -200 0. For a 1 bit-delay. We further observe that with narrowband filtering.8 1 1.4 MZDI bit-delay ( T/T0) (a) Chromatic dispersion (ps/nm) Optical filter bandwidth (GHz) 200 90 80 70 60 50 40 30 20 0.4 0. The destructive component.17: Chromatic dispersion (a.16.4. The improvement in optical filter tolerance for 42. we note that the chromatic dispersion tolerance and the filter bandwidth are dependent on each other as well as on the MZDI bit-delay.17c-d). For an OSNR requirement of 16-dB (2. for an 16-dB required OSNR.8-Gb/s NRZ-DPSK with a shortened MZDI is discussed in [264.65 bit-delay MZDI the narrowband filter tolerance is improved to 24 GHz. the chromatic dispersion tolerance increases from 80-ps/nm to 95-ps/nm. At the same time. For RZ-DPSK.Chapter 4. 265]. We note that this is computed with a 60-GHz optical filter bandwidth.5-dB penalty). Binary modulation formats nent. combined with a shortened 0. the narrowband filter tolerance is 35-GHz. which in turn reduces the narrowband filtering penalties. including a broad optical spectrum. partial DPSK is the DPSK format of choice for deployed transmission systems. When narrowband optical filtering or a shortened MZDI are considered separately. an OSNR penalty is observed for NRZ-DPSK. However. the tolerance can be further increased.17. For RZ-DPSK (Figure 4. When the shortened bit-delay is combined with narrowband filtering. A shortened bit-delay results in a signal that has similar properties as RZ-duobinary. the penalty is more or less symmetrical with respect to the 1 bit-delay. The observed ’w’-shape in the dispersion tolerance for small bit-delays confirms that the signal is similar to duobinary in the absence of narrowband filtering. 86 . This is depicted in Figure 4. the dependence is significantly reduced. No significant improvement in narrowband filtering tolerance is therefore observed at low OSNR penalties [266]. Finally. Only for high OSNR penalties a similar improvement in narrowband filtering tolerance is observed. As a result. The higher OSNR requirement.1 the structure of a DQPSK transmitter and receiver are explained. multi-level modulation formats are a logical upgrade to either increase the spectral efficiency above 1-b/s/Hz. A significant number of different multi-level modulation formats have been proposed. c42. or to improve the robustness against transmission impairments. c50. In Section 5. In Chapter 6 we subsequently focus on long-haul transmission using DQPSK modulation.5 we discuss in detail the use of multi-level random sequences for evaluation of DQPSK transmission performance. In order to minimize the OSNR requirements and maximize nonlinear tolerance for long-haul transmission systems.3 the properties of DQPSK modulation are discussed. phase or polarization domain [267. Subsequently. c53 87 . Phase modulated formats have only modestly worse OSNR requirements compared to DPSK [10]. chromatic dispersion and PMD. 245. Section 5. as well as the reduced nonlinear tolerance of multi-level modulation in the amplitude domain [270] makes it impractical for long-haul transmission. 1 The results described in this chapter are published in c11.5 Differential quadrature phase shift keying For high-speed optical transmission systems. This chapter discusses the properties of DQPSK modulation. c24. especially modulation formats based on either phase and/or polarization modulation appear to be the most suitable. using either modulation in the amplitude. 268].4 analyzes the nonlinear tolerance of DQPSK modulation and in Section 5. As well. including the tolerance against narrowband filtering. c35. The use of polarization as a selective agent is discuses in Chapter 7 The multi-level modulation format that received the most interest in recent years is return-to-zero differential quadrature phase shift keying (RZ-DQPSK). the lack of a strong optical carrier reduces the generation of XPM when compared to amplitude modulation formats [269]. in Section 5. Comparing DPSK and DQPSK modulation. Two independent electrical drive signals are fed to the DQPSK modulator and only binary drive signals are required. The main drawback of using a phase modulator for DQPSK modulation is the higher residual chirp in the signal. DQPSK therefore doubles the total bit rate. 274] and two EAMs in a three-arm interferometer structure [275]. al. ideally. In such a parallel DQPSK modulator.3 depicts the signal constellation for several of the DQPSK modulator configurations. it is evident that the number of constellation points is doubled and the distance between the constellation points is halved. but in somewhat reduced amounts as it occurs only during the symbol transitions. 274]. This has the advantage that standard drive amplifiers at half the bandwidth of DPSK modulation can be used to amplify the electrical drive signals to a 2 ·Vπ voltage swing. respectively. which reduces the tolerance against chromatic dispersion and nonlinear impairments [273. The higher signal chirp is also evident from the signal constellations of both the MZM and phase modulator in series as well as the 4-level phase modulator. More commonly. the signal is split and each tributary is. DQPSK modulation is subsequently obtained by interfering the two tributaries with a suitable chosen phase shift (either −π/2 or π/2). Differential quadrature phase shift keying 5. At the same symbol rate. RZ pulse carving reduces the residual chirp in the modulated signal and is 88 .1 Transmitter & receiver structure Figure 5. ’00’ as a reference. a 3-dB higher OSNR for the same BER. DQPSK is used at half the symbol rate of binary modulation to obtain the same total bit rate. as the distance between the constellation points is halved it requires. π and 3π/2. Taking. DQPSK modulation can be realized using a variety of modulator configurations. a single phase modulator with a 4-level drive signal [273. [271]. DQPSK has then. However.2 shows a double intensity dip when the MZM switches over either ∆φ = π/2 or ∆φ = π. DPSK modulated. We note that modulation with a parallel DQPSK modulator also result in residual chirp.1 depicts the signal constellations of both binary DPSK and quaternary DQPSK modulation. Figure 5.2 using a so called ’Super MachZehnder’ structure as first introduced by Griffin et.1: Signal constellations for binary DPSK and quaternary DQPSK modulation. then the symbols ’01’.Chapter 5. DPSK: Im{E} DQPSK: j Im{E} -1 Es 1 Re{E} -1 2 Es 1 Re{E} 1 symbol/bit 2 symbol/bit -j Figure 5. ’10’ and ’11’ correspond to a phase difference π/2. for example. Other modulator configurations for DQPSK modulation include a MZM and phase modulator in series [272]. at least. The eye diagram in Figure 5. in effect. this is characteristic for DQPSK modulation with a parallel modulator. no OSNR penalty in comparison to DPSK modulation. The most common DQPSK modulator configuration is depicted in Figure 5. 278]. therefore desirable for DQPSK modulation. the phase shift between the two arms of the MZDI is +45o and −45o to demodulated the inphase (I) and quadrature (Q) component. Figure 5.5). For experimental evaluation the BER tester is normally programmed for the expected output sequence (post-coding). Each MZDI has a constructive and destructive output and therefore 4 photodiodes are required for balanced detection of DQPSK. In most reported transmission experiments.3: Simulated signal constellations for DQPSK modulation with (a) a parallel ’Super MachZehnder’ structure. This is illustrated by optical time-divisionmultiplexing experiments where a MZM plus phase modulator has been used for DQPSK modulation with excellent performance [276].5. The thick line shows the signal in the middle 50% of the symbol period. (b) a cascaded MZM and PM and (c) a PM with 4-level drive signal. A phase control for DQPSK demodulation is described in [280]. Q (normalized) Q (normalized) Q (normalized) -1 0 I (normalized) 1 1 1 1 0 0 0 -1 -1 0 I (normalized) 1 -1 -1 -1 0 I (normalized) 1 (a) (b) (c) Figure 5.1. a pseudo random quaternary sequence (PRQS) can be used to ensure that all possible sequences up to a given length are tested (see Section 5. Transmitter & receiver structure Parallel DQPSK modulator MZ MZ /2 Constellation diagram =0 = /2 = DQPSK eye diagram Figure 5. Either pre-coding or post-coding is therefore required to evaluate DQPSK modulation. a mix of the two transmitted data sequences. When two separate MZDI interferometers are used. The data sequences obtained after balanced detection are. due to the differential demodulation in the 1-bit delay MZDI. Although it is also possible to demodulate both tributaries at the same time using a 1x4 star coupler [277. two separate MZDIs are used in the receiver to convert the modulation from the phase to amplitude domain.2: Operation of the ’super’ Mach-Zehnder structure for DQPSK modulation.4 depicts the transmitter and receiver structure using a parallel DQPSK modulator. or a 90o hybrid with one of its inputs delayed over one symbol period [279]. For experimental evaluation of DQPSK modulation. The performance of all three modulation structures is nearly identical for 33% RZ pulse carving [273]. respectively. This limits the PRBS length to ∼ 215 − 1 because 89 . data I u v (a) DQPSK precoder clock MZ “Super Mach-Zehnder” structure MZDI T PD + In-phase ( = /4) + data u Rx MZM MZ /2 laser optional -j Prec. in [281]. (e) 42. pre-coding of the transmitted sequence is required [281. Such a high-speed feedback path can be avoided by using toggle flip-flops. 283]. (b) 42.u) (c) (d) (e) 47ps 47ps 47ps 47ps Figure 5.8-Gb/s NRZ-DQPSK after phase demodulation. I(k − 1) and Q(k − 1).8-Gb/s NRZ-DQPSK. programming the expected output sequence makes longer sequences impractical.2) + u(k − 1) ⊕ v(k) − v(k − 1) ⊕ u(k) In a commercial transponder.4: (a) Transmitter and receiver structure of RZ-DQPSK. al. which implies that a high-speed feedback is required that operates at the symbol rate. 282.Chapter 5. data Q -1 j j 1 -j T Quadrature ( data v Rx = . u(k). a parallel implementation can be used to reduce the speed of the feedback path 90 . Each bit I(k) and Q(k) in the post-coded sequences is dependent on four bits of the transmitted sequence.1) − u(k − 1) ⊕ v(k) + v(k − 1) ⊕ u(k) Q(k − 1) = 1 u(k − 1) ⊕ u(k) + v(k − 1) ⊕ v(k) 2 (5. This shows that each pre-coded bit depends on its predecessor.8-Gb/s RZDQPSK. (b-e) Measured eye diagrams showing. The post-coded bits for a parallel DQPSK modulator are given by. u(k − 1) and v(k − 1).8-Gb/s RZ-DQPSK after phase demodulation. Differential quadrature phase shift keying Prec. (c) 42. v(k). I(k − 1) = 1 u(k − 1) ⊕ u(k) + v(k − 1) ⊕ v(k) 2 (5. as shown by Serbay et. Each bit of the pre-coded sequence is dependent on the bits u(k). Alternatively. on the other hand. (d) 42. v(k)./4) (b) Power (a. 5. but can be minimized by controlling the bias voltage of the three interferometers within a parallel DQPSK modulator.and RZ-DQPSK modulation before and after demodulation. But for a parallel DQPSK modulator. in particular the phase and amplitude mismatches between the two DPSK modulated tributaries is important. by minimizing the power envelope variance.4) I(k − 1) ⊕ Q(k − 1) · I(k − 1) ⊕ v(k) I(k) = u(k) · v(k) · I(k − 1) + u(k) · v(k) · Q(k − 1) (5. Transmitter & receiver structure [283]. but for a commercial transponder they have to be controlled. In this case three different pilot tones can be used. In the transmission experiments reported here these bias voltages are set manually.4 further shows the measured eye diagrams for NRZ. The pre-coded bits of a parallel DQPSK modulator are given by [271]. Such imperfections depend on the specifications of the modulator. where each pilot tone separately controls one of the three bias voltages. The broadened ’1’-rail in a DQPSK signal can be partially suppressed through RZ pulse-carving. We note that the amplitude noise in the signal is not clearly evident in the back-to-back OSNR requirement.6) + u(k) · v(k) · I(k − 1) + u(k) · v(k) · Q(k − 1) Figure 5. for example. an additional light source at the modulator output can be used to implement a control of the bias voltages by minimizing the power of the backward propagating light [284].5) + u(k) · v(k) · I(k − 1) + u(k) · v(k) · Q(k − 1) Q(k) = u(k) · v(k) · Q(k − 1) + u(k) · v(k) · I(k − 1) (5.3) I(k − 1) ⊕ Q(k − 1) · I(k − 1) ⊕ u(k) Q(k) = + which can be re-written as [283]. Typical modulator imperfections result from mismatches between the Vπ of the modulator and the 2 ·Vπ amplitude swing of the driver amplifiers. 91 .1. but results in an increased impact of nonlinear phase noise along the transmission link. I(k − 1) ⊕ Q(k − 1) · I(k − 1) ⊕ u(k) (5. The amplitude noise results from modulator imperfections. This shows a relatively broad ’1’-rail in the NRZ-DQPSK modulated eye diagram due to amplitude noise. but the amplitude of the pulse remains noisy. I(k) = + I(k − 1) ⊕ Q(k − 1) · I(k − 1) ⊕ v(k) (5. Alternatively. For a 10−9 BER the difference is 6. -2 FEC limit -3 8 4 OSNR (dB) 4. for direct detection receivers the OSNR requirement differs between both modulation formats as DQPSK suffers from a higher MZDI demodulation penalty.4-Gb/s RZ-DPSK as a reference. The crosstalk is removed through balanced detection as the ghost pulse is subtracted from the other component.6 dB 0 -2 -4 -6 -8 -10 -12 OSNR/0.6: OSNR difference between DPSK and DQPSK modulation at a 42. ideally.5: Measured BER versus OSNR for 42. The constructive and destructive components show a ghost pulse in the ’0’.2 dB 16 18 20 16 22 0. For DQPSK modulation both the constructive and destructive outputs are neither duobinary or AMI modulated. In-phase 42. which translates into a higher OSNR requirement.4-Gb/s RZ-DPSK. This is clearly visible in Figure 5. The difference between simulated and measured penalty results from transmitter and receiver imperfections. Quadrature 21. This indicates that the difference in OSNR requirement between RZ-DPSK and RZ-DQPSK is BER dependent.8-Gb/s RZDQPSK. whereas for a 10−3 BER the difference reduces to 4. a measured penalty is left that varies between 1.4 dB.7 dB 2 log(BER) -5 -6 -8 -10 -12 6 8 10 12 14 Q (dB) -4 1 6.Chapter 5. the constructive component is duobinary modulated and the destructive component is AMI modulated. Figure 5.8-Gb/s bit rate. the same as for DPSK modulation at the same total bit rate. which is ∼0.1nm(dB) log(BER) Figure 5.8-Gb/s RZ-DQPSK modulation. Differential quadrature phase shift keying 5.2 Back-to-back OSNR requirement The OSNR requirement of DQPSK modulation is.2 dB.2 dB. with 21. which in a sense results from crosstalk of the other tributary. This causes a loss of signal power. For DPSK.5 shows the measured OSNR requirement for 42. simulated measured.7 which depicts eye diagrams of the constructive and destructive components as well as the (slightly skewed) eye diagram after balanced detection for the in-phase tributary of 42. Figure 5. In an ideal DPSK receiver.6 depicts this excess OSNR penalty for both the measurements as well as simulations. 92 . The measured penalty is slightly higher than the penalty predicted by simulations.6 dB for a BER close to the FEC limit and increases to 1.4 dB and 3. both components are (nearly) orthogonal to each other.8-Gb/s RZ-DQPSK. Figure 5. However. The higher OSNR requirement for DQPSK demodulation can be explained as follows.4 dB 10 12 14 3 1.6 dB for a 10−9 BER. When we do not take the 3-dB difference into account that results from doubling the bit rate.8-Gb/s RZ-DQPSK modulation. The simulation assumes ideal signal constellations and matched filtering at the receiver to match with the theoretical performance of the coherent detection schemes. We note that the curve for 42.10 show the impact of some of the receiver impairments on the demodulated signal after balanced detection. ∆φ = 0.u) Power (a.u) 47 ps 47 ps 47 ps (a) (b) (c) Figure 5. (b) constructive and (c) after balanced detection.8 depicts the BER as a function of OSNR for self-homodyne demodulation of DQPSK and homodyne demodulation of DQPSK and QPSK. As an example.8-Gb/s DQPSK modulation with interferometric detection is computed using Monte-Carlo simulations. r(t) = 1. 93 .8 as we assume ideal matched filtering. (a) destructive.8-Gb/s RZ-DQPSK with 34-GHz optical filtering.7: Measured eye diagrams for the in-phase tributary of 42. and that the phase shift in the MZDI is ideal. we assume that the input signal is an ideal unmodulated signal. Figure 5.7) In comparison. this gives u(t) = 1. The higher OSNR requirement of DQPSK modulation can be computed using Equation 4.5. i. 2 2 4 2 2 4 (5. Transmitter & receiver properties Power (a.85 dB for DQPSK. a direct detection DQPSK receiver is vulnerable to receiver impairments such as amplitude or time imbalance between the photodiodes and an offset in the phase and timedelay of the MZDI. For homodyne demodulation in a coherent receiver. Figure 5. with NRZ-DPSK as a reference.4 dB.e. for DPSK modulation.5 dB when converted to logarithmic units. √ 1 1 π π 1 1 u(t) = | + exp( j )|2 − | − exp( j )|2 = 2.4.3. ∆φ = π/4.3 Transmitter & receiver properties Similar to DPSK. The excess OSNR penalty of DQPSK demodulation with an MZDI can be compensated using electrical post-processing algorithms such as multi-symbol phase estimation (see Chapter 9). i.9a depicts the tolerance of NRZ-DQPSK against phase offsets in the MZDI. DPSK and DQPSK modulation have the same OSNR requirement. as the differential decoding of DQPSK doubles the BER. The eye diagrams in Figure 5. Note that the simulated penalty is slightly higher than the difference between the theoretical curves in Figure 5. Comparing DQPSK with coherent QPSK detection the OSNR difference increases to 2.u) Power (a. The output signal after balanced detection can then be denoted as. For a 10−3 BER the difference between coherent and interferometric detection is 1. 5.e. The difference is equal to 1. Measurements of the phase offset penalty in [259] shows a slightly larger penalty which most likely results from transmitter impairments. the allowable phase offset is 6. as for example used by Kim and Winzer in [259]. For a 1-dB OSNR penalty. 94 .1 Narrowband optical filtering One of the more important advantages of DQPSK modulation over binary modulation formats is its robustness against narrowband filtering in densely spaced WDM transmission. We conjecture that the more narrow filtering bandwidth is beneficial in the measurements because it removes impairments in the optical signal resulting from imperfections in the modulator.1nm) 14 16 15 Q (dB) Figure 5. which results for both cases in a BER of approximately 4 · 10−6 .11b show for 42. Although the use of a <1-bit delay MZDI improves the narrowband filtering tolerance somewhat [286. In the simulations an ideal RZ-DQPSK signal is used and hence no modulator imperfections are taken into account. The penalty as a function of differential delay offset is very similar to DPSK modulation.9b depicts the impact of an offset in the MZDI differential delay. The receiver structure in the simulations is modeled to match the experimental receiver. When the penalty is expressed as a percentage of the bit rate. with a 3rd order Gaussian optical filter and a 15-GHz 5th order Bessel electrical low-pass filter. conventional direct detection. respectively.11a and 5.8-Gb/s QPSK with coherent detection.8: Theoretical performance of 42.8-Gb/s DQPSK with herent detection with differential decoding.11a and 5. Differential quadrature phase shift keying -2 log(BER) -3 -4 -6 -8 -10 7 FEC limit 8 10 12 14 8 9 10 11 12 13 OSNR (dB/0. Figures 5.11b show a similar tendency but a different optimal filtering bandwidth of 32 GHz (experimental) and 45 GHz (simulations).5o for DPSK [285].5o for a DQPSK signal compared to 20. DQPSK is about a factor of three more sensitive than DPSK to MZDI phase offsets. Comparing Figures 5. 5. 42. The BER is computed with the eigenfunction evaluation method [288].8-Gb/s RZ-DQPSK the tolerance towards narrowband optical filtering for back-to-back simulations and measurements. the phase offset tolerance is a factor of six lower due to the factor of two difference in symbol rate. respectively. co- Because the phase difference between the constellation points is halved.3.Chapter 5. Figure 5. For a <1-bit delay MZDI the partially deterministic interference results in a smaller penalty than for a >1-bit delay where three symbols are interfering and the symbol transition of the delayed symbol falls within the symbol period. 287]. This indicates that partial-DQPSK does not to provide a significant benefit over DQPSK modulation. its effectiveness is reduced through the mixing of the duobinary and AMI component in the MZDI. The OSNR at the receiver is set to 17 dB in the measurements and 15 dB in the simulation. as evident from Figure 5. 42.8-Gb/s RZ-DQPSK is compatible with a narrow channel spacing down to 25 GHz. Gb/s NRZ-DQPSK. (b) time imbalance and (c) phase offset.8 1 1.6-Gb/s RZ-DQPSK on a 50-GHz WDM grid is measured.4 MZDI phase mismatch (degrees) (a) MZDI differential delay ( T/T0) (b) Figure 5.4-Gb/s RZ-DQPSK is compatible with a 12.2 1.8-Gb/s NRZ-DPSK. Transmitter & receiver properties 21 20 19 18 17 16 15 14 13 -60 -40 13 o Required OSNR (dB/0.5. but this does not impact the signal quality after the MZDI. it has been shown that 21.4 Required OSNR(dB/0.1nm) 21 20 19 18 17 16 15 14 13 0. An offset between the filters center frequency and the optical spectrum result in asymmetric filtering. For an even narrower filtering bandwidth. However. (a) amplitude imbalance.6 0.8-Gb/s RZ-DQPSK with 100GHz optical filtering. only a 1-dB penalty is measured for a 24-GHz filtering bandwidth (Figure 5.5-GHz WDM grid and in [290] the performance of 85.1nm) BER = 10 -5 41o -20 0 20 40 60 BER = 10 -5 0.u) Power (a. Besides the optical filter bandwidth. Hence. The ’0’ level is broadened due to ISI.10: Measured eye diagrams for the quadrature tributary of 42. the additional ISI causes performance impairments. the filters center frequency is an important parameter to take into account. The modulator imperfections are also evident from the eye diagrams depicted in Figure 5.9: Simulated (a) MZDI phase mismatch and (b) MZDI differential delay mismatch.8-Gb/s RZ-DQPSK modulation is well suited for optical meshed networks [291].12b. as discussed in Section 3.8- Power (a. This indicates that 42. This shows that 42.5.12c). Note that the eye diagrams are measured at high OSNR. In [289]. With narrowband filtering (36 GHz) the amplitude fluctuations are reduced. so that practically no ASE is present. which show the amplitude fluctuations in the broadened ’1’-rail of the optical signal.12a. For optical meshed networks.u) 47 ps 47 ps 47 ps (a) (b) (c) Figure 5.3. 42. For most optical filters the center frequency will change slightly over the 95 . the available optical bandwidth after cascaded optical filtering is approximately 35-GHz.u) Power (a. narrowband optical filtering results in a performance improvement for a filtering bandwidth down to ∼ 34 GHz. as this is typical for cascaded optical filtering on a 50-GHz grid. Figure 5.13a shows the measured tolerance with respect to filter center frequency offset. This is similar as observed for narrowband optical filtering and we attribute this to a reduction in modulator imperfections.12: Measured eye diagrams for 42. Figure 5. the allowable frequency offset window with a penalty below 1 dB is as large as 32-GHz. in the case of cascaded optical filters.u) Power (a.11: (a) simulated and (b) measured narrowband filtering penalty for 42.13a shows that for a 37.u) Power (a.8-Gb/s RZ-DQPSK before (upper row) and after (lower row) phase demodulation for (a) 50-GHz filtering (b) 36-GHz filtering and (c) 24-GHz filtering. When the optical filter bandwidth is reduced. the filter offset results in crosstalk as some energy of the other channel is passed through.Chapter 5. for example. Furthermore. The depicted measurements are for a single WDM channel.5-GHz optical filter bandwidth the allowable filter offset range 96 .u) 47 ps 47 ps Power (a. the performance slightly improves. This can.u) 47 ps Power (a. When other channels would be present at a 50-GHz channels spacing. course of the filters lifetime. Power (a.8-Gb/s RZ-DQPSK. Note that for a center frequency offset of up to ±10 GHz. every filter can have a slightly different center frequency. the tolerance to center frequency offsets is consequently lowered. Differential quadrature phase shift keying FEC limit log(BER) -3 log(BER) FEC limit -3 -4 -5 -7 10 20 30 40 50 60 70 80 3-dB filter bandwidth (GHz) 15 90 11 13 Q (dB) 9 11 13 Q (dB) 9 -4 -5 -7 10 20 30 40 50 60 70 80 3-dB Filter bandwidth (GHz) 15 90 (a) (b) Figure 5.u) Power (a. This shows that 42.8-Gb/s RZ-DQPSK modulation on a 50-GHz WDM grid is still very tolerant to de-tuning of the optical filter [292].u) 47 ps 47 ps 47 ps (a) (b) (c) Figure 5. For a broad 50-GHz optical filter. An important consideration is therefore the tolerance for filter bandwidths in the range of 35 to 40 GHz. results from temperature induced changes or component aging. 13c-e.u) 47 ps Power (a.8-Gbit/s RZ-DQPSK for a 3-dB filter bandwidth of 50 GHz. Figure 5. Combined.8-Gb/s RZ-DQPSK after passing through a 40-GHz 3-dB bandwidth filter for different offsets from the center frequency. NRZ-DQPSK and duobinary modulation. but no significant degradation is observed in the middle of the symbol period.14a shows simulations that compare the chromatic dispersion tolerance of 42.5 1555 Center frequency offset (GHz) (a) Wavelength (nm) (b) Power (a.5. is still ∼10 GHz with a penalty below 1 dB. For DQPSK. The impact of asymmetric filtering is also evident from the measured spectra and eye diagrams in Figures 5. The difference results 97 .5-GHz optical filter bandwidth and 10-GHz center frequency offsets tolerance should be sufficient to counter the (random) drift in center frequency of a number of cascaded 50-GHz optical filters (with 42-GHz 3-dB bandwidth) over the course of their lifetime. 37. This is lower than the factor of four that one would expect by simply scaling the symbol rate.5 GHz and 25 GHz. such as chromatic dispersion and PMD.3. When we compare 42. 5.2 Chromatic dispersion & DGD tolerance A further advantage of DQPSK over DPSK modulation is the higher tolerance against linear transmission impairments. (b-e) 42.8-Gb/s NRZ-DPSK and NRZ-DQPSK. (b) measured spectra and eye diagrams for an offset of (c) 0 GHz. (d) 10 GHz and (e) 20 GHz.u) 47 ps (c) (d) (e) Figure 5.13: (a) measured filter center frequency offset for 42.3.u) 47 ps Power (a.3. a 37. the chromatic dispersion tolerance increases from 96 ps/nm to 221 ps/nm for a 1-dB OSNR penalty. mainly the ’0’ level in between two symbols is broadened due to ISI. For a 10-GHz center frequency offset. Transmitter & receiver properties 6 0 Relative Power (dB) -2 8 -10 -20 -30 -40 -50 20 GHz 10 GHz 0 GHz log(BER) FEC limit -3 -4 12 -6 -20 -10 0 10 20 10 Q (dB) 14 -60 1554 1554. a factor of 2.13b and 5.8-Gb/s NRZ-DPSK. the increased tolerance against chromatic dispersion results from the doubled symbol period as well as the more narrow optical spectrum. 42.D B OSNR PENALTY.14: Simulated comparison of (a) chromatic dispersion and (b) DGD tolerance. duobinary has a somewhat lower chromatic dispersion tolerance for a 1-dB OSNR penalty. which improves the chromatic dispersion tolerance. Differential quadrature phase shift keying Required OSNR(dB/0. in contrast to the chromatic dispersion tolerance.14b shows the DGD tolerance for the same modulation formats. When we now compare 42.6. duobinary has a larger chromatic dispersion tolerance but also an increased OSNR requirement.8-Gb/s NRZ-DPSK.8-Gb/s RZ-DPSK and RZ-DQPSK. the chromatic dispersion tolerance increases from 63 ps/nm to 226 ps/nm for a 1-dB OSNR penalty.1nm) 22 20 18 16 14 0 10 20 -5 BER = 10 200 BER = 10 30 400 40 Chromatic dispersion (ps/nm) (a) Differential group delay (ps) (b) Figure 5.800 300 from the residual chirp in the signal. 42.PS OF DGD PER SPAN .1 − ps/ km PLUS 0. This is summarized in Table 5.8-Gb/s Table 5.2: DGD 1. which compares favorably with other 42. In order to compare NRZ-DQPSK with duobinary modulation. This can be reduced through 50% RZ pulse carving.D B OSNR PENALTY. Optical filter [GHz] DPSK DQPSK Duobinary Duobinary 90 42 90 32 NRZ [ps/nm] 96 221 350 157 RZ [ps/nm] 63 226 NRZ-DPSK NRZ-DQPSK Duobinary DGD PMD-limited tolerance reach [ps] [km] 9. the optical filter bandwidth plays a critical role. For a 1-dB OSNR penalty.1-ps/ km PMD coefficient for the transmission fiber and 0. mainly dependent on the symbol period. We now consider a link with 0. a factor of 3. NRZ-DQPSK. This gives a 1. PMD. Without narrow-band optical filtering.898 .8-Gb/s filtered duobinary. Figure 5. which decreases the chromatic dispersion tolerance.5 18. 42.1. This gives DQPSK modulation a clear advantage over either DPSK or duobinary modulation.5 ps.Chapter 5.800-km feasible transmission distance for DQPSK.3-ps DGD for each span to account for PMD in the EDFAs and DCF. which translates into a ∼6-ps √ PMD tolerance. The DGD tolerance is.5 6 650 1.3.1nm) 22 20 18 16 14 -400 -200 0 -5 Required OSNR(dB/0.1: C HROMATIC ANCE FOR A DISPERSION TOLER - Table 5. With optimal narrowband filtering (32-GHz).LIMITED REACH FOR √ 0. the DGD tolerance equals 18. TOLERANCE FOR A 1. 9 dB and 15. In this case. This is illustrated in Figure 5. the difference between single-channel and 50-GHz spaced WDM transmission is only slightly over 1 dB.. on the other hand. the channels are de-correlated with -510 ps/nm of pre-compensation.7-Gb/s RZ-DPSK and 21.7Gb/s DPSK modulation or a parallel DQPSK modulator for 21.9 nm) are combined in a 16:1 coupler. Nonlinear tolerance Gb/s modulation formats as denoted in Table 5. The loss of the SSMF spans and DCF varied between 21 dB .7-Gb/s clock signal is used for pulse-carving. The second modulator is a standard MZM driven with a 231 − 1 PRBS for 10.7-Gb/s RZ-DPSK and 21. respectively. and this includes degradations due 100km SSMF DCM TX DCM 8x Postcompensation 25-GHz CSF Precompensation TDC ~ ~ ~ RX Figure 5. two 10.. as depicted in Figure 5. 5.4 Nonlinear tolerance The smaller phase difference between the constellation points in DQPSK modulation results also in a reduced nonlinear tolerance.5. as discussed in Section 4.4-Gb/s DQPSK modulation.4-Gb/s RZ-DQPSK.15: Experimental setup 99 .2.3 dB (DPSK).7-Gb/s 215 − 1 PRBS sequences with a relative delay of 5 bits for de-correlation of the bit sequences are used for modulation of the DQPSK signal.. We now take a 10−5 BER as a measure for the nonlinear tolerance in Figure 5. In particular the feasible PMD-limited reach of duobinary modulation is limited in comparison to both DPSK and DQPSK modulation. a difference of 6. With a 50-GHz WDM channel spacing and 9 co-propagating channels the nonlinear tolerance is 4. For WDM transmission. the impact of XPM reduces the difference between both modulation formats.4-Gb/s RZ-DQPSK.4 ps/nm. the nonlinear tolerance reduces from 12.5 dB (DQPSK) and 8. the OSNR is set such that a 10−9 back-to-back BER is obtained. the outputs of 1 to 9 ECL on a 50-GHz grid (center wavelength at 1550.16. After each span the chromatic dispersion is compensated with an average undercompensation of 78.16 by comparing the nonlinear tolerance of 10.5 dB lower nonlinear tolerance indicates a severe XPM penalty for DPSK.2. Particulary the SPM-induced nonlinear phase shift has a more severe impact on DQPSK modulation compared to DPSK. The transmission line consists of eight 100 km spans of SSMF with EDFA amplification in between the spans. 11 dB.4-Gb/s RZ-DQPSK on a 800km SSMF transmission link. The 4. In this experiment. A MZM driven with a 10.9 dB for 10. respectively. Before transmission. which is 10. At the receiver a 37-GHz CSF selects the desired WDM channel and the accumulated dispersion is compensated to approximately 0 ps/nm. respectively. Subsequently.15..8 dB for 10.7-Gb/s RZ-DPSK to 6. 24 dB and 8 dB .2 dB for 21. For DQPSK modulation.6 dB.4. For the single-channel case. 8-Gb/s DQPSK transmission. is upgraded to a 42. As this is an important aspect for the deployment of 42. Figure 5.8-Gb/s DQPSK. In particular the signal constellation before phase demodulation is clearly degraded through a pattern-dependent XPMinduced phase shift. which indicates a strong correlation between the XPM-induced phase shift of consecutive symbols. even at a 10. as discussed in Chapter 10.8-Gb/s bit rate. 295. in [293].7-Gb/s NRZ-OOK channels. Simulated is a 2000-km transmission link with -2-dBm input power per channel.17 shows the impact of XPM-induced impairments using signal constellations.4-Gb/s RZ-DQPSK with single channel.7-Gb SK /s Q(dB) -4 -5 -6 Si n 4. Figure 5. We can therefore conclude that RZ-DQPSK is strongly SPM-limited. 9 channels on a 50-GHz grid. 42. when the four co-propagating channels are 10. Such a configuration might occurs when a deployed system.6 dB 12 14 14 -8 -10 0 2 4 6 8 10 12 14 16 16 gl e -10 -2 0 2 4 6 8 10 12 14 16 16 Input power (dBm/ch/span) (a) Input power (dBm/ch/span) (b) Figure 5.17 further shows that the phase distortions are strongly reduced through differential demodulation.8-Gb/s RZ-DQPSK is XPM rather than SPM limited with co-propagating 10.16 are not the result of a high XPM tolerance.16: Measured nonlinear tolerance for 800-km transmission (a) 10. GHz grid and 3 channels on a 200-GHz grid.e.4-Gb/s RZ-DPSK modulation will have a reduced nonlinear tolerance compared to 10.8-Gb/s DPSK compared to 42. In the case of DQPSKonly transmission. This is important for digital coherent receivers. 296. al.7-Gb/s RZ-DPSK and (b) 21. the denser signal constellation of DQPSK in comparison to DPSK modulation makes it more sensitive to XPM-induced distortions. i. This is however difficult. at the same bit rate.8-Gb/s RZ-DQPSK modulation is therefore the impact of copropagating 10. it has been extensively studied in the literature [294. We can therefore conclude that 42. Alternatively. the difference in nonlinear tolerance is still ∼2-3dB.5dB 12 6. However.Chapter 5. the XPM impact is much stronger.7-Gb/s NRZ-OOK modulated. and hence the comparison is here somewhat undue. The small inter-channel impairments that are observed for DQPSK in Figure 5. as the system design of the deployed NRZ-OOK channels is based on high input powers (typically 3 dB per channel). The strong XPM impact can be reduced through a lower input power. However. as first observed by Spinnler et. An important consideration for 42. carrying 10. whereas RZ-DPSK is largely XPM limited. We note that 21.7-Gb/s symbol rate. 100 Q(dB) .7-Gb/s RZ-DPSK. the wavelength spacing between the DQPSK and NRZ-OOK channels can be increased to ≥100 GHz. 297]. and often impossible. On the contrary. 5 channels on a 100- to amplifier gain tilt.7-Gb/s NRZ-OOK channels. Differential quadrature phase shift keying -2 8 FEC limit FEC limit -2 8 -3 log(BER) -3 -4 -5 -6 -8 10 log(BER) 10 cha nn DP el 10 .7-Gb/s NRZ-OOK channels. which do not necessarily use differential demodulation. a very similar constellation diagram is obtained with either single-channel or five WDM channels on a 50-GHz grid. In transmission experiments. To assess the linear and nonlinear transmission properties of DQPSK.7-Gb/s NRZ-OOK channels. inter-symbol interference as occurs along the transmission line should be properly modeled. the same data stream is used twice with a relative delay for de-correlation.8-Gb/s RZDQPSK. For DQPSK modulation. 5.5. generally.5. For DQPSK modulation. Pseudo random quaternary sequences Optical spectra 0 -10 -20 -30 -40 -150 0 -10 -20 -30 -40 -150 0 -10 -20 -30 -40 -150 PSD (dB) PSD (dB) -100 -50 0 50 Frequency (GHz) 100 150 -100 -50 0 50 Frequency (GHz) 100 150 PSD (dB) -100 -50 0 50 Frequency (GHz) 100 150 Constellation before demodulation 1 Q (normalized) Q (normalized) 1 Q (normalized) -1 0 I (normalized) 1 1 0 0 0 -1 -1 0 I (normalized) 1 -1 -1 -1 0 I (normalized) 1 Constellation after demodulation 1 Q (normalized) Q (normalized) 1 Q (normalized) -1 0 I (normalized) 1 1 0 0 0 -1 -1 0 I (normalized) 1 -1 -1 -1 0 I (normalized) 1 (a) (b) (c) Figure 5. (b) 5 co-propagating 42. Wickham et.8-Gb/s RZ-DQPSK channels and (c) a 42.8-Gb/s RZ-DQPSK center channel with 4 co-propagating 10.5 Pseudo random quaternary sequences We now discuss in more detail the impact of the pseudo-random bit sequence in DQPSK transmission experiments.17: Simulated impact of XPM on 42.8-Gb/s RZ-DQPSK. For example in [298]. (a) single-channel 42. showed that for transmission systems limited by intra-channel nonlinear impairments the bit pattern length can be critical in correctly evaluating the transmission performance. al. the transmission performance is best assessed by using pseudo-random quaternary sequences (PRQS). Binary modulation formats are routinely modeled using a PRBS. but for quaternary modulation formats no such standard exists. 101 . two bit streams at half the bit rate are fed to the modulator. i.18: Simulated BER for 42. which results in a back-to-back BER of 10−9 . doted lines denote in-phase and quadrature tributaries.e.8-Gb/s NRZDQPSK transmission. At the receiver. Note that De Bruijn sequences are equal to standard PRBS with length kn − 1 with the exception that the subsequence with n consecutive zeros is omitted.3 dB. it does not contain all possible subsequences up to length n/2. (b) PRBS 28 .(c) PRBS 210 . The OSNR is set to 18. Assume a sequence to have length kn .Chapter 5. Differential quadrature phase shift keying A pseudo-random sequence should. However. Comparing multi-level (k > 4) modulation with binary modulation. contain all possible combinations of symbols up to a given length. for multilevel modulation formats it becomes difficult in both simulations as well as experimental verification to correctly model the interaction of long bit patterns. To verify the impact of bit pattern dependence we now simulated the influence of different 4-level sequences on 42. phase demodulated with an MZDI. The input power is 4 dBm per channel into the SSMF and -1 dBm into the DCF. Single channel transmission over 12x95-km (1140 km) of SSMF is simulated with a pre-compensation of 680-ps/nm. Two PRBS with a cyclic shift for de-correlation can be multiplexed to construct a 4-level sequence. We use NRZ rather than RZ-DQPSK modulation here as RZ carving would somewhat mask the impact of bit-sequence dependence. the signal is filtered with a 45-GHz optical Gauss filter. solid line denote the average of both tributaries. ideally. Hence.8-Gb/s NRZ-DQPSK after 1140 km for all possible cyclic shifts and (a) PRBS 26 . The BER is computed using a Karhunen-Loeve series expansion 102 . 85ps/nm/span in-line under-compensation and zero residual dispersion. -4 log(BER) log(BER) -4 -5 -6 -7 -5 -6 -7 -8 1 PRBS 2 10 6 20 30 40 50 Cyclic shift (symbols) 64 -8 1 PRBS 2 50 8 100 150 200 Cyclic shift (symbols) 256 (a) -4 log(BER) -5 -6 -7 (b) -8 1 100 200 300 400 500 600 700 800 900 1024 Cyclic shift (symbols) PRBS 2 10 (c) Figure 5. A pseudo random sequence (also know as de Bruijn sequence) can then be defined as a sequence that contains all possible combinations of symbols up to length n (subsequences) exactly once. the required sequence length to consider all possible subsequences of a given length n grows exponentially. where k is the alphabet size and n an integer value. differentially detected and subsequently filtered with a 17-GHz electrical Bessel filter. this results in a sequence with length 4n/2 = 2n which is generally not a pseudo-random sequence. but differences of more than an order of magnitude are still apparent. 1 The 103 .5. The proposed PRQS results in a BER close to the median value over all possible cyclic shifts. As evident from Figure 5. From Figure 5.19: Fraction of existing sequences with length 4 as a function of the cyclic shift. The observed transmission performance difference can be avoided by a proper choice of the bit pattern. Fraction of all possible subsequences (%) 100 80 log(BER) -4 -5 13 -6 PRQS -7 64 128 256 512 Sequence length (symbols) 1024 14 PRBS 12 Q (dB) 60 40 20 0 PRBS 28 50 100 90 4 8 12 16 20 24 100 150 200 Cyclic shift (symbols) 250 Figure 5. Figure 5.18 shows the obtained BER after transmission for different bit pattern lengths. as depicted in Figure 5. Figure 5.20.5. This shows that even for long sequences an arbitrary cyclic shift can potentially result in inaccurate modeling of transmission penalties. median and best-case BERs for all cyclic shifts compared to the BER of a PRQS. This gives a straightforward and simple method to generate true PRQS for the simulation and experimental verification of 4-level modulation formats such as DQPSK1 . For each bit pattern length. For a longer bit pattern length (e. This indicates that such sequences are suitable for the assessment of DQPSK transmission performance. This method can also be extended to create pseudo-random sequences for modulation formats with k > 4.18 we now take the worst-case. An exception is the transmission experiment discussed in Section 10. Comparing Figure 5. Figure 5.g.20: Worst-case. For this purpose we analyze which fraction of all possible 4-level subsequences with length n/2 exists as a function of the cyclic shift between the two PRBS sequences u and v with length 2n . median and best-case obtained BER for all possible cyclic shifts between u and v larger than two (to ensure all symbol transitions exist). For a bit use of PRQS for DQPSK modulation is based on more recent work and is therefore not used in most of the transmission experiments discussed in this thesis.18 this results in significant performance differences. Pseudo random quaternary sequences [299]. Note that shifting v over -n/2 symbols is equal to shifting v over +n/2 symbols and inverting it. It is evident that all possible subsequences of length 4 exist only when v is cyclically shifted over ±4 symbols with respect to u. two PRBS (u and v) are used to modulate the in-phase and quadrature component of the DQPSK signal. such as polarizationmultiplexed DQPSK modulation (see Chapter 8).3. It can be shown that for a 2n PRBS and a cyclic shift of ±n/2 symbols (for n is even) always a PRQS with length 4n/2 is obtained. 1024 symbols) the variation in BER as a function of the cyclic shift is reduced. clearly indicating that the choice of bit pattern severely affects the obtained transmission performance. The bit pattern dependence is observed by cyclically shifting both sequences with respect to each other and computing the BER for each cyclic shift.19 shows the obtained results for a PRBS length of 28 and a subsequence length of 4.18a-c shows that a shorter bit pattern length result on average in a lower BER.6. of which the parallel ’Super Mach-Zehnder’ structure is most widely used. which potentially makes the tolerance comparable to DPSK at the same symbol rate. → DQPSK modulation is strongly limited by inter-channel nonlinear impairments. An important consideration for the choice in modulator architecture is the residual frequency chirp in the modulation signal. DQPSK modulation has an increased transponder complexity compared to DPSK or duobinary modulation. No significant narrowband filtering penalty is evident down to a 28-GHz filter bandwidth. 104 . 5. As it encodes 2 bits per symbol. DQPSK further allows for a 10-GHz filter offset with an OSNR penalty smaller than 1-dB.7-Gbaud symbol rate. For 50% RZ-DQPSK modulation the chromatic dispersion tolerance is approximately a factor of three higher when compared to DPSK at the same bit rate. → DQPSK is normally demodulated with two separate MZDI with a ±π/4 phase shift between both arms. The most significant properties of DQPSK modulation can be summarized as follows: → DQPSK modulation is possible using a variety of modulator architectures. In addition. it allows for a higher spectral efficiency and a higher tolerance towards linear transmission impairments compared to binary modulation formats. the difference is limited to approximately 1 dB. → The chromatic dispersion tolerance of DQPSK modulation is lowered due to the residual chirp in the modulated signal. This residual frequency chirp can be reduced through RZ pulse carving. → DQPSK modulation has a doubled PMD tolerance compared to DPSK modulation. Due to the suboptimal phase demodulation. We note that PRQS can also be generated using 4-level generator polynomials [300]. which indicates this bit pattern length is sufficient to properly determine transmission penalties. For a 10. DQPSK has a higher OSNR requirement in comparison to DPSK modulation. Near the FEC limit.Chapter 5. This significantly reduces the nonlinear tolerance of DQPSK modulation compared to DPSK modulation. → The narrowband filtering tolerance is one of the most significant advantages of DQPSK in comparison to binary modulation formats.6 Summary & conclusions DQPSK modulation is one of the most suitable multi-level modulation formats for long-haul transmission links. the difference is approximately 4 dB for a 50-GHz WDM system. similar to the method used for PRBS. Differential quadrature phase shift keying pattern length larger than 256 symbols the median value is relatively constant. On a 50-GHz grid. At the same bit rate the difference in nonlinear tolerance is 2-3 dB. This negates the need for active PMD compensation on fibers with even moderately high PMD. This makes a higher degree of optical integration attractive for DQPSK modulation. 4-Gb/s RZ-DQPSK modulation. Subsequently. Subsequently. We shows that OPC can enable both lumped dispersion compensation as well as a significant increase in transmission distance through the compensation of intra-channel nonlinear impairments. c32-c33.5 focuses on the combination of DQPSK modulation and OPC-supported long-haul transmission. In this chapter we focus in more detail on the properties of DQPSK in long-haul transmission.4. at the cost of a less optimized dispersion map that somewhat reduces the nonlinear tolerance. In Section 6.8-Gb/s RZ-DQPSK modulation. c46.8-Gb/s RZ-DQPSK modulation. Finally. in Section 6. c12. In particular. This allows for simplified EDFAs in most of the transmission link.2 the bit rate is doubled and we focus on long-haul transmission with 42. in Section 6. First of all. c38.6 we compare some of the DQPSK transmission experiments that have been reported in the literature. in Section 6. c5. 1 The results described in this chapter are published in c1.3 we simplify dispersion compensation using a lumped dispersion map. c27. In Section 6. The second part of this chapter focuses on alternative dispersion compensation technologies for long-haul transmission systems. c40-c41. chirped-FBGs are discussed as a means of dispersion compensation in more costsensitive transmission systems. we particulary focus on the impact of phase ripple induced impairments on 42. Here.1 we discuss an ultra long-haul transmission experiment using 21. c8-c10. c51 105 . Section 6. we discuss the optimization of the dispersion map and the use of different technologies for chromatic dispersion compensation. c44.6 Long-haul DQPSK transmission The previous chapter focused on the properties of DQPSK modulation in comparison to binary modulation formats. the SSMF span loss is compensated.5 km SSMF DCM WSS 44 DCM 25-GHz RX TDC ~ ~ ~ CSF 3x Raman EDFA Figure 6. Approximately 20% of the DCF is placed between the Raman pump and the first amplifier stage to balance the DCF insertion loss. Afterwards.4-Gb/s RZ-DQPSK modulation. In order to emulate ultra long-haul transmission. the accumulated dispersion is optimized on a per-channel basis. Afterwards. Afterwards. The transmission link consists of three 94. In order to maximize transmission performance. with an average 11-dB ON/OFF Raman gain from counterdirectional pumping. The parallel DQPSK modulator is driven with two 10. When the first switch (Tx switch) is open. the SSMF input power. At the transmitter. with an average span loss of 21. inline-under compensation and pre-compensation are optimized after 4. an optical burst from the transmitter enters the re-circulating loop. a 25-GHz CSF selects the desired WDM channel.1: Experimental setup for long-haul 21. Two optical switches are used to control the propagation of the signal. The signal is then fed into a one-bit (∆T = 94ps) MZDI and subsequently detected with a balanced photodiode.4-Gb/s RZ-DQPSK transmission Figure 6.5 km spans of SSMF.7Gb/s PRBS with length 215 − 1 and shifted over 5 bits for de-correlation. 1 A W G Tx switch TX Precompensation Loop switch LSPS 94. Using hybrid EDFA/Raman amplification. the outputs of 44 DFB lasers on a 50 GHz ITU grid are multiplexed using an AWG. Long-haul DQPSK transmission 6.4-Gb/s RZ-DQPSK transmission. Once the signal has propagated over the predetermined transmission distance (a multiple of the re-circulating loop length) a trigger signal to the receiver starts the measurements. The input power is set to 106 . two cascaded modulators are used for RZ pulse-carving with a 50% duty cycle and DQPSK modulation. The transmission performance is evaluated using a BER tester programmed for the expected output sequence.5 dB. The re-circulating loop further contains a loop-synchronous polarization scrambler (LSPS) in order to obtain the correct polarization distribution and a WSS to emulated cascaded optical filtering and power equalization. After each span a DCF module is used to compensate for the chromatic dispersion. the first switch closes and the second switch (Loop switch) is opened which allows the optical burst signal to propagate around the re-circulating loop.Chapter 6.1 depicts the experimental setup for ultra long-haul 21.1 21. At the receiver. Subsequently. the signal is re-circulated and passes multiple times through the same transmission link. the first switch opens again and another optical burst starts to propagate around the re-circulating loop.500-km transmission. We conjecture that this accelerated BER increase results partially from the impact of SPM-induced nonlinear phase noise which is more significant at low OSNR.1.100 km. we optimize the pre-compensation. We note that the optimum input power per channel will be slightly lower after transmission over 7. λ = 1549. λ = 1553. the BER of a typical channel (in-phase tributary. but we observe that a higher amount of pre-compensation is slightly better. the transmission performance is relatively tolerant to power variations as the input power can be varied between -7 dBm and -1 dBm for a 1-dB Q-factor penalty. The optimum input power per channel is lowered through the hybrid EDFA/Raman amplification and has its optimum at -4 dB/channel. the measured log(BER) deviates from the linear increase due to the accumulated nonlinear impairments. This has only a minor impact on the transmission performance. -2 log(BER) -3 -4 -5 -6 -7 -9 -2 8 log(BER) 8 Q (dB) 10 12 14 -100 Q (dB) 10 12 14 1 -3 -4 -7 -5 -3 -1 Input power (dBm/ch/span) -5 -6 -7 -1. This limits the feasible transmission distance in this configuration to 7. Secondly. 1550.500 km. Next. the pre-compensation to -850 ps/nm and the inline-under compensation is fixed at 80 ps/nm/span.7 nm.100 -900 -700 -500 -300 Pre-compensation (ps/nm) (a) -2 log(BER) -3 -4 -5 -6 -7 10 8 Q (dB) 10 12 14 30 50 70 90 110 130 Inline under-compensation (ps/nm/span) (b) (c) Figure 6. we optimize the inline under-compensation per span.4-Gb/s RZ-DQPSK transmission -4 dBm/channel. However.7 nm. A lower input power would therefore 107 . as previously observed in [302].000km transmission. A clear penalty is evident for low inline under-compensation per span as this results in an enlarged impact of XPM due to insufficient spreading between the channels [301].5 nm. whereas for higher input powers the penalty is dominated by nonlinear impairments. 21.7 nm) is assessed as a function of the transmission distance (Figure 6.2: BER as function of (a) input power per channel. (b) pre-compensation and (c) inline-under compensation.100 km compared to 4. For shorter distances. After 5.6. For an inline under-compensation higher than >60 ps/nm/span the performance differences are insignificant. with λ = 1533. the log(BER) increases linearly with an exponential increase in transmission distance. Subsequently each parameter is varied to assess its influence on the transmission performance (Figure 6.2). Using the optimized parameters. For lower input powers. transmission is OSNR limited.3a). The 21.100-km transmission. see Appendix B for the difference. Figure 6. The WDM channels are modulated using two parallel modulator chains for separate modulation of the even and odd channels. 1 The 108 . FEC limit -3 log(BER) -4 -5 -6 -8 2000 16 4000 6000 8000 10000 Distance (km) 8 8 FEC limit log(BER) Q (dB) 10 12 14 9 10 11 Q (dB) -3 -4 1530 1535 1540 1545 1550 Wavelength (nm) 1555 12 (a) (b) Figure 6. In Figure 6.4-Gbaud symbol rate.8-Gb/s RZ-DQPSK modulation. at a 21. The highest measured BER is 1.4 depicts the transmitter and receiver structure for 42.4-Gb/s electrical bit sequences for DQPSK modulation is created by electrically multiplexing two 10. Here. Long-haul DQPSK transmission somewhat improve the feasible transmission distance beyond the limit measured here as less nonlinear impairments accumulate and transmission is more limited by the OSNR.8-Gb/s RZ-DQPSK transmission RZ-DQPSK modulation is the most promising for a 42. 6.8-Gb/s bit rate (21. Optical filtering is therefore required to reduce the linear crosstalk between neighboring WDM channels.4-Gbaud symbol rate). as is used by the majority of the deployed transmission systems. After modulation. absolute performance is expressed here in terms of the BER. In addition. It can be seen that the performance is similar for all WDM channels and no spectral dependence is measured. which is a 0.6 · 10−3 after 7. Quadrature tributary.100-km transmission (25 re-circulations).3: (a) Measured BER as a function of transmission distance (b) BER of all channels after 7.4-Gb/s data stream is subsequently split and fed to both inputs of the 42.100 km.2 42. In-phase tributary.8-Gb/s RZ-DQPSK signal is >50 GHz.8-Gb/s transmission on a 50-GHz wavelength grid.Chapter 6. In this section we optimize the power and dispersion map for 42.4-dB Q-factor margin with respect to the FEC limit1 . followed by a parallel DQPSK modulator. whereas a penalty or margin is expressed in terms of the Q-factor.8-Gb/s DQPSK modulator with a relative delay of 10 bits. the spectral width of an unfiltered 42.8-Gb/s RZ-DQPSK modulation and analyze the long-haul transmission performance.3b the BER of both the in-phase and quadrature components of all 44 WDM channels is assessed after 7. The 21. Each RZ-DQPSK modulator chain consists of a MZM for RZ pulse-carving.4-GHz clock signal to carve out pulses with a 50% duty cycle.7-Gb/s PRBS signals with a length of 215 − 1 and a relative delay of 16 bits. This enables robust 42. The pulse-carver MZM is driven with a 21. the bandwidth requirement for the electrical components in the transponder is still modest. the channels are filtered when the odd and even WDM channels are combined in the 50-GHz interleaver. Figure 6. as shown in Figure 6. At the receiver.4: Experimental setup for long-haul 42. 18 WDM channels are multiplexed on a 50-GHz ITU grid. The inline under-compensation is changed by stepwise substituting the DCF spools in the link such that the average inline under-compensation increases or decreases.8-Gb/s RZ-DQPSK transmission RZ-DQPSK Tx – odd channels RZ-DQPSK Tx – even channels clock 2 A W G MZM 21. hence it is sufficient to measure only one 10. The inline under-compensation is set to ∼33 ps/nm/span and the precompensation is fixed at -1020 ps/nm.25 nm to 1537. Subsequently.7-Gb/s with a 1:2 de-multiplexer and evaluated using a BER tester programmed for the expected bit sequence. The optimal input power is found to be -3.5 dBm per channel. In order to model worst-case nonlinear interaction between the WDM channels. This is due to amplifier gain tilt and intra-band SRS. First of all.52 nm).5-dBm channel input power.1). In this experiment.6. The re-circulating loop setup is the same as used in the 21. followed by balanced detection. as depicted in Figure 6. which increases the noise factor of the lower wavelengths. the measured BER as a function of the input power per channel is depicted in Figure 6. the signal is de-multiplexed to 10. the signal is split and one part is used for clock-recovery. a PBS after the interleaver ensures that all WDM channels are co-polarized.4-Gb/s signal.7-Gb/s tributary instead of the multiplexed 21.40 nm) and 9 channels in the higher part of the C-band (from 1549. 42.5a. Note that the 25-GHz bandwidth of the optical filter results in a 1-dB OSNR penalty. The other part is fed to a two-bit (∆T = 94 ps) MZDI. With a two-bit MZDI.9 nm and 1551. The two separate wavelength bands are used here to investigate the presence of wavelength dependent performance differences due to a change in amplifier noise figure or gain tilt across the C-band. A pre-compensation of -1020 ps/nm is used as well as a -3.8-Gb/s RZ-DQPSK after 2.4G MZ data I I N T /2 CR 1:2 PBS BERT + T PD (b) MZDI MZ 18 21. Subsequently. For this purpose.2.7-Gb/s tributary of the 21.4-Gb/s signal.7-Gb/s BER tester this considerably simplifies the DQPSK post-coding.5 shows the optimization of the dispersion map for 42. For a 109 .4G data Q (a) Figure 6.260km transmission.0 nm). As the BER is measured using a 10.8-Gb/s RZ-DQPSK transmission (a) transmitter and (b) receiver.5b. The 18 WDM channels are divided over the lower and higher part of the C-band. the BER tester requires only programming for the expected 10. The performance of the two tributaries is averaged through loop operation. For high input powers a slight performance difference is measured between both channels.4-Gb/s RZ-DQPSK transmission experiment (see Figure 6. the BER is measured for the center channels of both the higher and lower wavelength band (1535. The use of a two-bit instead of a one-bit MZDI might result in slightly higher penalties [262] but it is used here to simplify the post-coding of the DQPSK sequences. the chromatic dispersion is optimized on a per-channel basis and a narrowband 25-GHz CSF is used to select the desired WDM channel.32 nm to 1552.5c. the inline under-compensation per span is optimized. After balanced detection. 9 channels in the lower part of the C-band (from 1534. λ = 15551.9 nm. The optimal pre-compensation is -1020 ps/nm. λ = 1535. which indicates a large tolerance for 42. 110 Q(dB) -3 . The optimal value is found to be an inline under-compensation of ∼60 ps/nm/span. (c) pre-compensation.5: Dispersion and power map optimization for 42.9 nm.260 km. Similar to the measured results for 21. Long-haul DQPSK transmission -2 0 Relative power (dB) 8 log(BER) 9 10 11 12 1535 1540 1545 1550 Wavelength (nm) 1555 -10 -20 -30 -4 -5 -6 13 -8 -6 -4 -2 Input power (dBm/ch/span) 0 (a) -2 8 log(BER) Q(dB) -3 -4 -5 -6 -100 log(BER) -2 (b) 8 9 10 11 12 13 -2000 -1500 -1000 -500 Pre-compensation (ps/nm) 0 Q(dB) Q (dB) 9 10 11 12 13 -50 0 50 100 150 200 Inline under-compensation (ps/nm/span) -3 -4 -5 -6 (c) -2 8 log(BER) 10 11 12 -5 -6 -200 -100 0 100 Accumulated dispersion (ps/nm) 13 200 Q (dB) -3 -4 (d) 8 FEC limit log(BER) -3 -4 12 -5 -6 1000 14 2000 3000 4500 6000 800010000 Transmission distance (km) 10 9 (e) (f) Figure 6.0 nm.4-Gb/s RZ-DQPSK. 21.8-Gb/s RZ-DQPSK after 2. (b-e) BER as a function of (b) input power per channel.8-Gb/s RZ-DQPSK modulation towards suboptimal dispersion maps.4-Gb/s RZ-DQPSK. A further increase in inline under-compensation decreases the measured performance only by a small amount. (e) accumulated dispersion and (f) transmission distance. In this experiment the input power is again set to -3. λ = 1551. In-phase tributary. Figure 6. Quadrature tributary. In-phase tributary. Next.Chapter 6. (a) Optical spectra of the 18 WDM channels.5 dBm per channel and the inline under-compensation is fixed at ∼60 ps/nm/span. Quadrature tributary. Only when the pre-compensation value is close to zero. the amount of pre-compensation has no strong influence on the transmission performance. λ = 1535. (d) inline under-compensation per span.0 nm. insufficient pulse spreading occurs and the measured performance decreases.5d plots the BER performance as a function of pre-compensation. lower under-compensation the walk-off between the WDM channels is reduced which clearly raises the transmission penalty. But for longer transmission distances.260-km as a function of the accumulated dispersion excursion. The re-circulating loop consists of three 94.260-km transmission the measured BER is 9 · 10−5 . The transmitter and receiver structure that is used for 42. 100GHz interleaved Raman 3x 11x TDC Postcompensation RX ~ ~ ~ 34-GHz CSF LSPS WSS EDFA Figure 6. This indicates that 42.3. respectively.3 Lumped dispersion compensation In order to explore the possibility of simplified dispersion management. which gives a ∼2.5e shows the BER after 2.7-Gb/s NRZ-OOK legacy transmission systems. This is somewhat lower as the simulated back-to-back tolerance in Figure 5.3 in feasible transmission distance. Lumped dispersion compensation The optimal dispersion map for 42.6: Re-circulating loop setup with lumped dispersion compensation.5km SSMF Raman odd ch. 6. the log(BER) degradation accelerates due to the accumulation of nonlinear impairments.8-Gb/s RZ-DQPSK modulation is similar to other modulation formats as well as to the optimum values found in the previous section for 21. from 1549. which is depicted as a reference. For a 1-dB and 2-dB Q-factor penalty.8Gb/s RZ-DQPSK transmission with a lumped dispersion map. 100GHz ITU TX TX I N T PBS Tx switch Precompensation Loop switch DCF -4783 ps/nm 94. After 2. with the exception that a 34-GHz CSF is now used to de-multiplex the WDM channels.6 depicts the re-circulating loop setup. Figure 6.6. we now discuss 42. Figure 6. This improves the back-to-back OSNR requirement with ∼1 dB.500 km transmission distance the log(BER) degrades in a linear fashion.0 nm) as a function of the transmission distance.14a. the feasible transmission distance is therefore approximately 3. this is a reduction by a factor 2.4-Gb/s RZ-DQPSK transmission. Compared to the reach of 21. even ch. Figure 6.0 nm.0 nm to 1555. Before entering the re-circulating loop. For a 10−3 BER. A Hybrid 111 . In this experiment 16 DFB outputs are combined on a 50-GHz ITU grid.2.5-km spans of SSMF with an average span loss of 21. the WDM channels are de-correlated with -1020 ps/nm of pre-compensation. Up to a 2. which probably results from the accumulation of nonlinear impairments after 2.260-km transmission.8-Gb/s RZ-DQPSK should be compatible with a dispersion maps optimized for 10.8-Gb/s RZ-DQPSK modulation is identical to the one described in Section 6.4-dB margin with respect to the FEC limit.9 nm and 1551.5 dB.500 km.5f depicts the measured BER of both center channels (1535.4-Gb/s RZ-DQPSK. the chromatic dispersion window is in excess of 160 ps/nm and 250 ps/nm. 5 dBm for the lumped and periodic dispersion map. there is a trade-off between nonlinear tolerance and OSNR requirement and only a negligible difference in BER is measured between the lumped and periodic dispersion map. Note that the transmission distance is slightly different in both experiments (2. The BER is measured for the center channel at 1552.8-Gb/s RZ-DQPSK with a periodic dispersion map. From Figure 6. is compensated using DCF placed after the third span. in order to avoid nonlinear impairments in the DCF.Chapter 6. Figure 6. When either inline under. lumped dispersion map. 112 .5 dB difference indicates that the lumped dispersion map suffers from a somewhat larger influence of nonlinear impairments.5-km SSMF spans combined (-4783 ps/nm). Hence. the performance improves and optimal performance is obtained for an inline under-compensation of more than 60 ps/nm. the influence of the inline under-compensation on the measured BER is still significant.or over-compensation is used.550 km). The DCF insertion loss is compensated using backwards Raman pumping with an ON/OFF Raman gain of 18 dB. However. the dispersion compensation has effectively no insertion loss. Long-haul DQPSK transmission Raman/EDFA structure with backward pumping is used for signal amplification with an average ON/OFF Raman gain of ∼11 dB.260 km and 2. The chromatic dispersion of the three 94. 42.550km transmission versus (a) inline under-compensation and (b) input power variation. Note that the Raman pump powers launched into the DCF are significantly lower than the pump powers used for Raman amplification in the SSMF. as described in the previous section. This slightly increases the OSNR at the receiver. respectively.7b shows the input power variation for a 107-ps/nm inline under-compensation per re-circulation. is shown as a reference.7b show the dependence of the transmission performance on the inline undercompensation per recirculation and input power. with the lumped dispersion map the number of EDFA’s in the re-circulating loop is reduced (single-stage versus double-stage amplifiers). 8 log(BER) log(BER) 8 9 -3 10 11 -4 -9 -7 -5 -3 -1 Input power (dBm/ch) 12 1 Q (dB) 9 -3 10 11 -4 12 -100 -50 0 50 100 150 200 250 300 Inline under-compensation per recirculation (ps/nm) Q (dB) (a) (b) Figure 6. This can be attributed to a reduction of XPM-induced impairments from co-propagating channels. As the combined loss of DCF and Raman coupler is 17.6 dB.7a it is clear that even though the accumulated dispersion is only compensated every 285 km. The worst performance is obtained with full dispersion compensation after every three spans. Hence. periodic dispersion map. respectively.550-km transmission. which results in approximately a 2-dB penalty.7: Measured BER after 2. The 0. the total gain of the EDFA/Raman amplification for dispersion compensation is 23 dB. However. the input power is ∼5 dB reduced with respect to the SSMF. Figures 6.7a and 6. The optimal input power is -4 dBm and -3.12 nm and after 2. 3. Quadrature tributary.8-Gb/s RZ-DQPSK modulation. For chirped-FBGs that have a channelized dispersion compensation profile. FEC limit -3 log(BER) -4 -5 -6 -8 500 1000 2000 3000 Transmission distance (km) 16 4500 8 log(BER) 8 FEC limit 9 10 11 1548 1550 1552 1554 Wavelength (nm) 12 1556 Q (dB) 10 Q (dB) 12 14 -3 -4 (a) (b) Figure 6. This has the further advantage that the PR penalty is generally smaller for phase modulated formats in comparison to amplitude modulation [303]. where the PR-induced transmission impairments might make it difficult to realize long-haul transmission.4 Chirped-FBGs based dispersion compensation Cost-sensitive optical transmission systems nowadays might use chirped-FBGs for dispersion compensation. This is particulary important for 42.8-Gb/s RZ-DQPSK modulation. This indicates that more cost effective dispersion management is feasible by accumulating the DCF at specific points and using single-stage amplifiers in the remainder of the transmission link. the broad optical spectrum can further increase the penalty because the FBGs incur narrowband filtering and have an increased PR near the edge of the pass-band. 6. The channel spacing is limited to 100 GHz because of the channelized profile of 113 .8-Gb/s transmission systems. Quadrature tributary. In-phase tributary.100-km transmission. From this comparison we conjecture that the use of a lumped dispersion map does not reduce the transmission performance of 42.6. Lumped map. Chirped-FBGs based dispersion compensation Figure 6. But the accumulation of phase ripple (PR)induced transmission impairments limit the feasible transmission distance. As discussed in Section 3. Periodic map.0 nm.8-Gb/s RZ-DQPSK.100-km transmission.3.8b shows the measured BER for all 16 channels after 3. Lumped map. from 1538. The dispersion map and input powers are separately optimized for the periodic and lumped dispersion map. In the transmitter.8a shows the BER as a function of transmission distance for both the periodic and lumped dispersion map.4. 32 DFB outputs are combined on a 100-GHz ITU grid. the low insertion loss and negligible nonlinearity of a FBG allow for a simpler EDFA structure. In-phase tributary.8-Gb/s modulation format with a relatively narrow optical spectrum such as 42. It is therefore advantageous to use a 42. This section describes a long-haul transmission experiment using 42.2 nm to 1563. as discussed here (see Figure 3. Periodic map. Figure 6.8: Measured BER (a) as a function of transmission distance and (b) for all 16 WDM channels after 3. In order to assess the impact of using cascaded FBGs for chromatic dispersion compensation we compare long-haul transmission with either FBGs or DCF based chromatic dispersion compensation.14). The worst-case WDM channel still has a ∼1 dB margin with respect to the FEC limit. The FBG-based DCM have an average insertion loss of 2 dB and an average GDR of 0. The FBG and transmission fiber are not cascaded here because the EDFA used in this experiment are optimized for DCF-based dispersion compensation.Chapter 6.5 dB. It consist of 6 x 95-km SSMF spans with an average span loss of 19. The use of a double-stage EDFAs structure is therefore necessary to control the tilt of the WDM spectrum.9. The 32 WDM channels are 42.2.02rad.2). which is found to be the optimum for this configuration.8-Gb/s RZ-DQPSK modulated with the transmitter discussed in Section 6. However. The span loss is ∼2 dB lower in this experiment compared to the previous experiments as no Raman coupler are included.2. The PR penalty is clearly visible through the large (3. Tx switch TX Loop switch circ FBG 95 km SSMF FBG 6x 34-GHz RX 2x LSPS LSPS DCM DGE WSS TDC ~ ~ ~ CSF circ DCM EDFA Figure 6.9: Re-circulating loop setup with FBG-based dispersion compensation.8-Gb/s RZDQPSK receiver discussed in Section 6. The SSMF input power is ∼0. despite the significant PR-induced penalty the measured BER is below the FEC limit for all channels.2 and the re-circulating loop setup as shown in Figure 6.0 dB) spread in performance between the 32 WDM channels. This has the advantage that the accumulated dispersion after every six spans is close to zero. For cascaded FBGs the PR can add up constructively or destructively.5 dBm per channel.074rad with a standard deviation of 0. the input power into the DCF is ∼7 dB reduced with respect to the SSMF input power. The 6 in-line DCMs in the re-circulating loop have either a chromatic dispersion of -1345 ps/nm (5x) or -1681 ps/nm (1x). As the motivation of this experiment is the feasibility of FBG-based dispersion compensation for cost-effective transmission systems. First. Figure 6. EDFA-only amplification is used (see Section 3. the performance for all 32 WDM channels is measured after two circulations (1140 km). Afterwards. which at the same time is also used as pre-compensation. The chromatic dispersion is compensated with chirped-FBGs and a double periodic dispersion map is used in the transmission experiments. Long-haul DQPSK transmission the FBGs. Hence. after two recirculation a total number of 14 FBGs is cascaded. The double-periodic dispersion map is realized using a FBG-based DCM with -1020 ps/nm of chromatic dispersion (at 1550 nm) before the first span.10a depicts the measured BER for all WDM channels. in-line dispersion compensation with only FBG-based DCMs is considered. To analyze the impairments that result from cascaded FBGs. When DCF-based DCMs are used for chromatic dispersion compensation. the signal is fed into the 42. 114 . At the receiver the desired WDM channel is selected using a narrowband 34-GHz CSF and the residual chromatic dispersion is per channel optimized with a (DCF/SSMF-based) TDC. as a results some WDM channels will be affected significantly where other WDM channels show only minor PR related impairments. This indicates that the residual dispersion optimization can be important to reduce the PR associated penalty [303.6. FEC limit log(BER) -3 -4 -6 -8 1535 1540 1545 1550 1555 Wavelength (nm) 1560 16 1565 8 log(BER) FEC limit -3 -4 -6 -8 1535 1540 1545 1550 1555 Wavelength (nm) 1560 16 1565 8 10 12 14 Q (dB) 10 12 14 Q (dB) (a) FEC limit -3 log(BER) -4 -6 -8 1535 1540 1545 1550 1555 Wavelength (nm) 1560 16 1565 8 10 12 14 (b) (c) Figure 6. but the average 115 Q (dB) . The in-line dispersion map consists now of DCF modules with either -1345 ps/nm (3x) or -1512 ps/nm (3x) of chromatic dispersion. 304]. This reduces the spread between the WDM channels to below 1.11c is approximately 220 ps/nm. Figure 6. The in-line dispersion compensation now consist of FBG-DCMs (-1345 ps/nm. 152].10c shows the measured performance when all FBG DCMs are replaced by DCF except for the pre-compensation DCM. The measured difference in optimal post-compensation between the channels shown in Figures 6. Next. (b) mixed DCF and FBGs and (c) only DCF.5 · 10−4 ) than the eye diagram in Figure 6. which results in nearly a 3 dB margin with respect to the FEC limit. the combination of residual dispersion and PR impairments results in a WDM channel dependent eye shape. Chirped-FBGs based dispersion compensation Figure 6. Note that in the absence of PR impairments the residual dispersion would be close to zero. After transmission. In-phase tributary.2·10−5 . Note that in the experiment the residual dispersion is optimized on a per-channel basis to minimize the BER.4.11b and 6. The eye diagram in Figure 6. Finally.11b shows a more severe PR penalty (BER 1. 3x). Quadrature tributary.10b.9 · 10−5 ). Using DCF-only for dispersion compensation further reduces the spread between adjacent WDM channels to approximately 1 dB. for example through the use of a thermally-tuned FBG [151. In deployed systems this would require per-channel tunable dispersion compensation at the receiver.5 dB and decreases the average BER to 1. The smaller number of cascaded FBG clearly improves the transmission performance.11c (BER 1. 3x) and DCF (-1512 ps/nm.10: Measured BER for 32 WDM channels after 1140-km (12 x 95 km) of SSMF using dispersion compensation with (a) only FBGs. every second FBG-based DCMs is replaced with DCF-based DCMs and the measured performance for all WDM channels is depicted in Figure 6.11 shows measured eye diagrams before and after phase demodulation (Quadrature tributary). 3 nm (b) and λ = 1538. a smaller number of FBGs (up to ∼10) result in an acceptable penalty. Long-haul DQPSK transmission BER is 2.24 dB.11: Eye diagrams showing the signal before phase demodulation (upper row) and the quadrature tributary after demodulation (lower row).u) 47 ps 47 ps (a) (b) (c) Figure 6. 6.6 dB.12 depicts the measured BER as a function of the wavelength de-tuning. This translates into a Q-factor penalty per FBG of 0.0 dB and the Q-factor of the worst-case WDM with FBG-based dispersion compensation is 9. which in turn increases the measured BER. long-haul transmission with only FBGs for in-line dispersion compensation might not be feasible. Although this penalty is clearly overestimated.8Gb/s transmission. This is a results of the performance difference between the lower and higher part of the WDM spectrum. slightly higher compared to the mixed FBG/DCF in-line dispersion compensation.Chapter 6. Note that the 116 .1 Wavelength de-tuning Figure 6. We conjecture that this difference is due a spectral tilt. We now assess the impact of laser de-tuning on the PR-induced penalties. Back-to-back (a) and after 1140 km transmission for λ = 1553.u) 47 ps Power (a. The higher power increases nonlinear impairments. whereas PR-induced penalties can change significantly with only a small change in center wavelength [305].u) 47 ps Power (a. which makes it difficult to allocate a 2-dB penalty to PR-related impairments. which increases the power of the channels in the upper part of the WDM spectrum.8 · 10−5 . Power (a.4.u) Power (a. This illustrates that the lower insertion loss and nonlinearity of FBG-based inline dispersion compensation can simplify EDFA spectral tilt control.2 nm (c). This particularly results from the small margins available with 42.u) 47 ps Power (a. Figure 6. The Q-factor of the best-case channel with DCF for dispersion compensation is 13. We can now compute the Q-factor penalty from using FBGs instead of DCF-based dispersion compensation. comparable to or smaller than the increased nonlinear penalty when DCF is used for in-line dispersion compensation. However.10 depict the measured BER when the WDM channel is centered on the ITU grid.u) 47 ps Power (a. 4.6. which suffers only from a small PR penalty whereas the channel at 1544.5 nm is severely affected (Figure 6. In-phase tributary. Quadrature tributary 6.5 GHz.7-Gb/s NRZ-OOK modulation and chirped-FBGs for dispersion compensation.12a shows the measured BER for the WDM channel at 1538. 5x) or 100 km of SSMF (1681 ps/nm.5 nm. The wavelength de-tuning range is thus in principe not limited by the bandwidth of the channelized FBGs. However.2 nm. For two re-circulations. For the in-line dispersion compensation. the DCMs have a chromatic dispersion equivalent to 80 km (1345 ps/nm. which is consistent with the input powers that are used in deployed 10.2 10.12b). As evident from Figure 6. the measured BER increases to above the FEC limit within the de-tuning range. In this experiment. both the wavelength of the transmitter laser and the center wavelength of the receiver-side CSF are changed. the same 32 channels are used as in the previous section (from 1538.0 nm) and the transmitter and receiver structure are depicted in Figure 6. Figure 6. The SSMF input power is increased to ∼3 dBm per WDM channel. which is more narrow than the 65-GHz 3-dB bandwidth of a single FBG.2 nm to 1563. Note though that a typical laser wavelength drift over the system lifetime would be ±1. Hence. But the PR-induced penalty is artificially enlarged in these results as each of the FBGs is passed twice within the re-circulating loop. 6 -2 log(BER) FEC limit -3 -4 -5 -6 -10 Q (dB) log(BER) 8 10 12 = 1538. The same re-circulating loop setup is used here as described in the previous section (Figure 6. with the difference that the number of spans in the re-circulating loop is increased to 8. At the receiver the 117 . the peak-to-peak PR would increase statistically in comparison to a linear addition when the same FBGs are passed multiple times.4. the peak-topeak PR increases by a factor of 2. Chirped-FBGs based dispersion compensation channelized WSS used in the re-circulating loop has a 42-GHz 3-dB bandwidth. 3x).13.12: Measured BER versus wavelength detuning from the ITU grid after 1140-km.7-Gb/s NRZ-OOK In order to analyze the PR-induced penalties that occur when multiple FBG are cascaded. To measure the penalty as a function of wavelength de-tuning. both channels show that the PR penalty can easily change with up to 3 dB within a ±5-GHz de-tuning range.7-Gb/s transmission systems. but the difference is OSNR penalty can be more significant. for the WDM channels at (a) 1538. we now discuss a long-haul transmission experiment using 10. the peak-to-peak PR will be higher for a re-circulating loop with two re-circulations in comparison to √ straight-line transmission. The impact of using a re-circulating loop in the evaluation of PR-induced penalties is discussed in more detail in the next section.2 nm -5 0 5 Detuning from ITU grid (GHz) 10 14 -2 -3 FEC limit -4 -5 -6 -10 6 8 10 12 = 1544. When independent FBGs are cascaded.5 nm -5 0 5 Detuning from ITU grid (GHz) 10 14 Q (dB) (a) (b) Figure 6.2 nm and (b) 1544.9).12b. 040-km and 3. Figures 6.800-km transmission distance. Hence.040-km transmission the measured BER is below 10−4 for the worst channel. 1 MZM A W G (a) 32 (b) 10.800-km transmission. We now compute the OSNR penalty between FBG and DCF-based dispersion compensation.14b show the measured BER after 3.040-km and 3. Figure 6. which consists of a photo-diode. the OSNR penalty range increases and we measure penalties 118 .5 dB after 3. limiting the feasible transmission distance to 3.7-Gb/s receiver (Rx).7 dB and 18.800-km of transmission.7-Gb/s NRZ-OOK.Chapter 6.800 km.7 dB and 15. The impact of PR-related impairments is apparent through the large ∼5 dB spread in performance between the WDM channels whereas the spread would be in the range of ∼1 dB for a similar DCF-based transmission experiment.7 nm and (b) 1551. for respectively a 3. The OSNR penalty is now computed by subtracting the required back-to-back (B2B) OSNR for the measured BER from the measured OSNR after transmission. but no transmission is simulated (”back-to-back”).7G data BERT CDR PD Figure 6. (6. which gives a 2. which gives a variation in OSNR penalty between 4 dB and 8.14a and 6. respectively. respectively. For comparison.1 nm the PR has evidently a more severe impact. After transmission the average OSNR is 19. The eye diagrams at (a) 1543.15 shows in the upper row the measured eye diagrams after 3. After a 3. The lower row in Figure 6. the measured BER is below the FEC limit for all 32 WDM channels.15 shows the eye diagrams for the same WDM channels when the amplitude and phase response of the cascaded FBGs are simulated. the signal is fed to a standard 10. for the channels at (c) 1552. In the simulations the measured amplitude and phase response of the FBGs from the transmission experiment are used. Based on this similarity we conjecture that the phase distortion in the measured eye diagrams result mainly from PR-induced penalties. CDR and BER tester. ∆OSNR = OSNRRx − OSNRB2B (BERRx ). By measuring a large number of WDM channels a certain measured of statistics for the PR penalties is obtained.15 show a strong broadening of the ’1’ rail through phase distortions. And even for a 3. On the other hand. This shows that after 3. Afterwards. cascading 36 and 45 FBGs. Both the simulated and measured eye diagrams in Figure 6.7 nm show WDM channels where the PR has a relatively small influence.3 dB for a 10−3 and 10−9 BER.040 km transmission.800 km transmission distance. the simulation shows only the PR related impairments resulting from the cascaded FBGs.13: Transmitter and receiver structure for 10.8 dB.5 nm and (d) 1554. Long-haul DQPSK transmission desired WDM channel is selected using a 18-GHz CSF and the residual chromatic dispersion is per channel optimized with a (DCF/SSMF-based) TDC.800-km transmission distance. back-to-back the required OSNR is 9.1) We compute this way the OSNR penalty for the best-case and worst-case measured BER.5 dB margin with respect to the FEC limit. Figure 6. Power (a. the measured penalty is artificially increased due to the cascade of the same FBGs for each re-circulation.6.1 nm. This is visualized through simulations in Figure 6. we can conclude that the PR related impairments become more severe with an increasing number of cascaded FBGs.14: Measured BER for 32 WDM channels after (a) 3. in comparison to 3 dB for an ideal (linear) transmission line2 .5 nm. The mean value and the standard deviation of the GDRpp are computed from a large number (> 100) of measured FBGs for statistical averaging.800 km with small (a and b) and large (c and d) PR related penalties. (b) 1551.7 nm. Chirped-FBGs based dispersion compensation FEC limit 8 -3 log(BER) -4 -6 Q (dB) log(BER) 2. 2 This 119 .5 dB when the transmission distance is doubled. Both the mean GDRpp and the mean GDRpp plus twice the standard deviation (2 · σ ) are shown.24 dB.4.u) Power (a.u) Power (a.11 dB and 0. In Figure 6. including channels that suffer from small as well as large PR penalties.u) 93 ps 93 ps 93 ps 93 ps (a) (b) (c) (d) Figure 6.800-km transmission. However. the decrease is ∼2. If the Q-factor is assessed as a function of the transmission distance for a fixed input power. lower row: simulated back-to-back eye diagrams using measured amplitude and phase response.7 nm.16b we assume is slightly different in a nonlinear transmission link. Hence.u) Power (a.16b and 6. in the re-circulating loop experiment. The Q-factor decrease with ∼6. we can compute the OSNR penalty per FBG.16c.5 dB margin 10 12 14 16 1540 1545 1550 1555 Wavelength (nm) 1560 1565 FEC limit -3 -4 -6 8 10 12 14 16 Q (dB) -8 -10 1535 -8 -10 1535 1540 1545 1550 1555 Wavelength (nm) 1560 1565 (a) (b) Figure 6.16b shows the BER increase with transmission distance for a number of WDM channels. (c) 1552. we obtain an OSNR penalty per cascaded FBG between 0.15: upper row: Eye diagrams after 3. which show the growth of the peak-to-peak GDR (GDRpp) when an increasing number of FBGs is cascaded. When we now assume that the OSNR penalty is only related to PRinduced impairments.040-km and (b) 3. (a) 1543.2 dB for a doubling in transmission distance. (d) 1554. between 5 dB and 10 dB. Dividing the penalty through the number of FBGs passed along the transmission link. However. We note that it is not straightforward how the PR related penalty scales as a function of the bit rate.7nm 2000 3000 4000 6000 Transmission distance (km) 1552. Peak-to-peak group-delay ripple (b) when arbitrary FBGs are cascaded and (c) when 8 FBGs are cascaded in a re-circulating loop.1 dB when we assume that a larger number of FBGs are cascaded. the peak-to-peak GDR grows linearly. Hence. mean GDRpp.8-Gb/s modulation. The ripple period on the other hand is usually well below the modulation frequency for 42. mean GDRpp + 2 · σ .8-Gb/s compared to a 10. the penalty we find here assume per-channel optimization of the accumulated dispersion. In addition. In [152] it was shown that the PR penalty is somewhat larger for a 42. However.5nm 7 9 11 13 15 Q (dB) 300 Group delay ripple (ps) 250 Linear fit 200 150 100 50 10 20 30 40 Number of FBGs 0 0 10 20 30 40 Number of FBGs 250 200 Square root fit 150 100 50 0 0 (a) (b) (c) Figure 6.7-Gb/s bit rate. up to approximately 2000 km. When we allow a maximum 2-dB penalty resulting from PR-induced impairments this implies that FBG fabrication technology has matured into an appealing alternative for cost-sensitive long-haul links. which reduces the ripple impact [172]. Figure 6.16: (a) Measured BER versus transmission distance for a channel with small (1551.5 nm) PR penalties as well as several arbitrary WDM channels.16c depicts the case when 8 arbitrary FBG are cascaded in a re-circulating loop. where the PR of the cascaded FBGs adds randomly. Comparing the PR-induced penalty for 10. The transmission experiment shows that the PR of state-of-the-art FBGs is small enough for dispersion compensation in a long-haul transmission link. but the difference is relatively small. as occurs in field deployment.8Gb/s modulated signals in comparison to 10.7-Gb/s modulation.7 nm) and large (1552. The PR of the cascaded FBGs is then uncorrelated and grows statistically (square-root) [305]. Consequently. the penalties associated with cascading an even large number of FBGs (> 30) implies that FBGs are not yet suitable for ultra long-haul applications.8-Gb/s RZ-DQPSK appears to support this conclusion. the worst-case OSNR penalty per FBG is ∼0.7-Gb/s NRZ-OOK and 42. In a straight-line. Long-haul DQPSK transmission that arbitrary FBGs are cascaded. 300 Group delay ripple (ps) -2 FEC limit log(BER) -3 -4 -6 -8 1500 1551. The FBG peak-to-peak ripple amplitude is a much larger fraction of the bit period for 42. in this transmission experiment 8 FBGs are cascaded in a re-circulating loop and the optical signal is thus passed multiple times through the same FBG. we conjecture that for arbitrary cascaded FBGs the drop-off with transmission distance is less steep and a significant larger number of FBGs can be cascaded with acceptable PR-induced impairments. Without tunable dispersion compensation the OSNR penalty per FBG will be higher. tremendously worsening the associated penalty. 120 .Chapter 6. with one branch containing the OPC subsystem. which consists only of the 22 WDM channels in the upper part of the C-band. This is shown in Figure 6.5 nm. The optical spectrum at this point is depicted in Figure 6.4-Gb/s RZ-DQPSK transmission In this transmission experiment. After half the re-circulations. The other branch contains only a VOA to match the output power of both branches . as observed in Section 5. where the conversion efficiency is the difference between the lower (after OPC) and upper (before OPC) wavelength band.4 dB.4.1. The optical spectrum at the output of the OPC subsystem consists of the pump signal.6.3 nm to 1540. 44 wavelengths on a 50-GHz ITU grid are 21. The input power of the WDM channels is approximately 10 dBm per channel at the input of the polarization diversity structure.3o Celsius. The wavelengths range from 1532. as it can be used to improve the nonlinear tolerance and thereby increases the feasible transmission reach.3 nm to 1540. This feeds the phase conjugated signal into the loop. In this section we therefore discuss OPC-aided long-haul transmission experiments using RZ-DQPSK modulation and compare it with the DCF-aided transmission experiment discussed in Section 6.4 nm. it is operated at 202. from 1546. after amplification to ∼26 dBm. as depicted in Figure 6. 6.1 21.6.17c. i. This makes OPC of particular interest to DQPSK modulation. OPC-supported long-haul transmission 6.17b.5.4-Gb/s RZDQPSK modulated. In order to reduce the photo-refractive effect in the PPLN waveguide.1 nm to 1554. with the output of an ECL at 1543. are optical phase conjugated. The insertion loss of the OPC subsystem and subsequent filters is comparable 121 .5 nm in the upper part of the C-band. e.1 and has a measured PDL of less than 0. QPM inside the PPLN waveguide is realized by reversing the sign of the nonlinear susceptibility every 16. the loop switch is closed and the re-entrant switch is opened for one re-circulation. the remaining 22 channels. Mid-link OPC is realized here with a re-entrant re-circulating loop structure. The conversion efficiency of the PPLN waveguide.5 OPC-supported long-haul transmission DQPSK has a somewhat lower nonlinear in comparison to DPSK modulation. as depicted in Figure 6. The experimental setup of the OPC-aided transmission link is depicted in Figure 6. is 9.17c.6 nm in the lower part of the C-band and from 1546. as these channels are only used to balance the amplifiers in the re-circulating loop.17a. the difference between the input signal and the conjugated signal at the output of the OPC subsystem. The OPC subsystem is pumped. In both experiments. The phase conjugated signals are present mirrored with respect to the pump and range from 1532.3µm. the signals are optically phase conjugated.1 nm to 1554.6 nm. the same transmitter and receiver structure is used. the link with DCF for dispersion compensation in Figure 6.5.1. The re-circulating loop is split in two branches. The OPC subsystem that is used in this experiment is based on the counter-propagating polarization-diversity scheme discussed in Section 3. Subsequently. After half the re-circulations (18x).3 nm to 1540. The OPC subsystem first removes the 22 channels in the lower part of the C-band. input signals and phase conjugated signals.2 dB. which range from 1532.17a.6 nm. which then propagates for another 18 re-circulations. 2 dB -60 1530 1535 1535 1540 1545 1550 Wavelength (nm) 1555 (b) (c) (d) Figure 6.200-km transmission (all spectra 0. At shorter distances. In the OPC-aided transmission experiment. the input channels. the pump signal is suppressed through a pump block filter (PBF) and the original input signals are removed using a band selection filter (BSF). This is 1 dB higher than the optimal input power in the transmission experiment with DCFbased dispersion compensation.Chapter 6. the nonlinear impairments are not compensated. For the OPC-aided transmission experiment the in-phase tributary at 1535.1 nm to 1554. are recombined with the phase conjugated channels to balance the amplifiers when the signal propagates for another 18 re-circulations through the re-circulating loop.18 depicts the BER as a function of the transmission distance. which results in worsening of the performance after 5. The amplitude fluctuations result in signal dependent nonlinear phase shift variations. Figure 6.4-Gb/s RZ-DQPSK transmission. Long-haul DQPSK transmission (a) Precompensation 1 A W G Re-entrant switch B S F ~ ~ ~ PBF OPC subsystem B S F TX 44 Tx switch 25-GHz Loop switch 94.) to a single fiber span (with hybrid EDFA/Raman amplification). But after 5. which 122 . As well. Finally. and the OPC has therefore no significant impact on the OSNR after transmission. In the absence of OPC.1 nm is measured. an extra penalty arises in this experiment due to transmitter-side imperfections of the parallel DQPSK modulator. the Q-factor of the configuration with DCF is about 0.5 dB lower than that of the OPC-aided transmission system. As RZ-DQPSK is mainly limited by single channel impairments this likely results from SPM induced nonlinear impairments and the impact of nonlinear phase noise. After the OPC subsystem.5 km SSMF VOA RX TDC ~ ~ ~ CSF WSS LSPS EDFA 3x 10 0 Relative Power (dB) -10 -20 -30 -40 -50 Raman 10 Relative Power (dB) 1540 1545 1550 Wavelength (nm) 1555 0 -10 -20 -30 -40 1530 10 0 Relative Power (dB) -10 -20 -30 -40 -50 -60 -70 1530 1535 1540 1545 1550 Wavelength (nm) 1555 9.5 nm.01 nm res. (c) spectra at the output of the OPC subsystem and (d) received spectra after 10. whereas for the configuration with DCF the in-phase tributary at 1550.000-km transmission. the optimal SSMF input power is -3 dBm per channel. the performance of the DCF configuration deviates from the linear increase in log(BER) whereas the OPC based performance is virtually unaffected.7 nm is depicted.000-km transmission.17: (a) Experimental setup for OPC-aided long-haul 21. ranging from 1546. bw. (b) spectra at the input of the OPC subsystem. before as well as after phase demodulation. without OPC. And even after 10. Quadrature.200 km transmission all WDM channels are well below the FEC limit.200 km. Quadrature.980 km.980 km (28 circulations) and 10. When we compare mid-link OPC and the configuration with DCF for dispersion compensation.u) 93 ps (a) (b) Figure 6. After 7.5.200 km transmission. OPC-supported long-haul transmission 8 FEC limit FEC limit 8 9 10 11 12 -5 13 1528 1530 1532 1534 1536 1538 1540 1542 -3 10 log(BER) log(BER) Q (dB) -4 12 -5 -6 -7 -8 -9 1000 2000 4000 6000 14 10200 km 7980 km -4 16 10000 Transmission distance (km) Wavelength (nm) Figure 6. Quadrature. 10. The BER of all WDM channels after 7. mid-link OPC reduces both conventional SPM-induced nonlinear impairments as well as the increased nonlinear phase noise due to modulator imperfections.19: BER of all channels after transmission for the OPC-aided configuration. the single OPC unit compensates for an accumulated chromatic dispersion of over 160. a second OPC subsystem would be required. Power (a. In order to conjugate the other 22 channels. respectively.20: Eye diagrams after 10. In-phase.200 km. 10.6.200 km transmission distance.980 km there is an average 2 dB margin with respect to the FEC limit. (b) after demodulation. 123 Q (dB) -3 . causes additional nonlinear phase noise impairments along the transmission link. 7.19. the transmission reach of 21. In the OPCaided transmission experiment. Figure 6. with OPC and Figure 6.20 depicts the measured eye diagrams after 10. 7.200 km (36 circulations) is depicted in Figure 6.4-Gb/s RZ-DQPSK is 10. In-phase.200-km transmission (a) before demodulation.980 km. Note that for a 10.000 ps/nm.200 km.200 km and 7.u) 93 ps Power (a.18: BER of a typical channel as a function of the transmission distance. This indicates that the use of a single mid-link OPC unit increases the transmission distance by 44%. The performance is only evaluated for the 22 phase conjugated channels. 2 dB 1535 1535 1540 1545 1550 Wavelength (nm) 1555 (a) (b) Power (a.9 dBm in the OPC-aided configuration.2 and the re-circulating loop has the same configuration as shown in Figure 6. The channels are first de-correlated with -2040 ps/nm of pre-compensation before entering the re-circulating loop.u) 46 ps (c) (d) (e) Figure 6.8-Gb/s RZ-DQPSK transmission The concept of mid-link OPC for simultaneous chromatic dispersion and nonlinearity compensation is even more promising for higher bit rates. Mid-link. We now discuss a transmission experiment where mid-link OPC is combined with 42.500-km transmission.8-Gb/s RZ-DQPSK modulation.1 nm to 1556.5. As an increase in bit rate severely reduces the feasible transmission distance.bw.01nm res. compared to -3.1 nm in the higher wavelength band. which results from further optimization as well as a higher pump power (27 dBm). The signal then propagates for 8 re-circulations (2270 km) around the re-circulating loop.21b. 124 . The conversion efficiency is with 7.u) Power (a.Chapter 6. the signal is transmitted for another 8 circulations around the re-circulating loop and subsequently fed into the 42.17a.6 nm in the lower wavelength band and from 1546. 0 Relative Power (dB) -10 -20 -30 -40 -50 1530 Relative Power (dB) 1540 1545 1550 Wavelength (nm) 1555 0 -10 -20 -30 -40 1530 7.21: (a) Optical spectrum after the PPLN subsystem. (b) Optical spectrum at the receiver after 4.2 dB slightly higher in this experiment. In this transmission experiment.5 dBm for the configuration with DCF for dispersion compensation.8 nm to 1540. After phase conjugation. (c) eye diagram before demodulation without narrowband filtering.8-Gb/s RZ-DQPSK receiver. the signals are fed through the re-entrant branch of the loop and the signal is phase conjugated using the same polarizationdiversity OPC subsystem as described in the previous section. The optical spectrum at the receiver is depicted in Figure 6.u) 46 ps 46 ps Power (a. (d) eye diagram before demodulation with narrowband filtering and (e) eye diagram after demodulation (all spectra 0. The input power per channel into the SSMF is -2.8-Gb/s RZ-DQPSK modulated using the transmitter architecture discussed in Section 6. Long-haul DQPSK transmission 6.2 42. ranging from 1530. the gain in transmission reach provided through OPC can be an enabling technology for long-haul transmission.). 52 wavelengths on a 50-GHz ITU grid are used. The channels are 42. 4-Gb/s RZ-DQPSK experiment. narrowband filtering with a 25-GHz bandwidth results in approximately a 1-dB penalty.6. Hence. When we compare the performance of both configurations. without OPC and Figure 6. and the additional 9 channels (from 1534.500 km for the OPC-aided configuration.52 nm).8-Gb/s RZ-DQPSK with a periodic DCF-based dispersion map.3.22. Figure 6. For this measurement. the RZ shape is clearly recognizable.500-km transmission when the nearest neighbors are switched off and the signal is not passed through the 25-GHz CSF. The narrowband optical filtering is clearly visible in the eye diagram. The measured difference between the 9 channel and 52 channel WDM spectrum is approximately 1 dB in Q-factor. OPC-supported long-haul transmission Figure 6. Although the low OSNR after transmission (∼15.1.500 km with a periodic dispersion map to 6. which indicates that the nonlinear impairments are (partially) compensated. Similar to the 21. In this case the upper 9 channels are phase conjugated (from 1549. As discussed in Section 5. Figure 6. When the nearest neighbors are switched on and the signal passes at the receiver through the 25-CSF. the eye diagram in Figure 6. a single OPC provides a >50% improvement in transmission reach.700 km up to 5.22 further depicts the BER versus transmission distance of 42. a clear advantage is evident for mid-link OPC. the same 18 WDM channels are used as in the configuration with the periodic dispersion map.40 nm) are used to balance the amplifiers.5.700 km.21d is obtained.000 km with the mid-link OPC.25 nm to 1537.5 dB) is evident from the eye diagram.22: BER of a typical channel as a function of transmission distance. 8 FEC limit -3 10 8 FEC limit 9 log(BER) Q (dB) 12 -5 -6 -7 -8 -9 500 1000 2000 14 -3 10 11 -4 16 4000 6000 1530 1532 1534 1536 1538 1540 12 1542 Transmission distance (km) Wavelength (nm) Figure 6. we measure for the mid-link OPC a linear dependency between transmission distance and log(BER). This increases the feasible transmission distance from 3. In-phase.32 nm to 1552.23: BER of the in-phase and quadrature tributary after 4. the BER is measured as a function of transmission distance from 1. with OPC. The measured performance as a function of transmission distance is depicted in Figure 6.21c depicts the measured eye diagram after 4.8 nm).21e depicts the eye diagram after phase demodulation and balanced detection. which improves the amplifier noise figure. 125 Q (dB) -4 log(BER) . Quadrature. Reducing the number of WDM channels resulted in a slight improvement in transmission performance because the more narrow spectrum requires less gain tilt compensation in the EFDA. For the center channel (at 1535. This percentage can be used as a figure of merit to estimate the feasible transmission distance for the other transmission experiments discussed in this chapter when EDFA-only amplification would be used.Chapter 6.6 Comparison of DQPSK transmission experiments The previously discussed long-haul transmission experiments focus on the feasible transmission distance near the FEC limit. severely restricts the feasible transmission distance when compared to DPSK modulation. The BER of the worst measured channel is 1. Both tributaries show a similar average BER.500-km transmission is approximately 15.8-b/s/Hz spectral efficiency in the presence of strong optical filtering. This is used to account for chromatic dispersion and PMD penalties as well as aging.4 and Section 8. However. deployed transmission systems operate often with a considerable margin with respect to the FEC limit. the BER of both the in-phase and quadrature channels are depicted. Hence. The received OSNR of all channels after 4. This indicates that there is only a minor impact of nonlinear distortions.080 km. But the lower nonlinear tolerance of RZDQPSK coupled with the higher OSNR requirement. al.24a uses EDFA-only amplification. Both experiments are discussed in more detail in Section 6. For example.500-km transmission for the 26 phase conjugated WDM channels.8-Gb/s RZ-DQPSK transmission experiments with a ∼3-dB margin with respect to the FEC limit. the vast majority of the deployed transmission system uses EDFA-only amplification. with a slightly better performance for the in-phase tributary due to modulator imperfections. but due to the small impact of XPM on DQPSK modulation this will not significantly affect the comparison. The transmission experiment in Figure 6. Long-haul DQPSK transmission The WDM performance with mid-link OPC is evaluated after 4. Table 6. In Figure 6.24a shows that a ∼1000-km reach is feasible for 42. which corresponds to a 2-dB OSNR penalty compared with the back-to-back performance.1 summarizes some of the long-haul transmission experiments that have been reported in recent years using >40-Gb/s DQPSK modulation. respectively.24b hybrid EDFA/Raman amplification is used. component variations and temperature differences.700 km. whereas in Figure 6.5 dB averaged over all WDM channels.2.8Gb/s RZ-DQPSK modulation with EDFA-only amplification and a 3-dB margin with respect to the FEC limit. For long-haul transmission systems that can use hybrid EDFA/Raman amplification the feasible transmission distance can be extended to around 1. This shows that the use of hybrid EDFA/Raman amplification increases the feasible transmission distance with ∼60%. In addition. the feasible transmission distance is reduced from 6. In [291].8-Gb/s RZ-DQPSK enabled long-haul transmission with a 0. Figure 6. and we observe no evidence of severe nonlinear phase noise impairments.8-Gb/s RZ-DQPSK transmission.120 km to 4. Gnauck et.24 shows two 42.8-Gb/s RZ-DPSK modulation in [306] and 42. comparing the long-haul transmission experiments using 42. were the first to show that 42. 126 . 6. OPC effectively improves the nonlinear tolerance and thereby extends the reach of 42.23.8-Gb/s RZ-DQPSK modulation in [122]. hence all measured channels are below the FEC limit.3 · 10−3 . The transmission experiment in Figure 6. We note that in the first experiment a 100-GHz channel spacing is used. 6. which makes it unsuitable for a 50-GHz channel spacing. The performance of 100Gb/s DQPSK modulation is currently limited by the immature components.0-b/s/Hz spectral efficiency.8-Gb/s RZ-DQPSK transmission.700-km with hybrid EDFA/Raman amplification. which allows to use modulation formats with different spectral width for the odd and even wavelength grid. which reduces the feasible spectral efficiency and therefore offsets one of the main advantage of DQPSK modulation. in [15]. Binary modulation formats are challenging to use at such bit rates. al. In-phase Hence. However. However. a field trail was reported using 107-Gb/s DQPSK modulation to cover a 500 km distance. particulary as there is a considerable difference in feasible transmission reach. Note that bit-wise alternating polarization or phase modulation results in spectral broadening. al. We note that 100-Gb/s DQPSK modulation can be compatible with a 50-GHz wavelength grid using asymmetric interleavers [311]. When we assume the use of EDFA-only amplification and taking into account a 3 dB margin with respect to the FEC limit. A commercial 43-Gb/s RZ-DQPSK transponder is discussed by Hoshida et. Comparison of DQPSK transmission experiments FEC limit -3 log(BER) -4 -5 -6 -8 1. as the required bandwidth of the electrical components in the transponder is difficult and costly to realize. predominantly the DQPSK modulator. the lower symbol rate of DQPSK modulation is of particular interest. in [309]. the OSNR requirement (1 dB) and lower nonlinear tolerance (2-3 dB) result on average in a 50% reduction in feasible transmission distance.24: Long-haul 42. When used with a 100-GHz channel spacing. 107-Gb/s DQPSK transmission can enable long-haul transmission with a 1. In [310].140 km transmission 1535 1540 1545 1550 1555 Wavelength (nm) 8 10 FEC limit -3 log(BER) Q (dB) 8 10 12 14 Q (dB) 12 14 1560 16 1565 -4 -5 -6 -8 1. A further drawback of 100-Gb/s DQPSK modulation is its spectral width. even for an optimized 100-Gb/s DQPSK signal. the feasible transmission distance is not likely to exceed ∼600 km. this performance is likely to increase in the near future as components are better optimized for the required ∼55-Gbaud symbol rate. the advantage over 40-Gb/s transmission with a 50-GHz channel spacing is limited. in the transponder. tributary. albeit using all-Raman amplification. the nonlinear tolerance of RZDQPSK can potentially be improved through all-Raman amplification [122].6.700 km transmission 1535 1540 1545 1550 1555 Wavelength (nm) 1560 16 1565 (a) (b) Figure 6. Finally. in [294] a field trail using 43-Gb/s DQPSK modulation was reported with full implementation of the transmitter and receiver control circuits. Quadrature tributary. 127 . CRZ modulation [307]. (a) BER after 1. Asymmetric interleavers have a broad and a narrow pass-band.140-km transmission with EDFA-only amplification (b) BER after 1. As shown by Winzer et. bit-wise alternating polarization (APol) [307] or optical phase conjugation (OPC) [308]. For the next generation of 100-Gb/s transmission systems. The disadvantage of 100-Gb/s DQPSK modulation is the limited transmission reach. 080 2.4-Gb/s RZ-DQPSK modulation. → In an ultra long-haul transmission experiment using 21.1: S ELECTED LONG .5 SSMF 45 -D/+D/-D ∼90 SSMF 100 NZDSF 100 NZDSF Remarks Company / Ref Lucent [291] TU/e. Siemens [308] Alcatel [122] TU/e.8 0.8 0. This shows that ultra-long haul transmission with a 0. The re-circulating loop used in the transmission experiment contains a narrowband optical filtering nodes with 42-GHz bandwidth.800 4.000 1.3 Distance (km) 2.8-Gb/s RZ-DQPSK transmission we obtain a feasible transmission distance of 2. we described a number of long-haul transmission experiments using RZ-DQPSK modulation.8-Gb/s RZ-DQPSK modulation.7 43 # of WDM channels 25 26 151 18 28 1+38 Spectral efficiency (b/s/Hz) 0.7 42.100-km.4-Gb/s and 42.200 6.550 1. This shows that a large number of cascaded optical filtering nodes can be passed in a longhaul transmission link using 42.66 1. 128 .047 Spans (km) / fiber type 100 93.8 42. Siemens [312] Tyco [307] Ericsson.800 6.8 0.HAUL (> 1. bit rate (Gb/s) 42.5 SSMF 65 -D/+D/-D 93.500 4.7-Gb/s NRZ-OOK modulation as used in most deployed transmission systems.8 43 42. → Both for a 21.4-b/s/Hz spectral efficiency is possible using only 10-Gb/s optical and electrical components and a 50-GHz channel spacing.8 0. → For 42.8-Gb/s bit rate. CoreOptics [294] Lucent [14] Alcatel-Lucent [15] year 2004 2005 2005 2006 2006 2006 EDFA/Raman SSMF EDFA/Raman OPC all-Raman EDFA/Raman EDFA-only APoL/CRZ EDFA-only field-trail EDFA/Raman EDFA/Raman NRZ 2006 2007 107 107 10 10 0. the feasible transmission distance is 7.7 Summary & conclusions In this chapter.0 2. the optimized dispersion map for DQPSK modulation is comparable to a dispersion map optimized for 10. Long-haul DQPSK transmission Table 6.000 KM ) TRANSMISSION EXPERIMENTS USING DIRECT DE TECTED >40-G B / S RZ-DQPSK MODULATION .8-b/s/Hz spectral efficiency.800 km with a 0.Chapter 6. 8-Gb/s RZ-DQPSK modulation. A single DCM unit can then compensate the chromatic dispersion between two OADM nodes (up to ∼ 500 km) and simpler EDFAs can be used in the remainder of the link. In a long-haul transmission experiment with 42. When the accumulated dispersion is optimized. It can therefore be instrumental in the realization of long-haul transmission systems with a high spectral efficiency. which negates the need for inter-stage access in the EDFA. This indicates that use of OPC extends the feasible transmission reach and enables transmission links without any periodic dispersion compensation. This implies that FBG-based dispersion compensation can be used for links up to 2000 km with 10. Summary & conclusions → For deployed transmission systems with EDFA-only amplification and a 3 dB margin with respect to the FEC limit. the lumped dispersion map might result in a lower nonlinear tolerance.7-Gb/s NRZ-OOK modulated channels are co-propagating on the same link. We further discussed long-haul transmission experiments using a number of different technologies for chromatic dispersion compensation. The use of chirped-FBGs for dispersion compensation results in PR-induced impairments that limit the feasible transmission distance.6. The results discussed in Chapters 5 and 6 shows that DQPSK modulation has a number of significant advantages over binary modulation formats in terms of chromatic dispersion and PMD tolerance.7-Gb/s NRZ-OOK modulation. On the other hand. 129 .7. → Lumped dispersion compensation requires only minor changes to the transmission link design. the cascade of a large number of FBGs results in an OSNR penalty of ∼0. In summary. For 42.8-Gb/s RZ-DQPSK.1 dB per FBG. → Fiber Bragg gratings (FBG) have a low insertion loss (2 dB to compensate for 100 km of SSMF) and negligible nonlinearity. When 10. → Optical phase conjugation (OPC) allows the compensation of both chromatic dispersion and intra-channel nonlinear impairments in a long-haul transmission link. The FBG can therefore be cascaded with transmission fiber.8-Gb/s makes it challenging to use FBG-based dispersion compensation at this bit rate. a ∼1000 km transmission reach seems feasible for 42. the higher OSNR requirement and lower nonlinear tolerance somewhat restrict the feasible transmission distance. The long-haul transmission experiments shows that a high accumulated chromatic dispersion does not severely affect the nonlinear tolerance of 42. The lumped dispersion map discussed here compensates the DCF insertion loss with backwards-pumped raman amplification. but the smaller available margin for 42. This PR-related penalty can be significantly reduced by optimizing the chromatic dispersion at the receiver. as well as spectral efficiency.7-Gb/s NRZ-OOK modulation. OPC is modulation format and bit rate transparent and a single device can conjugate multiple WDM channels.8-Gb/s RZ-DQPSK.8-Gb/s RZ-DQPSK the penalty per FBG is only slightly higher than for 10. the use of a single mid-link OPC unit increases the feasible transmission distance with >50% when compared to a conventional transmission link with an optimized periodic dispersion map. for example.Chapter 6. Long-haul DQPSK transmission 43-Gb/s DQPSK modulation seems to be particulary promising for transmission systems that require a high tolerance against transmission impairments rather than maximize the transmission reach. optical phase conjugation might be instrumental in realizing ultra long-haul transmission with 43-Gb/s DQPSK modulation. The compensation of nonlinear impairments through. 130 . al. After the advent of WDM transmission systems. Polarization-multiplexed (POLMUX) transmission. used POLMUX transmission to demonstrate for the first time a 1-Tb/s transmission capacity [316].56-Tb/s in a single wavelength channel [276]. This can be useful to increase both linear and nonlinear transmission tolerances. 1 The results described in this chapter are published in c13. c37.7 Polarization-multiplexing So far. c48-c49. is the most widely used polarization-sensitive modulation format. This ultimately resulted in a transmission experiment where POLMUXDQPSK was used to transmit 2. A different approach towards multi-level modulation formats is the use of the polarization dimension of the optical signal. c16-c18. first proposed in 1992 the use of polarization-multiplexing in long-haul transmission systems using soliton transmission [313]. In 1996. POLMUX signaling has mainly be used to double the spectral efficiency for high-capacity WDM transmission experiments. c55 131 . 315]. but at the same time has a lower OSNR requirement and higher SPM tolerance. we have limited the discussion to modulation formats that employ either the amplitude or phase dimension to transmit information. For instance. It transmits two independent tributaries in each of the orthogonal polarizations and can therefore be used to double the spectral efficiency in comparison to single polarization modulation. This is mainly due to the fact that such modulation formats require a polarization sensitive receiver. Later on. modulation using the polarization dimension has attracted only modest attention. different groups used POLMUX signaling in transmission experiments as a means to increase the bit rate in a single wavelength channel [314. al. sometimes also referred to as polarization division multiplexing (PDM). In addition. In comparison to the extensive use of amplitude or phase shift keying in fiber-optic research. POLMUX signaling reduces the symbol rate by a factor of two when compared with binary modulation formats at the same total bit rate. Chraplyvy et. Evangelides et. POLMUX-DPSK features a comparably high chromatic dispersion tolerance and narrow spectral width as DQPSK modulation. POLMUX signaling has been used in a number of record-capacity breaking laboratory experiments [317.2 discusses the transmitter and receiver architecture required for POLMUX signaling. PolSK uses the SOP of the signal to encode the information rather then multiplexing two orthogonal polarizations.. The main advantage of POLMUX over APol modulation is the potentially higher spectral efficiency. 34] and field trails [322]. APol modulation can be used either with a polarization sensitive or polarization insensitive receiver.e. Section 7. has a more complicated transmitter and receiver structure. 320. POLMUX is only one representative of a broader family of polarization sensitive modulation formats. the possibility of multiplexing using the polarization as a selective agent can be derived by considering the matrix multiplication that is required for polarization (de-)multiplexing. E2 . which includes bit-wise alternating-polarization (APol) modulation and polarization-shiftkeying (PolSK). optical polarization de-multiplexing reduces the PMD tolerance. It therefore requires an even more complicated transmitter and receiver structure. The K signals have an equally spaced linear SOP. In particular. Mathematically. on the other hand. Chapter 10 will consider digital coherent detection. This chapter therefore focuses on the interaction between PMD and various signal impairments. with polarization de-multiplexing in the optical domain. 318.3 then reviews the tolerance of POLMUX signaling with respect to linear transmission impairments with a focuss on PMD related impairments. . such record-capacity breaking experiments are generally limited to comparably short transmission distances. POLMUX. π θk = (k − 1) .1 Principle of polarization-multiplexing The possibility to multiplex two channels in the polarization domain is intuitive when considering the two degenerate polarization modes of an optical fiber. In Section 7. it is more sensitive to polarization related impairments. Polarization-multiplexing Later on. 7.. However.1 we introduce the concept of POLMUX mathematically and show that up to three channels can be multiplexed. Section 7. Finally. which makes this a key issue to consider. This chapter discussed POLMUX modulation with a direct detection receiver. We assume therefore that the signals E1 .Chapter 7. in total K logical channels. Because POLMUX signaling transfers the information in the polarization of the optical signal.4 analyzes the impact of single-channel and WDM nonlinear impairments on POLMUX signaling. K 132 (7. are multiplexed and transmitted over an optical fiber. but can potentially provide an even higher spectral efficiency. which opens up the possibility of electrical polarization de-multiplexing. 321. This can be realized either in the optical or electrical domain. Due to the random birefringence in optical fibers.1) . i. Section 7.. This is in part due to the sensitivity of POLMUX to PMD-related impairments in long-haul transmission systems. 319. a polarization sensitive receiver requires polarization de-multiplexing at the receiver. Ek . Subsequently. This describes the polarization change in an optical device. The maximum of three multiplexed channels can also be related to the generalized description of a two-by-two Jones matrix. (7. the phase difference between the polarization states [324]. This is in a sense very similar to PolSK.4) 3 ⎜ 4 4 ⎟ 3⎝ 3 ⎠ −2 − 2 10 1 1 4 4 1 The negative elements in the inverse matrix A−1 shows that not all of the three channels can have 3 a linear SOP. the transfer matrix A3 and its inverse A−1 3 are denoted by. ⎛ 1 ⎞ 1 1 4 4 ⎛ ⎞ ⎜ ⎟ 10 − 2 − 2 ⎟ 1⎜ 1 A3 = ⎜ 1 1 1 ⎟ . This shows that multiplexing two channels in the 2 polarization is possible with each channel having a linear polarization.3) 0 1 1 cos2 ( π ) 1 cos2 (0) 2 2 2 Where it should be noted that A2 equals A−1 . K n=1 K n=1 K (7.1. It can be shown that the inverse K matrix A−1 only exists when the determinant of matrix AK is nonzero [323]. Principle of polarization-multiplexing In the receiver the intensity received for channel k after a polarizer with polarization angle θk is given by Malus law [43] and can be denoted through Ek . A2 = ⎝ (7.5) 133 . This is possible K when K ≤ 3. we look at the case that two channels are multiplexed in the polarization. In its most general form the Jones matrix is denoted through [325]. The possibility of transmitting K signals multiplexed in the polarization domain is therefore dependent on the existence of an inverse matrix A−1 .1. which shows that for three-fold POLMUX the symbol are also spaced more closely together. The three-fold multiplexing is therefore only possible by employing the elipticity of the transmitted signals. When we extend this to multiplexing three channels in the polarization domain. Hence.2) where the summation over the K channels describes the amount of energy of input channel Ek that contributes to Ek .7. It is straightforward that proper decoding of the transmitted signal at the receiver is only possible when this matrix can be inverted. This results in a slightly higher OSNR requirement for the same total bit rate. including optical fiber. 1 K 1 K π 2 Ek = ∑ En cos [θk − θn ] = ∑ En cos2 [(k − n) ]. cos θ exp( jφ ) − sin θ exp(− jψ) sin θ exp( jψ) cos θ exp(− jφ ) .3 ⎛ 1 2 ⎞ 1 π 2 2 cos (0) 2 cos (− 2 ) ⎠= 1 0 . a K ×K matrix AK characterizes the received signal for all channels by denoting the transferred power from the input to the output signals. The distribution on the Poincar´ sphere for two and three-fold POLMUX signaling is visualized e in Figure 7. i. The channel matrix A2 is then given by Equation 7. (7. A−1 = ⎝ −2 10 − 2 ⎠ . First. although only binary signals are multiplexed at the transmitter.e. but a single laser source is generally used as this is more cost-effective and prevents impairments through beating between the two lasers in the presence of PMD [326]. as well as eye diagrams for (N)RZ-OOK and (N)RZ-DPSK with POLMUX signaling. Afterwards a PBS recombines the two polarization tributaries channels into a single POLMUX channel. with a MZM in each branch to modulate the orthogonal signal components with independent electrical drive signals. Note that the laser output. In this section we discuss the transmitter and receiver structure required for POLMUX signaling with two orthogonal polarizations. not all channels have a linear SOP.3. We therefore focus in the remainder of this thesis on POLMUX signaling with two orthogonal polarization channels. In addition. The output of the laser source is split into two branches. but orthogonal. PBS and modulators should use polarization maintaining fiber to ensure that both polarization tributaries have an equal optical power.1: Poincar´ sphere for (a) two-fold and (b) three-fold polarization-multiplexing. Fig134 . Figure 7.2 depicts the transmitter and receiver structure for POLMUX-RZ-OOK modulation. The transmitter can either use a single laser source or two different laser sources. This also implies that in the case of threefold multiplexing in the polarization domain. SOPs.2 Transmitter & receiver structure Following Equation 7. two channels can be multiplexed using linear. Multiplexing three channels in the polarization domain is generally not used in optical transmission because it would require careful control of the relative phase differences between the polarization states. each polarizae tion tributary is DQPSK modulated where θ .2 depicts the basic layout of a POLMUX transmitter and receiver. For two-fold multiplexing. on the other hand. only the linear part of the SOP has to be controlled. Polarization-multiplexing (a) (b) Figure 7. 7.Chapter 7. the impact of PMD and fiber nonlinearities in realistic optical fiber links are likely to make three-fold multiplexing impractical. φ and ψ are independent real variables. Figure 7. respectively.1) 2Es (0.1) (1. POLMUX signaling requires a polarization-sensitive receiver in order to separate both polarization tributaries.u) Power (a.4-Gb/s back-to-back eye diagrams for (b) POLMUX-NRZ-OOK.4-Gb/s POLMUX-NRZ modulation.3 depicts the signal constellation for POLMUX-OOK and POLMUX-DPSK modulation. Note that the penalty curve for both polarization tributaries is asymmetric because the misalignment results in crosstalk that adds either constructively or destructively with the signal on the orthogonal polarization. (c) POLMUX-RZ-OOK. Transmitter & receiver structure (a) clock MZM data H MZM PD PC PBS data H data V PD PBS laser optional MZM (0. POLMUX-OOK modulation.u) 93 ps 93 ps 93 ps Power (a.-1) (1.1) (0.7. POLMUX-DPSK is still a constant intensity modulation format. Destructive crosstalk results in a higher OSNR penalty.0) Es (0.1) (0.u) 93 ps Figure 7. When 135 .1) (-1. (d) POLMUX-NRZ-DPSK and (e) POLMUX-RZ-DPSK.1) (-1. two conventional polarizationindependent receivers can be used.2: Transmitter and receiver structure for POLMUX modulation.3: Signal constellations for POLMUX-OOK and POLMUX-DPSK modulation.5o and 9o misalignment angle between the PBS axis and the polarization tributaries results in a 1-dB and 2-dB OSNR penalty.4 for linearly polarized 21. results in a ’quasi’ 3-level amplitude signal. After polarization de-multiplexing.2.0) (1. POLMUX-OOK: POLMUX-DPSK: (1. As discussed in Section 2. This shows that a 4.0) data V polarization control feedback (b) (c) (d) (e) Power (a.0) (1. on the other hand.-1) 2Es (1.1) (1.u) Power (a. The optical polarization de-multiplexing consists of a PBS preceded by an automatic polarization control. ure 7. This misalignment penalty as a function of the angle θ is depicted in Figure 7. This shows that combined with DPSK modulation. the birefringence in an optical fiber results in a random and time-variant SOP at the receiver. When the polarization axis of the PBS are not aligned with the two polarization tributaries. 21. a misalignment penalty occurs.1) Figure 7.3. Chapter 7. after filtering and signal processing in order to integrate over time.4: (a) OSNR penalty versus misalignment angle θ for 21. 136 . The most practical approach is to add a low-frequency phase modulated pilot tone to one of the polarization tributaries [327].4c.4). 327]. A number of feedback principles have been proposed in the literature. This is evident by comparing the optical signals in Figures 7.4-Gb/s POLMUX-NRZ-OOK with the 0o tributary and the 90o tributary. the randomly varying interference results in a noise-band that characterize suboptimal polarization de-multiplexing. To limit the OSNR penalty to < 0. different line rates for each polarization tributary [328] or the magnitude of the clock recovery output [77. measured optical signals show de-multiplexing (b) without crosstalk and (c) with crosstalk. and fast in order to track the randomly changing polarization that can occur in optical fibers (see Section 3. FEC error counting. 316]. provides a measure for the degree of misalignment. the crosstalk interferes only partially.u) 1 ns BER = 10 -20 -10 0 10 20 -5 (c) 30 (degrees) (a) Power (a. Including the use of pilot tones [322.5 dB the de-multiplexing needs to have an accuracy of θ < 2o .u) 1 ns Figure 7. 187]. The phase modulation varies the crosstalk between constructive and destructive interference which. The response time of the automatic polarization control should therefore be in the order of 200 µs when we assume that a full revolution around the Poincar´ e sphere can occur in 20 ms [185. compared to approximately θ ≤ 10o for a polarization insensitive receiver. The tracking speed of an automatic polarization control for polarization de-multiplexing needs to be faster than the tracking speed required for PMD compensation in a polarization insensitive receiver. 186. Polarization-multiplexing the polarization of both polarization tributaries is not linear but elliptical.1nm) 25 23 (b) 21 19 17 15 -30 Power (a. The automatic polarization control in front of the PBS should be both accurate to minimize the de-multiplexing penalty. the automatic polarization control requires a feedback signal that provides a measure of the interference between the two polarization tributaries. Averaged over time. In order to track the polarization.4b and 7. Required OSNR (dB/0. combined with the impact of optical polarization de-multiplexing has a significant impact on the tolerance against linear transmission impairments.5: Measured OSNR requirement for (a) NRZ and (b) RZ modulation. The combination -2 FEC limit -3 -4 -2 8 FEC limit 8 10 12 14 16 log(BER) log(BER) Q (dB) 12 -6 14 -8 -10 NRZ modulation -12 4 6 8 10 16 12 14 16 18 20 -4 -6 -8 -10 RZ modulation -12 4 6 8 10 12 14 16 18 20 OSNR/0.7 dB and 18.2). The OSNR tolerance improves with ∼0. where the impact 137 Q (dB) 10 -3 .7-Gb/s DPSK.1 Back-to-back OSNR requirement The use of different multi-level modulation formats such as amplitude phase shift keying and DQPSK (with direct detection) results in a >3 dB increase in OSNR for a doubling in the bit rate.3 Transmitter & receiver properties The lower symbol rate of POLMUX signaling compared to binary modulation formats. The chromatic dispersion tolerance and OSNR requirement are improved.1).4-Gb/s DQPSK. 10.3.3. Note that the advantage of using a polarization sensitive receiver increases slightly for higher BER.3 dB in a polarization sensitive receiver because the ASE in the orthogonal polarization is filtered out. which worsens the OSNR tolerance through spontaneous–spontaneous beat noise in a polarization insensitive receiver.7.7-Gb/s OOK. PMD (Section 7. One of the main advantages of POLMUX signaling is therefore that it allows a doubling of the bit rate with a ≤3 dB increase in OSNR requirement. This is valid under the assumption that without POLMUX signaling a polarization-insensitive receiver is used. of POLMUX signaling with different binary modulation formats is depicted in Figure 7.1. But polarization related signal impairments. such as PMD and PDL. 10.3-dB improvement which results from the use of a polarization sensitive receiver. chromatic dispersion (Section 7.3.4-Gb/s POLMUX-OOK.5a and the OSNR requirements for a 10−3 and 10−9 BER are listed in Table 7. 21.3) and polarization dependent loss (Section 7. The 2. 7.7-Gb/s POLMUX-DPSK and 10.4 dB.3.3.1nm) (b) Figure 7.3. This section discusses the tolerance of POLMUX signaling with respect to OSNR (Section 7.4).1nm(dB) (a) OSNR (dB/0.7-dB difference in OSNR requirement results from a 3-dB penalty due to the doubled bit rate and a 0. At a 10−9 BER the required OSNR for NRZ-OOK and POLMUX-NRZ-OOK is respectively 15. Transmitter & receiver properties 7. are more critical. 21. in the presence of PMD.5b compares the OSNR tolerance of 21.0 / 14. It indicates that the advantage of a polarization sensitive receiver is somewhat higher for D(Q)PSK compared to OOK modulation. Only when the POLMUX tributaries are exactly coupled into the PSP’s of the fiber. the PDλ of the MZDI is irrelevant.Chapter 7.7 / 15.2 Polarization-mode dispersion In the absence of PMD and nonlinear impairments both orthogonal polarization modes do not interact with each other. We note that for DPSK modulation there is some measurement uncertainty as the drift of both polarization and MZDI phase offset is controlled manually in the experiment.4 11. 138 .2 7. The improved OSNR requirement is a combination of the use of a polarization sensitive receiver and the absence of a phase demodulation penalty as observed for direct detection DQPSK.1 / 11.1: M EASURED OSNR MODULATION FORMATS AT TOLERANCE FOR DIFFERENT 10 G BAUD (BER 10−3 AND 10−9 ) single polarization (10. 7. As a polarization sensitive receiver filters out the orthogonal polarization. This lower difference might result from the absence of a PDλ induced penalty in the polarization sensitive DPSK receiver.7 of spontaneous–spontaneous beat noise is stronger for a polarization independent receiver.7 6. which explains the smaller difference between OOK and DPSK at low BER.3. This shows that POLMUX modulation allows for a 1.9 dB at a 10−3 BER. However.4-Gb/s RZ-DQPSK. For a high BER this measurement uncertainty is averaged out.8 / 10. but for 10−9 BER it results in some residual penalty.7 / 14. Even in the presence of random fiber birefringence. the coupling between the polarization modes will generally result in a transmission impairment for POLMUX signaling.3 9.2 / 17.9 POLMUX (21. the DGD results only in a time delay and no de-multiplexing penalty occurs.2 9.7 8. The difference between NRZ-DPSK and POLMUX-NRZ-DPSK is only 1.4-Gb/s POLMUX-RZ-DPSK with 21.1 / 15.7-Gb/s) NRZ-OOK RZ-OOK NRZ-DPSK RZ-DPSK 9.9 single polarization 21. In this case POLMUX can truly be considered a transparent multiplexing technique. the SOP is only rotated and both polarization modes remain orthogonal to each other.0 / 13.4-Gb/s) 12. Polarization-multiplexing Table 7.4-Gb/s) RZ-DQPSK 10.1 dB improvement in OSNR requirement compared to direct detection RZ-DQPSK.2 / 18. Figure 7. 1 nm) 10 8 6 4 2 0 BER = 10 -5 Power (a.4-Gb/s NRZ-OOK. the part of the signal in the slower PSP is delayed. The over. ’011’ or ’110’). (d) with 40-ps DGD and (e) with 40-ps DGD after polarization de-multiplexing. Transmitter & receiver properties Required OSNR (dB/0. which results in over. At the receiver. This is illustrated in Figure 7.4-Gb/s POLMUX-NRZ-OOK and 21.and undershoots in a 21. For other sequences (e. PSP coupling is however not realistic for a deployed transmission systems and the polarization de-multiplexing will therefore introduce a DGD induced penalty. The measured eye diagrams in Figure 7. the ISI results in mixing of the tributaries at the leading and falling edges of the symbol.and undershoots are in effect crosstalk between the polarization tributaries.u) 93 ps (e) Polarization rotation + DGD Inverse polarization rotation (b) Figure 7. which results in amplitude fluctuations when the tributaries are polarization de-multiplexed. the ghost pulse will interfere either constructively or destructively with the trailing or leading pulse. If the POLMUX tributaries are not coupled into the PSPs.7.3. When DGD is added to the POLMUX signal.and undershoots. 139 .6ce clearly show the DGD induced over. 21. For POLMUX signaling this results in higher penalties because the DGD changes the SOP along the symbol period. (c-e) measured eye diagrams for 21.g. (b) polarization changes within a symbol period resulting due to DGD. We assume therefore that the polarization control will align the polarization in the middle part of the symbol period.6: (a) Simulated OSNR penalty versus DGD for 10.u) 93 ps (c) 93 ps (d) 0 20 40 60 80 Differential Group Delay (ps) (a) Power (a. to the axis of the PBS. which contains the majority of the pulse energy.7-Gb/s NRZ-OOK. But the polarization control cannot correct for polarization changes on the time scale of a single symbol period.6b for a ’010’ sequence in both polarization tributaries.4-Gb/s POLMUX-NRZ-OOK with (c) back-to-back. This is most easily understood by noting that DGD results in ISI between neighboring bits.4-Gb/s POLMUX-NRZ-OOK signal with 40-ps DGD. the polarization tracking aligns the polarization tributaries again with the PSPs.u) Power (a. The part of the pulse at the leading and falling edge which has been coupled to the orthogonal polarization will then appear as a ghost pulse. In the wave-plate model. which shift the DGD induced over. To compute the OSNR requirement.7.7 shows the distributions obtained with 10-Gb/s NRZ-OOK and 20-Gb/s POLMUX-NRZ-OOK with different amounts of average PMD.4Gb/s POLMUX-NRZ-OOK for a worst-case 45o offset with respect to the PSP’s. We can consider the case when both POLMUX tributaries are exactly interleaved.7·B bandwidth. the worstcase penalty is approximately 1. This can be understood by noting that the crosstalk occurs mainly at the rising and falling edge of the pulse and not in the middle of the symbol period. the difference with single polarization modulation is relatively small. both tributaries are orthogonal and the offset between the two polarization tributaries 140 . Although POLMUX is more sensitive to PMD-induced impairments. When we adapt this to OSNR penalties (3x) and scale it to a 21. the optical EOP is used. but the resulting penalty is approximately a factor of 2-3 smaller than the OSNR penalty [330].7: Simulated scatter plots showing the penalty for different average PMD (a) 10-Gb/s NRZOOK and (b) 20-Gb/s POLMUX-NRZ-OOK. This indicates that 21-4-Gb/s POLMUX-NRZ-OOK has a ∼11-ps PMD tolerance for a 1-dB OSNR penalty. we find a 16-ps tolerance for a 1-dB OSNR penalty.6a shows a comparison between the DGD tolerance of 10. for 21. this also translates into a ∼11-ps PMD tolerance. The PMD is generated with a wave-plate model that uses 100 randomly oriented wave-plates. which is based on the error probability in the electrical signal. the average PMD per wave-plate is constant whereas the coupling angles between the 100 wave-plates change for each of the 10.4-Gb/s bit rate to account for FEC. when the symbol rate is doubled the DGD tolerance is reduced by a factor of two (e. the worst-case penalty for a 12-ps average PMD is approximately a 0.35 dB EOP. this approximates a Maxwellian PMD distribution [329]. The difference results from the use of the optical EOP to quantify the penalty rather than the OSNR requirement. while the bit rate is doubled. This indicates a clear advantage of POLMUX signaling over an increase in symbol rate.Chapter 7.1 dB.6 show a 34ps DGD tolerance for a 1-dB OSNR penalty.and undershoot more towards the middle of the symbol. The allowable DGD for a 2-dB OSNR penalty reduces from 42 ps to 34 ps for POLMUX signaling. Polarization-multiplexing Figure 7. the signal is low-pass electrical filtered with 0. This gives a performance indication with less computational effort.7-Gb/s NRZ-OOK.8b).7-Gb/s NRZ-OOK and 21. In the absence of DGD. To quantify the PMD penalty. Figure 7.4-Gb/s NRZ-OOK). Using the same approach to compute the PMD tolerance of 10. In comparison. The results depicted in Figure 7. (a) (b) Figure 7. We now extend the discussion to randomly distributed PMD. When we take into account that the average PMD tolerance for a 10−5 outage probability is approximately a factor of three lower than the DGD tolerance.000 simulations. The impact of DGD becomes more complicated when other impairments are present in the signal. In Figure 7.g. A good example is the inter-symbol delay between both polarization tributaries (see Figure 7. The interaction between these transmission impairments will be discussed in the remainder of this chapter. but is shifted to the middle of the symbol period [331]. the OSNR penalty increases to more than 4 dB.6 0. (c-d) simulated eye diagrams for 20-Gb/s POLMUX-NRZ-OOK with (c) tributaries aligned and (d) tributaries interleaved. but signal impairments such as chromatic dispersion and nonlinear impairments have a similar effect on the PMD tolerance. (b) definition of the inter-symbol delay between the POLMUX tributaries. the polarization tributaries are time-interleaved. Transmitter & receiver properties 5 -5 OSNR penalty (dB/0.2 0.7.5 1 1. When. as it also incurs a wavelength dependent change in the SOP. both polarization tributaries should be synchronized such that the rising and falling edges of the pulse occurs at the same time. This shows that in order to minimize the OSNR penalty. DGD induces also a periodic change of the SOP [332].8a for worst-case coupling of the POLMUX tributaries in between the PSP. For high symbol rates (and hence a broad optical spectrum) the wavelength dependent polarization change can be dominating. the crosstalk between both polarization tributaries occurs not anymore at the leading and falling edge of the symbol. In effect the SOP of the carrier wavelength. The difference in PMD tolerance between POLMUX and 141 . i.5 0 -150 -100 -50 0.e. The polarization control at the receiver aligns the signal such that crosstalk is minimized.5 1 0. Afterwards the signal is passed through a polarizer. does not result in an OSNR penalty. The alignment of both tributaries can be easily realized by a proper design of the transmitter. which shows the depolarization in the signal. In the presence of DGD this results in crosstalk between both polarization channels for all other components of the signal spectrum. The impact of DGD induced depolarization is illustrated in Figure 7. which contains the majority of the transmitted power. A DGD equal to one symbol period is added to a (single-polarization) NRZ-OOK signal which is coupled exactly in between both PSP’s. depolarization. 25 ps of DGD results in a 1-dB OSNR penalty.9.5 0 -150 -100 -50 0. When both polarization tributaries are synchronized. In addition to ISI between consecutive symbols.1nm) BER = 10 4 3 2 1 0 0 T (b) Power (mW) Power (mW) 1. The impact of SOPMD on POLMUX signaling is similar.4 0.3. Note that the periodicity between the minima in the optical spectrum in [T Hz] is equal to the inverse of the DGD in [ps].8 1 0 50 100 150 0 50 100 150 Inter-symbol delay (normalized) (a) Time (ps) Time (ps) (c) (d) Figure 7. This is depicted in Figure 7.8: (a) Simulated OSNR penalty versus the inter-symbol delay between the POLMUX tributaries with 34-ps of DGD. on the other hand. is aligned with the axes of the PBS. But when DGD is added to the signal. 4-Gb/s POLMUX-NRZ-OOK. but a sharply reduced tolerance for 21. They investigate POLMUX signaling combined with 40-Gb/s RZ-OOK modulation and find a reduction in PMD tolerance up to a factor of 5 compared to single-polarization modulation.7-Gbaud symbol rate.4-Gb/s POLMUX-NRZ-OOK with 34-ps of DGD.10: (a) Simulated OSNR penalty versus chromatic dispersion.3 Chromatic dispersion The lower symbol rate of POLMUX signaling compared to binary modulation formats improves the chromatic dispersion tolerance with a factor of 4.1 nm) 6 40 30 20 10 0 0 16 22 20 22 18 20 BER = 10 -5 4 22 18 20 22 16 18 20 2 0 -2000 BER = 10 -1000 0 1000 -5 2000 500 1000 1500 Chromatic dispersion (ps/nm) (a) Chromatic dispersion (ps/nm) (b) Figure 7. Polarization-multiplexing DGD equal to T0 2B0 Polarization filter Figure 7.7-Gb/s NRZOOK and 21.4-Gb/s NRZOOK.4-Gb/s NRZ-OOK and 21. 7. (b) OSNR penalty versus chromatic dispersion and DGD.g. 21. 10. This is evident from the comparison in Figure 7.9: Depolarization when a signal is passed through a polarizer in the presence of a DGD equal to the symbol period. 333. the contribution of time domain ISI is normally dominant (in the absence of DGD compensation).Chapter 7. On the other hand. Differential group delay (ps) 8 OSNR penalty (dB/0. for POLMUX signaling at a 10. 334]. This difference is for example evident by comparing the PMD induced penalties with and without POLMUX signaling for 10-Gb/s NRZ-OOK. which shows a nearly identical chromatic dispersion tolerance for 10. non-POLMUX therefore increases for higher symbol rates. Especially at a high symbol rate (e. with the results reported by Nelson and Kogelnik in [326]. as discussed here.7-Gb/s NRZ-OOK.10a. 40 Gbaud).3. 21.4Gb/s POLMUX-NRZ-OOK. 142 . depolarization can become the dominant impairment and significantly worsens the PMD tolerance of POLMUX signaling [326. In comparison. we assume here for the moment a single PDL element.4 Polarization dependent loss For polarization insensitive receivers PDL is a relatively insignificant impairment.3. 7. the PDL attenuates one tributary and leaves the other tributary unaffected. With a 0o offset between the POLMUX tributaries and the axis of the PDL element. Figure 7. The POLMUX tributaries are no longer orthogonal to each other. The OSNR for each of the POLMUX tributaries can then be denoted as. either 650-ps/nm of chromatic dispersion or 34-ps of DGD can be tolerated.and undershoots in the signal that normally occur near the symbol transition are now broadened and shift more towards the middle of the symbol period. The combined penalty is further evident from Figure 7.11b. 143 . For POLMUX signaling. At the receiver. To simplify the discussion on PDL.10b the required OSNR is depicted as a function of both chromatic dispersion and DGD. A lower de-multiplexing penalty is then obtained when each of the polarization tributaries is demultiplexed with a separate polarizer and polarization control [313. This is shown in Figure 7. a polarization-sensitive receiver demultiplexes the POLMUX tributaries using only a single PBS. The over. For a 2dB OSNR penalty.10a.5 dB of PDL. which results in crosstalk upon polarization de-multiplexing. If we assume that in the absence of PDL the optimum de-multiplexing angles are θ = 0o and θ = 90o . Normally. PDL results in depolarization of the signal when the POLMUX tributaries are 45o offset with respect to the axis of the PDL element. 340-ps/nm of chromatic dispersion and 20-ps of DGD together result in a 2-dB OSNR penalty. The PDL induced penalty in POLMUX signaling then depends on the alignment between the POLMUX tributaries and the axis of the PDL element.3.3. (7. In the absence of PDL. In this case a 2-dB OSNR penalty is obtained for ∼3. 2 ∆OSNRbest−case = 10log10 ( S+1 ) 2·S ∆OSNRworst−case = 10log10 ( S+1 ) . When on the other hand both signal impairments are present simultaneously. 316]. In Figure 7. But this is suboptimal when the signal is severely depolarized due to PDL. when we consider PMD and chromatic dispersion simultaneously. the dispersion tolerance is somewhat reduced. when comparing the tolerance without DGD and with 34-ps of DGD (2-dB OSNR penalty). as only large amount of PDL results in a noticeable penalty (see Section 2.6) where 0 < S < 1 denotes the PDL-induced attenuation in linear units. This clearly indicates that both signal impairments are strongly correlated. on the other hand.3). respectively.11c illustrates this by showing the impact of PDL-induced depolarization on the signal constellation.7. and assuming a constant total signal power. S equals 1. the impact of PDL is more detrimental as it effects the orthogonality between both tributaries. The performance of the worst-case POLMUX tributary is generally used as a measure of the OSNR penalty. for single polarization modulation both signal impairments can be considered nearly independently of each other. this reduces the OSNR of one tributary while increasing the OSNR of the other tributary. Transmitter & receiver properties However. We therefore only consider here the impact of PDL-induced depolarization on a POLMUX signal. This shows that PDL-induced depolarization results in a slightly lower OSNR penalty than PDL-induced attenuation of one of the polarization tributaries. 90 10 80 Depolarization (degrees) 70 60 50 40 OSNR penalty (dB/0. all curves show the worst-case of both POLMUX tributaries. on the other hand. π 4 (7. ) impact of PDL parallel to one of the polarization tributaries.11a depicts the impact of PDL-induced depolarization when unpolarized noise is assumed. the OSNR penalty due to depolarization is limited to 2-dB. (b. We note that the case of two separate polarizers applies to the digital coherent receiver discussed in Chapter 10. The OSNR decrease is negligible when the noise is polarized through the PDL. there still is an OSNR penalty when two separate polarizers are used.11 then shows that if we take 3 dB of PDL as a typical value for a long-haul link. This assumes that the noise in unpolarized. However. (c) impact of PDL with a 45o offset to the polarization tributaries with separate polarizers ( ) and for a single PBS ( ). which results in the worst-case penalty. Polarization-multiplexing the two polarizers should filter the signal with an angle. The impact of PDL in a long-haul transmission link is more difficult to estimate as it also interacts with other transmission impairments such as PMD.1nm) PDL with no offset PDL with 45o offset PDL 8 6 4 2 0 0 PDL BER = 10 2 4 6 8 -5 10 (b) (c) Polarization dependent loss (dB) (a) Figure 7. which is likely to be the dominant PDLrelated impairment. This penalty is a result of the smaller fraction of the total signal power that now passes through the polarizers. 144 .11: (a) Simulated OSNR tolerance versus polarization dependent loss. Figure 7.Chapter 7. The combination of a lower signal power but constant noise power results in a reduced OSNR. θ= √ 180o π ( ± arctan( S)).7) Even in the presence of severe PDL. is reduced with only 3-dB when the signal passes through the polarizer. this separates the two POLMUX tributaries without any crosstalk. both with a single PBS and with separate polarizers. Figure 7. The noise power. which lower the signal power by >>3 dB. 7-Gb/s RZ- We now assess the nonlinear tolerance of POLMUX signaling on an 800-km transmission link. which is analyzed in Section 7.1 Self-phase modulation The nonlinear interaction between both orthogonal polarization modes at the same wavelength results in XPolM. POLMUX signaling suffers from polarization scattering through XPM-induced depolarization. -2 FEC limit 8 log(BER) -3 -4 10 12 -6 -8 2 4 6 8 10 12 14 16 16 18 14 Input power (dBm/ch) Figure 7. Section 7. which is depicted in Figure 5.4.4. Section 7. XPolM results in a crosstalk between both tributaries that is more similar to XPM.9 nm) are combined in a 16:1 coupler.7. Nonlinear tolerance 7.4 introduces polarization-interleaved POLMUX transmission as a concept to reduce the impact of XPM-induced depolarization. We then focus on POLMUX signaling in a WDM transmission system. on the other hand.2 studies in more detail the interaction between PMD and single-channel nonlinear impairments. depending on the bias voltage and drive signal amplitude swing applied to the modulator.4 Nonlinear tolerance We now extend the discussion on POLMUX signaling to include nonlinear transmission impairments.7-Gb/s 231 − 1 PRBS is used to drive a second MZM for modulation. 10. A MZM driven with a 10. For modulation formats that do not modulate the polarization of the optical signal. For POLMUX signaling.7-Gb/s clock signal is used for pulse-carving and a 10. The signal is subsequently polarization-multiplexed by splitting the signal. 21. both polarization modes carry a portion of the same signal and the XPolM interaction is similar to SPM.4. The second MZM generates either OOK or DPSK modulation.4. Subsequently.15. Q(dB) 10. 21. The 800-km transmission link 145 .4.12: Measured single channel nonlinear tolerance for OOK. 7. The outputs of 1 to 9 ECL on a 50-GHz grid (center wavelength at 1550.7-Gb/s RZ-DPSK. In WDM systems.3.1 discusses the nonlinear tolerance of POLMUX signaling in the absence of co-propagating WDM channels.4. delaying one tributary by 23 ns and then recombining both tributaries with orthogonal polarizations. Section 7.4-Gb/s POLMUX-RZ-DPSK.4-Gb/s POLMUX-RZ-OOK. Finally. 7.4. it is desirable to avoid PMD in the transmission link. 146 . the propagating signal in each of the polarization modes is a mix between both POLMUX tributaries. And when the signals are polarization-multiplexed.2 Self-phase modulation & PMD As a next step.Chapter 7. a slightly higher nonlinear tolerance is measured for DPSK compared to OOK modulation. In POLMUX transmission the interaction between PMD and nonlinear impairments results unfortunately in increased transmission impairments.36 indicates that the nonlinear phase shift in a single channel is the same for both POLMUX signaling and single polarization modulation. When we take POLMUX-NRZ-OOK modulation as an example. At the receiver a 37-GHz CSF selects the desired WDM channel. In conventional transmission systems. The SPM-induced nonlinear impairments shift the DGD-induced over. The signal is then manually polarization de-multiplexed using a PBS preceded by a polarization controller (PC).13. The nonlinear phase shift is therefore not related to the power per polarization channel. as evident from Figure 7.12 shows the single channel1 nonlinear tolerance of 10. A significant amount of PMD can even reduce nonlinear impairments to a certain degree [335].4. on the contrary. However. as the PMD-induced penalty is normally much larger than the improvement in nonlinear tolerance. we observe no significant penalty for the same amount of DGD and nonlinear phase shift. This is illustrated through the simulated eye diagrams in Figure 7. both impairments combined results in higher penalties as when they would occur separately. Figure 7. As a result. there is no significant change in the nonlinear tolerance for either OOK or DPSK modulation. Substituting the power per polarization channel into Equation 2. 1 Single channel refers to a single wavelength channel. as is also the case in the absence of POLMUX signaling. When the signal is not coupled into the PSP’s.13.and undershoots more to the middle of the symbol period. Polarization-multiplexing consists of 8x100-km SSMF spans and the dispersion map is described in Section 5. However. we consider the impact of PMD on the single channel nonlinear tolerance. but to the power per wavelength channel. the nonlinear penalty for such a ’3-level’ signal will generally be slightly higher compared to a conventional NRZ-OOK signal. Due to the interaction with chromatic dispersion. this implies that a quasi ’3-level’ amplitude modulated signal propagates along the fiber. This similarity in nonlinear tolerance can be understood when we take into account that POLMUX signaling divides the channel power over both polarization modes.7-Gb/s NRZ-OOK and 10. For 10-Gb/s NRZ-OOK. the impact of PMD on the nonlinear tolerance is small. For RZ-DPSK the detector consists of a 1-bit MZDI followed by balanced detection and for RZ-OOK direct detection is used.7Gb/s NRZ-DPSK with both single polarization and POLMUX signaling. Because the SOP of the signal changes on the bit-level. Without POLMUX signaling. the average propagating power is equally divided over both orthogonal PSP. the interaction between the nonlinear phase shift and chromatic dispersion is slightly different. 7.4. Nonlinear tolerance Power (a.u) Power (a.u) Power (a.u) 100 ps 100 ps 100 ps Power (a.u) 100 ps (a) (b) (c) (d) Figure 7.13: Simulated eye diagrams for (a) 20-Gb/s POLMUX-NRZ-OOK with 40 ps of DGD, (b) 20Gb/s POLMUX-NRZ-OOK after transmission over 100-km SSMF with 15-dBm input power (c) 20-Gb/s POLMUX-NRZ-OOK after transmission and with 40 ps of DGD, (d) 10-Gb/s NRZ-OOK after transmission and with 40 ps of DGD. (b) (a) (c) Figure 7.14: Statistical simulation results for 10-Gb/s NRZ-OOK and 20-Gb/s POLMUX-NRZ-OOK; (a) Monte-Carlo simulation (10,000 simulations) of the probability distribution for 8-ps, 12-ps and 16-ps of PMD, dots denote linear and circles denote nonlinear simulations for a 100-km link and 15-dBm input power. (b-c) PMD scatter plots for a 100-km link and 12-ps of average PMD with (b) 10-Gb/s NRZ-OOK and (c) 20-Gb/s POLMUX-NRZ-OOK. The precise interaction between DGD and fiber nonlinearity is rather difficult to quantize as it depends on the evolution of the SOP along the fiber. As an alternative, the interaction between PMD and nonlinear impairments is quantified using statistical simulations. Figure 7.14 shows statistical simulations of the combined penalty for 10-Gb/s NRZ-OOK and 20-Gb/s POLMUXNRZ-OOK modulation. Only the interaction between nonlinearity and DGD is considered, ASE noise is neglected in the simulations and the performance is evaluated using the EOP. A single 100-km SSMF fiber span is simulated with -510-ps/nm pre-dispersion and zero accumulated dispersion. The input power is equal to 15 dBm into the SSMF and 5.5 dBm into the DCF. Different amount of PMD are added distributed along the SSMF through random coupling between the wave-plates. The fiber parameters for the SSMF and DCF are depicted in Table 7.2. At the receiver, the polarization channels are de-multiplexed using a PBS. We assumes here perfect alignment between the SOP at the carrier frequency and the axis of the PBS. In addition, the worst-case EOP of both POLMUX tributaries is used. 147 Chapter 7. Polarization-multiplexing Table 7.2: S IMULATED FIBER PARAMETERS . SSMF Insertion loss (α) Dispersion (D) Dispersion slope (S) Nonlinearity (γ) 0.2 17 0.057 1.3 DCF 0.5 -102 -0.34 2.95 unit dB/km ps/km/nm ps/km/nm2 1/W /km The linear and nonlinear simulation for an average PMD of 8 ps, 12 ps, and 16 ps are depicted in Figure 7.14a. For the linear simulations, only a small penalty is obtained. The penalty is Maxwellian distributed and shows a longer tail for higher average PMD. In the nonlinear simulations the worst-case penalty is significantly increased beyond the penalty for the linear case. As an example we consider the simulation with 16-ps average PMD, where the worst-case PMDonly penalty extends to 1.1 dB. But combined with nonlinear impairments, the worst-case penalty equals 2.5 dB whereas the mean nonlinear penalty is only 0.4 dB. This interaction is also evident from a comparison between Figures 7.14b and 7.14c. Whereas we observe a clear correlation between PMD and nonlinear impairments for 20-Gb/s POLMUX-NRZ-OOK, the penalty for 10-Gb/s NRZ-OOK is uncorrelated or decreases slightly with higher PMD. When we take the worst-case penalty from the statistical simulations as a measure, the interaction between nonlinear impairments and PMD results in a ∼2 dB decrease in nonlinear tolerance. Next, a fixed set of coupling angles between the birefringent wave plates is used and the strength of the birefringence is varied to simulate different amounts of DGD. The polarization channels are launched with a worst-case 45o misalignment angle with respect to the PSP. This simplification allows for significantly reduced computation effort in the study of the interaction between DGD and nonlinearity. For a fixed DGD and input power a single EOP is now obtained instead of a probability distribution. Note that the results only represent an average case with respect to DGD and nonlinear tolerance due to the fixed evolution of the SOP along the fiber link. For the selected set of coupling angles the SOPMD is 0.228 ps2 for a 1-ps DGD, and can therefore be neglected. Figure 7.15 shows the EOP as a function of both DGD and input power into the SSMF. In order to compare penalties, both 20-Gb/s POLMUX-NRZ-OOK (Figure 7.15a) as well as NRZ-OOK transmission with 10 Gb/s and 20 Gb/s (Figures 7.15b and 7.15c) are shown. First of all, we compare 10-Gb/s NRZ-OOK and 20-Gb/s POLMUX-NRZ-OOK. In this case the simulations show a clear reduction in both nonlinear and DGD tolerance. In the absence of nonlinear interaction, the DGD tolerance is respectively 54 ps and 42 ps for a 1-dB EOP. The nonlinear tolerance in the absence of DGD decreases from 17.5 dBm to 16.2 dBm, which is comparable to the measurements in Figure 7.12. As well, and similar to the previously discussed statistical simulations, the penalty increases when both DGD and nonlinear impairments are present. This contrasts with 10-Gb/s NRZ-OOK modulation where no interaction between DGD and nonlinear impairments is observed. Although a comparison between 20-Gb/s POLMUXNRZ-OOK and 10-Gb/s NRZ-OOK gives insight in how POLMUX signaling changes the transmission penalties, it is more realistic to compare the penalties at the same total bit rate, i.e. 20-Gb/s POLMUX-NRZ-OOK with 20-Gb/s NRZ-OOK. This results in a very different comparison between the DGD and nonlinear tolerances. Similar to Figure 7.6, the DGD tolerance 148 7.4. Nonlinear tolerance of NRZ-OOK is approximately halved and the nonlinear tolerances decrease even more when the symbol rate is doubled. Consequently, 20-Gb/s POLMUX-NRZ-OOK has a clear advantage over 20-Gb/s NRZ-OOK in both DGD and nonlinear tolerances. The DGD tolerance of 20-Gb/s POLMUX-NRZ-OOK is 42 ps compared with 26 ps for 20-Gb/s NRZ-OOK and the nonlinear tolerance equals 16.2 dBm and 11.9 dBm, respectively. We note that this difference in nonlinear tolerance gives only an indication and might change slightly when long-haul transmission with an optimized dispersion map is considered. 50 5 1 2 10 3 5 10 1 2 3 50 0.5 2 1 0.5 1 0.5 2 3 2 DGD (ps) DGD (ps) 40 30 20 10 11 40 30 20 10 1 13 15 17 Input power (dBm) 19 11 13 15 17 Input power (dBm) 19 (a) 50 50 5 5 3 1 2 3 5 10 10 10 (b) 1 DGD (ps) DGD (ps) 10 2 3 5 10 40 30 20 10 11 40 30 20 10 1 2 3 1 2 3 13 15 17 Input power (dBm) 19 11 13 15 17 Input power (dBm) 19 (c) (d) Figure 7.15: Simulated EOP as a function of DGD and input power for transmission over 100 km of SSMF, (a) 20-Gb/s POLMUX-NRZ-OOK, (b) 10-Gb/s NRZ-OOK, (c) 20-Gb/s NRZ-OOK and (d) 20-Gb/s POLMUX-NRZ-OOK with DGD compensation. We now investigate the de-multiplexing penalties when the DGD is compensated at the receiver. First-order PMD compensation is used, i.e. the DGD at the carrier frequency is reduced to zero, and any influence of higher-order PMD is not compensated. In this case, Figure 7.15d shows that no penalties are associated with the de-multiplexing of the polarization multiplexed channels. The nonlinear tolerance is comparable to the case without DGD compensation (Figure 7.15a) and no further penalties are observed up to a 50-ps DGD. This confirms that the increased penalties in POLMUX signaling result from the polarization de-multiplexing at the receiver and do not result from nonlinear interaction along the transmission link. This implies that for a DGD compensated transmission link, PMD and nonlinear effects can be treated independently, similar as observed in Figures 7.15b and 7.15c for NRZ-OOK. A final consideration is that PMD compensation normally uses the DOP as a feedback signal. In a POLMUX transmission system, the PMD compensation cannot be based on DOP measurement as the time-averaged DOP is close to zero. An alternative feedback signal that has been reported for POLMUX signals is the monitoring of spectral components in the electrical spectrum [336]. Alternatively, the impact of PMD can be compensated using a digital coherent receiver, as discussed in Chapter 10. 149 Chapter 7. Polarization-multiplexing 7.4.3 Cross polarization modulation We now extend the discussion to POLMUX-specific inter-channel nonlinear impairments. In POLMUX transmission systems, XPM-induced XPolM results in a polarization dependent nonlinear phase shift. This nonlinear phase shift depends on the transmitted bit-sequence in the co-propagating channels which leads to a noise-like change of the SOP, and hence depolarization. Due to the polarization sensitive receiver, the depolarization is converted into crosstalk between the POLMUX tributaries. This was first observed for two co-propagating polarizationmultiplexed solitons by Mollenauer et. al. in [77]. The nonlinear induced depolarization does not affect polarization insensitive modulation formats, as the penalty occurs only in the receiver when the POLMUX tributaries are de-multiplexed [78]. In order to study the effects of XPM-induced XPolM, we compare the nonlinear tolerance for transmission with and without POLMUX signaling. The nonlinear tolerance is measured for RZOOK or RZ-DPSK nodulation with different numbers of co-propagating channels and different channel spacings. The experimental setup consists of an 800-km transmission link, as discussed in Section 5.4. Figures 7.16a-d shows the BER as a function of the channel input power with co-propagating channels on a 50-GHz ITU grid. First of all, we compare single channel and WDM transmission with 9 co-propagating channels for RZ-OOK and RZ-DPSK. This shows that the nonlinear tolerance decreases with 2.4 dB and 4.8 dB, respectively, which results mainly from XPM impairments between the co-propagating WDM channels. Linear crosstalk between neighboring channels can also contribute slightly to the penalty as the channels are multiplexed using a 16:1 coupler, which does not filter out the out-of-band components. This comparison shows that at a 10.7-Gb/s symbol rate, RZ-DPSK is more affected by XPM impairments than RZ-OOK. This is straightforward when we take into account that for DPSK, the XPM-induced nonlinear phase shift results in a direct penalty. For OOK, on the other hand, the XPM-induced nonlinear phase shift results only indirectly in a transmission penalty through the interaction with chromatic dispersion. We note that for RZ-DPSK, the large inter-channel penalty could partially be a result of the high input powers used in this comparison, which enhances the influence of nonlinear phase noise. Next, we compare the nonlinear tolerance of RZ-OOK and POLMUX-RZ-OOK, which is shown in Figures 7.16a and 7.16c, respectively. For RZ-OOK, the nonlinear tolerance decreases with 2.4 dB when we compare single channel transmission with 9 co-propagating WDM channels on a 50-GHz grid. On the other hand, for POLMUX-RZ-OOK modulation the decrease equals 6.7 dB. This indicates a strong impact of XPM-induced XPolM impairments for POLMUX-RZ-OOK modulation. Where RZ-OOK is mainly limited by (intra-channel) SPM, POLMUX-RZ-OOK is clearly limited by inter-channel nonlinear impairments. A comparison between RZ-DPSK (Figure 7.16b) and POLMUX-RZ-DPSK (Figure 7.16d), on the other hand, shows only an additional 0.9-dB penalty. This is related to the more symmetric signal constellation of POLMUX-DPSK, which reduces the impact of XPolM. In summary; RZ-OOK has a higher nonlinear tolerance when compared to RZ-DPSK on a 50-GHz WDM grid. But for POLMUX signaling, the impact of XPolM results in a lower nonlinear tolerance for POLMUX-RZ-OOK when compared to POLMUX-RZ-DPSK. 150 7.4. Nonlinear tolerance -2 FEC limit 8 -2 8 log(BER) log(BER) Q(dB) -4 -5 -7 -9 -12 0 12 14 1.1dB 2 4 6 8 10 12 14 16 16 -4 -5 -7 -9 -12 0 12 14 4.0dB 10 12 16 14 16 2 4 6 8 Input power (dBm/cd/span) (a) -2 FEC limit 8 Input power (dBm/ch/span) (b) -2 FEC limit log(BER) -3 -4 -5 -7 -9 -12 0 5.7dB 8 log(BER) -4 -5 -7 -9 -12 0 Q(dB) 12 14 6.7dB 8 10 16 12 14 16 12 14 16 2 4 6 8 10 12 14 16 2 4 6 Input power (dBm/ch/span) (c) Input power (dBm/ch/span) (d) Figure 7.16: Measured nonlinear tolerance after 800-km for (a) 10.7-Gb/s RZ-OOK, (b) 10.7-Gb/s RZDPSK, (c) 21.4-Gb/s POLMUX-RZ-OOK and (d) 21.4-Gb/s POLMUX-RZ-DPSK with single channel, 3 WDM channel, 50-GHz spacing, 5 WDM channel, 50-GHz spacing, 9 WDM channel, 50-GHz spacing. Figures 7.17e-h compares the influence of different channel spacings with 3 co-propagating channels on a 50-GHz, 100-GHz and 200-GHz WDM grid. For both RZ-OOK (Figure 7.17e) and RZ-DPSK (Figure 7.17f), the penalty is sharply reduced for a channel spacing larger than 50 GHz. With POLMUX-RZ-OOK (Figure 7.17g) and POLMUX-RZ-DPSK (Figure 7.17h), on the other hand, a reduced nonlinear tolerance is also observed when the co-propagating channels are spaced 100-GHz and 200-GHz away. In particular POLMUX-RZ-OOK shows still a significant penalty (2.9 dB) between single channel and 3 co-propagating channels on a 200-GHz grid. For RZ-OOK, on the other hand, almost no difference is measured between 3 channels on a 200-GHz grid and single-channel transmission. This larger bandwidth is typical for XPolMinduced depolarization in POLMUX transmission. In conventional transmission systems, where the receiver is not polarization sensitive, a low-pass behavior characterizes the influence of XPM [337] and therefore results in a penalty which scales strongly with the channel spacing. Whereas XPM is normally not significant for a channel spacing in excess of 100-GHz (for SSMF and 10-Gbaud), XPolM can be a significant impairment for channel spacing up to 200-GHz. The difference in nonlinear penalty as a function of channel spacing is less significant for RZ-DPSK and POLMUX-RZ-DPSK, which confirms the observation that DPSK is mainly XPM and not XPolM limited. We note that this results in particulary large transmission impairments when a D(Q)PSK signal co-propagates with an OOK modulated channel. This case is discussed in Section 10.6.2. 151 Q(dB) -3 10 10 Q(dB) -3 10 -3 10 Chapter 7. Polarization-multiplexing -2 FEC limit -2 8 8 log(BER) log(BER) Q(dB) -4 -5 -7 -9 -12 0 12 14 1.1dB 2 4 6 8 10 12 14 16 16 -4 -5 -7 -9 -12 0 12 14 4.0dB 10 12 16 14 16 2 4 6 8 Input power (dBm/cd/span) (a) -2 8 Input power (dBm/ch/span) (b) -2 8 log(BER) Q(dB) -4 -5 -7 -9 -12 0 2.9dB 12 14 -4 -5 -7 -9 -12 0 2.0dB 12 14 5.2dB 10 12 16 14 16 2 4 6 5.3dB 8 10 16 12 14 16 2 4 6 8 Input power (dBm/ch/span) (c) Input power (dBm/ch/span) (d) Figure 7.17: Measured nonlinear tolerance after 800-km for (a) 10.7-Gb/s RZ-OOK, (b) 10.7-Gb/s RZDPSK, (c) 21.4-Gb/s POLMUX-RZ-OOK and (d) 21.4-Gb/s POLMUX-RZ-DPSK with single channel, 3 WDM channel, 50-GHz spacing, 3 WDM channel, 100-GHz spacing, 3 WDM channel, 200-GHz spacing. 7.4.4 Polarization-interleaved POLMUX systems The impact of XPolM-induced transmission penalties can be reduced through orthogonal polarization interleaving of adjacent POLMUX channels. Interleaved POLMUX transmission deterministically spreads out the SOP of the channels over the Poincar´ sphere, by changing the e SOP of the even wavelength channels with respect to the uneven channels. Polarization interleaved POLMUX transmission therefore bears a strong similarity to conventional polarization interleaved transmission, where adjacent WDM channels are transmitted in orthogonal SOPs [71, 72]. In polarization interleaved POLMUX systems, a signal is transmitted in both orthogonal SOPs of each co-propagating wavelength channel, as illustrated in Figure 7.18. The decrease in transmission penalties is based on the observation that the sum of the Stokes vectors of two copropagating wavelength channels is constant during transmission, which cancels the influence of XPolM. Using the Manakov Equation [338], one can show that the nonlinear polarization shift induced on a pulse in channel ω1 through a second co-propagating pulse in channel ω2 is equal to, S ω1 8 = γP0 (Sω1 xSω2 ), (7.8) z 9 where Sn denotes the Stokes vector of channel n, P0 is the channel input power and z the transmission distance. Assuming a sum vector S0 with S0 = 1 (Sω1 + Sω2 ) it can be shown that this is 2 152 Q(dB) 10 log(BER) -3 -3 10 Q(dB) -3 10 -3 10 The output of up to 9 DFB lasers. This show an improvement of 0. the sum vector S0 equals zero and the nonlinear polarization shift only depends on the pulse in channel ω1 itself.19. The SOP of the POLMUX channels are adjusted using the polarization controllers in between both interleavers. the signals are polarization-multiplexed to 20-Gb/s POLMUX-NRZ-OOK.5 dB for 3 and 5 co-propagating channels. data 1 A W G MZM VOA PC V PC 100km SSMF I N T DCM H delay PC I N T 25-GHz PC PBS CSF PC 9 POL-MUX Interleaving ~ ~ ~ RX POLdeMUX Figure 7. Nonlinear tolerance equal to.20a. the impact of polarization interleaving on 10-Gb/s NRZ-OOK is depicted.9) z 9 which only depends on Sω1 and the sum vector S0 . The signals are then transmitted over 100 km of SSMF and matching DCF. In effect. the signal is fed into a direct detection receiver and the nonlinear tolerance is measured for the center channel at 1551. a 25-GHz CSF filters out the center channel and the signal is manually polarization de-multiplexed with a PBS preceded by a polarization controller.18: Principle of interleaved POLMUX transmission.19: Experimental setup for interleaved POLMUX transmission. Using a similar argument it can be shown that also for multiple co-propagating channels polarization interleaving minimizes the variance in nonlinear polarization shift.9 dB and 0. As it is difficult to measure the SOP difference between the WDM channels. respectively 153 . are 10-Gb/s NRZ-OOK modulated (PRBS 231 -1). (7. The WDM channels are polarization interleaved by splitting the channels into two subsets using a 50-GHz interleaver and afterwards recombining the channels with a second 50-GHz interleaver.6 nm. Afterwards. spaced on a 50-GHz grid. Non-interleaved ’10’ ’11’ ’10’ ’11’ ’10’ 90° polarization interleaved ’11’ ’11’ ’10’ ’00’ Channel ’01’ 1 ’00’ Channel ’01’ 2 ’00’ Channel ’01’ 1 ’01’ ’00’ Channel 2 Figure 7. Sω1 16 = γP0 (Sω1 xS0 ). the polarization interleaving rotates the linear polarization components of the even WDM channels 90o with respect to the uneven WDM channels. Afterwards. we adjust the SOP of one of the channel subsets such that the measured BER is minimized.7. In Figure 7. We experimentally verify the principle of interleaved POLMUX transmission with the setup depicted in Figure 7. After transmission. where the same input power is used for both SSMF and DCF to generate sufficient nonlinear impairments.4. When the two pulses in channels ω1 and ω2 have an orthogonal SOP. When the channel spacing is increased. The difference between 3 and 9 co-propagating channels is more significant here than previously discussed (Figure 7. This improvement results mainly from a reduction in XPM impairments between the co-propagating channels. For 3 copropagating channels. 3 channel 50-GHz spacing. 3 channel 300-GHz spacing. Polarization-multiplexing -2 FEC Limit 8 -2 FEC Limit 8 10 12 14 log(BER) log(BER) -3 -4 -5 -7 -9 5 6 7 8 9 10 11 12 Q(dB) 12 14 16 13 -4 -5 -7 -9 2 4 6 8 10 12 16 Input power (dBm/ch) (a) -2 FEC Limit Input power (dBm/ch) (b) 8 10 12 14 6 7 8 9 10 11 12 16 13 log(BER) -3 -4 -5 -7 -9 5 Input power (dBm/ch) (c) Figure 7.2 dB to 0. The influence of the channel spacing is evident from the measurement results depicted in Figure 7. 9 3 (at 10−5 BER). channel 300-GHz spacing. We can therefore conclude that polarization interleaved POLMUX transmission does not sufficiently reduce the impact of XPolM to be practical in long-haul transmission systems. This reduces the benefit of polarization interleaving. a much lower nonlinear tolerance is measured compared to 10-Gb/s NRZ-OOK. The efficiency of interleaved POLMUX transmission is relatively small compared to the XPolM penalty. But when the number of co-propagating channels increases. as it requires an accurate alignment of the SOP of the WDM channels. the beneficial influence of polarization interleaved transmission decreases as channels spaced further away contribute to the XPolM penalty.20c. interleaved. interleaved. 9 channel 50-GHz spacing.2 dB. 154 Q(dB) Q(dB) 10 -3 . For 20-Gb/s POLMUX-NRZ-OOK. interleaved. which changes the SOP as a function of wavelength.16c). as there is no dispersion map used here to reduce the impact of XPM.20: Measured nonlinear tolerance after 100-km for (a) 10-Gb/s NRZ-OOK and (b-c) 20-Gb/s POLMUX-NRZ-OOK with 3 channel 50-GHz spacing. In particular for WDM channels that are spaced further apart. channel 50-GHz spacing.20b. the orthogonality between the WDM channels is maintained only over a short transmission distance. as depicted in Figure 7. polarization interleaving increases the nonlinear tolerance with 1. which compares a 50 GHz and a 300-GHz channel spacing for 3 co-propagating channels. This is mainly due to the impact of DGD and SOPMD.Chapter 7.2 dB. the nonlinear tolerance improvement reduces from 1. which reduces the impact of XPolM. → PMD results in crosstalk between the POLMUX tributaries due to over. It suffers therefore only a ∼1 dB penalty from XPolM impairments. 155 . → For POLMUX-OOK modulation. But at the same bit rate. shifts the DGD induced edge over. → POLMUX-DPSK modulation has a more symmetric signal constellation. → A polarization-sensitive receiver improves the OSNR requirement by filtering out the noise in the orthogonal polarization. POLMUX signaling significantly increases the transmission tolerance when compared to binary modulation at the same bit rate. This causes crosstalk between the POLMUX tributaries after the polarization sensitive receiver. the impact of XPolM results in a reduction of the nonlinear tolerance with 4-5 dB in comparison to WDM transmission without POLMUX signaling (10 Gbaud. the nonlinear tolerance decreases due to the cumulative edge effects of DGD and SPM. PDL can either result in an OSNR fluctuation for one of the tributaries or a loss of orthogonality between the tributaries. the single-channel nonlinear tolerance is comparable with and without POLMUX signaling. → The lower symbol rate increases the chromatic dispersion tolerance by a factor of 4 in the absence of a PMD. the impact of XPolM results in a reduced nonlinear tolerance for POLMUX transmission systems. 50-GHz grid). Summary & conclusions 7. A 3-dB PDL results approximately in a 2-dB worst-case OSNR penalty.and undershoots near the edge of the pulse. For POLMUX-OOK modulation. In addition we find that for WDM transmission systems. → At a 10-Gbaud symbol rate. → The XPolM-induced nonlinear phase shift result in a noise-like change in the SOP. However.and undershoots from the edge to the center of the pulse.1 dB advantage in OSNR requirement. In comparison to DQPSK modulation.5.5 Summary & conclusions In this chapter we analyzed and compared the transmission tolerances of POLMUX signaling with polarization insensitive modulation formats. This reduces the tolerance by ∼30% (2-dB OSNR penalty) in comparison to single-polarization transmission at the same symbol rate. This makes POLMUX-OOK modulation generally impractical for long-haul transmission. POLMUX-DPSK modulation has a 1. the difference is ∼2. In the presence of PMD. the combination of chromatic dispersion and PMD.7 dB for a doubling in the total bit rate. Statistical simulations show for this case a reduction in nonlinear tolerance with up to ∼2 dB in comparison to singlepolarization transmission at the same symbol rate.7. the PMD tolerance of POLMUX signaling is significantly higher in comparison to binary modulation formats. This shows that for most linear and nonlinear transmission impairments separately. → For POLMUX signaling. → Deterministically spreading the SOP of co-propagating WDM channels reduces the impact of XPolM. have to be designed with simple engineering rules. POLMUX-DPSK has a 3-dB advantage in nonlinear tolerance compared to DQPSK modulation at a 10-Gbaud symbol rate and 50-GHz channel spacing. optical compensation of PMD might not be practical due to high polarization tracking speeds that are required. ideally. The use of phase modulation reduces the impact of XPolM and makes POLMUX signaling practical for long-haul transmission systems. 156 . When the PMD-related impairments are compensated. However. This is undesirable for long-haul transmission systems which. The interaction between PMD. chromatic dispersion and nonlinear impairment complicates system design for POLMUX transmission systems.Chapter 7. either through optical or electrical means. which decreases the efficiency of polarization interleaving. cancels out the XPolM penalty. Polarization-multiplexing This indicates that POLMUX-DPSK can be a suitable modulation format for long-haul transmission systems. Polarization interleaving of the WDM channels therefore. the high transmission tolerances combined with the doubled spectral efficiency of POLMUX signaling make it an attractive option for high-capacity transmission systems. if possible. It is therefore attractive to apply PMD compensation for POLMUX transmission systems. the orthogonality between the co-propagating channels is lost through PMD. However. as shown in the previous chapter the use of multi-level modulation formats is challenging for long-haul transmission systems. Section 8. To further increase the number of bits per symbol.1 describes the transmitter and receiver structure of POLMUX-RZ-DQPSK modulation. DQPSK modulation and POLMUX signaling as possible approaches to double the spectral efficiency over binary modulation. This chapter combines DQPSK modulation and POLMUX signaling to realize modulation with 4 bits per symbol.3 we then compare the high-spectrally efficient transmission experiments that have been studied in the literature. Chapters 5 and 7 have discussed. Subsequently. phase and polarization dimensions of an optical signal has allowed multi-level modulation at high bit rates with up to 5 and 6 bits per symbol [340. 1 The results described in this chapter are published in c7.6-b/s/Hz spectral efficiency. An example of orthogonal coding that combines amplitude and phase shift keying is amplitude differential phase shift keying [339]. Such a high-density signal constellation opens up the possibility for a ≥1. This requires transmission formats with a narrow optical bandwidth while maintaining sound linear and nonlinear transmission tolerances to enable long-haul transmission with >1 b/s/Hz.2 discusses long-haul POLMUX-RZ-DQPSK transmission with a 1. It can result in reduced transmission reach through higher OSNR requirements and a lower nonlinear tolerance. the OSNR requirement as well as the tolerance against narrowband filtering. In Section 8. c36 157 . The simultaneous modulation of the amplitude.6 b/s/Hz spectral efficiency in long-haul transmission systems. which presents a trade-off between the nonlinear and PMD tolerance. orthogonal coding can be used to exploit two or more degrees of freedom at the same time. We particulary focus on the influence of interleaved polarization multiplexing. However. respectively.8 Polarization-multiplexed DQPSK Future state-of-the-art optical transmission systems are expected to transmit high bit rates in even more densely spaced WDM channels. Section 8. 341]. 3) vI (t) = ℜ{Ev } = ℜ{ vQ (t) = ℑ{Ev } = ℑ{ j Im{E } h 1 Re{Eh} Pv exp( j∆ϕv (t))} Pv exp( j∆ϕv (t))}. Assuming ϕ and ∆ψ √ are equal to zero this gives Ph exp( j∆ϕ√ = hI (t) + j · hQ (t) as the complex envelope of the h (t)) horizontal polarization components and Pv exp( j∆ϕv (t)) = vI (t) + j · vQ (t) as the complex envelope of the vertical polarization component. hI (t) = ℜ{Eh } = ℜ{ Ph exp( j∆ϕh (t))} hQ (t) = ℑ{Eh } = ℑ{ Ph exp( j∆ϕh (t))} (8.1 Transmitter & receiver structure A POLMUX-DQPSK transmitter consists of two DQPSK transmitters which are afterwards multiplexed on the two orthogonal polarizations of the signal. π. Each DQPSK signal encodes 2 bits per symbol. which results in a total 2 · 2 = 4 bits per symbol for POLMUX-DQPSK modulation.1 shows only 8 158 . (8. The information is carried in ∆ϕh (t) and ∆ϕv (t) which are independent of each other and take a value from the set [0. √ P · exp( j[ω0t + ϕ + ∆ϕh (t)]) r(t) = √ h .Chapter 8. as a DQPSK modulated signal on each of the two orthogonal polarizations.2) Pv · exp( j[ω0t + ϕ + ∆ϕv (t) + ∆ψ]) where ϕ is the absolute phase of the transmitter laser and ∆ψ is the phase difference between both orthogonal polarization components. This can be slightly counterintuitive. π/2.1 shows the signal constellation diagram for POLMUX-DQPSK. we can also denote the signal as. 3π/2].1) r(t) = Ev Pv exp( j[ω0t + ϕv (t)]) As POLMUX-DQPSK modulation encodes the information in the differential phase ∆φ . as the constellation diagram in Figure 8. j Im{E } v 1 Re{Ev} h v -1 X -1 -j -j Figure 8. (8. √ P exp( j[ω0t + ϕh (t)]) Eh = √ h . Polarization-multiplexed DQPSK 8. This results in a transmitted signal. The signals in each of the 4 signaling dimensions can therefore be defined as.1: 2-dimensional signal constellation diagram for POLMUX-DQPSK modulation Figure 8. x(∆ϕh . the signal is first split into two orthogonal polarization tributaries with a polarization controller followed by a PBS. Figure 8. Note that when visualized on a Poincar´ sphere.1a). We note that all fibers in the transmitter would normally be polarization-maintaining. Transmitter & receiver structure signal points. The polarization rotation for one of the DQPSK tributaries is shown explicitly here.e. but is normally integrated into the PBS. The signal constellation diagram is now shown as a 4-dimensional hypercube. the signal constellation can be defined in a three-dimensional coordinate system (x. see Figure 7. For RZ modulation. which is the product of two coplanar circles. At the receiver. Each of the polarization tributaries is split again with a 3-dB 159 .2: 4-dimensional signal constellation diagram for POLMUX-DQPSK modulation The transmitter and direct detection receiver structure for POLMUX-RZ-DQPSK modulation are both depicted in Figure 8. z) as. As an alternative representation. a total of 4 independent binary electrical data streams are modulated onto the POLMUX-DQPSK signal. Different hypercubes can be used to represent the signal constellation but we use here a torus. ∆ϕv ) = [R + r · cos(∆ϕv )] · cos(∆ϕh ) y(∆ϕh . the signal is split and each of the tributaries is DQPSK modulated with a parallel DQPSK modulator.4) z y x Figure 8. ∆ϕv ) = r · sin(∆ϕv ). whereas the other circle denotes exp( j∆ϕv ). Assuming that ∆ψ is equal to zero. respectively. the output of the laser is first RZ pulse carved. y. both tributaries are then multiplexed together on orthogonal polarizations. Hence.2 depicts both orthogonal polarizations combined in a single constellation diagram. (8. ∆ϕv ) = [R + r · cos(∆ϕv )] · sin(∆ϕh ) z(∆ϕh .3. We use here one circle to denote exp( j∆ϕh ).1. Afterwards. ∆ϕv − ∆ψ − ∆ϕh . where R and r.8. with R > r defines the distance from the center of the tube to the center of the torus and the radius of the tube. e the constellation diagram of POLMUX-DQPSK modulation consist of 4 signal points as only the phase difference between both polarization modes is denoted (i. With a PBS. Note that it is switched off in the actual measurement and has no influence on the discussed results. The optical switch can be triggered (switch 1) to change between POLMUX-RZ-DQPSK. the transmitter and receiver structure is somewhat different from the one discussed in Section 8. Polarization-multiplexed DQPSK MZDI T MZ Prec. which enables multiple components on a single optical dei [342.1. 8. After DQPSK modulation. the channels are fed to a polarization-multiplexing stage.-j) (j.6 ns relative to each other. For simplicity.Chapter 8.15 nm and 1563. aligned on a 50-GHz ITU grid between 1548.1. The signal is power split to create two tributaries (H and V).3: Transmitter and receiver structure for POLMUX-(RZ)-DQPSK modulation fused-fiber coupler and all four tributaries are fed to separate MZDIs.1 Back-to-back OSNR requirement Figure 8. Hence. This would for example be possible using InP technology.1.-j) + =+ /4 data VB Figure 8. the even and odd channels are combined with a 50-GHz interleaver.2. the output signals of 40 DFB lasers. The MZDIs demodulate the in-phase and quadrature tributaries of each of the polarization components which is followed by balanced detection.88 nm. One branch of the polarization-multiplexing stage contains an optical switch and phase modulator. data HA TE TM /2 PD + =+ /4 PC T data HA clock Prec.j) (j.1) (-1. laser PBS PBS =+ /4 T data HB optional + MZ /2 =+ /4 T data VA Prec. 278. This is discussed in more detail in Section 8. 343]. which are delayed with 16. This shows that the number of optical components in both the transmitter and receiver is significant for POLMUX-RZ-DQPSK modulation.6-Gb/s POLMUX-RZ-DQPSK transmitter and receiver as used in the experimental verification. and is hence used to identify which polarization tributary is measured. are modulated using two parallel modulator chains for separate modulation of the even and odd wavelength channels. At the transmitter.6-Gb/s POLMUX-RZ-DQPSK modulation. The two polarization tributaries can be bit-aligned or they can be offset from each other. Subsequently. having a 3-dB bandwidth of 44 GHz. The RZ-DQPSK modulator is the same as discussed in Section 6. and (single polarization) RZ-DQPSK modulation for the reference measurements. to make such a modulation format more practical further optical integration of the components is a prerequisite. 160 .-1) (-j. The tributaries H and V are recombined with orthogonal polarizations in a PBS to generate 85.2. The phase modulator (PM) causes synchronization loss in tributary V when switched on (switch 2).4 depicts the configuration of the 85.-1)(1. MZM MZ data HB data VA MZ + Prec. data VB (-j. 5 shows the back-to-back OSNR requirement of 42. Figure 8.5: Measured (points) and simulated (lines) back-to-back sensitivity for 42.8-Gb/s RZDQPSK (dashed line) and 85.8-Gb/s RZ-DQPSK and all four tributaries of 85.8-Gbit/s RZ-DQPSK 12 14 16 18 20 22 OSNR/0.1nm(dB) 24 14 16 26 -30 1556 1556.0 dB for measurements and simulations.4G data A 2 A W G MZM MZ /2 MZ Switch VOA -2 PM I N T Switch -1 RZ-DQPSK Rx POL-DEMUX CR PD MZDI T V switch-1 H delay PBS PC DE BERT MUX + - 40 21. the simulative and experimentally measured OSNR requirement are in good agreement and show only a 1.8. 85.3.4 dB and 3. 161 .4 dB 12 6 -2 0 Relative Power (dB) 8 10 Q(dB) (b) (c) -10 (a) -20 (d) log(BER) -3 -4 -6 -8 -10 -12 10 42.0 dB and 15. (b) transmitted spectrum (c) received spectrum before the CSF (d) received spectrum after the CSF.6: High resolution optical spectrum with: (a) single channel. Hence.5 Wavelength (nm) 1557 Figure 8. In the simulations.8 dB 85. This sensitivity reduction is similar to the reduction observed in Section 7.1. The simulated back-to-back OSNR requirements are shown as a reference.3.6-Gbit/s POLMUX RZ-DQPSK 2. respectively. respectively.1 are used.2 dB difference due transmitter and receiver impairments (for a 10−3 BER).1 and results from a 3-dB penalty due to the doubled bit rate and a 0.8-Gb/s RZ-DQPSK and 85.6-Gb/s POLMUX-RZ-DQPSK modulation. For both simulations and experiments the respective optimized filter bandwidths discussed in the Section 5. respectively.4G data B POL-MUX PBS (a) (b) Figure 8.6-Gb/s POLMUXRZ-DQPSK (dotted line). For a fixed OSNR.8 dB for 42. the back-to-back Q-factor difference between RZ-DQPSK and POLMUX-RZ-DQPSK equals 2. 2. The required OSNR for a 10−3 BER is 13. the required OSNR is 11.8-Gb/s RZ-DQPSK.6-Gb/s POLMUX-RZ-DQPSK.4G clock 21. Figure 8.8 dB and 14.8 dB higher OSNR with respect to 42.4: Experimental setup: (a) transmitter and (b) receiver. Transmitter & receiver structure RZ-DQPSK Tx – odd channels RZ-DQPSK Tx – even channels 21.6 dB for 42.2-dB benefit which originates from the polarization sensitive receiver.6-Gb/s POLMUX-RZ-DQPSK. Hence.8-Gb/s RZ-DQPSK and 85.6-Gb/s POLMUX-RZ-DQPSK requires a 2. The transmittance spectrum of the in-line WSS used in the experiment is shown in Figure 3.6-Gb/s POLMUX-RZDQPSK modulation on a 50-GHz WDM grid. the WDM signal is de-multiplexed using a CSF with a 34-GHz 3-dB bandwidth. Spectra (a) shows the single channel optical spectrum of 85.7: (a) re-circulating loop setup. This indicates that 85.6-Gb/s POLMUX-RZ-DQPSK can be transmitted over multiple cascaded adddrop nodes on a 50-GHz WDM grid. Tx switch TX Precompensation Postcompensation Loop switch DCM DCM 94.1.5 ps/nm (at 1550 nm). the bandwidth of the optical filters is important to consider.6-Gb/s POLMUX-RZ-DQPSK with a 50-GHz channel spacing.8-Gb/s RZ-DQPSK as discussed in Section 6.6Gb/s POLMUX-RZ-DQPSK is similar to 42.6Gb/s POLMUX-RZ-DQPSK before optical filtering.5 km SSMF 3x 6x LSPS (a) Raman 34-GHz CSF RX ~ ~ ~ TDC WSS 40 x 85. which is close to the optimum for 42. The in-line spectral filtering is evident by comparing the spectral dip between WDM channels in spectra (b) after the 50-GHz interleaver and spectra (c) after 6 passes through the re-circulation loop. Spectra (d) is obtained after de-multiplexing of the WDM channels. A comparison of spectra (a) and (b) shows the influence of the 50-GHz interleaver at the transmitter. It shows that the spectral width of the received signal after 6 passes through the re-circulating loop is similar to the back-to-back optimized de-multiplexing filter bandwidth of 34-GHz. (b) optical spectrum after transmission. 8.6-b/s/Hz spectral efficiency while maintaining a sound tolerance with respect to narrowband optical filtering. This enables a high 1.16.2 Narrowband optical filtering In order to transmit 85.5 dB. The narrowband filtering tolerance of 85.2. further narrowing the optical bandwidth.8-Gb/s RZ-DQPSK as both modulation formats are DQPSK modulated and have the same symbol rate. The re-circulating loop consists of three 94. At the receiver. The optical filtering in the in-line WSS reduces the optical bandwidth with every pass through the re-circulating loop.6 shows in more detail the narrowband filtering as it occurs along the transmission line in the long-haul transmission experiment discussed later in this chapter.5km spans of SSMF with an average span loss of 21. The inline under-compensation per span is 33. The input power into the SSMF is -3 dBm per WDM channel and a 162 . Before transmission the channels are de-correlated with -1020 ps/nm of pre-compensation. Figure 8.2 Long-haul transmission In this section we discuss a long-haul transmission experiment with 85. Polarization-multiplexed DQPSK 8.6-Gb/s POLMUX-RZ-DQPSK (b) Figure 8.Chapter 8. 6-Gb/s POLMUX-RZ-DQPSK . the signal is fed into the conventional 42. We note though that the difference is small and can also partially result from measurement inaccuracies. This is depicted in Figure 8. In-phase.Z-D .6-Gb/s POLMUX-RZ-DQPSK modulation format for longhaul transmission.8-Gb/s RZ-DQPSK modulation and it can thus be concluded that no POLMUX specific impairments are measured. pol. Quadrature.8. Initially the measured log(BER) shows a linear increase with an exponential increase in transmission distance. pol. (b) Measured BER of all 40 WDM channels after 1. the performance is assessed as a function of the transmission distance. pol. A LSPS with a deterministic sequence of polarization states equal to the number of re-circulations is used in the re-circulating loop.8-Gb/s RZ-DQPSK and 85. Quadrature. However. pol. This is likely a result of the lower peak power in comparison to RZDQPSK.V. for RZ-DQPSK In-phase. which results in an improved nonlinear tolerance.2.H.2 dB 12 13 14 -6 -8 1545 42.6-Gb/s POLMUX-RZ-DQPSK is strongly limited by single-channel impairments and that the influence of XPM-induced depolarization is minimal. 8 FEC limit -3 FEC limit 10 -3 8 9 10 11 log(BER) Q (dB) -4 -5 -6 -8 500 . the desired channel is selected with a narrowband 34-GHz CSF and afterwards fed into the receiver (depicted in Figure 8. The signal is first manually polarization de-multiplexed using a PC followed by a PBS.2.V. A similar performance decrease is observed for 42. To analyze the suitability of the 85.8 42 1000 G RZ s b/ 12 -4 2. averaging out PMD and PDL influences. The lack of POLMUX specific impairments such as XPM induced cross polarization modulation confirms that 85. the LSPS does not influence the polarization at the receiver and is as such not used to de-multiplex the polarization tributaries.2 5.000 km it deviates from the linear increase due to an increased impact of nonlinear impairments such as SPM and nonlinear phase noise.4-dB back-to-back difference in Q-factor between 42.8-Gb/s DQPSK receiver as discussed in Section 6.H. After 2. configured as a channel-based DGE.3b).2 dB. Power equalization of the WDM channels is provided by the WSS. Using a TDC. 163 Q (dB) K PS DQ log(BER) UX M OL K s P PS / Gb Q dB 6.8b. The polarization in each re-circulation of the loop is thus randomized with respect to the other re-circulations. The optical spectrum at the receiver is depicted in Figure 8. Subsequently.8-Gb/s RZ-DQPSK 1550 1555 1560 14 15 1565 2000 3000 4000 16 Transmission distance (km) (a) Wavelength (nm) (b) Figure 8. the accumulated dispersion at the receiver is optimized on a per-channel basis. Quadrature and POLMUX-RZ-DQPSK In-phase.700 km. The 2.8: (a) Measured BER as a function of transmission distance. Afterwards. R 2 8 85.6-Gb/s POLMUX-RZ-DQPSK is slightly reduced to 2. Long-haul transmission hybrid backward pumped Raman/EDFA structure is used for signal amplification with an average ON/OFF Raman gain of ∼11 dB.7b. which is defined as the peak power divided by the minimum power in the eye diagram. the RZ pulse shape of RZ-DQPSK is to a high degree maintained and a high extinction ratio is measured.700-km transmission.2.Chapter 8. 10 Extinction ratio (dB) 8 6 4 (a) (b) 2 (a) (c) -10 0 10 20 30 (b) (c) 0 -20 Normalized optical delay (ps) Figure 8. all 40 RZ-DQPSK channels have more than 3-dB margin with respect to the FEC limit.6-Gb/s POLMUX-RZ-DQPSK. a maximum 2 dB difference in Q-factor is measured. as shown in Section 7.8-Gb/s RZ-DQPSK and 85. The difference in inter-pulse delay can be denoted by the optical extinction ratio before polarization de-multiplexing and phase demodulation. partly because the quasi CW signal of interleaved polarization tributaries caused instable operation of the phase-locked loop based clock-recovery.2. 164 .3. After 1. It can be changed such that both tributaries are either bit-aligned or interleaved.1 Interleaved vs.2).6-Gb/s POLMUX-RZ-DQPSK signals before polarization demultiplexing and phase demodulation as a function of the normalized inter-pulse delay. The small performance variance among the WDM channels indicates that there is no strong wavelength dependency across the upper part of the C-band. the inter-pulse delay is set in between both extremes. 8. Polarization-multiplexed DQPSK Figure 8. bit-aligned polarization-multiplexing The optical inter-pulse delay is defined as the delay between both polarization tributaries within one symbol period (see Section 7. In Figure 8.3.6-Gb/s POLMUX-RZDQPSK the worst channel is more than 1 dB above the FEC limit. In the case both polarization tributaries are interleaved. a quasi CW signal is obtained and the extinction ratio is close to zero. It is observed in the transmission experiment that interleaving the polarization tributaries reduces nonlinear impairments considerably.8a shows the BER for all WDM channels and tributaries for both 42. as evident from the eye diagrams in Figure 8. For 85. When the polarization tributaries are bit-aligned on the other hand. For RZ pulse carved signals. In the experimental results reported here.6-Gb/s POLMUX-RZDQPSK. it can be particulary interesting to interleave both polarization tributaries as this lowers the peak power of the signal and therefore improves the nonlinear tolerance. On the other hand the influence of PMD related impairments is enhanced for interleaved polarization tributaries.9.9 the influence of the inter-pulse delay on the optical extinction ratio is depicted for 85.9: Extinction ratio of the 85. 10b.10a shows the simulated DGD tolerance for both cases.1 THz) is an integer multiple [331]. the performance fluctuations might be attributed to the reduced PMD tolerance of 85. the generated RZ-DQPSK signal is split. For RZ-DQPSK the results shown here are the worst-case (maximum) EOP obtained from the in-phase or quadrature channel. the impact of SOPMD is also important to consider as it results in a polarization change along the optical bandwidth. for the doubled bit rate.6-Gb/s POLMUX-RZ-DQPSK with interleaved tributaries. which depicts the penalty versus the inter-symbol delay between the polarization tributaries in the presence of 8.2 Differential group delay The polarization de-multiplexing in the POLMUX receiver.and undershoots near the edges of the symbol. We therefore restrict our comparison here to the DGD tolerance. the denoted EOP is the maximum EOP obtained among the 4 tributaries.8-Gb/s RZ-DPSK.6-Gb/s POLMUX-RZ-DQPSK the DGD tolerance is strongly dependent on the inter-pulse delay between the two polarization tributaries.0 ps of DGD. A DGD results in a polarization change across the symbol period. For 85. For high bit rates. With a simulative comparison the influence of the inter-pulse delay on the PMD and nonlinear tolerance of POLMUX-RZ-DQPSK is discussed in more detail. The inset eye diagrams show 165 . which is modeled as linear birefringence. For the POLMUX signals.5 dB decrease in measured Q-factor.6Gb/s POLMUX-RZ-DQPSK. results in a penalty when the signal polarization is not constant (1) over the symbol period or (2) across the optical spectrum. but in the middle of the symbol period. In this case the misalignment between the received polarization and the axis of the PBS does not occur in between two symbols. Hence. For 85. For interleaved polarization tributaries. This is true when the DGD times the center frequency (193.2. When the polarization tributaries are bit-aligned the DGD tolerance is only slightly worse than 42. because the inter-pulse delay has no influence on the optical spectrum. In the case of POLMUX signaling. the EOP is normalized with respect to the back-to-back EOP.8.8-Gb/s RZ-DQPSK shows an increase in DGD tolerance with about a factor of two for 42. with 42. Setting the inter-pulse delay in between both extremes resulted in more stable operation but a ∼0. This clearly shows a relatively low penalty for aligned polarization tributaries and a large increase in penalty when the tributaries are interleaved.2. In the simulations the penalties are denoted through the EOP.4-Gb/s symbol rate. In addition.8-Gb/s RZ-DQPSK as a reference. Figure 8. the DGD tolerance is further reduced by about a factor of two in comparison to bit-aligned 85. on the other hand. In particular the difference between interleaved and bit-aligned POLMUX is not likely to be significantly affected by higher order PMD.8-Gb/s RZ-DPSK and 42. delayed over 17 bits and recombined with orthogonal polarizations. which causes over. it does not include the difference in OSNR requirement for the various modulation formats.6-Gb/s POLMUX-RZ-DQPSK the influence of a wavelength dependent polarization mismatch should be relatively small due to the 21. Long-haul transmission Additionally. The reduced DGD tolerance of interleaved POLMUX-RZ-DQPSK is even more evident from Figure 8. Comparing the DGD tolerance of 42.8-Gb/s RZ-DQPSK [122]. as is the case for bit-aligned polarization tributaries.8-Gb/s RZDPSK and 42. the simulated DGD is chosen such that the output SOP equals the input SOP. 8. Polarization-multiplexed DQPSK 8 6 normalized EOP (dB) normalized EOP (dB) 10 20 30 40 50 5 4 3 2 1 6 4 2 0 0 0 0 10 20 30 40 50 DGD (ps) (a) Optical delay (ps) (b) Figure 8.6-Gb/s POLMUX-RZ-DQPSK. severe overshoots are evident in the middle of the eye diagram which clearly shows the cause of the reduced DGD tolerance.6-Gb/s POLMUX-RZDQPSK with 8-ps DGD. interleaved. bit-aligned 85. For interleaved polarization tributaries on the other hand. EDFA-only amplification is used and the dispersion map is chosen such that it is typical for a transmission link optimized for 10-Gb/s bit rate. the polarization is randomized through random coupling between wave-plates every 1 km.Chapter 8. Table 8.3 Nonlinear tolerance The more constant intensity level of interleaved POLMUX-RZ-DQPSK modulation reduces the impact of nonlinear impairments through a lower peak power.10: (a) Simulated comparison of the DGD tolerance with 42. In the simulated transmission link.6-Gb/s POLMUX-RZ-DQPSK. This increases the EOP to in excess of 4 dB.2.8Gb/s RZ-DQPSK 85.2.1: S IMULATED LINK AND RECEIVER PARAMETERS . To show the relation between nonlinear tolerance and inter-pulse delay we simulate single-channel transmission over an 8x100km link of SSMF. 166 . When the tributaries are bitaligned the DGD mainly results in jitter between consecutive symbols and the penalty is below 1 dB. Dotted lines denote tributaries whereas the denote worst case result among all tributaries. The simulation parameters of the transmission link are listed in Table 8. 8.1 whereas the fiber parameters are the same as denoted in Table 7. 42. (b) normalized EOP as a function of the inter-pulse delay for 85. Link parameters Transmission length 8 x 100 Amplification EDFA Pre-compensation -510 Inline under-compensation 90 Post-compensation 0 unit km ps/nm ps/nm ps/nm the additional degradation for interleaved polarization tributaries.8-Gb/s RZ-DPSK. The eye diagram of 42. for RZ-DPSK the phase demodulation is more ideal in comparison to RZ-DQPSK.11 depicts the simulated eye diagrams for the four considered modulation formats with a 9-dBm input power into each span. From the eye diagrams after balanced detection.8-Gb/s RZ-DQPSK. The variance of the ’1’ rail in the eye diagrams after polarization de-multiplexing is comparable for bit-aligned POLMUX-RZ-DQPSK and 42. However. it follows that the nonlinear tolerance of interleaved 85.8-Gb/s RZ-DPSK. which is not as evident in the POLMUX eye diagrams.6-Gb/s interleaved POLMUX RZ-DQPSK Before pol-demux 47 ps 47 ps After pol-demux before phase demodulation Power (a. Long-haul transmission 85. For bit-aligned POLMUX-RZ-DQPSK. although the bit rate is doubled.2. the nonlin167 .8-Gb/s RZ-DPSK is therefore clearly higher than for both POLMUX and single polarization RZ-DQPSK. respectively.8-Gb/s RZ-DQPSK shows a strong timing jitter.6-Gb/s bit-aligned POLMUX RZ-DQPSK Power (a.11: Simulated eye diagrams.6-Gb/s POLMUX-RZ-DQPSK is slightly better than 42.8-Gb/s RZ-DQPSK. After polarization de-multiplexing. This results in an eye diagram after balanced detection that is wide open despite the broadened ’1’-rail in the phase domain.u) 23 ps 47 ps 47 ps 47 ps After phase demodulation and balanced detection Power (a. Figure 8. on the other hand. After phase demodulation and balanced detection the increased eye closing is evident.u) 23 ps 47 ps 47 ps 47 ps Figure 8. increased broadening of the ’1’-rail is evident for bit-aligned POLMUX.8-Gb/s RZ-DQPSK 85. The received eye diagram of bit-aligned and interleaved POLMUX-RZ-DQPSK before polarization de-multiplexing shows the RZ and quasi CW shape. The reduced jitter for POLMUX-RZ-DQPSK might be due to a more constant spread of the optical power over both polarization modes. This relatively high input power is chosen here to point out the difference in nonlinear tolerance between the modulation formats. which is in agreement with the measured results in Section 6.8-Gb/s RZ-DPSK 42. The nonlinear tolerance of 42. before polarization de-multiplexing as well as before and after phase demodulation and balanced detection. This indicates that.u) 42. the nonlinear tolerance is somewhat reduced compared to 42.8. showing the lower nonlinear tolerance for bit-aligned POLMUX. whereas for interleaved POLMUX a much cleaner RZ shape is obtained. The trade-off between nonlinear and DGD tolerance for interleaved in comparison to bit-aligned POLMUXRZ-DQPSK has significant implications for the use of POLMUX-RZ-DQPSK as a modulation format for long-haul transmission. This also confirms the observation in the experimental results that 85. The dotted horizontal line denotes the penalty obtained for 42. For 85. and worst-case results are denoted here. bit-aligned 85.6-Gb/s POLMUX-RZ-DQPSK has a slightly higher nonlinear tolerance in comparison to 42. 21 symbols).8-Gb/s RZ-DQPSK modulation. In the absence of PMD compensation.5 dB.8-Gb/s RZ-DQPSK is 2. (b) normalized EOP versus inter-pulse delay for a 9-dBm input power. The use of ultra-low PMD fiber would be required to enable long-haul transmission with interleaved POLMUX-RZ-DQPSK and benefit from its higher nonlinear tolerance.8-Gb/s RZ-DQPSK 85.8-Gb/s RZ-DPSK and 42.Chapter 8.6-Gbit/s POLMUX-RZ-DQPSK 10 20 30 40 50 42. interleaved POLMUXRZ-DQPSK transmission can be used to enable long-haul transmission with a high spectral efficiency. Together with PMD compensation. A severe bitpattern dependence is observed in the simulations due to the limited length of the De Bruijn sequence.6-Gb/s POLMUX-RZ-DPSK. Polarization-multiplexed DQPSK ear tolerance could be improved using POLMUX signaling. the difference in input power between 42.12b shows a similar observation when the inter-pulse delay is varied. 17. 16. only the DGD tolerance of bit-aligned POLMUX-RZ-DQPSK seems to be large enough to enable medium or long-haul transmission with realistic fiber PMD coefficients.6Gb/s POLMUX-RZ-DPSK. Figure 8.6-Gb/s POLMUX-RZ-DQPSK with respect to 42. 168 .8 dB for bit-aligned polarization tributaries.12: (a) Simulated comparison of the nonlinear tolerance for 800-km transmission with 42.0 dB for interleaved polarization tributaries and decreased with 1. 42. 12 6 normalized EOP (dB) 10 8 6 4 2 0 0 2 4 6 8 10 12 14 normalized EOP (dB) 5 4 3 2 1 0 0 85. a digital coherent receiver can realize both polarization control as well as PMD compensation simultaneously. Therefore simulations have been conducted with different delay between the two polarization tributaries (13. In addition. Dotted lines denote tributaries whereas denote worst case result among all tributaries.8-Gb/s RZ-DPSK.12a shows the nonlinear tolerance of the four considered modulation formats. For a normalized EOP penalty of 2 dB.8-Gb/s RZ-DQPSK.8-Gbit/s RZ-DQPSK Input power (dBm/ch/span) (a) Optical delay (ps) (b) Figure 8.8-Gb/s RZ-DQPSK the nonlinear tolerance is increased with 1. Since POLMUX signaling requires anyhow polarization control at the receiver the additional effort of PMD compensation does not significantly increase the transponder complexity. interleaved. Figure 8. . the need for active PMD compensation makes it difficult to realize POLMUX signaling at such a symbol rate. For binary modulation formats.800-km (see Chapter 6 and [291]) using terrestrial length fiber spans and over 4. receiver and add-drop points along the link. In addition. However. which often have a limited bandwidth. In particular.55-Gbaud symbol rate.5-Gbaud symbol rate [348. Most other transmission experiments with a high spectral efficiency have been reported using POLMUX-RZ-DQPSK modulation. chromatic dispersion and PMD tolerance are more relaxed for a ∼10-Gbaud symbol rate. For shorter span length.080-km with shorter fiber spans [122].3.5 b/s/Hz [354] and 3.. phase modulator) and receiver. experimental long-haul transmission results have been reported with a spectral efficiency of 0. Using terrestrial length fiber spans. This requires narrow (de-)multiplexing filters with a near rectangular bandwidth profile at the transmitter. making intra-channel nonlinearities the dominant transmission impairment. 349. the OSNR requirement. a transmission distance of 2.2 b/s/Hz [34]. In order to realize a >1-b/s/Hz spectral efficiency. On the other hand. 321] channel spacing is required.8.6-b/s/Hz spectral efficiency using narrowband filtered RZ-DQPSK. respectively. 350. 169 . In addition.700-km [344] and 3. The higher symbol rate poses furthermore challenges to the electrical components in the transmitter (MZM. 349. On the other hand. the main challenge to obtain a high spectral efficiency is the (de-)multiplexing of the ≤ 25-GHz spaced WDM channels.8 b/s/Hz. Yoshikane et. RZ-DQPSK modulation has to be severely bandlimited to reach a 1. al. which might not be practical in the presence of optical add-drop multiplexing. longhaul transmission has been reported over 2. for closely spaced WDM channels the XPM induced crosstalk can be a significant source of transmission impairments. In addition. transmission distances up to 8. 352. In [290]. Transmission with a high spectral efficiency 8. the reduced chromatic dispersion and PMD tolerance at a >40-Gbaud symbol rate will require tunable compensators for most long-haul transmission systems. For a 10.6 b/s/Hz [347. Using less optimal filters results in linear crosstalk between neighboring WDM channels as well asymmetric filtering due to the limited wavelength stability of the laser sources. as common for undersea deployment. 321. the OSNR requirement and nonlinear tolerance might limit the feasible transmission distance. respectively.3 Transmission with a high spectral efficiency We now consider the feasibility of high-spectrally efficient transmission in more detail.. a suitable choice of both the channel spacing and bit rate is necessary. multiplexing and de-multiplexing is significantly relaxed as only a 100-GHz [347. i. 2.2.200-km have been bridged [346]. 2. at 1.e. A higher spectral efficiency of 1-b/s/Hz can be realized using DQPSK modulation and a direct detection receiver [15].0 b/s/Hz [352.8-b/s/Hz spectral efficiency. 353].200-km [345] is feasible for duobinary and RZ-DPSK. showed the feasibility of 1. 348. the wider channel spacing and higher symbol rate increase the walk-off between WDM channels. This shows that a spectral efficiency <1-b/s/Hz can be realized in long-haul transmission systems using a number of different modulation formats. 351].6-b/s/Hz spectral efficiency. The transmission experiments are listed in Table 8.. 354].12. At a 40. For RZ-DQPSK modulation with a 0. 2-b/s/Hz spectral efficiency can be realized using 170.5 SSMF 80 NZDSF 80 SSMF 95 SSMF 65 +D/-D/+D Remarks Company / Ref NICT [347] U.6 1.8 111 85.550 Spans (km) / fiber type 40 -D/+D 100 SSMF 80 SSMF 100 SSMF 100 DSF 81 SSMF 94. TU/e. U NLESS NOTES OTHERWISE ALL EXPERIMENTS USE POLMUX-DQPSK MODULATION . The nonlinear tolerance of a 20. As shown in this chapter.. al.0 1.0 3.8Gb/s POLMUX-DQPSK modulation and a 50-GHz channel spacing.6 1. hence avoiding POLMUX-specific nonlinear impairments.g NZDSF) inter-channel nonlinear impairments might still be significant. This indicates that future 170 ..6 222 170. as intra-channel nonlinear impairments are generally dominant for SSMF-based transmission systems. In [34]. Gnauck et. Paderborn [349] TU/e. Siemens [353] Alcatel-Lucent [351] 2001 2003 2004 2004 2005 2005 2006 2007 2007 2007 2007 EDFA-only EDFA-only EDFA/Raman RZ-DQPSK EDFA-only EDFA/Raman EDFA/Raman EDFA/Raman EDFA/Raman EDFA/Raman EDFA/Raman all-Raman The majority of the deployed WDM transmission systems uses a channel spacing of 50-GHz. TRANSMISSION EXPERIMENTS WITH A SPECTRAL EFFICIENCY Table 8.4 50 40 160 85.700 240 240 2.0 2. showed that a 3..5 1..2 2.2: S ELECTED year bit rate (Gb/s) 160 40 85. Siemens [350] NTT [321] Alcatel-Lucent.375 2.Chapter 8. A symbol rate around 20.30 Gbaud symbol rate also compares favorably with lower symbol rates.6 1.30 Gbaud [350. This limits the penalty due to either XPM or XPolM.6 2.6. NICT. for other fiber types with a lower chromatic dispersion coefficient (e.6 # of WDM channels 40 8 64 14 3 8 40 102 160 10 160 Spectral efficiency (b/s/Hz) 1. 351.6 2.4-Gbaud symbol enables long-haul transmission due to a combination of component maturity and low OSNR requirement.6 Distance (km) 80 200 320 400 200 324 1. Kiel. of Tokyo [355] U. the 21.B / S /H Z . Siemens [348] KDDI [290] CeLight [352] U. Although. Sumitomo [34] CoreOptics. 353] is therefore the most suitable choice to realize high-spectrally efficient transmission with a sound tolerance towards (de)-multiplexing and optical filtering on a 50-GHz WDM grid. Polarization-multiplexed DQPSK ≥1. As OFDM inherently uses multi-level signals at the transmitter. it is more straightforward to use more dense signal constellations. showed OFDM-based POLMUX-QPSK modulation and in [357]. when both tributaries are interleaved the nonlinear tolerance is increased by about 2 dB. Schmidt et. showed the implementation of 4 and 5 bits per symbol using (single-polarization) quadrature amplitude modulation.6-Gb/s POLMUX-RZDQPSK modulation. realizing a 1. al.8. → Using POLMUX-RZ-DQPSK modulation combined with a direct detection receiver. longhaul transmission with a 1.6-Gb/s POLMUX-RZ-DQPSK modulation combined with a direct detection receiver (10−3 BER). this will likely require the use of modulation formats with more than 4 bits per symbol in order to realize a sound tolerance to narrowband optical filtering. However.6-Gb/s POLMUX-RZ-DQPSK modulation is 14. → An optical filter bandwidth of 34-GHz is found to be optimal for 85. al. This shows that long-haul transmission with a >1-b/s/Hz spectral efficiency is feasible over a long-haul transmission distance. In contrast. This shows that the transmission characteristics of POLMUX-RZ-DQPSK modulation are well suited for long-haul transmission as long as PMD is not the dominant transmission impairment. Summary & conclusions high-capacity optical transmission systems might use a spectral efficiency well above 2-b/s/Hz. A potential candidate for modulation with more than 4 bits per symbol is orthogonal frequency division multiplexing (OFDM).6-b/s/Hz spectral efficiency is discussed. For example in [356] Jansen et.6 dB.4.6-Gb/s POLMUX-RZ-DQPSK modulation the feasibility of high spectrally efficient long-haul transmission is discussed in this chapter. → An OSNR requirement of 15. 8. This enables long-haul transmission with cascaded optical filtering in a 50-GHz wavelength grid.8-dB is measured for 85. → For POLMUX modulation. The theoretical OSNR requirements for 85. This allows an increase in nonlinear tolerance when POLMUX signaling is used to double the bit rate. When both POLMUX tributaries are bit-aligned the DGD tolerance is maximized. 171 . the inter-pulse delay has a significant impact on both the DGD tolerance as well as the impact of intra-channel nonlinear impairments.6-b/s/Hz spectral efficiency.4 Summary & conclusions Using direct detected 85.700-km feasible transmission distance and 1. Polarization-multiplexed DQPSK 172 .Chapter 8. 9 Digital direct detection receivers As discussed in Chapters 4 to 8, the choice of the optical modulation format can substantially increase the transmission tolerances in long-haul transmission links. However, no modulation format has the ideal combination of transmission properties. For example, POLMUX-DPSK modulation has an excellent OSNR requirement and nonlinear tolerance but suffers from a reduced PMD tolerance. DQPSK modulation, on the other hand, supports a high PMD tolerance but has a reduced OSNR requirement and lower tolerance against nonlinear impairments. It is therefore advantageous to combine robust optical modulation formats with analog or digital signal processing, as this can further improve transmission tolerances and can negate some of the drawbacks of the modulation format. Digital signal processing can be applied either at the transmitter to pre-distort the optical signal or at the receiver. At the transmitter, digital signal processing can be used to electronically precompensate for chromatic dispersion [358, 359], intra-channel nonlinear impairments [360, 361] or both impairments simultaneously [362]. The main drawback of pre-distortion is the significant reduction in nonlinear tolerance that occurs when chromatic dispersion is fully compensated at the transmitter [363]. Although intra-channel nonlinear impairments can be compensated using pre-distortion, this is not possible for inter-channel nonlinear impairments. In addition, predistortion can not compensate for PMD, which can be a limiting transmission impairment in high bit rate long-haul transmission. This makes pre-distortion a less likely candidate for high bit-rate systems. In this chapter we therefore focus on digital signal processing at the receiver. In the receiver, the applications of digital signal processing are more extensive and includes the compensation of chromatic dispersion, PMD, nonlinear impairments as well as electrical polarization de-multiplexing and improvements in the back-to-back OSNR requirement [364]. To 1 The results described in this chapter are published in c3, c19, c23, c39, c43 173 Chapter 9. Digital direct detection receivers realize most of these receiver-side digital signal processing applications with a minimal performance penalty, the full optical field has to be transferred to the electrical domain. This is the case for a (digital) intra-dyne coherent receiver, as will be discussed in Chapter 10. However, digital signal processing is not limited to coherent receivers. In direct detection receivers, only the amplitude information is transferred to the electrical domain. This reduces the efficiency of digital signal processing, but it can still allow for a significant increase in transmission robustness. A number of different signal processing algorithms can be used together with direct detection receivers, for example: → Linear feed-forward or decision-feedback equalizers → Nonlinear equalizers → Optical field reconstruction algorithms → Maximum likelihood sequence estimation (MLSE) In order to compensate for signal distortions, an equalizer can be used that approximates the inverse of the channel impulse response. The simplest equalizer structure is a linear feed-forward or decision-feedback equalizer [365, 366, 367]. However, such a linear equalizer can only compensate for limited signal distortions as a direct detection receiver is inherently nonlinear due to the squaring function of the photodiode. This can be alleviated through the use of nonlinear equalizers, as shown by Xia et. al. in [368] using structures based on nonlinear Volterra theory. Optical field reconstruction algorithms do not equalize signal impairments but rather generate an improved decision variable. Such algorithms use the amplitude information from the in-phase and quadrature tributary to (partially) reconstruct the optical field in the receiver. This includes multi-symbol phase estimation (MSPE) and field reconstruction based on the inverse tangent of the direct detected components [369]. Once the optical field is reconstructed in the receiver, linear equalizers can be used with higher efficiency. In Section 9.1, MSPE is discussed as a means to improve the OSNR requirement and nonlinear tolerance of D(Q)PSK modulation. MLSE is another approach to increase the tolerance against linear and nonlinear transmission impairments. It improves the decision variable by basing it on a sequence of symbols rather than on a single symbol. MLSE is a more complex, but also a more versatile approach to distortion compensation than a linear equalizer. The use of MLSE can improve the tolerance against chromatic dispersion, PMD and narrowband filtering [19, 20, 370]. In addition, it can under certain conditions improve the tolerance towards nonlinear transmission impairments [74, 75]. MLSE has shown to provide excellent performance when combined with NRZ-OOK and duobinary modulation [371]. In Section 9.2 we discuss the application of MLSE to DPSK and DQPSK modulation. 174 9.1. Multi-symbol phase estimation 9.1 Multi-symbol phase estimation In a direct detection D(Q)PSK receiver, the received signal is demodulated using one or more MZDIs. As discussed in Chapters 4 and 5, this demodulation is suboptimal and results in an OSNR penalty when compared to a coherent receiver. MSPE is a signal processing algorithm that can be used to overcome some of the drawbacks of direct detection and achieve an OSNR requirement close to theoretical optimal performance. It is based on techniques previously proposed for wireless communications [372, 373, 374]. In addition, MSPE can reduce impairments due to nonlinear phase noise and therefore improve the nonlinear tolerance. Section 9.1.1 introduces the concept of MSPE and Section 9.1.2 discusses the MSPE algorithm. The improvement in back-to-back OSNR requirement is subsequently discussed for 10.7-Gb/s DPSK and 42.8-Gb/s DQPSK (Section 9.1.3). In Section 9.1.4 we analyze the implications of a finite laser linewidth to the MSPE demodulation scheme. Finally, in Section 9.1.5 we focuses on reducing the nonlinear phase noise penalty using MSPE demodulation. 9.1.1 Multi-symbol phase estimation MSPE generates an improved decision variable in the electrical domain by using not only the last received symbol but a sequence of the latest received symbols. As this improved decision variable is based on a long sequence of previous symbols, the phase noise in the individual symbols is averaged out. The main difference of the MSPE in comparison to conventional MZDI-based demodulation schemes is therefore that the improved decision variable is less degraded by phase noise. Ideally, the improved decision variable is only impaired by the phase noise of the last received symbol x(k) instead of the last two symbols as is the case with the decision variable x(k)x∗ (k − 1) in a conventional direct detection receiver. Note that this is equal to coherent detection, where the decision variable is also based only on the last received symbol x(k). Hence, MSPE potentially closes the performance gap between direct detection and coherent detection. MSPE demodulates the signal by comparing each symbol from the DPSK signal with the previous symbol of the demodulated sequence. Since the previous symbol is itself based on its predecessor a decision variable is generated that is based on a long sequence of received symbols. In other words, MSPE uses the received in-phase and quadrature components to generate a decision variable that depends recursively on the past received symbols. The recursive algorithm gives a correction term which is added to the conventional decision variable to generate an improved decision variable. In order to make the scheme adaptive and prevent an infinite memory, a forgetting factor w slowly fades out the contribution from previous symbols. Because MSPE is based on interferometric phase demodulation and does not involve a local oscillator, the forgetting factor w can be chosen relatively close to 1 without any performance impairments. The scheme proposed in [374] is based on coherent detection and as such suffers a penalty due to the phase drift of the local oscillator, which limits the highest acceptable value of w. In [375, 376] a similar approach is discussed, which used MZDIs with different bit-delays to generate a more accurate phase estimation in the optical domain. 175 Chapter 9. Digital direct detection receivers Figure 9.1 shows the receiver structure that is required for MSPE demodulation. In order to generate the improved decision variable, the MSPE demodulation scheme requires the phase information in the electrical domain. However, as no coherent detection is applied, the phase information cannot be directly transferred to the electrical domain. This is solved by detecting both the in-phase and quadrature component of the received symbol, which together also contain the phase of the received signal. Hence, two MZDIs are necessary with a π/2 difference in the phase shift between both arms. This is can be either a −π/4 and π/4 phase difference as in a conventional DQPSK receiver or a 0 and π/2 phase difference for the two MZDIs, respectively. MZDI T PD + - data A Rx Recursive algorithm T + - data B Rx Figure 9.1: MSPE receiver structure for either DPSK or DQPSK modulation. The MSPE algorithm can also be used for modulation formats that combine phase and amplitude modulation. This requires a third branch in the receiver with a single-ended photodiode to detect the intensity of the optical field [377]. 9.1.2 The MSPE algorithm The recursive MSPE algorithm is now based on the following principle. Consider a received signal, √ r(t) = Ps exp( j[ω0t + ϕ(t)]), (9.1) √ where Ps exp( jϕ(t)) = xI (t) + j · xQ (t) is the complex envelope of the signal x(t) in the absence of phase noise. After balanced detection and electrical low-pass filtering two components uI (t) and uQ (t) are obtained containing the in-phase and quadrature components, respectively: uI (t) = ℜ{x(t)x∗ (t − ∆T )} uQ (t) = ℑ{x(t)x∗ (t − ∆T )}. (9.2) This can be realized with two MZDIs, one with a phase shift between the arms of ∆φ = 0 and one with a phase shift of ∆φ = π/2 For simplicity we now introduce a time discrete notation where t = kT0 + t , with −T0 /2 ≤ t ≤ T0 /2. Considering the optimal sampling point in the bit interval we assume t = 0 and the signals are further denoted as time discrete samples. The recursive algorithm now replaces the conventional decision variable x(k)x∗ (k − 1) with the improved decision variable x(k)z∗ (k − 1) [374], where x(k) is the currently received symbol. z(k) is a recursive component, z(k − 1) = x(k − 1) + w · exp(+ jc(k − 1)) · z(k − 2), 176 (9.3) 9.1. Multi-symbol phase estimation where 0 ≤ w ≤ 1 is the forgetting factor. The binary factor c(k − 1) rotates the previous symbol z(k − 2) to align it with x(k − 1). However, Equation 9.3 can only be implemented together with coherent detection because not x(k), but only x(k)x∗ (k − 1) is available after demodulation with an MZDI. As a result, Equation 9.3 cannot be directly implemented. The recursive component z(k) in Equation 9.3 is therefore replaced by the following approximation, y(k) = uI (k) + w · u(k) · exp(− jc(k − 1)) · y(k − 1), (9.4) where u(k) = uI (k) + j · uQ (k). Note that the term exp(− jc(k − 1)) is a straightforward multiplication with either −1 or 1, depending on the binary value of c(k − 1). We now show that a similar OSNR requirement can be expected for a receiver that uses either the algorithm in Equations 9.3 or 9.4. When we assume that the MSPE receiver demodulates the correct symbol we can express y(k − 1) as, y(k − 1) = y(k − 1) · exp(− jc(k − 1)). ˜ Equation 9.4 can then be written (for DPSK modulation) as, ˜ y(k) = uI (k) + w · u(k) · y(k − 1). The output of the MZDI u(k) equals x(k)x∗ (k − 1) which changes Equation 9.6 into, ˜ y(k) = ℜ{x(k)x∗ (k − 1)} + w · x(k)x∗ (k − 1) · y(k − 1). (9.7) (9.6) (9.5) We can unroll the recursion in Equation 9.6, but for simplicity we assume that for symbol y(k −1) the conventional and improved decision variable are equal, e.g. y(k − 1) = u(k − 1) = x(k − 1)x∗ (k − 2). Using this approximation in Equation 9.7 results in, ˜ ˜ y(k) ≈ ℜ{x(k)x∗ (k − 1)} + w · x(k)x∗ (k − 1) · x(k − 1)x∗ (k − 2), where x(k) = x(k) · exp(− jc(k)). This gives, ˜ ˜ y(k) ≈ ℜ{x(k)x∗ (k − 1)} + w · x(k)x∗ (k − 2), (9.9) (9.8) The improved decision variable thus consists partly of the most recent symbol x(k) and a contribution from the previous symbols x(k − 1) and x(k − 2). In Equation 9.3 there is no contribution ˜ from previous symbols, and it therefore results in the theoretically optimal performance. The contribution from the previous symbols in Equation 9.4 somewhat impacts the performance of the MSPE algorithm, and this causes the slight difference in OSNR requirement that we will find between MSPE and the theoretically optimal performance of a coherent receiver. In Figure 9.2 the principle of MSPE is visualized using a signal constellation diagram after interferometric demodulation. Combining the in-phase and quadrature components, each received symbol can be considered as a vector in the complex phase plane. In a conventional direct detection receiver, the binary decision would be ’0’ for ℜ{u(k)} < 0 and ’1’ for ℜ{u(k)} > 0. 177 Chapter 9. Digital direct detection receivers Re{u(k)} u(k-2) u(k-1) y(k) Im{u(k)} u(k) Figure 9.2: Generation of the improved decision variable. The MSPE algorithm now constructs an improved decision variable y(k) using the sequence of received symbols in Figure 9.2 such that, y(k) = ℜ{u(k)} + w · u(k) · ℜ{u(k − 1)} (9.10) − w · u(k − 1) · ℜ{u(k − 2)} + w · u(k − 2) · ℜ{u(k − 3)} + ... 2 3 The MSPE demodulation scheme can be implemented with either analog, as discussed here, or digital signal processing [378]. In the case of digital signal processing, the most straightforward implementation is to convert the decision variables uI (k) and uQ (k) into digital samples. Note that the performance of the MSPE demodulation scheme with a digital implementation depends on the granularity of the ADCs, which is not consider here. An analog implementation of the MSPE demodulator for DPSK modulation is shown in Figure 9.3. This implementation requires a complex four-quadrant multiplication, an attenuation to implement the forgetting factor w and a delay line with a bit-delay ∆T to multiply u(k) with the previous decision variable x(k − 1). The improved decision variable c(k) is obtained from the real part of the improved decision variable x(k) after binary decision with a D-flip-flop (D-FF). Note that the upper MZDI on itself demodulates the in-phase tributary of the DPSK signal, which gives the conventional decision variable uI (k) and is therefore equivalent to a conventional direct detection DPSK receiver. 9.1.3 MSPE demodulation for 10.7-Gb/s DPSK & 42.8-Gb/s DQPSK Figure 9.4a shows the improvement in OSNR requirement with MSPE demodulation when only Gaussian noise is present. Simulations are based on the Monte-Carlo approach with a random bit sequence of 5 · 106 bits. The simulated BER is compared for a 10−4 BER because lower BERs are impractical to simulate using the Monte-Carlo approach. The sensitivity improvement due to MSPE increases for higher values of the forgetting factor w, approaching the performance of coherent detection with differential decoding. For a 10−4 BER, the difference between MSPE (w = 0.9) and conventional direct detection is ∼0.5 dB. The difference between MSPE (w = 0.9) and differential coherent detection is negligible, effectively closing the gap in OSNR requirement between coherent detection and direct detection. 178 9.5. An analog implementation of the MSPE demodulator for DQPSK modulation is shown in Figure 9. j.4b shows the performance of the MSPE demodulation scheme with DQPSK modulation when only Gaussian noise is present. The ±1 multipliers are exchanged with a complex ±1 multiplier because both the cI (k) and cQ (k) outputs have to be taken into account and c(k) now takes a value of the set {1. two MZDIs are necessary to demodulate the signal.3: Implementation of the MSPE algorithm for DPSK. MSPE with w = 0. differential coherent detection MSPE The MSPE demodulation scheme can be easily extended to DQPSK modulation. MSPE with w = 0. − j}. Monte-Carlo 179 .9. Multi-symbol phase estimation Re{y(k)} MZDI T PD + x(k) MZDI T ~ ~ uI(k) uQ(k) w + T D. -2 8 FEC limit log(BER) -3 0.7-Gb/s DPSK and (b) 42. √ Note that the forgetting factor w now has to be scaled with a factor 2.8 dB 11 12 -5 13 -6 8 10 12 OSNR (dB/0. the quadrature part of the signal is used to obtain the second output cQ (k) from the imaginary part of the improved decision variable y(k).4: Performance of (a) 10.1.1 nm) 14 -4 (a) (b) Figure 9. conventional direct detection with w = 0. the overhead of using MSPE in combination with DQPSK modulation is limited to (potentially inexpensive) electronic signal processing. Similar to the results for DPSK modulation.2. Similar to a conventional direct detection DQPSK receiver.8-Gb/s DQPSK modulation with MSPE for Gaussian noise and several values of the forgetting factor w. Figure 9. −1.output FF +/-1 multiplier +/-1 multiplier - Complex four quadrant multiplier PD + /2 ~ ~ + + c(k) w Im{y(k)} T Figure 9.5 dB 11 -4 12 -5 13 -6 2 3 4 5 6 OSNR (dB) 7 8 9 Q (dB) 10 -2 8 FEC limit log(BER) -3 9 Q (dB) 10 1.5. Hence. The optical components necessary to realize the MSPE demodulation scheme are the equal to a conventional DQPSK receiver. In comparison to the MSPE implementation for DPSK. 8 dB for a 10−4 BER. When the phase noise between those symbols is uncorrelated (zero mean) the estimate will be improved by using more symbols. the phase noise resulting from a finite laser linewidth is correlated and therefore does not average out when more symbols are taken into account.Q w 2 T Im{y(k)} Figure 9. However.Chapter 9. for example. Digital direct detection receivers Re{y(k)} MZDI T PD + w - 2 - T + + D.1.7-Gb/s bit rate. At a 10. The performance gain with MSPE demodulation is considerably larger due to the larger theoretical difference between coherent and direct detection DQPSK. simulations are used and every point is simulated with a 2 · 106 symbols long random sequence.2-dB difference with respect to coherent detection (with differential decoding). For MSPE with w = 0. The phase noise of a Lorentzian-shaped laser linewidth can be described as a random walk Wiener process using φPN (t) = 180 m=t m=−∞ ∑ νm . 9.5: Implementation of the MSPE algorithm for DQPSK. Savory and Hadjifotiou derived for a similar penalty the maximum allowable linewidth with DQPSK modulation and a self-homodyne receiver. only the phase difference between two subsequent symbols determines the sensitivity penalty. When one considers that the same optical components and nearly the same signal processing is required for MSPE with either DPSK or DQPSK modulation.1 multiplier ~ ~ uI(k) uQ(k) + x(k) MZDI T Complex four quadrant multiplier PD + /2 ~ ~ + + + - cQ(k) DFF output .output .4 Laser linewidth requirements PSK modulation is generally sensitive to phase noise. MSPE uses a sequences of symbols to compute the improved decision variable. which is only a 0. the difference amounts to 1.9. which equals 8 MHz [380].5-dB OSNR penalty the transmitter laser requires a linewidth less than 30-MHz linewidth [379]. With conventional direct detection. DQPSK seems to be the most logical application of MSPE demodulation. Standard DFB lasers can have a linewidth in the order of 1-3 MHz [381]. (9. This makes direct detection robust against phase noise.11) . resulting from a finite laser linewidth.7-Gb/s bit rate and for a 0. which is sufficient for both DPSK and DQPSK direct detection at a 10.I FF cI(k) Complex +/. the number of symbols that is taken into account to compute the decision variable depends strongly on the forgetting factor. respectively. 2π∆νT0 ). With MSPE demodulation. When we scale this to a 42. as shown in Figure 9. However. And for a 2-dB penalty.5 MHz (for a 1-dB penalty).5.7Gb/s DPSK. the forgetting factor is upper bounded. such lasers are generally not used in conventional optical transponders as it is difficult to realize full C-band tunable ECL. φPN (t) = φPN (t − T0 ) + N(0.5-dB penalty). This is a significant reduction in comparison to conventional direct detection. when a w ∼ 0. In the time discrete simulations the laser linewidth is now modeled as random walk phase noise [383].9 forgetting factor.8-Gb/s DQPSK modulation the linewidth requirements are significantly higher. Norimatsu derived in [384] that both transmitter and LO laser require a laser linewidth below 8 MHz. ∆ν is the beat linewidth. In [385]. When the laser linewidth is not negligible. generally.8 MHz. it can be beneficial to make the forgetting factor w adaptive in order to obtain the maximum performance for a certain laser linewidth. A too high linewidth will result in a performance penalty because linewidth-induced phase noise reduces the accuracy of the improved decision variable. the linewidth requirement increases to 10 MHz by sufficiently lowering the forgetting factor to ∼ w = = 0. (9. For 42. Barry and Kahn reported that a beat linewidth lower than 500 kHz is required (at 5-Gbaud and for a 0. requires a much narrower linewidth compared to direct detection. we obtain 500 kHz or 1 MHz for 10-Gbaud POLMUX-QPSK and 20-Gbaud QPSK modulation. which is similar to the requirement for MSPE. For coherent detection. For 42. Multi-symbol phase estimation where νm are independently Gaussian distributed random variables with zero mean and variance σ 2 = 2π∆νT0 . σ 2 ) is a Gaussian distribution random variable. For 10-Gbaud (D)PSK modulation and a 0. This tolerance is not sufficient to use standard DFB lasers and an analog coherent receiver requires therefore ECL. We can compare the linewidth tolerance of MSPE with (analog) coherent detection.4 MHz is reported for a 1-dB OSNR penalty at 10−3 BER [382]. but the tolerance is still sufficient to use a typical DFB laser.13) sPN (t) = s(t)exp[iφPN (t)]. Figure 9. Coherent detection therefore. a too high laser linewidth results in phase noise degradations through beating between transmitter and local oscillator (LO) laser. A laser linewidth lower than ∼4 MHz is required for a w = 0.8 = forgetting factor is used the linewidth tolerance increases to ∼3 MHz.8-Gb/s POLMUX-QPSK with a digital coherent receiver. and T0 is the symbol period [382]. a beat linewidth of 1. However.9.5-dB sensitivity penalty.1. The phase-noise degraded signal is then defined according to.9 forgetting factor the maximum allowable linewidth is now 1. With the exception that MSPE uses only a transmitter laser whereas for digital coherent detection the 181 .12) where N(0. With ECL a linewidth below 200 kHz is feasible [386]. which is the sum of the 3-dB linewidth of the signal and LO lasers. This implies that both the transmitter and LO laser require a laser linewidth narrower than 250 kHz. Digital coherent detection is largely similar in terms of its tolerance against laser linewidth.6b. For coherent detection of QPSK. (9.6a shows the performance of MSPE as a function of laser linewidth for 10. Scaling this to a 20-Gbaud symbol rate gives a beat linewidth of 2. For a w = 0. the allowable laser linewidth is reduced even further. Hence.8-Gb/s bit rate. Simulated is single channel transmission over 30 x 90-km spans with the ASE added along the transmission line.8-Gb/s DQPSK modulation with MSPE for different laser linewidth and several values of the forgetting factor w.3 W−1 km−1 .5.7-Gb/s DPSK and (b) 42. Another advantage of the nonlinear phase noise reduction through MSPE is that it is unimportant what the source of the phase noise is.8. With MSPE. nonlinear phase noise can also degrades signal quality in PSK systems. conventional direct detection.9.1. MSPE with w = 0.7-Gb/s DPSK the performance improvement of MSPE in the presence of nonlinear phase noise. which averages out the phase uncertainty over a long sequence of received symbols. 9. Another detection scheme that is very tolerant to laser linewidth is proposed in [387]. Digital direct detection receivers beat linewidth is divided over the LO and transmitter laser. as long as the noise sequence is uncorrelated and has a zero-mean distribution. where a LO is used in combination with differential detection. Figure 9. MSPE with w = 0. For low 182 .2. MSPE with w = 0. Fiber attenuation is α = 0.5 Nonlinear phase noise compensation Besides a finite laser linewidth.7a shows for 10.7.6: Performance of (a) 10. the impact of XPM induced nonlinear phase noise is also reduced through the use of MSPE. the influence of dispersion is neglected for simplicity [95]. -2 8 -2 8 FEC limit FEC limit 9 9 10 11 Q (dB) -3 log(BER) Q (dB) log(BER) -3 10 11 -4 12 -5 13 -6 -7 -1 10 14 10 10 Laser Linewidth (MHz) 0 1 -4 12 -5 -1 10 10 10 Laser Linewidth (MHz) 0 1 10 2 10 2 (a) (b) Figure 9. which can significantly reduce the associated penalty. This can for example be important for D(Q)PSK transmission in the presence of co-propagating OOK modulated channels [293].4.25 dB/km and fiber nonlinearity γ = 1. Hence. The reduction of nonlinear phase noise through MSPE results from the recursive decision variable. as discussed in Section 2. MSPE therefore potentially halves the magnitude of nonlinear phase noise. However. MSPE reduces the influence of phase noise in general. the decision variable ideally only depends on a single symbol x(k) instead of x(k)x∗ (k − 1) as for interferometric demodulation. the noise figure of the in-line amplifiers along the link is changed. MSPE with w = 0.Chapter 9. Compensation schemes that use the correlation between intensity and nonlinear phase shift in the received symbol are restricted to compensation of SPM induced nonlinear phase noise. In order to change the OSNR. However this scheme comes at the cost of an >3 dB increase in OSNR requirement. 6 dB and 13.1 nm) BER = 10 -4 Input power (dBm/span) (b) Figure 9. MSPE with w = 0. which gives a 1.7-Gb/s DPSK and 42.8-Gb/s DQPSK modulation.7.9) the required OSNR is only 6. for MSPE (w=0. which is also observed in the back-to-back case. When chromatic dispersion is included. differential coherent detection.1.1 dBm to 3.9 dB.7b further shows that the different in nonlinear tolerance between DPSK and DQPSK is 0.1 dB BER = 10 -4 Required OSNR (db/0. The same link parameters are used as in Figure 9.4 results from the interaction between fiber nonlinearity and chromatic dispersion.2.1 dB comparable to the performance gain in the presence of only Gaussian noise. This indicates that the lack of an improvement in nonlinear tolerance through MSPE demodulation is a result of the smaller impact of nonlinear phase noise for 42. with a 3-dBm input power per span.6 dBm per span. Alternatively.1 dBm per span.7-Gb/s DPSK modulation is a result of the lower OSNR along the link.7-Gb/s DPSK. MSPE with w = 0.8-Gb/s DQPSK signal with nonlinear phase noise.5 dB between MSPE and conventional direct detection. This indicates that the larger difference observed in Section 5. we can define the nonlinear tolerance as the input power for which a 3-dB OSNR penalty is obtained. The received OSNR is 5. the required OSNR for the conventional direct detection receiver is 8. Comparing the two constellation diagrams shows a significantly larger nonlinear phase noise impact in the case of 10. which result backto-back in a BER of 10−4 . the performance of MSPE in the presence of nonlinear phase noise is shown in Figure 9. conventional direct detection MSPE with w = 0.8. The link parameters used in the simulation are the same as for 10.7: Nonlinear tolerance of (a) 10. For 42. The MSPE improvement with (w = 0.7a and 9.7-Gb/s DPSK and (b) 42.1 dB.8 dB improvement over conventional direct detection.5. When the input power is increased to 2. input power the simulated OSNR requirement differs 0. Comparing Figures 9. We note that the simulations discussed here do not include chromatic dispersion and therefore only the reduction in nonlinear phase noise is observed.8-Gb/s DQPSK transmission. However.8 dB 0.7-dB (3-dB penalty). This can be understood from the constellation diagrams in Figure 9.8 dB 2. despite the fact that the nonlinear phase shift is the same for both cases. Multi-symbol phase estimation 18 24 22 20 18 16 14 12 10 -8 -6 -4 -2 0 2 4 6 8 1. as experimentally shown by Lui 183 . the improvement in nonlinear tolerance can be more significant.1 nm) 16 14 12 10 8 6 4 -6 1.9) for a 10−4 BER is with 2.8 dB (for a 3-dB OSNR penalty). In this case MSPE increases the nonlinear tolerance from 2.9. The more pronounced impact of nonlinear phase noise for 10.9. respectively.5 dB -4 -2 0 2 4 6 8 Input power (dBm/span) (a) Required OSNR (dB/0. rather than from nonlinear phase noise.7b.8-Gb/s DQPSK with MSPE and several values of the forgetting factor w.7-Gb/s DPSK. which show a 10. Chapter 9. Digital direct detection receivers 10-3 Probability 10-3 Probability Im(E) Im(E) 10-4 10-5 10-6 10-4 10-5 10-6 Re(E) (a) Re(E) (b) Figure 9. To improve the performance of MLSE with DPSK modulation.1 we introduce the principle of MLSE and a Viterbi receiver. Finally. 9.9a shows a received OOK modulated sequence with significant chromatic dispersion induced pulse broadening. As this difference is deterministic. This has been shown to provide an improvement of the nonlinear tolerance when a digital coherent receiver is used [256].2.2.1 The MLSE algorithm Figure 9. A maximum likelihood sequence estimation (MLSE) receiver searches for the transmitted sequence that has the highest probability of producing the received sequence. This implies that the ’0’ amplitude differs depending on the two surrounding symbols and will be higher for a ’101’ than for a ’001’ sequence (e.2. et. This allows for simpler system design and can alleviate the need for optical compensation of these transmission impairments.2. al. in [378]. for DQPSK modulation we discuss in Section 9.g. 9.2. In Section 9.2 and 9.4) or partial DPSK (Section 9. A further improvement in nonlinear tolerance might be realized by combining MSPE with a nonlinear phase noise compensation scheme that employs the correlation between intensity and nonlinear phase shift. at 6T ).6) can be used. Subsequently.8: Simulated constellation diagrams of (a) DPSK and (b) DQPSK modulation with nonlinear phase noise.2.2.2 Maximum likelihood sequence estimation Arguably the most important application of signal processing in an optical receiver is increasing the tolerance with respect to (linear) transmission impairments such as chromatic dispersion and PMD. respectively. The amplitude of the middle ’0’ of a ’101’ sequence (at 4T ) is broadened through the ISI of the trailing and leading ’1’s. either joint-decision MLSE (Section 9.3 we discuss the performance of MLSE with OOK and DPSK modulation. the receiver can assign a different 184 . in Sections 9.7 the use of joint-symbol MLSE. Such a receiver is therefore the theoretically optimal receiver for a transmission channel with ISI. . The term argmax(P(rk |Ai )) defines the value of Ai that maximizes P(rk ).g. i (9. e. the number of surrounding symbols that is taken into account. This simplifies Equation 9. State Transition 000 0 10 001 101 010 110 01 1 111 Amplitude 1 0 1 > 010 10 1 > 100 0 4T 00 01 10 00 01 10 11 T 00 01 10 11 2T 00 01 10 11 nT 0 T 1 2T 1 3T 1 5T 0 6T 0 Time 7T 11 (a) (b) Figure 9.14 to. with the surrounding symbols as the condition. For example. ˆ A= 0 1 P(rk |A0 ) > P(rk |A1 ) otherwise (9. According to Bayer’s theorem of probability. . AN } consists of N possible symbols and each symbol is transmitted with an equal probability 1/N. if the PDF takes only the two surrounding symbols into account. This can be described using conditional probability density functions (PDF). for a binary signal A = {0.9.g. P(Ai |rk ) > P(A j |rk ) ∀ i = j. The signal’s alphabet A = {A1 . with −T0 /2 ≤ t ≤ T0 /2. Maximum likelihood sequence estimation probability to each of the possible received sequences as a function of the received amplitude in the ’0’. . N. because the decision is made after receiving the sample rk [388].9: (a) Deterministic ISI resulting from chromatic dispersion and (b) trellis diagram with 4 states. 2. . To discuss the concept of MLSE we first consider a channel with no memory.2. A2 . Note that the alphabet size is defined through the bits per symbol of the modulation format (e. The a posteriori probability P(Ai |rk ) can now be defined as the probability that the symbol Ai is transmitted when the sample rk is detected. . 1} the decision can then be written as. the a posteriori probability can be written as. (9. which contains K samples taken from the continuous received signal r(t) at sample points t = kT0 + t . (9.14) This is known as the a posteriori probability. ˆ A = argmax(P(rk |Ai )) ∀ i = 1. P(rk |Ai ) · P(Ai ) P(Ai |rk ) = . The received sequences is a vector r(k). The optimal decision then looks for the symbol that has the maximum a posteriori probability among all of the symbols in the alphabet A.15) P(rk ) The terms P(rk ) and P(Ai ) are equal for all a posteriori probabilities and can therefore be neglected. . 2 for OOK/DPSK and 4 for DQPSK). For example.17) 185 . .16) where P(rk |Ai ) is the probability that rk is received when the symbol Ai is transmitted. . it assumes that the channel has an impulse response of three symbol periods. The accuracy in which the PDF models the channel characteristics is determined by the channel memory. the metric of the state transition mi (k) can be expressed as. 186 (9. . The MLSE estimation process is therefore based on the Viterbi algorithm as first proposed by Forney in 1972 [389]. Each transition mi (k) in the trellis diagram is associated with one of the PDFs of the channel. the a posteriori probabilities for each state transition at each quantization level P(r|Si ) are determined. . Alternatively. The natural logarithm function is monotonic and Equation 9. This can be simplified by changing the multiplication into a summation by taking the natural logarithm function of the a posteriori probability. This is possible through different algorithms of which we use here both the histograms method and the Gaussian model method. Digital direct detection receivers This is equal to the decision of a conventional CDR receiver as discussed in Section 3. the channel histogram is used to find the conditional probability P(rk |Si ) associated with each of the channels conditional PDFs. This is possible by training the MLSE with a known sequence. The look-up tables are then used to compute the metric for each of the transitions in the trellis. which is the probability that the sample rk represents a ’1’ symbol.19) Equation 9. ˆ S = argmax( ∏ P(rk |Ak )) ∀ i = 1.Chapter 9. 2. i i k=1 K (9. This increases exponentially with the length of the sequence and the alphabet size. which contains a total of 2Q · N L+1 values. Subsequently. . N. preceded and followed by ’0’ symbols. i i k=1 K (9. For instance. mi (k) = m j (k − 1) + ln[P(rk |Si )]. . N. Once the PDFs are obtained this information can be used to calculate the metrics of the trellis’s state transitions.2. . which is not practical. This can be written as. .20) . The histograms are stored in a look-up table. To make the optimum decision on a received symbol. The trellis diagram has 22 possible states and 23 state transitions. blind estimation can be used through feedback signals from the forward error correction or more advanced blind channel estimation algorithms [390].19 implies that N K sequences have to be taken into account to determine the maximum a posteriori probability. For example.1. ˆ S = argmax( ∑ ln[P(rk |Ak )]) ∀ i = 1.18) ˆ where S is the sequence with the maximum a posteriori probability and Ak is the set of all the i possible symbols representing sample r(k). The Viterbi algorithm can be represented by means of a trellis diagram that consists of N L states and N L+1 states transitions. where N is the alphabet size and L is the memory length. . . MLSE requires that the PDFs correctly represent the distortions in the optical channel. Figure 9. which gives the PDFs or histograms [391].18 can now be rewritten as. for L = 2 the transition ’010’ is associated with the PDF P(rk |010). After sample k is received and quantized with quantization level rk . but rather the received sequence in order to obtain the maximum a posteriori probability decision. 2. which are quantized with a vertical resolution of Q bits.9b shows an example of a trellis diagram for a two bit channel memory and binary modulation. This means that a received ’1’ has four different conditional PDF functions. An MLSE receiver does not consider only the received symbol. The histograms technique builds discrete PDFs for all of the possible transitions in the trellis diagram. N. Maximum likelihood sequence estimation where m j (k − 1) is the metric of the transition that leads to state Si . This implies that using the Viterbi algorithm.10: MLSE histograms for (a) 0-ps/nm chromatic dispersion and (b) 2000-ps/nm chromatic dispersion. S = argmax ∑ ln( √ 2σi2 2πσi i k=1 (9.22) The Gaussian model method assumes that the sample belongs to the state Si of which the mean is nearest to the received sample rk [392]. where the x-axis represents the quantization bins for a 4-bit vertical resolution. Equation 9. .06 0.10b depict two examples of histograms.10a and 9. each having a different total metric and a different path through the trellis. the complexity is reduced from searching through N K down to K · N L+1 sequences. This method determines the sequence that maximizes the Gaussian a posteriori probability defined as.05 0 10 Quant 15 ization bins 5 Y X 1 1 11 10110 1 0 00 on 01011 siti 00 n 000 1 Tra 1 1 11 10110 1 0 00 on 01011 siti 001 an 000 Tr (a) (b) Figure 9. When the variance of all PDFs is assumed to be equal.02 0 10 Quant 15 ization bins 5 Y X Z Probability 0.9. Figures 9. . . The y-axis shows the transitions in the trellis diagram for a channel with a 2-symbol memory.21 can be simplified into. . Z Probability 0. 2. respectively. 2. . K 1 (rk − µi )2 ˆ exp(− )) ∀ i = 1. Repeating this procedure for K samples results in N L surviving paths.2. N.1 0. . For each of the N L states in the trellis. The z-axis shows the probability for each quantization bin/transition. Minimizing the sum of these distances for K successive samples maximizes the probability that the sequence has been correctly estimated. while the others are canceled out. The trellis path of the sequence with the maximum probability is considered to represent the maximum likelihood sequence. Only the 187 . i k=1 K (9. ˆ S = argmin ∑ (rk − µi )2 ∀ i = 1. and σi is the PDF variance. for back-to-back and 2000 ps/nm of chromatic dispersion.04 0. the metrics of the N incoming paths are compared and the path with the highest metric survives.21) where µi is the mean of the Gaussian PDF associated with state transition mi . . . The Gaussian model method uses a somewhat simpler channel model as it assumes that the PDF functions associated with a specific channel have Gaussian distributions. Digital direct detection receivers mean of each of the PDFs is now extracted from the training sequence and a total of N L+1 values are stored in the look-up table.k |Ak )] i H h=1 H ∀ i = 1.7-Gb/s 231 − 1 PRBS to generate NRZ-OOK modulation.12b shows that the use of an MLSE receiver also significantly improves the DGD tolerance. the tolerance increases to ±2000 ps/nm for a 2-dB OSNR penalty. At the transmitter side. It is therefore advantageous to sample at a multiple of the baud rate in an MLSE receiver. .7-Gb/s OOK modulation. . .24) where H is the number of samples per symbol. either a conventional threshold CDR or an MLSE receiver is used.11. the signal is filtered with a CSF having a 27-GHz 3-dB bandwidth.12a shows the measured chromatic dispersion tolerance of the MLSE receiver compared with the CDR receiver. Hence. 9.Chapter 9. as shown by Poggiolini et. The channel model is based on the analysis of amplitude histograms. The real-time MLSE receiver has a 3-bit ADC with a twofold over-sampling rate of 21.2 MLSE combined with OOK For 10. a MZM is driven with a 10. the MLSE receiver outperforms the threshold CDR receiver by more than a factor of two. Hence. (9. Figures 9. MLSE can substantially increase the tolerance against linear transmission impairments [19]. Equations 9. al. Note that this increases the size of the lookup table but does not change the size of the trellis. The chromatic dispersion tolerance of 10. respectively. For MLSE receivers without over-sampling. This is verified using the experimental setup depicted in Figure 9.11c depict the CDR and MLSE receiver. Figure 9. ˆ S = argmax ∑ i K k=1 h=1 ∑ ln[P(rh. After detection with a single-ended photodiode.4 Gsample/s and a 2-bit channel memory [19]. the most significant 188 . At the receiver. Sampling at twice the baud rate (H=2) is generally used in the literature. 395]. Chromatic dispersion between -4500 ps/nm and 4500 ps/nm is subsequently added to the signal using SSMF and DCF of different lengths.k |Si )]. while a low input power (<5 dBm) is used to avoid nonlinear impairments. An MLSE receiver with two-fold over-sampling can tolerate an arbitrary amount of chromatic dispersion given that it uses a sufficiently large channel memory. the Gaussian model method is somewhat less complex in comparison to the histogram technique.11b and 9. 2.2.23) mi (k) = m j (k − 1) + ∑ ln[P(rh. Figure 9.20 then changes into. The assumption that all PDFs have the same variance is generally valid in the presence of significant signal distortions. in [393].19 and 9. . N (9. The DGD is measured by splitting the signal in two orthogonal polarizations with equal power and recombining them with a time delay between 0 ps and 200 ps. But combined with the MLSE receiver. However.7-Gb/s NRZ-OOK is ±800 ps/nm for a 2-dB OSNR penalty. the dispersion tolerance can be increased through narrowband optical filtering in the receiver [394. An additional property of electronic equalization is that only limited signal distortions can be tolerated using baud rate sampling (1 sample per symbol)[392]. This shows that the 3-dB benefit of DPSK with 189 . DPSK with balanced detection and CDR receiver. Maximum likelihood sequence estimation improvement occurs only when the allowable OSNR penalty is in excess of 6 dB where the DGD tolerance is doubled.12a depicts the measured dispersion tolerance of MLSE combined with DPSK modulation. When we compare the performance of DPSK with a CDR and MLSE receiver. 20 Required OSNR (dB/0. OOK with CDR receiver.3 MLSE combined with DPSK The improved chromatic dispersion and DGD tolerance of an MLSE receiver would be ideally combined with DPSK modulation. The experimental setup depicted in Figure 9. (b) conventional CDR receiver and (c) MLSE receiver.16 is used to evaluate MLSE with DPSK modulation and Figure 9. OOK with MLSE receiver. This would combine the high tolerance against linear impairments of MLSE with the improved OSNR requirement and nonlinear tolerance of DPSK. no performance improvement is measured between 0 ps/nm to 1600 ps/nm of chromatic dispersion.1 nm) 18 16 14 12 10 8 6 -4500 -3000 -1500 BER = 10-3 0 1500 3000 4500 Required OSNR (dB/0.9. a 30% improvement over a conventional CDR receiver. balanced detection and MLSE receiver.12: Measured OSNR requirement versus (a) chromatic dispersion and (b) differential group delay.1 nm) 20 18 16 14 12 10 8 BER = 10-3 6 0 20 40 60 80 100 120 140 160 180 Chromatic dispersion (ps/nm) (a) Differential group delay (ps) (b) Figure 9. For higher chromatic dispersion the improvement is small and approaches the results obtained with NRZ-OOK modulation. This shows that the improvement in dispersion tolerance that is observed for OOK is not replicated for DPSK modulation. data Tx (a) laser MZM (b) r(t) PD CD DGD VOA 27-GHz CSF ~ ~ ~ r(t) ~ ~ CDR BERT (c) r(t) PD ~ ~ A/D MLSE BERT Figure 9. For a 2-dB OSNR penalty the allowable DGD is 60 ps. DPSK with 9.2.11: (a) Experimental setup.2. Figure 9. Hence.Chapter 9. The eye diagrams are complemented with simulated PDF histograms of the signal samples and the simulation parameters are set according to the measurement conditions. the 3-dB benefit of DPSK remains when using an MLSE receiver. For 2400-ps/nm chromatic dispersion. and therefore the 3-dB OSNR benefit of DPSK. balanced detection fades away when chromatic dispersion is the dominant impairment. For DGD. the majority of the samples shift towards the middle of the histogram.13: Simulated PDF histograms of signal samples. Figure 9. As chromatic dispersion becomes more dominant.5. (b) 2400-ps/nm chromatic dispersion and (c) 140-ps differential group delay. even when used together with an MLSE receiver. The insignificant advantage of MLSE combined with DPSK modulation was also reported in [396]. Figure 9.13a shows that back-to-back the eye diagram is wide open and the samples have a high probability in the normalized voltage range around 1 and -1. This is particulary true for the destructive signal component.12b shows that when the DGD tolerance is considered. the samples are concentrated with a high probability around a voltage of -0.2. Figure 9. on the other hand. 190 . the constructive and destructive outputs of the MZDI are correlated to a lesser degree which preserves more of the symbol distance. reducing the symbol distance that is the basis for the 3-dB OSNR benefit of DPSK. In contrast.5 and 0. which confirms the difference in dispersion tolerance of the constructive and destructive components as discussed in Section 4.13 shows measured eye diagrams at the output of the balanced photodiode in the presence of significant chromatic dispersion and DGD. However.3. Digital direct detection receivers Eye diagram after balanced detection Signal constellation Re PDF histograms Normalized voltage (a) Backto-back Im Probability Normalized voltage Re (b) 2400-ps/nm chromatic dispersion Im Probability Normalized voltage (c) 140-ps DGD Im Probability Figure 9. measured eye diagrams at the output of the balanced photodiode and signal constellation for (a) back-to-back.12c shows that for 140 ps the eye is highly distorted which confirms the high measured OSNR penalty. in contrary to chromatic dispersion there is still a high probability that the samples occur around ±1 in the histogram. the duobinary modulation of the constructive components improves the dispersion tolerance. constructive. more severely distorted.2. which in turn results in a higher OSNR requirement.14a). 9. The lower dispersion tolerance of the destructive component closes the eye diagram after balanced detection. separately (Figure 9.4 Joint-decision MLSE To overcome the low chromatic dispersion tolerance of D(Q)PSK combined with MLSE.u) Back-to-back 1510 ps/nm Required OSNR (dB/0. This confirms that in the presence of chromatic dispersion the destructive component is. This is similar to the difference in chromatic dispersion tolerance as observed with a CDR receiver (see Section 4. JD-MLSE is characterized by having more than one input into the MLSE receiver in order to provide it with additional information about the signal. Hence. in the presence of >1200 ps/nm chromatic dispersion. A joint-decision MLSE can thus be considered as a two input. al.1 nm) 93 ps 93 ps Chromatic dispersion (ps/nm) (a) (b) Figure 9.5). 191 . As a result of this correlation. which reduces the MLSE performance.2. this does not explain why. the constructive and destructive component partially cancel each other out with balanced detection. destructive. This reduces the signal power. Cavallari et. However.u) Power (a. We conjecture that this results from a correlation between the constructive and destructive components in the presence of chromatic dispersion.14: (a) Experimental comparison of DPSK with single-ended or balanced detection input to the MLSE receiver. Maximum likelihood sequence estimation 18 16 14 12 10 8 BER = 10-4 -3000 -2000 -1000 0 1000 2000 3000 93 ps 93 ps Power (a.3. balanced detection and (b) measured eye diagrams comparing constructive (upper row) and destructive (lower row) components back-to-back and with chromatic dispersion. we measure the dispersion tolerance of the constructive and destructive ports. Figure 9.14b show measured eye diagrams of the constructive and destructive components for back-to-back and with 1900 ps/nm of chromatic dispersion. proposed in [397] the use of joint-decision MLSE (JD-MLSE). The destructive component clearly shows a smaller dispersion tolerance than the constructive component. in comparison to the constructive component. whereas the AMI modulation on the destructive components broadens the optical spectrum and results in a lower dispersion tolerance. To better understand the ineffectiveness of MLSE with DPSK modulation. the OSNR requirement with balanced detection is worse compared to the constructive component.9. k k The principle of JD-MLSE is similar to the histograms method. another degree of confinement is added to the conditional PDF. where the y-axis represents the quantization bins for the second input. However. But the JD-MLSE constructs N L+1 3-dimensional discrete PDFs instead of the conventional 2-dimensional PDFs used in the histograms method.01 0 15 Z Y X Qu ant 10 iz for ation 5 inp ut bins 1 15 bins 5 ation 2 n t iz Qua r input fo 10 Figure 9.03 0. u− k u+ k 0. JD-MLSE therefore requires a significantly larger look-up table to compute the trellis metrics. u+ |Si )]. which now has to store the 3-dimensional PDFs. In addition slightly more hardware is required. The z-axis gives the probability for each point in this 2-dimensional plane. In addition. the trellis diagram has the same complexity for the conventional MLSE with balanced detection (B-MLSE) and JD-MLSE. k k i k=1 K (9. when two different signals (carrying the same information) are input into the JD-MLSE. 192 . since both methods build discrete PDFs containing the probability of occurrence for each state transition.Chapter 9. Digital direct detection receivers single output receiver. the two inputs of the JD-MLSE are the constructive and destructive output ports of the MZDI. Obviously. when the two input signals are the same. as two ADC are necessary to convert the received signals into the digital domain. u+ |Si ) is the a posteriori k k probability that samples u− and u+ are received when the state Si is transmitted [397]. The JD-MLSE therefore maximizes the a posteriori probability. to a total of 4Q · N L+1 values.02 0. ˆ S = argmax ∑ ln[P(u− .15: Joint-decision MLSE histogram for transition ’010’ with 2000-ps/nm chromatic dispersion. the PDF will be symmetric with respect to the x and y-axis. In the case of DPSK modulation. This increases the required training sequence length or the accuracy of the blind estimation algorithms.04 0. The x-axis represents the quantization bins for the first input.25) where and represent the constructive and destructive components of the demodulated DPSK signal that are used as input sequences of the JD-MLSE. more information is necessary to compute the PDFs with a high enough accuracy. The computational effort required for the JD-MLSE is therefore comparable to the B-MLSE based on histograms (except for slightly higher memory requirements due to the larger number of PDFs).15 shows a 3-dimensional PDF for the ’010’ state transition with a two bits memory length. This increases the size of the look-up table. P(u− . Figure 9. On the other hand. where T0 is the symbol period. Subsequently. the signal is input into either a threshold CDR receiver or a DSO. This shows a clear advantage for the JD-MLSE. Maximum likelihood sequence estimation 9. the stored signal is re-sampled to a sample rate of 21. The measured dispersion tolerance for both the conventional CDR receiver. which is sub-optimal in the presence of large signal distortions. (b) CDR receiver. At the receiver. 1A 193 . The balanced MLSE show no significant improvement in dispersion tolerance over the conventional CDR receiver. a set of data is stored using a DSO (Tektronix TDS 6804B) and afterwards post-processed on a desktop computer. MLSE is applied to the sequences stored with the DSO.3. The JD-MLSE used here has a 2-symbol memory and it builds therefore eight 3-dimensional histograms similar to the one shown in Figure 9. the signal is sampled at −T0 /4 and +T0 /4. which gives an accuracy of 99. data Tx (a) laser MZM (b) u-(t) u+(t) + VOA SSMF or DCF BERT CDR 50-GHz CSF MZDI r(t) T PD u-(t) u+(t) ~ ~ ~ - ~ ~ A/D MLSE (c) u-(t) u+(t) + - ~ ~ ~ ~ ~ ~ A/D MLSE BERT (d) ~ ~ u (t) + u-(t) or BERT (e) u-(t) u+(t) A/D A/D MLSE BERT Figure 9. Figure 9. this slightly increases the back-to-back OSNR requirement.5 Joint-decision MLSE combined with DPSK We now evaluate the impact of JD-MLSE on DPSK modulation using the experimental setup shown in Figure 9.16: (a) Experimental setup and (b-e) different receiver configurations. This is attributed to the re-timing required for the off-line MLSE. which nearly doubles the chromatic dispersion tolerance over both the B-MLSE as well as the CDR receiver. the signal is re-timed using the digital filter and square timing recovery algorithm. B-MLSE as well as JD-MLSE are depicted in Figure 9. (d) MLSE with single-ended detection and (e) joint-decision MLSE.12). After re-timing.2 with the exception that a 50-GHz CSF filter is used in the receiver.99% for a BER of 10−3 [398]. To determine the MLSE performance.2. In the off-line measurements.2.9. data sequences of 1 · 106 bits are processed by the MLSE algorithm. (c) MLSE with balanced detection. The bandwidth of the DSO is 8 GHz and it samples at a sampling rate of 20 Gsample/s. For a 2-dB OSNR penalty the measured chromatic dispersion tolerance is 2000 ps/nm real-time JD-MLSE receiver was not available in this experimental evaluation and the measurements discussed here are therefore ’off-line’.161 . It is similar as discussed in Section 9. To obtain exactly 2 samples/symbol.4 Gsample/s. as discussed in Section 10. The MLSE has a 4-bit quantization resolution and 4-state Viterbi decoder.17a compares the chromatic dispersion tolerance of the B-MLSE and JD-MLSE.17. which is similar to results obtained in the previous section with the real-time MLSE (see Figure 9. Only for large accumulated dispersion we find a difference between the real-time MLSE and off-line MLSE.15.2. Using off-line processing.1. this signal is multiplied with the impulse response of the desired amount of chromatic dispersion. respectively. 194 . The simulations use a similar configuration as shown in Figure 9. A 27 bits long 10. 9. a data sequence with a length of 106 bits is constructed from the received 29 bits by using the overlap-and add-method [398]. Figures 9. DPSK with balanced detection and MLSE receiver.17b. for the JD-MLSE. DPSK with balanced detection and CDR receiver. Digital direct detection receivers Required OSNR (dB/0.7-Gb/s DPSK is compared when JD-MLSE is used for the DPSK receiver.1 nm) Chromatic dispersion (ps/nm) (b) Figure 9. OOK with MLSE receiver.1 nm) 18 16 14 12 10 8 6 BER = -3000 -2000 -1000 0 10-3 1000 2000 3000 18 16 14 12 10 8 BER = 10-3 6 -3000 -2000 -1000 0 1000 2000 3000 Chromatic dispersion (ps/nm) (a) Required OSNR (dB/0. To determine the impact of partial DPSK. Either a conventional CDR receiver or MLSE receiver is subsequently used to determine the chromatic dispersion tolerance.7-Gb/s OOK and 10. After balanced detection.18b depict the simulated influence of the MZDI bit-delay on the chromatic dispersion tolerance of the CDR and MLSE receiver. To determine the chromatic dispersion tolerance. the MZDI bit-delay is varied from 0. compared to only 1100 ps/nm for the CDR and B-MLSE receivers. DPSK with joint-decision MLSE receiver.Chapter 9.0 · T0 bit in steps of 0. In this section we show that combined with MLSE the improvement is further enhanced. the chromatic dispersion tolerance obtained for 10.18a and 9.5 · T0 to 1. At the receiver.6 MLSE combined with partial DPSK A different approach to improve the chromatic dispersion tolerance of DPSK modulation and MLSE is the use of partial DPSK. Additive white Gaussian noise is added to the signal.1 · T0 . This shows that JD-MLSE preserves the 3-dB difference in OSNR requirement between OOK and DPSK in the dispersion-limited regime.17: (a) DPSK with different MLSE configurations and (b) comparison between OOK and DPSK modulation.4. the electrical signal is filtered with a 10th -order Bessel filter with a bandwidth of 7 GHz. which is then used to construct a DPSK modulated signal.16. In Figure 9. As shown in Section 4.7-Gb/s PRBS sequence is repeated 4 times to obtain a total block length of 29 bits. which is subsequently filtered with a 2nd -order Gaussian shaped 50-GHz filter. the use of MZDI with a delay of less that one bit can considerably increase the chromatic dispersion tolerance. OOK with CDR receiver.2. The measured chromatic dispersion tolerance for both the CDR and real-time MLSE with a 0. The choice of the optimum MZDI bit-delay should therefore take both the back-to-back OSNR requirement and chromatic dispersion tolerance into account.1nm) 18 16 14 12 10 8 0 1. Subsequently.5-bit delay.0 bit-delay 14 12 10 8 0 BER = 10 -4 1000 2000 3000 4000 Chromatic dispersion (ps/nm) 0.0 · T0 to 0.5 or 0. For a 0.5 · T0 (2-dB OSNR penalty).18a shows that for the CDR receiver the chromatic dispersion tolerance improves from 1140 ps/nm to 1890 ps/nm when the bit-delay is decreased from 1.9-bit delay. Maximum likelihood sequence estimation Figure 9. Figure 9. 0. Figure 9. The back-to-back OSNR requirement is somewhat higher with 2. 0.6. Consequently. To further point out the improvement obtained with partial DPSK and MLSE.19b compares the chromatic dispersion tolerance of partial DPSK with duobinary modulation. which indicates that MLSE causes a slight OSNR penalty for partial DPSK.5 bit-delay 0.g. one with a 1-bit delay. (2) a software based MLSE receiver for off-line processing and (3) a conventional CDR receiver. Two different MZDIs are employed.5-bit-delay.0-bit delay 16 1.1nm) Required OSNR (dB/0. a shorter bit-delay results in an increased back-to-back OSNR requirement. the output of the balanced photodiode is used as the input signal for (1) a real-time MLSE receiver [19].16 to verify the chromatic dispersion tolerance of partial DPSK combined with MLSE. For partial DPSK combined with MLSE no significant increase in OSNR requirement is measured for a chromatic dispersion up to 3500 ps/nm. the use of MLSE results in a nearly identical OSNR requirement for chromatic dispersion ranging from 0 ps/nm to in excess of 3000 ps/nm.19a. when a 0. delay.0-bit delay.7-bit delay. 18 Required OSNR (dB/0. followed by a balanced photodiode.0-bit delay MZDI is depicted in Figure 9.18b shows that the chromatic dispersion tolerance is optimum for a bit-delay of 0.5-bit delay MZDI is used.65-bit delay) is a more optimal choice in order to balance the chromatic dispersion tolerance and back-to-back OSNR requirement. But on the other hand.7 dB when a 0.0 · T0 to 0. On the other hand.6-bit delay. The chromatic dispersion tolerance is now increased from 1140 ps/nm to 3750 ps/nm when the bit-delay is decreased from 1. 0. the other with a 0.5 · T0 . which increases by 1. It further shows that there is a trade-off between chromatic dispersion tolerance and back-to-back OSNR requirement.18: Simulated chromatic dispersion tolerance of 10. 0. 0. which confirms the improvement observed through simulations.18b depicts the chromatic dispersion tolerance when we apply an MLSE receiver to the output of the balanced photo-diode. a slightly higher bit delay (e.5-bit delay. A comparison between the CDR and MLSE receiver for a 1-bit delay MZDI confirms the inefficiency of an MLSE for DPSK modulation. This shows both a clear OSNR improvement 195 .7-Gb/s NRZ-DPSK with different MZDI bitdelay (a) conventional CDR receiver and (b) MLSE receiver.5-bit delay MZDI is used a considerable improvement in chromatic dispersion tolerance is evident.5 and 1.8-bit We now use the experimental setup depicted in Figure 9.2.5-bit delay BER = 10 -4 1000 2000 3000 4000 Chromatic dispersion (ps/nm) (a) (b) Figure 9. Figure 9.9. 1. again for a 2dB OSNR penalty. 0.6 dB. This can be better understood from 196 . real-time measured. Conventional DPSK with a 1-bit delay MZDI is insensitive to the sampling phase when a twofold over-sampled MLSE receiver is used.1nm) 0. The x-axis depicts the sampling instant t of the first sample along the symbol period. BER = 10 -4 1000 2000 3000 4000 Chromatic dispersion (ps/nm) 18 Required OSNR (dB/0. the required OSNR shows a significant dependence on the sampling phase offset. duobinary with MLSE. When we compare the sample phase sensitivity of a 0.5-bit delay. In addition.5-bit delay 14 12 10 8 0 sampling phase [-T0/4.20: Sampling instant optimization with MLSE.5 dB) and a slightly higher chromatic dispersion tolerance for the partial DPSK scheme with MLSE.1nm) 12 10 8 6 0 1-bit delay 16 Required OSNR (dB/0. 14 Required OSNR (dB/0. the dependence on the sampling phase disappears in the dispersion-limited regime.0-bit delay.1nm) 16 14 12 10 8 0 0.5 Sampling phase (T/T0) BER = 10 -4 1000 2000 3000 4000 Chromatic dispersion (ps/nm) sampling phase [0. Figure 9. On the other hand.19: Measured chromatic dispersion tolerance of DPSK with CDR and 1.1nm) 1-bit delay 16 14 12 10 0 DPSK BER = 10 -4 1000 2000 3000 4000 Chromatic dispersion (ps/nm) Duobinary (a) (b) Figure 9. DPSK with MLSE and 0.1 0. the back-to-back OSNR requirement of partial DPSK can be improved by optimizing the MZDI bit-delay. 0-ps/nm. line simulated. 18 Required OSNR (dB/0. off-line measured. DPSK with CDR and 0. 3000-ps/nm. Figure 9. the output signal resembles an inverted RZ signal.20 shows the OSNR requirement of (partial)-DPSK with different sampling instants.3 0.Chapter 9. Digital direct detection receivers (∼2. real-time simulated. This is similar to what has been reported in [399] for NRZ-OOK. 0-ps/nm. which would further increase the difference with duobinary modulation.21: Difference between real-time and off-line processing. off- In [266] it is shown that due to the deterministic interference between consecutive symbols in an MZDI with ∆T < T0 bit-delay.0-bit delay. in the case of a 0. duobinary with CDR. +T0/4] BER = 10 -4 0.T0/2] Figure 9. whereas the second sample is taken at t + T0 /2. DPSK with MLSE and 1. 0.5-bit delay MZDI and 0-ps/nm chromatic dispersion.4 0. The optimum sampling phase of the two samples is at t = 0 and at t = T0 /2 as most of the information in RZ can be extracted from the middle of the symbol. the choice of the sampling phase is more sensitive in comparison to NRZ.5-bit delay.2 0.0-bit delay. 1.5-bit delay MZDI and a 1-bit delay MZDI. For a RZ signal.5-bit delay DPSK.5-bit delay. 0. However. the higher sensitivity of the RZ pulse shape becomes apparent.5-bit delay. 2 The 197 .9. but this difference disappears in the dispersion-limited regime. 9. it might be beneficial to over-sample more than two-fold with partial DPSK. Sampling at -T0 /4.21 now compares the chromatic dispersion tolerance of the off-line processed MLSE with the real-time MLSE. which is not adapted to the partial DPSK signal but to a NRZ-OOK modulated signal. In addition.5-bit delay MZDI and balanced detection (a) back-to-back (b) 1900-ps/nm of chromatic dispersion. Note that the real-time MLSE receiver could be easily modified to sample at the optimal sampling point. As well. As a result the impact of the sample phase is significantly reduced. Real time-MLSE -T0/4 T0/4 Offline-MLSE -T0/2 0 Real time-MLSE -T0/4 T0/4 Offline-MLSE 0 T0/2 Back-toback 1900 ps/nm Figure 9. Maximum likelihood sequence estimation the partial DPSK eye diagram demodulated with a 0. We compare three different MLSE schemes and a conventional CDR receiver. as shown in Figure 9. Figure 9. Simulated curves confirm the choice in sampling phase as the source of the difference in OSNR requirement. which results in a higher OSNR requirement. This explains why the OSNR requirement of the real-time and off-line MLSE converges in the dispersion-limited regime.7 Joint-decision and joint-symbol MLSE combined with DQPSK We now combine MLSE with DQPSK modulation.2. The real-time MLSE shows a slight OSNR penalty for low chromatic dispersion. Comparing the eye diagrams back-to-back and with 1900 ps/nm of chromatic dispersion. the choice of the sampling instant is less critical. This can be attributed to the sub-optimal choice of the sample phase.5-bit delay MZDI. limited by the sampling rate of the ADCs in the DSO that is used for experimental verification. In this section we discuss the combination of 21.22: Measured eye diagrams after phase demodulation with a 0. the higher PMD tolerance can be beneficial in PMD-limited transmission links. and combined with MLSE the necessity of an optical tunable dispersion compensation for a 43-Gb/s transponder might be alleviated2 . In order to assess MLSE combined required chromatic dispersion tolerance for a robust 43-Gb/s transponder depends on system design.4-Gb/s NRZ-DQPSK modulation with MLSE. 0 and +T0 /4 could somewhat reduce the ∼1 dB OSNR penalty that occurs when partial DPSK is combined with MLSE. on the other hand. DQPSK modulation on itself supports already an improved tolerance to chromatic dispersion and PMD. In the chromatic dispersion limited regime. but as a figure-of-merit we assume here a 1000-ps/nm chromatic dispersion window for a 1-dB OSNR penalty.22. The real-time MLSE samples the signal therefore at a different part of the symbol period (t = -T0 /4 and t = +T0 /4).23 shows the different MLSE receivers for DQPSK modulation.2. shows that the signal loses the RZ shape in the dispersion-limited regime. Figure 9. 4.23: (a) Experimental DQPSK setup with (b) conventional CDR receiver. (d) MLSE with joint-decision estimation and (e) MLSE with joint-symbol estimation. Either the histogram method or Gaussian model method is used. Digital direct detection receivers with DQPSK modulation. we can use the constructive and destructive components of the in-phase and quadrature tributaries. A 5-bit vertical quantization resolution. except that due to the quaternary alphabet the Viterbi decoder now has 42 = 16 states. the random drift of two MZDI poses a significant problem to the experimental assessment (see Section 5. with the exception that a quaternary alphabet (N = 4) is used instead of a binary alphabet (N = 2). MZDI data u MZ PD I-(t) I+(t) SSMF or DCF VOA 50-GHz CSF T (a) laser MZ /2 ~ ~ ~ = /4 T Q-(t) Q+(t) data v = . For JD-MLSE the same approach is used as described for DPSK modulation in Section 9.Chapter 9. This causes some residual penalty in the measurements. The Gaussian model method minimizes the Euclidean distance.2. MLSE with joint-decision estimation (JD-MLSE) and MLSE with joint-symbol estimation (JS-MLSE). As DQPSK modulation has a low tolerance to phase mismatches in the MZDI. 198 . The three considered MLSE schemes consists of MLSE with balanced detection (B-MLSE). (c) MLSE with balanced detection.3). The principle of JS-MLSE is the same as discussed for JD-MLSE. As inputs to an MLSE receiver for DQPSK modulation. This gives a total of 4 signals that are detected with either balanced or single-ended photodiodes. 2-symbol channel memory and two-fold over-sampling is used in all cases. Both the B-MLSE and JD-MLSE consider the in-phase and quadrature tributaries independent of each other and use a 22 = 4-state Viterbi decoder. the DSO has been used to store the in-phase and quadrature tributaries./4 I-(t) I+(t) + + ~ ~ CDR BERT I-(t) I+(t) + + ~ ~ ~ ~ ~ ~ ~ ~ A/D A/D MLSE BERT (b) Q-(t) Q+(t) (c) BERT Q-(t) Q+(t) - ~ ~ A/D A/D A/D A/D MLSE - MLSE BERT I-(t) I+(t) (d) Q-(t) Q+(t) ~ ~ ~ ~ ~ ~ ~ ~ BERT I-(t) I+(t) + + A/D MLSE BERT (e) Q-(t) MLSE BERT Q+(t) - A/D Figure 9. JS-MLSE uses the samples from the in-phase and quadrature tributaries simultaneously to compute the branch metrics in the Viterbi decoder. simultaneously. The JS-MLSE uses the same parameters as the JD-MLSE. we obtain a 800 ps/nm window. Maximum likelihood sequence estimation which is now defined as. This might be sufficient to alleviate the need for optical tunable dispersion compensation. N. When we scale the measured dispersion tolerance of DQPSK with JS-MLSE to a 43-Gb/s bit rate. improvement in the signal processing (e. But when we compare the impact of JD-MLSE for both DPSK and DQPSK modulation.24b show the OSNR requirement as a function of the chromatic dispersion for experiments and matching simulations. JS-MLSE takes the decision on both tributaries simultaneously.1 nm) 20 18 16 14 12 10 8 0 1000 2000 BER = 3000 10-3 4000 20 18 16 14 12 10 8 0 1000 2000 BER = 10-3 3000 4000 Chromatic dispersion (ps/nm) (a) Chromatic dispersion (ps/nm) (b) Figure 9. In the presence of significant chromatic dispersion this crosstalk can limit the MLSE efficiency. .24a shows that JS-MLSE provides a significantly higher dispersion tolerance of ∼1500 ps/nm compared to 700 ps/nm for the CDR receiver (at a 2-dB OSNR penalty). where Ik and Qk are the samples from the in-phase and quadrature tributary. respectively. method. JS-MLSE and Gaussian model method.2. this results in crosstalk between the in-phase and quadrature tributaries and therefore in a higher back-toback OSNR requirement. As well. . The small mismatch between simulations and experiments can be attributed to the phase drift in the MZDIs and suboptimal digital clock recovery at high accumulated dispersion. Figure 9. It is evident that B-MLSE provides little or no advantage in comparison to a conventional CDR receiver. JD-MLSE. and it can take the crosstalk between the two tributaries into account. In [400] it has been shown that the Gaussian model is a valid assumption for the channel statistics of DQPSK modulation with a direct detection receiver. a larger number of states in the MLSE decoder) will further increase this figure and meet the requirement of dispersion tolerance modulation format. We conjecture that this difference results from the suboptimal phase demodulation in the case of DQPSK modulation. Required OSNR (dB/0. .2.24: DQPSK with different MLSE configurations for (a) experimental and (b) simulated results. the dispersion tolerance is increased by ∼50% at an OSNR penalty of 2-dB. respectively and µi is a complex number.g. As discussed in Section 5. When JD-MLSE is used instead of the CDR receiver.26) Equation 9. except that the term rk is replaced by Ik + j · Qk . it is evident that the performance improvement is less significant for DQPSK. . ˆ S = argmin ∑ (Ik + j · Qk − µi )2 ∀ i = 1. i k=1 K (9. which is similar to the results obtained for DPSK modulation.24a and 9. conventional CDR receiver. 2. 199 .9. MLSE with balanced detection.22. JS-MLSE and histogram Figures 9.1 nm) Required OSNR (dB/0.26 follows from Equation 9. 0 dB and 0.5 JS-MLSE Gaussian 9. B-MLSE JD-MLSE JS-MLSE histograms histograms histograms 10. 200 . The back-to-back OSNR requirement of JS-MLSE is 1. this is similar to the improvement observed for MSPE.1: E STIMATED COMPLEXITY OF THE DIFFERENT MLSE SCHEMES APPLIED TO DQPSK MODULATION . al. In this work the MSPE is implemented in the optical domain using multiple MZDIs with different bit-delays.6 Figure 9.24 it is evident that both JD-MLSE as well as JS-MLSE have a slightly lower back-to-back OSNR requirement. when the Gaussian model method is used only the Euclidean distance has to be computed in the trellis diagram.4 9. From Figure 9.9 9.8 9. respectively. We note that the difference between the measurements and simulation probably results from phase offsets in both MZDIs. B-MLSE JD-MLSE JS-MLSE JS-MLSE histograms histograms histograms Gaussian Number of trellis Trellis states Dimensions of the PDF Size of the look-up table 2 2L 2-D Q · 2L+1 2 2 2L 3-D Q · 2L+1 4 1 4L 3-D Q · 4L+1 4 1 4L N. 4L+1 Table 9. As MLSE creates an improved decision variable based on a number of symbols.24a further shows that both joint-symbol algorithms to calculate the metrics of the trellis’s state transitions (histograms and Gaussian model) have a similar performance. which has been confirmed by Zhao et. in this case equal to the channel memory length.2: BACK . which is also summarized in Table 9.A. This suggests that a combination of MSPE and MLSE might be a suitable approach to realize robust DQPSK modulation.TO . This confirms that the Gaussian channel model is a valid assumption for direct detected DQPSK modulation. Digital direct detection receivers Table 9.Chapter 9.4 dB lowered in comparison to the CDR receiver for the measurements and simulation. The advantage of the Gaussian model method is a significantly reduced complexity to store and compute the branch metric. the size of the lookup tables is 4L+1 = 64 and 4Q · 4L+1 = 65536 for the Gaussian model and histogram method.BACK OSNR CDR Measured (dB) Simulated (dB) 10.2. The complexity of the different MLSE schemes is summarized in Table 9. As only the mean value for each state is stored. In addition. The limited improvement for MLSE compared to MSPE is due to the smaller number of symbols used to compute the improved decision variable. respectively.1. in [401.8 10.3 9.3 10. but similar results could be obtained using a digital signal processing implementation.9 10. 402].0 REQUIREMENT OF DQPSK MODULATION FOR A 10−3 BER AND DIFFERENT MLSE SCHEMES . It can therefore compensate for the crosstalk between both tributaries.3. → MSPE approaches the OSNR requirement of coherent detection. 201 .7-Gb/s DPSK modulation. → The combination of partial DPSK with a conventional MLSE provides a significant increase in chromatic dispersion tolerance at the cost of somewhat higher back-to-back OSNR requirement. which degrades the performance of a direct detection DQPSK receiver.7-Gb/s NRZ-DPSK. → In the presence of nonlinear phase noise. For lasers with a 1 MHz linewidth. no significant compensation of nonlinear phase noise is observed. a 3750-ps/nm dispersion tolerance is measured for a 2-dB OSNR penalty. Multi-symbol phase estimation (MSPE) generates an improved decision variable using a recursive signal processing algorithm. a conventional MLSE receiver does improve the DGD tolerance of DPSK modulation.8-dB improvement in back-to-back OSNR requirement for DPSK and DQPSK modulation.9.5-dB improvement in nonlinear tolerance for 10. → For DPSK modulation.5-dB and 1. → Using the signal after balanced detection as the input of a conventional MLSE receiver does not significantly improve the tolerance against chromatic dispersion for both DPSK and DQPSK modulation. For DQPSK modulation. A joint-decision MLSE operates using both the constructive and destructive component as separate inputs to the MLSE receiver. joint-symbol MLSE provides the best chromatic dispersion tolerance. It therefore allows for a 0. but on a received sequence of symbols. the advantage of MSPE over conventional direct detection increases. This makes a simultaneous decision on the in-phase and quadrature tributaries of the demodulated DQPSK signal. signal processing algorithms have been discussed that can increase the robustness of D(Q)PSK modulation with a direct detection receiver. the use of joint-decision MLSE significantly improves the chromatic dispersion tolerance. respectively. For 10. Maximum likelihood sequence estimation (MLSE) improves the tolerance with respect to transmission impairments by basing the decision variable not only on the most recent symbol. On the other hand. → For DQPSK modulation. the forgetting factor can be lowered as a trade-off between linewidth requirement and OSNR improvement. → MSPE demodulation has only a modest laser linewidth requirement as it is based on interferometric demodulation with an MZDI. It is more tolerant to laser linewidth than a digital coherent receiver with optimized carrier recovery. Summary & conclusions 9.3 Summary & conclusions In this chapter. This allows for a 1. signal processing in direct detection receivers seems promising to realize more robust optical transmission.Chapter 9. The chromatic dispersion tolerance and PMD tolerance of. 43-Gb/s DQPSK modulation can be increased to the extent that no optical chromatic dispersion or PMD compensation is required. Digital direct detection receivers In summary. 202 . in particular. c21-c22. also known as digital intra-dyne receivers. a small difference remains. For state-of-the-art transmission systems. polarization and phase-sensitive detection. Coherent detection has initially received significant research interest in the 1980’s. which results in detection mostly limited by the thermal noise of the photo diode and electrical amplifiers.10 Digital coherent receivers In this chapter we discuss digital coherent receivers. Hence for coherent detection. In addition. However. the interest in coherent detection declined. c25-c26 203 . this difference in receiver sensitivity can potentially improve the OSNR requirement and increase the feasible transmission distance. nearly the same receiver sensitivity can be obtained without many of the drawbacks of coherent detection. it can be used for coherent amplification. after the development of the EDFA as an optical pre-amplifier. c6.1 dB (DPSK) or 2. no pre-amplification was used in front of the receiver. the receiver sensitivity is only limited by optical shot noise. differential detection provides relatively poor performance with respect to digital equalization as 1 The results described in this chapter are published in c4. and therefore are a suitable candidate for robust optical transmission systems. As discussed in Chapter 4. Coherent detection of an optical signal implies that the received signal is mixed with the output signal of a LO laser. for amplitude.4 dB (DQPSK) when compared to coherent detection. At that time. The LO is normally a receiver-side semiconductor laser. Although the receiver sensitivity of direct detection is close to the theoretical optimum. Such receivers combine coherent detection with digital signal processing to compensate for transmission impairments. the phase demodulation with an MZDI results in an OSNR penalty of 1. As the LO signal typically has a much higher power than the received signal. This can potentially increase the receiver sensitivity with up to 20 dB in comparison to optically unamplified direct detection [403]. such as active polarization and phase control. With EDFA pre-amplification and direct detection. 3. 1 A coherent receiver does not necessarily require differential detection. There are a number of different technologies that allow the construction of an optical hybrid [404]. Using coherent detection not only the amplitude. Subsequently. 204 . Section 10. in the work described in this chapter.1. 10.Chapter 10. Finally. The principle of coherent detection is briefly treated in Section 10.6 discusses the performance of digital equalization in long-haul transmission experiments. Digital coherent receivers discussed in Chapter 9.7 analyzes the possibilities of baud-rate distortion compensation.2 and the required signal processing algorithms are reviewed in Section 10.5 the compensation of linear impairments is discussed for 43-Gb/s POLMUXNRZ-DQPSK and 111-Gb/s POLMUX-RZ-DQPSK. i.1 Analog coherent receivers Figure 10.1 shows the basic layout of a coherent receiver.e.1: Principle of a coherent receiver. The received signal is mixed with the output of the LO in an optical hybrid. the implementation of a digital coherent receiver is discussed in Section 10. the amplitude.1) √ rLO (t) = PLO exp( j[ωLOt + ϕLO ]). but the full (base-band) optical field. phase and polarization control Figure 10. In order to analyze coherent detection. However. √ rs (t) = Ps exp( j[ωst + ϕs ]) (10.4) and hence the modulation format is still referred to as POLMUX-DQPSK. This opens up the possibility of distortion compensation and polarization de-multiplexing in the electrical domain and has recently revived the interest in coherent detection. In Sections 10. respectively1 . Section 10. and POLMUX-QPSK would therefore be the correct acronym of the modulation format.4 and 10.3. In more detail. which simply produces an interference between the received signal and the LO at the output. This chapter is organized as follows. we define the received signal and LO signal at the input of the optical hybrid as. electrical differential decoding is used (see Section 10. phase and polarization information from the received signal is transferred into the electrical domain. The most straightforward realization is a 2x2 coupler. Polarization control feedback PC LO PD + Optical hybrid Signal processing data Rx Frequency control feedback LO frequency. R is the responsivity of the photodiode and ηsh (t) the photocurrent shot noise. Coherent detection can be realized using a homodyne. bit rates up to 10-Gb/s have been shown for 205 . As PLO Ps . Recently. This leaves a direct detection contribution from the modulation in Ps as well as amplitude noise contributions in PLO . Such a receiver has a reduced sensitivity of >3 dB in comparison to homodyne detection. 408]. √ R Ps + PLO + 2 Ps PLO sin[(ωs − ωLO )t + ϕs − ϕLO ] √ i= (10. which makes such a receiver easier to realize. The direct detection terms Ps and PLO can be filtered out through balanced detection. 2 Ps + PLO − 2 Ps PLO sin[(ωs − ωLO )t + ϕs − ϕLO ] √ The information is contained in the term ±2 Ps PLO · sin[ωs − ωLOt + ϕs − ϕLO ].3) + ηsh (t). After mixing. blocking. In a homodyne receiver the LO and transmitter laser have the same frequency and the phase difference should be zero (or a multiple of 2π). When balanced detection is used the RIN of the LO is canceled out [405]. Homodyne detection is the ideal coherent detection scheme in the sense that it allows for the optimal receiver sensitivity. active control of the frequency and phase of the LO is required in a homodyne receiver as the phase difference between the LO and the transmitter laser should be zero.1. However. Thermal noise has been neglected The coherent mixing term after detection with the photodiode is subsequently defined by the photocurrent. The linewidth requirements are however about an order of magnitude less stringent in comparison to homodyne detection. Analog coherent receivers Where the LO and transmitter laser are assumed to have different frequency and phase. A heterodyne receiver therefore needs broadband photodiodes and electrical amplifiers. the optical signal at the input of the two photodiodes is then equal to.e. only Ps and PLO can be removed through D. In heterodyne detection the difference between the LO and transmitter laser frequency is nonzero and equals a fixed intermediate frequency (IF). which generates the desired coherent mixing products. better known as relative intensity noise (RIN). The LO and received signal are mixed in the 180o hybrid (for example a 2x2 coupler). The phase-locked-loop operation puts however stringent requirements on the laser linewidth for both the LO and transmitter laser. Optical transmission using homodyne detection with a phase-locked-loop was first shown by Malyon in 1984 [406]. which makes homodyne detection difficult to realize using semiconductor lasers. (10. as the signal energy with homodyne detection is twice the signal energy of a heterodyned signal [407. The difference between the three receiver types is the required frequency difference between LO and transmitter laser. heterodyne or intra-dyne receiver. ωs − ωLO = ωIF .C.2) The current after the photodiode is given by i(t) = R · |y(t)y∗ (t)| + ηsh (t). i. which makes it challenging to realize high-speed transmission. When detection is quantum noise limited it requires 9 photon/bit for BPSK modulation to obtain a 10−9 BER [403]. This shows directly the advantage of coherent detection in a system without pre-amplification. 1 √ 2 rs (t) + j · rLO (t) j · rs (t) + rLO (t) . the magnitude of the coherent detected term becomes much larger with respect to the photocurrent shot noise ηsh (t) as can be the case for direct detection. The main drawback of heterodyne detection is that it requires a receiver bandwidth of at least twice the bit rate [409].10. Whereas for single-ended detection. in addition to active phase control. which can separate both components through electrical baseband processing. The phase-diversity reception makes the receiver robust against phase offsets between the LO and transmitter laser. in 1986 [411]. as first shown by Derr in 1991 [412. that the polarization of the received signal and the LO are matched. but non-ideal electrical components in the receiver make it difficult to match the performance of direct detection with an optical preamplifier. Intra-dyne detection relies on detection of both the in-phase and quadrature component of the received signal. which requires a total of 4 photo-diodes and an optical hybrid with 4 outputs. and the summation of both signals (for BPSK) will be independent of the phase difference. This makes it difficult to demodulate QPSK with an optical phase-locked loop. In comparison to a BPSK intra-dyne receiver demodulation. The optical phase-locked-loop can be avoided by analog-digital conversion after the photodiode and subsequent phase drift compensation through digital signal processing. heterodyne or intra-dyne QPSK demodulation. a 90o hybrid is required [404]. but approximately zero. The frequency difference between LO and transmitter laser than can be tolerated by an intra-dyne receiver depends on the signal processing. intra-dyne detection has a 3-dB sensitivity penalty in comparison to homodyne detection for shot noise limited reception.Chapter 10. each shifted by 90o degrees. with the exception that the frequency difference between the LO and transmitter laser is not exactly zero. there is no sensitivity difference between homodyne.4. it can as well be used for QPSK detection. For homodyne QPSK demodulation. This can be solved through balanced detection. PBS LO TE TM X + + Signal processing data Rx Y PD Signal processing Frequency control feedback LO frequency and phase control Figure 10. on the contrary. As an intra-dyne coherent receiver converts both the in-phase and quadrature component into the electrical domain. The main disadvantage of coherent QPSK demodulation is that the laser linewidth tolerance is strongly reduced in comparison to PSK demodulation. As the signal has to be split in two components. Coherent optical transmission systems require. 414]. and is therefore also referred to as a phase-diversity receiver. Hence.1. only the electrical baseband processing has to be modified [412. Digital coherent receivers heterodyne detection [410]. al. This can be achieved either through 206 . an intra-dyne receiver that uses single-ended detection is vulnerable to RIN from the LO. as discussed in Section 9. This is similar for heterodyne demodulation.2: Principle of a polarization-diversity coherent receiver. a second receiver is required which results in a 3-dB sensitivity penalty. 413]. Intra-dyne coherent detection at 680-Mbit/s was first shown by Davis et. When the signal in one of the arms fades to zero the other signal is still present. In order to detect both the in-phase as well as the quadrature component. Similar to heterodyne detection. Intra-dyne detection is similar to homodyne detection. 3. 10. Such a polarizationdiversity scheme results only in a 0. In this scheme two IF signals (heterodyne demodulation) obtained from orthogonal polarizations are combined after phase adjustment. The transmitter laser is either a DFB laser or an ECL.1 The optical front-end The digital coherent receiver discussed here uses polarization-diversity intra-dyne detection to convert the full optical field (i. This translates for a 10. 421. infrastructure to 43-Gb/s and 111-Gb/s bit rates.2. Together with digital signal processing this allows for a receiver implementation that is robust against the most significant transmission impairments. 420.3 · 10−4 [382].10. but orthogonal.a total of four signals. The allowable product of linewidth times symbol period for a digital coherent receiver is approximately 1.e. as discussed in Chapter 7 for POLMUX with direct detection. as first demonstrated by Okoshi et. The most advantageous modulation format to use is POLMUX-(D)QPSK [355. but is normally integrated into a PBS. and the combined IF signal is then demodulated. al. A digital coherent receiver enables the compensation of linear transmission impairments and polarization demultiplexing in the electrical domain. which is difficult to achieve with 207 . or polarization diversity [415]. Figure 10. results in a coherent receiver that translates all properties of the optical signal into the electrical domain.4-MHz beat linewidth.75-Gbaud symbol rate into a ∼1. This allows the use of optical and electrical components with a ∼10-GHz bandwidth. the coherent receiver only has to operate at 10. The typical setup of a digital coherent receiver using POLMUX-RZ-DQPSK modulation is shown in Figure 10. This provides in particular a high tolerance towards PMD and chromatic dispersion. in 1987 [419].4 dB receiver sensitivity penalty with respect to an ideal single-polarization receiver [418]. in 1983 [416].75 Gbaud to achieve a 43-Gb/s bit rate. a digital coherent receiver can operate with any kind of optical modulation format. 422]. As POLMUX-DQPSK encodes 4 bits per symbol. Note that the polarization rotation TM↔TE is shown here explicitly. This requires the detection of both the in-phase and quadrature components for two arbitrary. amplitude. A polarization-diversity receiver was first demonstrated by Okoshi et.2 shows the basic layout of a polarization-diversity coherent receiver. 10-Gb/s optimized. Because the full (baseband) optical field is transferred to the electrical domain. Digital coherent receivers active polarization control. as it does not require phase adjustment at an IF frequency [417]. 10.2 Digital coherent receivers As discussed in Chapter 9 the development of high-speed digital electronics allows for the use of powerful digital signal processing algorithms for distortion compensation.2. The high tolerance against transmission impairments of a digital coherent receiver enables the upgrade of existing. phase and polarization information) to the electrical domain. A more practical approach is to separately demodulate the two polarization components. polarization states . The combination of an intra-dyne receiver with polarization diversity. al. both polarization components are recombined using a PBS. In addition. For a 43-Gb/s bit rate it might be desirable to use NRZ instead of RZ pulse carving as this removes the need for the additional pulse carver. a set of data is sampled and stored using a DSO and afterwards processed on a personal computer 2A 208 . decoding Equalization X0° X90° Y0° Y90° ^ XI ^ XQ ^ YI ^ YQ data Rx Y Frequency control feedback Control Automatic gain control Figure 10. which results in POLMUX-RZ-DQPSK modulation. Digital coherent receivers Transmitter MZ data HI TE TM /2 clock MZM MZ H data HQ data VI optional MZ laser V PBS MZ /2 data VQ Receiver X PBS LO 0° 90° hyb 90° TE TM PD 0° 90° 90° hyb Digital coherent ASIC Carrier recovery Clock Recovery Diff. Moreover. Each of the components is then fed to an integrated QPSK modulator. The POLMUX-RZ-DQPSK modulator chain starts with a MZM for RZ pulse carving. Typically. it can be more attractive to use RZ pulse carving as it reduces (nonlinear) transmission impairments as well as residual chirp in the transmitted optical signal. The measurements discussed here are therefore ’off-line’. provides therefore the optimum performance.Chapter 10. when NRZ coding is used. on the other hand. In the off-line measurements2 described in this chapter a ∼1 dB OSNR tolerance degradation has been observed when using a DFB laser at the transmitter. which might be difficult to achieve at a 111-Gb/s bit rate.3: A digital coherent transmitter and receiver using POLMUX-DQPSK modulation. A too low modulator bandwidth results in increased transmission impairments due to the broad amplitude level of the transmitted signal. the requirements on the LO laser might be somewhat higher than on the transmitter laser as it should have both a narrow linewidth as well as a low RIN. After the RZ pulse carver the signal is split up in two components using a power splitter. After DQPSK modulation. with a typical linewidth of several hundred Kilohertz. In the off-line measurements. For a 111-Gb/s bit rate. standard DFB lasers. We therefore use ECL lasers for both the LO and transmitter laser in the results discussed in this chapter. real-time digital coherent receiver requires implementation of the digital signal processing into integrated circuits. An ECL. the required electro-optical bandwidth of the integrated QPSK modulator is higher. ECLs will therefore be used as LO in coherent transponders. The allowable frequency range depends on the signal processing algorithms that are used for carrier phase estimation. 18]. The required vertical resolution of the ADCs to have a negligible penalty resulting from quantization distortions is 5-6 bits [427]. ADCs can also be made with CMOS technology. The polarization rotation TM↔TE is once more shown explicitly. In order to use available vertical resolution as effectively as possible the dynamic range of the ADC should be fully used. The mixing of the received signal and LO in the 90o hybrids gives the in-phase and quadrature components. Each of the polarization components is then fed into a 90o hybrid and mixed with the output of a LO laser.2. for example resulting from optical transients or component aging. an electrical 3-dB bandwidth of 0. polarization components X and Y. However. which is discussed in Section 10. The LO can be fixed within this frequency range using a slow feedback signal generated through signal processing. the four signals are quantized using ADCs. but this requires the use of a number of slower converters which are then time interleaved to achieve a high total sampling rate [424.2 Analog-to-digital converters After the photodiodes. First.3. which are typically sampling at 2 samples/symbol. Generally. the direct detected LO component can be removed using a D. but is normally integrated into the PBS.5 times the baudrate is sufficient [428].3. The distortions from direct detected signal components are minimized using a high LO-signal power ratio of approximately 18 dB. 424. a PBS splits up the signal into two arbitrary. Finally.2. where the power dissipation requirements are less strict than for a transponder. In the electrical signal. Afterwards the four signals are digitalized using an ADCs. A 43-Gb/s transponder therefore requires ∼25-Gsample/s ADCs. as shown in [423]. A ∼25-Gbaud ADC implementation has been shown in different semiconductor technologies [17. At the time of writing. The LO is free-running and should be aligned with the transmitter laser within an approximate frequency range of several hundred megahertz.3.10. This requires an automatic gain control in front of the ADCs to adapt to changes in the received optical power. whereas a 111-Gb/s transponder would use ∼60-Gsample/s ADCs. block. And as the digital signal processing has an inherently parallel architecture this fits well with the parallel ADC architecture required for CMOS implementation. 209 . Digital coherent receivers The digital coherent receiver structure is shown in Figure 10. 10. 425]. 18]. The polarization components X and Y are therefore an arbitrary rotation of the two polarization components at the transmitter (H and V). but orthogonal. which are then fed to single-ended Pin/TIA photodiodes.C. Particulary BiCMOS technology allows for the realization of high speed ADCs. a 50Gsample/s ADC design has only been realized for digital storage oscilloscopes [426]. The most promising architecture is a full-flash topology where 2Q − 1 parallel comparators are used to convert the signal with a resolution of Q bits in a single step [17. Balanced photodiodes are not used in order to test a cost-efficient and lower complexity receiver architecture. also the electrical bandwidth of the ADCs is an important design parameter. Realizing the ADCs in CMOS technology has the important advantage that they can be combined on a single chip with the subsequent digital signal processing. the required bandwidth depends strongly on the roll-off with frequency and specifying only the 3-dB ADC bandwidth can be somewhat misleading. clock recovery is applied. We note that the digital signal processing algorithms would normally process the data in blocks in order to parallelize the processing and reduce the required clock rate of the hardware. the overlap-and-add method [429]. the digital signal processing algorithms that enables the electronic distortion compensation are discussed in detail. Figure 10. The block-wise processing results therefore in an overhead to the processing and memory requirements. Afterwards the linear distortions in the signal are equalized using finite impulse response (FIR) filters. This requires an overlap between consecutive blocks. such that the full impulse response of every symbol within the block is taken into account.4 shows the different steps used in the digital coherent receiver as discussed in this thesis. first of all. After detection and quantization. optimized with LMS Im{E} Im{E} Re{E} Re{E} Carrier recovery: Viterbi-and-Viterbi 4th power phase estimation Im{E} Im{E} Re{E} Re{E} Binary decision & differential decoding Figure 10. carrier phase estimation (CPE) is applied to cancel out the phase and frequency offset between the LO and transmitter laser. The overlap between consecutive blocks can be implemented using. In the final step a digital decision is taken and differential decoding is applied to prevent cycle slips between the LO and transmitter laser. Digital coherent receivers Polarization X Signal after A/D conversion Im{E} Polarization Y Im{E} Clock recovery: digital filtering and square timing recovery Re{E} Re{E} ~1. this step also realizes the polarization de-multiplexing. for example.Chapter 10. 10. 210 .4: Overview of the signal processing steps in a digital coherent receiver. Subsequently.3 Digital equalization algorithms In this section. which scales linearly with the number of equalizer taps and inversely with the block length.8 sample /symbol Im{E} Im{E} Re{E} Re{E} 2 sample /symbol Equalization: 4 complex FIR filer banks. signal constellations exemplify the signals obtained after each processing step. This is achieved by increasing the sampling rate from ∼1.) 2 2 sample /symbol e j 2 fst Figure 10. This typically leaves some residual timing offset caused by timing error and jitter that must be compensated using a clock-recovery scheme.. This translates in both cases to ∼1.4) where m is the block index for blocks of length N. In the first step the signal is approximately re-sampled to ∼2 sample/symbol.5: Clock recovery and re-sampling. The DSO samples at 20 Gbaud (for the 10. Note that the fraction k/L corresponds to the sample period fst. (10.8 sample/symbol to 4 sample/symbol through up-sampling. resample 4 sample/symbol Cubic Interpolator ~1. χm = (m+1)LN−1 k=mLN ∑ p(k)e− j2πk/L . and no re-timing of the signal is required. the ADCs would therefore sample at an exact multiple of the baud rate.8 sample/symbol.75-Gbaud symbol rate.10. The normalized ˆ phase ε of the Fourier coefficient χm is then a measure of the sampling phase error for block m and can be used to re-sample the data using a cubic interpolator.3.. a DSO is used to convert the analog signal to the digital domain and subsequently store the received signal for later off-line processing. In order to exactly re-sample to 2 sample/symbol the digital filter and square timing recovery algorithm is used as described by Oeder and Meyer in [430]. 2π (10. In addition this also saves the implementation complexity of the re-timing algorithm. and hence the sequence must be re-timed to obtain an integer number of samples per symbol (either 1 or 2).3. based on knowledge of the symbol rate and oscilloscope sampling rate. In a digital coherent receiver specifically designed for a 10.8 sample /symbol r (k ) |x|2 p(k ) LN x 1 1 arg(.75-Gsample/s experiments).1 Clock recovery and re-timing For the transmission experiment discussed in this chapter. Digital equalization algorithms 10.5) Re-timing the signal with the ”filter and square timing recovery” algorithm becomes very critical in the presence of large signal distortions. L is the over-sampling factor.75/27. Approx. 211 . The power 2 2 envelope p(k) is calculated from the square of the four received signal components (X0o + X90o + 2 Y02o + Y90o ). ˆ ε= 1 arg(χm ).75-Gbaud experiments) or at 50 Gsample/s (for the 27. In this scheme the timing function is derived from the power envelope of the received signal by block-wise computing the complex Fourier coefficient at the symbol rate χm . 2 sample/symbol). as shown in Figure 10. which translates into minimizing an error function.8) . The electronic equalization. CMA exploits the property of PSK modulation (e. X and Y are the detected polariˆ ˆ zation components and X and X are the recovered polarization tributaries after signal processing. hyx . 1 sample/symbol) or fractionally-spaced (T0 /2-spaced. Adapting the filter tap as a single complex filter tap is only possible when the signal is perfectly symmetrical. Fractionally-spaced equalizers generally provide better performance than baud-rate equalizers since they serve as both matched filter and equalizer.6b shows the FIR filter bank in more detail. εy = R ˆ 212 (10. as depicted in Figure 10. 435] or the decision-directed least mean squares (DD-LMS) algorithm [436]. The output signal of the equalization stage can be described as ˆ X ˆ Y equalized signal = ˆ yx ˆ xx h−1 ( f ) h−1 ( f ) −1 ( f ) h−1 ( f ) ˆ yy ˆ hxy equalizer · X Y . which is normally not the case. which are either baud-rate (T0 -spaced. the electronic equalization implements both polarization de-multiplexing as well as the compensation of (linear) transmission impairments.Chapter 10. 432].2 Distortion compensation & polarization de-multiplexing In the next step. hxy and hyy ).e. be implemented with a single tap structure and that longer FIR filters are necessary to compensate for chromatic dispersion and PMD. which are optimized independently. in principle. when the real and imaginary components have the same magnitude.6) detected signal ˆ where in principle the matrix h−1 is an approximation of the inverse of the channel matrix h which is defined as.g. The filter taps can be optimized using least mean squares (LMS) algorithms such as the constant modulus algorithm (CMA) [434. this structure is also known as a cross polarization interference canceler (XPIC) [431.7.7) transmitted signal H and V are the polarization tributaries of the transmitted signal. BPSK. X Y detected signal = hxx ( f ) hyx ( f ) hxy ( f ) hyy ( f ) channel · H V . Digital coherent receivers 10. The single complex-valued tap is therefore structured as four real-valued filter taps. Each bank consists of a number of taps. Note that the polarization de-multiplexing can. (10. is implemented by a bank of 4 FIR filters with complex tap weights (hxx . Figure 10. i. (10. εx = R2 − |x|2 ˆ 2 − |y|2 . The FIR filters are arranged in a butterfly structure to enable polarization de-multiplexing.6a. Figure 10.3. Fractionally-spaced equalizers can however have difficulty converging because the neighboring tap signals are highly correlated [433]. It therefore tries to choose the tap coefficients in such a way that the variance between the samples and the circle is minimized. QPSK) that all points in the signal constellation are located on a circle.6c shows the complex multiplication required for each filter tap. The update of the tap coefficients follows according to. Note that for N taps. (c) Filter tap structure Re{X} Re{h0} + h0 Re{h0X} = Im{X} Re{h0} Im{h0} + + Im{h0X} Im{h0} Figure 10. (10. which can be easily computed from the average optical power. The tap delay τ is equal to T0 for a baud-rate equalizer or T0 /2 for fractionally-spaced equalizers.9) where µ is a convergence parameter and x∗ is the complex conjugate of x. where R is the radius of the constellation points. CMA is not influenced by a phase rotation between consecutive symbols. the tap coefficients are now updated until the algorithm converges and the error function becomes small enough. CMA is therefore robust against a large frequency offset between the LO and transmitter laser.10) ˆn The tapweights h−1 therefore increase or decrease with µε. each tap n of the FIR filter is updated separately. Using the error function. (b) linear FIR filter structure and (c) filter tap structure.7: Principle of CMA. ∗ ˆn ˆn h−1 = h−1 + µεx xˆn · xn .6: Digital Equalization using linear FIR filters (a) butterfly structure for polarization demultiplexing. ˆ hyy (10. The speed of convergence depends on the magnitude of µ. ˆ xx ˆ xx h−1 = h−1 + µεx x · x∗ ˆ ˆ yx ˆ −1 = h−1 + µεy y · x∗ ˆ hyx ˆ xy ˆ xy ˆ h−1 = h−1 + µεx x · y∗ ˆ yy ˆ −1 = h−1 + µεy y · y∗ . where a larger value results in faster convergence but also increases the 213 . Digital equalization algorithms (a) Butterfly structure hxx hyx hxy Y hyy ^ Y hxx ^ X h0 h1 h2 h3 h4 (b) FIR filter bank structure X = Data on Xpol.10.3. Because of the squaring in the error function. R Figure 10. Equation 10. which implies that the algorithm makes a decision on the data in order to estimate the error function. Figure 10. first CMA can be applied to the data to roughly equalize the majority of the channel distortions. ⎧ [Re{x} > 0. For the off-line measurements described in the remainder of this chapter this results in slow processing as each new measurement starts by assuming an ideal channel model. In a realtime equalizer.13) (10. Ideally. in practice CMA is more robust to channel distortions and especially phase rotations. DD-LMS is still a blind equalization algorithm. is less robust to channel distortions and phase offset but is more likely to converge to the optimum solution. In the presence of significant phase distortion the convergence parameter µ should therefore be suitably small. However. Alternatively. Under such conditions. the convergence parameter µ should be smaller and the optimization process will require more iterations. Note that it is also possible to combine the DD-LMS algorithm with CPE. Im{x} < 0] . The DD-LMS algorithm. the DD-LMS optimization algorithm is more practical.Chapter 10.11 gives the DD-LMS error function.12) As there is no squaring in the DD-LMS algorithm.8 shows an example of the resulting equalizer taps after optimization with the CMA algorithm. it is sensitive to phase distortions. and it can be used either before or after the carrier phase estimation. This is a decision-directed algorithm. which can be preceded or combined with the carrier recovery. Im{x} < 0] The tap coefficients are then updated according to. the smaller µ generally should be chosen. (10. csgn(x) = [Re{x} < 0. However. A further consideration for the digital coherent receiver is the required number of taps to compensate for channel distortions. When only the DD-LMS algorithm is used for channel equalization. to equalize the remaining distortions [435]. In this case the error function is computed by comparison of the output sequence with a known training sequence. Digital coherent receivers residual error as well as the possibility that the algorithm does not converge to a solution. The described equalization scheme can compensate for linear 214 .11) εy = R · csgn(y)/ 2 − y ˆ ˆ where csgn(x) and csgn(y) are the complex sign functions defined by. which should make it more robust to a larger frequency offset between transmitter and LO laser [435]. ˆ xx ˆ xx h−1 = h−1 + µεx · x∗ ˆ yx ˆ yx h−1 = h−1 + µεy · x∗ ˆ xy ˆ xy h−1 = h−1 + µεx · y∗ . In a second step this is then followed by the DD-LMS algorithm. each processed block can start with the channel model of the previous block and update this using a limited number of iterations. The more severe the channel distortions are. A further possibility is to use DD-LMS with training sequences instead of the blind equalization [437]. on the other hand. √ ˆ ˆ εx = R · csgn(x)/√2 − x . ˆ yy ˆ yy h−1 = h−1 + µεy · y∗ (10. Im{x} > 0] ⎪ 1+ j ⎪ ⎨ 1− j [Re{x} > 0. Im{x} > 0] ⎪ −1 + j ⎪ ⎩ −1 − j [Re{x} < 0. The second algorithm that can be used for equalization is DD-LMS. both CMA and DD-LMS converge to the same solution. 4 hn. the amount of chromatic dispersion that should be compensated has to be roughly known. 440]. to realize in a real-time implementation. The polarization tracking and compensation.yx 0 -0. it is questionable if the optimization algorithms would always converge properly for a FIR filter bank with such large tap counts. distortions as long as the impulse response length of the equalizer is at least equal to the impulse response length of the channel distortion. The chromatic dispersion and PMD that can be compensated increases therefore linearly with the number of FIR filter taps.4 0 2 4 6 8 10 12 14 16 18 20 22 0.000 ps/nm of chromatic dispersion. This implementation has the further advantage that the carrier phase be approximately estimated before equalization. At a 10.2 0 2 4 6 8 10 12 14 16 18 20 22 -0.4 Taps Y-Y hn. which makes the subsequent equalization stage more efficient. as well as the compensation of any residual chromatic dispersion is implemented afterwards with shorter (typically 5 taps) FIR filter banks. as discussed in the next section and shown in [435].xy 10 12 14 16 18 20 22 tap number tap number Figure 10. When we assume a linear transmission channel with only chromatic dispersion and DGD the channel matrix can 215 .e. For certain applications it can be desirable that a digital coherent receiver can compensate for the full chromatic dispersion in a long-haul transmission link [422. A further advantage of digital coherent receivers is that the FIR tap values can be used to estimate the transmission impairments for optical performance monitoring [439.10.yy 0. 2000-ps/nm and a 30o polarization offset.9. it is therefore more efficient to implement a fixed FIR filter by converting the signal to the frequency domain using a fast-Fourier transform (FFT).4 0. 438]. An arbitrary amount of chromatic dispersion can then be compensated by a single multiplication with the desired frequency response.2 -0.2 0 -0. As well. the impulse response of such a channel broadens an impulse over ∼100 symbol periods.4 0. transmission over 3000-km of SSMF this requires the compensation of ∼50. The drawback of such a scheme is that it is not based on blind estimation. 435. This would require a FIR filter bank with >100 taps.if not impossible.2 0 -0.2 0.3.4 0 2 4 6 8 Taps X-Y hn.8: Resulting tap coefficients for a 21 tap FIR filter with 111-Gb/s POLMUX-RZ-DQPSK modulation. for example. Digital equalization algorithms Taps X-X imaginary 0. The lines depict the real and imaginary part part of the tap vector. This uses again the above mentioned butterfly structure and is optimized with either the CMA or the DD-LMS algorithm. For a larger number of taps (>16).75-Gbaud symbol rate.2 Taps Y-X 0. Assuming. Afterwards the signal is converted back to the time domain with an inverse FFT.2 -0.2 -0.xx 0 -0. i.4 0 2 4 6 real 8 10 12 14 16 18 20 22 hn. which would be difficult. The digital equalization steps in such a receiver architecture are shown in Figure 10.4 0. which is discussed in [440]. be written as. 10. as shown in Figure 10. which is shown in [439].9: Digital Equalization using a combination of FFT and linear FIR filters .10.17) where β2 L/2 is the accumulated dispersion. This is for example possible by integrating the phase change 216 . As a first step the frequency can be corrected approximately. 2 (10. the signal processing enables a much larger tolerance towards frequency deviations. is still desirable to tune the LO approximately to the center of this frequency range. (10. (10. |u( f ) · u∗ ( f ) − v( f ) · −v∗ ( f )| · d( f )2 = d( f )2 = exp( j f 2 β2 L). The accumulated PDL in the received signal can as well be estimated using signal processing in digital coherent receiver. For analog coherent receivers the frequency deviations between the transmitter and LO laser is one of the most critical design parameters. which is equal to d( f ) = exp( j f 2 β2 L ). equalization & carrier recovery Y hyx hxy ^ X hyy Diff.Chapter 10. However. .3.3.3 Carrier phase estimation After the electronic equalization a CPE stage is used to correct for the frequency and phase offset between transmitter and LO laser as described by Viterbi and Viterbi in [441]. d( f ) is the chromatic dispersion transfer function. a feedback from the signal processing to LO. that the absolute value of its determinant is equal to one. Digital coherent receivers Clock Recovery X90° Y0° Y90° Approx.14) u( f ) v( f ) −v∗ ( f ) u∗ ( f ) (10. For a digital coherent receiver.15) is a unitary matrix which denotes the transfer function of the DGD. decoding X0° X Carrier recovery FFT hxx ^ Y ^ XI ^ XQ ^ YI ^ YQ FFT Figure 10. The principle behind CPE is shown in more detail in Figure 10. The absolute value of u( f ) or v( f ) can subsequently be used to estimate the DGD.16) A property of a unitary matrix is. Depending on the signal processing algorithms a frequency de-tuning range of several hundred Megahertz [353] to several Gigahertz [435] is possible. H( f ) = where hxx ( f ) hyx ( f ) hxy ( f ) hyy ( f ) = u( f ) · d( f ) v( f ) · d( f ) ∗ ( f ) · d( f ) u∗ ( f ) · d( f ) −v . The argument then gives the phase correction factor θ (k) that is used to apply a correction to the original symbols. (10. s(k) = r(k)4 . (10. The CPE algorithm first takes the 4th power of the symbols in order to remove the phase modulation from the QPSK modulated signal.10. over a large number of symbols or by estimating the shift in the frequency domain after FFT. as shown by Savory et. Subsequently a running average is used over a predefined number of symbols of the complex vectors s(k).) 4 j (k ) e (a) (b) Figure 10.18) where r(k) is either the x or y vector obtained from the equalization stage.. On the other hand. Frequency corr. When ASE is the dominant impairment a larger number of symbols for CPE is more optimal as this will average out the (zero mean) Gaussian noise and obtain a better phase estimate. such as for example a Wiener filter [383]. in the presence of significant phase noise a smaller number of symbols will be preferable as this allows better tracking of the fast change in phase offset.3. The most likely sources of phase noise are a LO or transmitter laser with a broad 217 . r (k ) s (k ) k N i k N r (k ) 4 X slicer j DQPSK decoder slicer j DQPSK decoder ai s ( i ) Delay Y (k ) 1 arg(.. The number of symbols over which the CPE averages can have a critical influence on the performance of the digital coherent receiver. Note that the CPE algorithm works also when it is not preceded by approximate frequency correction. The parameter ai can implement a windowing function. Digital equalization algorithms Approx. but this will generally result in smaller frequency offset window and/or a performance penalty. in [435]. al.19) For an 2N + 1 symbol CPE the N pre-cursor and N post-cursor symbols are considered. k+N i=k−N ∑ ai si .10: (a) Carrier phase estimation and (b) slicer followed by a DQPSK decoder. However. The LO is a tunable ECL with 100-kHz linewidth. A 10. The output power of the LO is 9 dBm. Note that using 2 symbols for CPE is similar to differential detection in a direct detection receiver. with an input power of approximately -9 dBm.4 Distortion compensation at 43-Gb/s Section 10. This might be desirable as it lowers the OSNR requirement by 0. The digital differential decoding is used to avoid the possibility of cycle slips. a digital decision on each symbol is made on the symbols using a slicer.11b and 10. polarization components X and Y. The impact of XPM is especially severe when the adjacent channels are 10. The possibility of cycle slips is effectively avoided through differential detection.5-dB OSNR penalty [10]. as for example shown in [442] where a CPE length of 9 is found to be optimum.12 nm is modulated using an integrated DQPSK modulator.4 Differential decoding & error counting In the final stage of the electronic signal processing. a POLMUX signal is generated by dividing the signal into two tributaries (H and V) and recombining those with orthogonal polarizations and a 106 symbol delay between the tributaries for de-correlation. This results in 43-Gb/s POLMUXNRZ-DQPSK modulation. the differential decoding doubles the BER which results in a ∼0. The signal is then fed into the coherent receiver. When DFB lasers are used for the transmission and/or LO laser.75-Gb/s PRBS with a length of 215 − 1 and a relative delay of 9 bits for de-correlation is split and fed to both inputs (data I and Q) of the DQPSK modulator. Digital coherent receivers laser linewidth (∼MHz) or XPM-induced phase noise from neighboring WDM channels. a shorter CPE length will result in better performance.11c show the directly detected eye diagrams for NRZ-DQPSK with (43 Gb/s) and without (21. Figures 10. For 43-Gb/s POLMUX-NRZ-QPSK the optimum CPE length is found to be averaging over 17 symbols. Each of the polarization components is then fed into a fiber based 90o hybrids where it is mixed with the output of the LO laser. for example because of a sudden jump in phase difference between LO and transmitter laser. The digital coherent receiver setup discussed in Section 10. A cycle slip result in loss of synchronization.5 dB. Afterwards. The PBS splits the signal into two arbitrary.3. there are other algorithms that can be used to detect and correct for cycle slips.5 Gb/s) POLMUX signaling.2 is for simplicity somewhat modified in the experiments. 10. At the receiver the OSNR is set using a VOA followed by an EDFA and a 37-GHz CSF. However.7-Gb/s NRZ modulated. The output signal of an ECL at a wavelength of 1550. as shown in Figure 10. The 90o hybrids 218 .3 discussed the algorithms that are used for the distortion compensation with a digital coherent receiver.11a. manually aligned to within 400 MHz of the transmitter laser. In the experiments discussed in this chapter we use digital differential decoding.Chapter 10. respectively. 10. In this section we discuss the compensation of different impairments using experimental results obtained with a coherent receiver for 43-Gb/s POLMUX-NRZ-DQPSK. but orthogonal. This is discussed in more detail in Appendix C. Using a Tektronix TDS6154 digital storage oscilloscope.5-Gb/s NRZ-DQPSK and (c) 43-Gb/s POLMUX-NRZ-DQPSK. The polarization controllers (PC) between the LO and the 90o hybrids are required because the latter are not polarizationmaintaining.4. where the power variation results from the use of an asymmetric 2:2:1 coupler. Note that. This shows the expected 3-dB difference in OSNR tolerance with the doubling of the bit rate.u) ~ ~ ~ PBS LO PC Off-line signal processing X 0° 90° 90° hyb 93 ps (a) (c) Figure 10. respectively. This indicates that a digital coherent receiver is capable of electrical polarization de-multiplexing without a noticeable performance penalty. the BER is measured at a number of different OSNR values.2 dB and 13.1 Back-to-back OSNR requirement Figure 10.3. unlike the results described in Chapter 7. The in-phase and quadrature components of both polarizations are detected using four single-ended pin/TIA photodiodes. eye diagrams for (b) 21. 10. 219 . the receiver is polarization sensitive for both cases and the OSNR difference is therefore exactly 3 dB.184 bits each (in total ∼ 2 · 106 bits).11: (a) Experimental setup for the 43-Gb/s POLMUX-NRZ-DQPSK transmitter and coherent receiver.75G data B 93 ps Power (a. After processing the differentially decoded sequence is compared to the transmitted PRBS. and the OSNR required for a BER of 10−4 is interpolated. consist of asymmetric 3x3 fiber couplers with a 20%:40%:40% coupling ratio [420]. Distortion compensation at 43-Gb/s 10. Mixing of LO and signal components in the hybrids leads to orthogonal signals on the 20% and one of the 40% outputs. With 43-Gb/s POLMUX-NRZ-DQPSK.10.4. each of the four signals is then sampled with 20-Gbaud ADCs to obtain four data sets of 524. The four data sets are subsequently off-line post-processed with the digital equalization algorithms described in Section 10. the required OSNR is 11. The absolute power on the photodiodes (dominated by the LO) is between -2 and +1 dBm.12a depicts the required OSNR for single polarization 21. taking into account the differential decoding. For back-to-back measurements.5-Gb/s NRZ-DQPSK and 43-Gb/s POLMUX-NRZ-DQPSK with the digital coherent receiver.75G data A MZ VOA H /2 laser MZ delay PBS 10.1 dB for a 10−3 and 10−4 BER.u) V DGD CD SOPMD Arbitrary state of polarization (b) 20Gs/s Storage Oscilloscope 37GHz CSF X0° X90° Y0° Y90° VOA PC 0° 90° hyb 90° Set OSNR Y TE TM PD Power (a. as there is no easy optical compensation approach.12: (a) Back-to-back sensitivity for 43-Gb/s POLMUX-NRZ-DQPSK with the OSNR requirement for 21. 220 . The required OSNR as a function of the LO-signal power ratio is shown in Figure 10. (b) Required OSNR versus LO-signal ratio. As a first step.12b. A high LO-signal power ratio is beneficial as it reduces the impairments resulting from direct detection components. It can also be observed that the OSNR requirement is slightly reduced at 0-ps DGD when the number of filter taps increases.1nm) (a) LO-sig power ratio (dB) (b) Figure 10.1nm) BER = 10-4 18 20 22 24 14 16 OSNR (dB/0. the measured results shows that the OSNR penalty is minimal for a relatively broad range of LO-signal power ratios. and 18 dB is used in the remainder of the experiments. When the number of FIR taps is reduced to 5.5-Gb/s NRZ-DQPSK as a reference.5-Gb/s NRZ-DQPSK 12 13 14 18 Required OSNR (dB/0. For 13 taps no significant penalty is measured for a DGD up to 200 ps. the inverse channel constructed by the FIR filters can effectively cancel out the distortion induced through DGD. This corresponds to an mean DGD of about 60 ps for a 10−5 outage probability. 10. which is approximately the DGD tolerance of a direct detection 2.2 Differential group delay Probably the most significant impairment that can be compensated with a digital coherent receiver is PMD. which results in a worst-case alignment.5-Gb/s NRZ-OOK receiver. Figure 10.4. We conjecture that this results from the equalization of transmitter and receiver imperfections. Since a digital coherent receiver detects the linear optical field for both polarization states and DGD is a linear distortion in the optical field. The optimum LO-signal power ratio is between 18 dB and 20 dB. However.Chapter 10. A too high LO-signal power ratio results here in a higher OSNR requirement as the signal power becomes too small (the LO power is kept constant). only the DGD is considered using a DGD emulator.13a shows the DGD tolerance for different numbers of FIR taps. Digital coherent receivers -2 8 FEC limit 9 Q (dB) 16 15 14 13 12 11 10 16 log(BER) -3 -4 -5 -6 -7 6 8 10 12 43-Gb/s 10 POLMUX11 NRZ-DQPSK 21. a 1-dB OSNR penalty is evident for 60 ps of DGD. The input SOP into the DGD emulator is set to a 45o offset with respect to the transmitted polarization tributaries. 3. PDL is more detrimental for POLMUX signaling in comparison to polarization insensitive modulation as it results in a performance difference between the polarization channels. but as shown in Section 7. respectively. Required OSNR (dB/0. When the PDL is combined with up to 120 ps of DGD. coherent equalization can still recover the polarization tributaries.10.11b. Here. for this case we also expect to observe similar penalties with a digital coherent receiver. respectively. This is most likely the result of the attenuated tributary having insufficient signal power to use the full dynamic range of the ADCs. followed by a DGD emulator. PDL is added to the signal as a power imbalance by attenuating one of the polarization tributaries in the transmitter. slightly higher penalties are evident.4. In Figure 10.1nm) 5 taps 16 Required OSNR (dB/0. Hence.13: (a) required OSNR versus DGD for various tap lengths and (b) DGD tolerance PDL and in the presence of 2-dB and 5-dB of PDL.4 Higher-order polarization-mode dispersion Higher-order PMD can have a severe impact for POLMUX signaling as the polarization demultiplexing becomes wavelength dependent.13b the worst-case tributary is depicted for 2 dB and 5 dB of PDL.4.13b shows the influence of PDL on the digital coherent receiver. As a result. The experimental setup that is used here to evaluate the combined effect of DGD and SOPMD is depicted in Figure 10. BER = 10 BER = 10-4 0 50 100 150 200 0 20 40 60 80 100 120 140 Differential group delay (ps) (a) Differential group delay (ps) (b) Figure 10. The combined impact of PMD and PDL might have a more significant impact.14a. SOPMD is added to the signal using a NewRidge NRT-40133A emulator preceded by a second polarization scrambler. Distortion compensation at 43-Gb/s 10. without 10. This indicates that even with a severe power imbalance between both channels. which results in depolarization [326]. but is not considered here. both tributaries will also have a different OSNR at the receiver.4 the difference in penalty between both cases is marginal for a direct detection receiver. The signal passes first through a polarization scrambler to randomize the state of polarization.4. Subsequently.1nm) 18 20 18 16 14 12 10 -20 5 dB PDL 7 taps 2 dB PDL 14 13 taps 12 no PDL -4 13 taps.3 Polarization dependent loss Figure 10.1 dB and 3. The SOPMD 221 . Note that PDL induced depolarization is not considered here. The lower signal power in the worst-case tributary reduces the OSNR by 1.2 dB compared to the average OSNR. which equals the case shown in Figure 7. the line indicates back-to-back performance and a 13 tap FIR filter is used. 40 measurements for each setting/OSNR) no relevant penalty is observed. 270-ps2 SOPMD and a 13 tap FIR filter. emulator is set to add the maximum amount of 20 ps of DGD and 270 ps2 of SOPMD to the signal. For this configuration (Figure 10. (b-d) 270-ps2 SOPMD combined with different amounts of DGD.Chapter 10. Digital coherent receivers (a) TX 60 ps scrambler PBS PBS scrambler -2 SOPMD emulator -2 RX -2 20-ps DGD 20-ps + 60-ps 20-ps + 120-ps log(BER) -3 log(BER) -3 log(BER) DGD -3 DGD -4 -5 -6 8 10 12 14 16 18 -4 -5 -6 8 10 12 14 16 18 -4 -5 -6 8 10 12 14 16 18 OSNR (dB) (b) OSNR (dB) (c) OSNR (dB) (d) Figure 10. -2 Worst-case tributary 8 9 11 12 -5 -6 Best-case tributary -7 16:10 16:30 16:50 17:10 17:30 17:50 18:11 18:31 18:51 19:11 13 14 Q (dB) 10 log(BER) -3 -4 Measurement timestamp Figure 10. both best-case and worst-case polarization tributaries are depicted.15. measurements are depicted over a time period of three hours to show system stability. 270 ps2 of SOPMD will normally not result in a significant penalty due to the small spectral width of the signal. The measurement are taken with a 2 minutes interval. In Figure 10. To illustrate the successful 222 . Note that for a 10-Gbaud symbol rate. In Figure 10. The measured points below the back-to-back OSNR requirement are due to measurement uncertainty. This indicates that coherent equalization is not overly sensitive to SOPMD and meets the requirements of a 43-Gb/s transponder.14: (a) Experimental setup used for higher order PMD evaluation.15: Stability test over three hours with 2-dB PDL.14d the amount of DGD is increased to 120 ps + 20 ps of DGD and 270 ps2 of SOPMD and still the worst-case OSNR penalty is below ∼2 dB for a 10−4 BER.14b. 80-ps + 20-ps DGD. Further statistical measurements are required to understand the fundamental limits of coherent equalization with respect to higher order PMD impairments. 4. when the length of the FIR filters is sufficient to accurately synthesize the inverse transfer function of the channel impulse response. and the impulse energy is therefore spread out over multiple symbol periods. To verify the feasibility of chromatic dispersion compensation. Required OSNR (dB/0. With 13-tap T0 -spaced FIR filters in the equalizer. When the number of taps is reduced to 7.000 ps/nm of chromatic dispersion the OSNR penalty is only in the order of 1 dB for a 13-tap equalizer.1nm) 16 5 taps 7 taps 5 taps 16 7 taps 14 13 taps 14 13 taps -4 60-ps DGD. Distortion compensation at 43-Gb/s compensation of PMD related impairments. PDL. 223 .16.5 Chromatic dispersion The channel impulse response of chromatic dispersion is typically longer than the impulse response of DGD. the tolerance is measured using a combination of DCF/SSMF spools and a fiber-based TDC.1nm) 18 18 Required OSNR(dB/0. (a) only chromatic dispersion and (b) chromatic dispersion plus 60 ps of DGD. The combined compensation of chromatic dispersion and DGD impairments is shown by adding 60 ps of DGD together with different amounts of chromatic dispersion (see Figure 10. confirms the expectation that for such a receiver the chromatic dispersion and DGD tolerance is only limited by the number of FIR taps in the equalizer.10. DGD and SOPMD are added to the signal. only a small BER variation (∼1 dB) is evident over time. The resulting chromatic dispersion tolerance for different numbers of FIR taps is depicted in Figure 10.14b-d. BER = 10 12 BER = 10-4 -4000 -2000 0 2000 4000 12 -4000 -2000 0 2000 4000 Chromatic dispersion (ps/nm) (a) Chromatic dispersion (ps/nm) (b) Figure 10. However.16b). an arbitrary amount of chromatic dispersion can be compensated. This indicates that a digital coherent receiver does not require tunable optical chromatic dispersion or PMD compensation at the receiver. only a small penalty is measured and the tolerance is in excess of ±3000 ps/nm. the dispersion tolerance for a 1 dB penalty is about ±2000 ps/nm.16: Required OSNR versus chromatic dispersion for various tap lengths. For a reduced number of taps the chromatic dispersion tolerance decreases accordingly. The chromatic dispersion and DGD tolerance measured with the digital coherent receiver. The 2-dB of PDL is once again added by attenuating one of the tributaries at the transmitter. The results show that despite the presence of severe PMD impairments. DGD and SOPMD are added in the same way as previously described for the results depicted in Figure 10.4. Even for 60 ps of DGD and 4. 10. 5 nm and 1552. the possible application of digital coherent receivers to 111-Gb/s transmission is also of major interest. the need for either optical or electrical adaptive distortion compensation becomes increasingly more important for higher bit rates. And as a digital coherent receiver combines an excellent OSNR tolerance with the compensation of linear transmission impairments it is an attractive solution to realize robust 111-Gb/s long-haul transmission.Chapter 10.u) 36 ps 36 ps Off-line signal processing X 0° 90° hyb 90° 36 ps 36 ps (a) (b) (c) (d) Figure 10. because the 27. the transmitter and receiver structure shown in Figure 10.2 nm centered on a 50-GHz ITU grid are fed to two modulator chains for separate 224 .18: Eye diagrams for (a) 55.75G data B 50Gs/s Storage Oscilloscope VOA 62GHz CSF X0° X90° Y0° Y90° ~ ~ ~ PBS LO PC PC 0° 90° hyb 90° Set OSNR Y TE TM PD Figure 10.5-Gb/s NRZ-DQPSK. (c) 111-Gb/s POLMUX-NRZ-DQPSK and (d) 111-Gb/s POLMUX-RZ-DQPSK modulation In order to verify the electronic distortion compensation at a 111-Gb/s bit rate.18 shows NRZ and RZ eye diagrams for both DQPSK and POLMUX-DQPSK at a 27. Digital coherent receivers 10. Figure 10. RZ-DQPSK Tx – odd channels RZ-DQPSK Tx – even channels clock 27.75-Gbaud symbol rate. The use of POLMUX-DQPSK modulation is particulary important at a 111-Gb/s bit rate.75-Gbaud symbol rate is low enough to enable conversion to the digital domain using state-of-the-art ADCs.5 Distortion compensation at 111-Gb/s Besides 43-Gb/s transmission.17 are used. Power (a. The output of 10 ECL between 1548. As chromatic dispersion scale quadratically with the bit rate.5-Gb/s RZ-DQPSK.17: Experimental setup for the 111-Gb/s POLMUX-RZ-DQPSK transmitter and receiver. POLMUX-DQPSK is also the modulation format of choice for 111-Gb/s to combine with a digital coherent receiver. (b) 55. Similar to the 43-Gb/s bit rate.75G data A 2 A W G MZM MZ /2 MZ VOA V I N T H delay PBS DGD CD Arbitrary state of polarization 10 27. 7Gb/s NRZ-OOK requires a ∼10 dB of OSNR for a 0−3 BER. Figure 10.5-Gb/s RZDQPSK is shown as a reference. After DQPSK modulation a 50-GHz interleaver with a 45-GHz 3-dB bandwidth is used to combine the even and odd WDM channels.5-Gb/s RZ-DQPSK is significantly broader than 45-GHz. the OSNR requirement cannot be further reduced.19: Back-to-back sensitivity for 111Gb/s POLMUX-RZ-DQPSK with a coherent receiver. And the use of POLMUX-NRZ-DQPSK with coherent detection would further reduce this to ∼11 dB. DPSK requires only a ∼12 dB of OSNR. and the interleaver is therefore bandlimiting the signal. Because of the somewhat limited electro-optic bandwidth of the modulators. the OSNR requirement of the modulation format is particulary significant as it is much higher than for a 10.5. The digital coherent receiver is identical to the one described in Section 10. For the back-to-back measurement the nearest neighbor channels are turned off to allow OSNR measurements.20: Required OSNR for a 10−4 BER versus 3-dB optical filter bandwidth. the OSNR requirement of 55.7-Gb/s bit rate.1 Back-to-back OSNR requirement For a 111-Gb/s bit rate. After detection. a POLMUX signal is generated by dividing the signal in two tributaries and recombining those with orthogonal polarizations and a 353 symbol delay between the tributaries for de-correlation. Note that the optical spectrum of 55.5. NRZOOK is conventionally used as the modulation format for terrestrial long-haul systems. which results in a 48 PRQS. For example.1 nm) Q (dB) 111-Gb/s POLMUXRZ-DQPSK 10 3-dB filter bandwidth (GHz) Figure 10.1nm) -2 24 22 20 18 16 20 30 40 50 60 70 80 90 100 log(BER) -3 -4 -5 -6 -7 10 11 12 13 14 24 55-Gb/s RZ-DQPSK 12 14 16 18 20 22 OSNR (dB/0. 8 FEC limit 9 Required OSNR (dB/0. But this difference can be effectively reduced by using advanced modulation formats. 55-Gb/s RZ-DQPSK with direct detection. For a 10. 10. However. the required OSNR scales with 6 dB when increased from 10.4 with the exception that photodiodes with a ∼30-GHz bandwidth are used. a RZ pulse carver is included to generate RZ-DQPSK. This will result in a significant reduction in feasible transmission distance for 111-Gb/s in comparison to 43-Gb/s 225 . 10.10. the signals are sampled with 50-Gsample/s photodiodes using a Tektronix DSA72004 DSO. The electrical drive signals consist of a 216 PRBS that is split and fed to both inputs of the integrated DQPSK modulators with a 8 bit de-correlation. Distortion compensation at 111-Gb/s modulation of the odd and even WDM channels. When we simply scale the bit rate. Finally.7 Gb/s to 43 Gb/s. when upgrading from a 43-Gb/s to a 111-Gb/s line rate.7-Gb/s and 43-Gb/s bit rate. 111-Gb/s POLMUX-RZ-DQPSK with coherent detection. Interleaver with 44-GHz 3-dB bandwidth.20.2 Narrowband optical filtering The lower symbol rate of POLMUX-RZ-DQPSK in comparison to binary modulation formats is a significant advantage in term of achievable spectral efficiency.3-dB improvement over 107-Gb/s RZ-DQPSK [14] and a >4-dB improvement over 107-Gb/s NRZ-OOK (with an optical equalizer) [12]. The tolerance of 111-Gb/s POLMUX-RZ-DQPSK with respect to narrowband optical filtering is shown in Figure 10.5 Wavelength (nm) 1551 1549. CSF with 40-GHz 3-dB bandwidth.5.01nm/res). (b) 111-Gb/s POLMUX-RZ-DQPSK with filter curves and (c) 111-Gb/s POLMUX-RZ-DQPSK after filtering. respectively.21 depicts the measured optical spectra for 111-Gb/s POLMUX-(N)RZ-DQPSK with the filter curves of a 44-GHz interleaver and 40-GHz CSF superimposed.5 1550 1550. The optical filter used to assess the tolerance is a NetTest X-Tract filter with a nearly rectangular pass-band. Note that a nearly similar narrowband filtering tolerance is obtained when a direct detection receiver is used. which realizes a spectral efficiency of 2. This compares favorably with previously reported 100-Gb/s OSNR requirements as it is a 2. Figure 10.21: Measured optical spectra (0.5 Wavelength (nm) 1551 1549.5 1550 1550. but results mainly from the choice in modulation format.5 Wavelength (nm) 1551 (a) (b) (c) Figure 10. 10. It is therefore advantageous to keep the OSNR requirement as low as possible for 111-Gb/s transmission by using POLMUX-RZ-DQPSK modulation with coherent detection. a 15. As expected. This shows that both filters result in strong spectral narrowing in the case of RZ pulse carving.20. the doubling of the channel capacity results in a 3-dB OSNR penalty. It supports a 111-Gb/s bit rate on a 50-GHz WDM grid. This indicates that the narrowband filtering tolerance is not significantly improved by the coherent receiver. The back-to-back OSNR requirement of both 55.8-dB and 17.5-Gb/s RZ-DQPSK and 111-Gb/s POLMUXRZ-DQPSK is depicted in Figure 10. Digital coherent receivers transmission.21c depicts 226 . This clearly shows the absence of a noticeable filtering penalty until the 3-dB optical filtering drops below 30 GHz. For 111-Gb/s POLMUX-RZ-DQPSK.5 1550 1550.Chapter 10.19. (a) 111-Gb/s POLMUX-NRZ-DQPSK with filter curves. as evident from Figure 10. The sound tolerance toward narrowband optical filtering enables transmission through a large number of cascaded 50-GHz OADMs for 111-Gb/s POLMUX-RZ-DQPSK.8 dB OSNR is required to obtain a BER of 10−3 and 10−4 . The lower OSNR requirement of POLMUX-DQPSK modulation combined with a digital coherent receiver can therefore be instrumental in realizing long-haul transmission systems with a 111-Gb/s bit rate per wavelength channel 10 10 10 111-Gb/s POLMUX-NRZ-DQPSK Relative Power (dB) Relative Power (dB) 0 -10 -20 -30 -40 0 -10 -20 -30 -40 111-Gb/s POLMUX-RZ-DQPSK Relative Power (dB) 0 -10 -20 -30 -40 111-Gb/s POLMUX-RZ-DQPSK 1549. Figure 10.0-b/s/Hz. For 31 taps. 111-Gb/s RZ-DQPSK is normally limited to a 100-GHz WDM grid. 111-Gb/s POLMUX-RZ-DQPSK with coherent detection.10.3 Chromatic dispersion & differential group delay The OSNR requirement for a 10−4 BER as a function of the chromatic dispersion is shown in Figure 10. Required OSNR (dB/0. The RZ spectra after passing through the 40-GHz CSF shows a very similar shape as the NRZ spectra without filtering.5. 55-Gb/s RZ-DQPSK with direct detection. Whereas 111-Gb/s POLMUXRZ-DQPSK can be used on a 50-GHz WDM grid. Because the symbol rate is lowered by a factor of two.75-Gsymbol/s baud rate. This compares favorably with a ∼3-ps DGD tolerance using 107-Gb/s NRZ-OOK and ∼6 ps using 107-Gb/s RZ-DQPSK. Although this improvement is in part due to the 27. When one compares this tolerance to the ∼8-ps/nm chromatic dispersion tolerance of 107-Gb/s NRZ-OOK [14]. 111-Gb/s POLMUX-RZ-DQPSK with direct detection (simulated).22. the increased robustness is nearly two orders of magnitude.5-Gbaud RZ-DQPSK [13].1nm) 26 24 22 20 18 16 26 24 3 taps 22 5 taps 20 18 16 0 20 40 60 80 9 taps 13 taps 21 taps 31 taps BER = 10-4 -1500 -500 500 1500 2500 BER = 10-4 100 12 -2500 Chromatic dispersion (ps/nm) (a) Differential Group Delay (ps) (b) Figure 10. When we takes into account that 100 ps of DGD equals 2.1nm) Required OSNR (dB/0. the most significant contribution results from the coherent detection of the optical field and the subsequent distortion equalization. This indicates that the narrowband filtering results in a quasi-NRZ eye shape.8 symbol periods for a 27. both in comparison to direct detection (CDR receiver). 111-Gb/s POLMUX-RZ-DQPSK requires only half the optical bandwidth of 111-Gb/s (direct-detection) RZ-DQPSK. or ∼25 ps/nm using 55.22. this clearly demonstrates the flexibility of a digital coherent receiver.5. no significant penalty is evident for a dispersion window ranging from 2000 ps/nm to +2000 ps/nm. Distortion compensation at 111-Gb/s the spectra obtained after filtering for 111-Gb/s POLMUX-RZ-DQPSK. 10. 227 . The DGD tolerance for various FIR filter tap lengths is shown in Figure 10.75-Gbaud symbol rate of POLMUX-RZ-DQPSK. while a 9-tap FIR filter shows no penalty for a DGD in excess of 100 ps. It can be observed that a 3-tap FIR filter is effective for a DGD up to 30 ps. And even for 13 taps the measured chromatic dispersion tolerance is in excess of 750 ps/nm.22: Required OSNR for various tap lengths (a) chromatic dispersion and (b) DGD. The OSNR penalty is depicted for different numbers of filter taps in the FIR equalizer. as depicted in Figure 10.5 show that the combination of POLMUX-DQPSK modulation coupled with a digital coherent receiver has excellent tolerance against linear transmission impairments. Double-stage EDFA-only amplification is used and the input power per channel into the DCF is 6 dB reduced with respect to the SSMF.5 nm and 1552. The output of the 9 additional ECLs are modulated using two DQPSK modulators for separate modulation of the even and odd channels.12 nm is selected with a 37-GHz CSF. Digital coherent receivers 10. (b) transmitter with only 43-Gb/s POLMUX-NRZDQPSK modulated channels and (c) transmitter with a single 43-Gb/s POLMUX-NRZ-DQPSK channel surrounded with 10.23b.7-Gb/s NRZ Tx I N 10. 10. 9 co-propagating channels between 1548. The signal is pre-dispersed with DCF having -1360 ps/nm of chromatic dispersion and the in-line under compensation is ∼85 ps/nm/span.6 Long-haul transmission The results discussed in Sections 10.5Gb/s NRZ-DQPSK POLMUX POLMUX I N T POLMUX I N T (b) = 1550.23: (a) Experimental transmission link.12 nm (c) = 1550. Nonlinear transmission impairments are however a different challenge as a digital coherent receiver has limited capability to compensate for such impairments. The re-circulating loop (Figure 10.7Gb/s NRZ 21. Using 228 .6. Loop-induced polarization effects are reduced using a LSPS and power equalization of the WDM channels is provided by a channelbased WSS.5 dB.7-Gb/s NRZ-OOK modulated channels.7Gb/s NRZ T 10.23a) consists of five 95-km spans of SSMF with an average span loss of 18.Chapter 10.1 43-Gb/s POLMUX-NRZ-DQPSK transmission In order to evaluate the performance of 43-Gb/s POLMUX-NRZ-DQPSK modulation in a longhaul WDM transmission system.2 nm are added to the channel under test on a 50-GHz WDM grid. In this section we discuss the transmission performance of POLMUX-DQPSK coupled with a digital coherent receiver for both a 43-Gb/s and 111-Gb/s bit rate.12 nm Figure 10. At the receiver the channel at 1550. (a) TX PreCompensation DCM 37-GHz CSF RX Tx switch Loop switch DCM 95km SSMF 2-5x EDFA Postcompensation 5x EDFA TDC ~ ~ ~ WSS LSPS 43-Gb/s NRZ-DQPSK only Tx I N NRZ-DQPSK T NRZ-DQPSK NRZ-DQPSK Mixed 43-Gb/s + 10.4 and 10. 6. which is found to be -3 dBm. the POLMUX signaling will also somewhat reduce the nonlinear tolerance due to XPM induced nonlinear polarization modulation. When compared to 10. Figure 10. the transmission distance and input power per channel are both varied to obtain an estimate for the transmission reach. Note that the optimum input power of -5 dBm per channel after 900 km is likely due to measurement uncertainty. the nonlinear tolerance of 43-Gb/s POLMUX-NRZ-DQPSK is reduced by 4-5 dB. Number of loops -2 2 FEC limit 3 4 5 6 8 9 FEC limit -2 8 9 log(BER) log(BER) -3 -3 -4 -3 -5 -6 -7 -5 1000 -3 1500 -3 11 12 -4 2375 km -5 11 12 13 13 Optimum input power (dBm/ch) 14 2000 2500 3000 -6 -7 1548 14 1549 1550 1551 1552 Transmission distance (km) (a) Wavelength (nm) (b) Figure 10. each measurement is repeated on 10 separate time instants. the chromatic dispersion at the receiver is either set close to zero. as discussed in Chapter 7. Figure 10.24a shows the feasible transmission distance for the optimum input power per channel.24b further depicts the BER for the 10 co-propagating WDM channels after 2375-km (5 loops) transmission.10. To obtain sufficient measurement accuracy.24: Long-haul transmission results with 43-Gb/s POLMUX-NRZ-DQPSK. On the other hand. There is a slight variance between the even and odd WDM channels. to obtain a total of 2 · 107 bits for error detection. The nonlinear tolerance of 43-Gb/s POLMUX-DQPSK is mainly limited by SPM. (a) BER versus transmission distance and (b) BER for all WDM channels. which results from a slight performance difference between both DQPSK modulators. This results from a drift in bias voltages of the modulator.7-Gb/s NRZ. Long-haul transmission post-compensation and a TDC.24a shows that the feasible transmission distance of 43-Gb/s POLMUX-NRZ-DQPSK with EDFA-only amplification is approximately ∼3000 km. 229 Q (dB) 10 Q (dB) -3 10 . or offset from zero to measure the chromatic dispersion tolerance of the receiver. First of all. Figure 10. which is similar to 43-Gb/s DQPSK modulation. Afterwards the signal is fed into the coherent receiver. respectively. POLMUX signaling can result in XPolM-induced polarization modulation. co-propagating NRZ-OOK channels can result in significant XPM impairments for DQPSK modulated signals.7-Gb/s NRZ-OOK channels As shown in Section 5.1 discussed the nonlinear tolerance under the assumption that all co-propagating channels are 43-Gb/s POLMUX-NRZ-DQPSK modulated.7-Gb/s NRZ-OOK modulated channels clearly reduce the transmission performance.Chapter 10.7Gb/s NRZ-OOK modulated (as depicted in Figure 10. In this case the co-propagating 10. The impact of XPolM is illustrated using the Poincar´ spheres in Fige ure 10. When only a single channel is transmitted. Digital coherent receivers 10.4.7Gb/s NRZ-OOK modulated. Such links are likely to be upgraded in the near future to a 43-Gb/s bit rate.2 Co-propagating 10. the currently installed base of WDM links carries predominantly 10.25 compares the nonlinear tolerance for 43-Gb/s POLMUX-NRZ-DQPSK with and without 10. Figure 10. The XPM tolerance of 43-Gb/s POLMUX-NRZ-DQPSK is therefore a key parameter to determine its suitability for overlay on an existing 10-Gb/s infrastructure. In addition.6. However. the spread in 230 Q (dB) -2 -2 8 . For all measurements the CPE averages over 17 symbols.7-Gb/s NRZ-OOK modulated channels.7-Gb/s NRZ-OOK neighbors. In this case the transmission penalty can be even more severe as the XPM induced phase noise can potentially impair the CPE in the digital signal processing.26. as discussed in Chapter 7. We therefore consider the case that the neighboring channels of a 43-Gb/s POLMUX-NRZ-DQPSK modulated channel are 10. This shows simulated results for transmission over 20x100-km of SSMF with a 2 dBm input power per WDM channel. The transmitter is modified such that only the center channel is modulated with 43-Gb/s POLMUX-NRZ-DQPSK and that the 9 surrounding channels are 10. center channel 43-Gb/s POLMUX-NRZ-DQPSK 6 6 log(BER) log(BER) 8 10 12 14 2 Q (dB) -3 -4 -5 -6 -7 -6 -3 -4 -5 -6 -7 -5 -4 -3 -2 -1 0 1 -6 -5 -4 -3 950 km 10 1425 km 1900 km 12 2375 km 2850 km 14 -2 -1 Input power (dBm/ch) (a) Input power (dBm/ch) (b) Figure 10.25: BER of the center channel versus input power per channel for (a) all channels 43-Gb/s POLMUX-NRZ-DQPSK modulated and (b) 43-Gb/s POLMUX-NRZ-DQPSK center channel with 9 copropagating 10.7-Gb/s NRZ. whereas in a direct detection receiver the impact of XPM is reduced through differential detection. The optimum input power is lowered from -4 dBm to below -6 dBm.7-Gb/s NRZ-OOK neighbors is an important design consideration for 43-Gb/s POLMUX-NRZ-DQPSK. This confirms that XPM-induced phase noise from co-propagating 0.23c) -1 950 km 10ch x 43-Gb/s 1425 km POLMUX-NRZ-DQPSK 1900 km 2375 km 2850 km -1 9ch x 10. this is not the case for a digital coherent receiver.6. As a result the feasible transmission distance for 43-Gb/s POLMUX-NRZ-DQPSK modulation is reduced from ∼3000 km to ∼1800 km. However.7-Gb/s NRZ-OOK channels Section 10. This directly results from the increased XPM and XPolM impairments generated through the co-propagating NRZ-OOK channels. We find that the optimum input power per channel and CPE lengths are respectively -5 dBm and a 5 symbol CPE length. the XPM induced phase noise depends on the bit sequence of the neighboring channels and therefore does not average out when more symbols are taken into account. XPM induced impairments are less dominant and the performance is more OSNR limited. the impact of reducing the averaging in CPE. The shorter CPE (∼5 symbols) improves the reach from ∼1800 km to ∼2800 km.75-Gb/s neighbors when the CPE length is optimized.26c).10.6. the constellation points is minimal. As discussed in Section 10.3.7-Gb/s NRZ-OOK neighbors. In this case a longer CPE length is beneficial. Figure 10.27a shows. However. and no evidence of severe nonlinear impairments is observed.3.26b). Long-haul transmission 0 PSD (dB) -10 -20 -30 -40 -100 -50 0 50 Frequency (GHz) 100 -100 -50 0 50 Frequency (GHz) 100 -100 -50 0 50 Frequency (GHz) 100 (a) (b) (c) Figure 10. for transmission over 1900 km. the spread of the constellation point is marginally increased as long as the co-propagating channels are 43-Gb/s POLMUX-NRZ-DQPSK modulated (Figure 10.27b now depicts the feasible transmission distances for 43-Gb/s POLMUX-NRZ-DQPSK with 10. For high input powers XPM induced phase noise is the dominant impairment and CPE with a smaller number of symbols gives better performance. Figure 10. (a) single-channel. When we add co-propagating WDM transmission on a 50-GHz channel grid. The increased impact of XpolM can be partially alleviated by optimizing the number of symbols used for CPE.7-Gb/s NRZ-OOK modulated the spread of the constellation points increases dramatically (Figure 10. (b)43-Gb/s POLMUX-NRZ-DQPSK neighbors and (c) 10. With an optimized CPE length there is still a penalty evident when 231 . this is evident from the smaller difference between the measured CPE lengths. We now obtain similar depolarization penalties as observed for transmission with POLMUX-NRZ-OOK modulation in Chapter 7. when the neighboring channels are 10. For low input powers.26: Simulated spectra and Poincar´ spheres showing 43-Gb/s POLMUX-NRZ-DQPSK modue lation after 2000-km transmission. 3 111-Gb/s POLMUX-RZ-DQPSK transmission In this section we discuss the transmission performance of 111-Gb/s POLMUX-RZ-DQPSK modulation when combined with a digital coherent receiver.7-Gb/s modulated channels to ≥100 GHz. all 43-Gb/s POLMUX-NRZ-DQPSK neighbors.6.28: Experimental transmission setup. The same transmitter and receiver structure with 10 WDM 232 Q (dB) 6 log(BER) 9 10 -3 . but this penalty is relatively small. (b) BER versus transmission distance for.7-Gb/s NRZ neighbors and a 17 symbol CPE length.7-Gb/s NRZ neighbors and an optimized CPE length.27: (a) BER versus input power per channel after 1.900 km for 43-Gb/s POLMUX-NRZDQPSK with 10.Chapter 10. the residual penalty due to XPolM might make it beneficial to increase the wavelength spacing between the 43-Gb/s and 10. Tx switch TX PreCompensation DCM 40-GHz CSF RX Loop switch DCM 95km SSMF 2-6x Postcompensation 5x WSS LSPS Raman DCM EDFA TDC ~ ~ ~ Figure 10. 10. 10.7-Gb/s NRZ-OOK channels.7-Gb/s NRZ neighbors transmission. 10. The combination of 111-Gb/s POLMUX-RZ-DQPSK modulation with a 50-GHz WDM grid enables long-haul transmission with a 2. compared to transmission with 43-Gb/s POLMUX-NRZ-DQPSK modulated neighbors. This indicates that 43-Gb/s POLMUX-NRZ-DQPSK modulation can be used to upgrade transmission systems that carry legacy 10.0-b/s/Hz spectral efficiency. However. Digital coherent receivers Number of loops -1 3 symbol 5 symbol 7 symbol 9 symbol 17 symbol 2 -2 3 4 5 6 7 8 17 symbol CPE 4 FEC limit log(BER) -2 Q (dB) 8 -3 3 symbol CPE -4 -4 -5 11 12 10 13 -6 -7 1000 1500 2000 14 2500 3000 -6 -5 -4 -3 -2 Input power (dBm/ch) (a) Transmission distance (km) (b) Figure 10. 10.6. Long-haul transmission channels is used as depicted in Figure 10.17. The re-circulating loop setup used for the 111-Gb/s transmission experiment is shown in Figure 10.28. The re-circulating loop consisting of 5x95 km of SSMF and uses hybrid EDFA-Raman amplifiers. The dispersion map is similar as discussed in Section 10.6.1 for 43-Gb/s POLMUX-NRZDQPSK, with -1530 ps/nm of pre-compensation and 85 ps/nm of inline under-compensation per span. The ON/OFF Raman gain in the SSMF provided by the backwards pumped Raman amplifiers is ∼14 dB. Note that the same Raman pump powers are used here as previously described in this thesis. The higher Raman gain results from the use of ”water free” SSMF, which has a lower attenuation around 1450 nm, which is approximately the wavelength range of the Raman pumps. A WSS with a 3-dB channel bandwidth of 43-GHz equalizes the power spectrum for each re-circulation and emulates strong optical filtering as it would occur in cascaded OADMs. Because of the broad optical spectrum of 111-Gb/s POLMUX-RZ-DQPSK, the signal is severely bandlimited through the 43-GHz filtering. After 5 re-circulations, the received spectra of the signal has a bandwidth of 32 GHz and 36.5 GHz (3 dB and 10 dB point respectively). However, as shown in Section 10.5.2 this does not result in a significant penalty for 111-Gb/s POLMUX-RZ-DQPSK modulation. In the receiver the 40-GHz CSF selects the desired channel, and the chromatic dispersion is set to the desired value (either zero or a preselected offset). Subsequently, the signal is fed into the digital coherent receiver. Number of loops -2 2 FEC limit 3 4 5 6 8 9 X Q (dB) log(BER) -3 10 -6 -4 -5 -6 -7 11 -5 -5 -5 -4 1000 Optimum input power (dBm/ch) 1500 2000 12 13 14 2500 3000 Y Transmission distance (km) (a) (b) Figure 10.29: 111-Gb/s POLMUX-RZ-DQPSK; BER versus transmission distance for the optimum input power per channel. Figure 10.30: Measured signal constellation for (a) back-to-back with 25-dB OSNR and (b) after 2375-km transmission (BER 2x10−4 ). First of all, the performance of 111-Gb/s POLMUX-RZ-DQPSK is determined by measuring the BER of the center channel at 1550.1 nm as a function of both input power per channel and transmission distance (see Figure 10.29a). The optimum input power per channel is found to be -4 dBm after 950 km and decreases to -6 dBm after 2850 km of transmission. Note that Figure 10.29 plots the BER for each of the 10 separate measurements, which gives a good indication of the loop induced BER variation. The BER variance also increases for higher input powers as nonlinear impairments become more dominant. However, the BER variation is minimal for the optimum input power of -4 to -6 dBm. Figure 10.30 shows a comparison of the signal 233 Chapter 10. Digital coherent receivers constellations measured back-to-back and after 2375-km transmission. In the presence of strong nonlinear phase noise, the constellation point would normally become asymmetric, as discussed in Section 2.4.7. The symmetry of the constellation points therefore indicates that the impact of nonlinear phase noise is small. Figure 10.32 shows the measured performance for all 10 wavelength channels after 1900 km and 2375 km. All channels show a similar BER between 1 · 10−4 and 5 · 10−4 after 2375 km of transmission. Hence, all measured channels have a margin with respect to the FEC limit of ∼1.5 dB. By varying the post-compensation and the TDC at the receiver, the chromatic dispersion tolerance is measured after 2375 km (see Figure 10.32). Using a 13-tap FIR filter, a dispersion tolerance window of ∼1500 ps/nm is measured without a significant penalty. This is equal to the tolerance observed in the back-to-back measurement. -2 8 FEC limit 9 -2 8 FEC limit log(BER) Q (dB) -3 9 log(BER) -3 -4 -5 -6 -7 1548 1900 km 11 12 13 14 1549 1550 1551 1552 -4 -5 11 12 -6 -1500 -1000 after 2375 km transmission -500 0 500 1000 13 1500 Wavelength (nm) Chromatic dispersion (ps/nm) Figure 10.31: BER for all 111-Gb/s POLMUXRZ-DQPSK WDM channels after 2,375-km transmission. 1,900-km and Figure 10.32: Chromatic dispersion tolerance with a 13-tap equalizer after 2375-km transmission 10.7 Distortion compensation using baud-rate equalizers Although the current state-of-the-art ADCs allows for sampling rate as high as 50-Gsample/s in DSOs, the power consumption makes it unrealistic to integrate such ADCs in a commercial transponder. In addition, the ADCs in DSO are usually based on BiCMOS or SiGe technology, whereas integration in CMOS technology would be desirable for a single-chip solution. It might therefore takes some time before ∼60-Gsample/s ADCs can be integrated into optical transponders. A further concern besides the raw sample rate itself, is the total signal processing required in a 111-Gb/s digital coherent receiver. Assuming that a digital coherent receiver requires 5-6 bits of vertical resolution, over-sampling with 55.5 Gsample/s on 4 input channels requires the processing of 1100-1300 Gb/s. There is no doubt that given the exponential increase in capability of CMOS integrated circuits [16] this will be realizable in the long-term. In the short-term, sampling with only 1 sample/symbol would allow a receiver implementation with a lower complexity and less digital signal processing. On the other hand, sampling with 1 sample/symbol requires the 234 Q (dB) 2375 km 10 10 10.7. Distortion compensation using baud-rate equalizers use of a baud-rate (T0 -spaced) equalizer for the polarization de-multiplexing and distortion compensation. A T0 -spaced equalizer is normally not capable of compensating an arbitrary amount of chromatic dispersion and DGD, and the tolerance will therefore reduce accordingly. Required OSNR (dB/0.1 nm) 22 21 20 19 18 17 16 4 8 12 16 20 BER = 10 -3 22 21 BER = 10 -3 -2 8 FEC limit log(BER) 20 19 18 17 16 4 8 12 16 20 9 10 11 Q (dB) -3 -4 -5 -1500 -1000 after 2375 km transmission -500 0 500 1000 12 1500 3-dB Filter bandwidth (GHz) (b) (a) Chromatic dispersion (ps/nm) Figure 10.33: Required OSNR versus Bessel filtering bandwidth for (a) T0 /2-spaced and (b) T0 spaced equalization; 0 ps/nm, -250 ps/nm and -500 ps/nm chromatic dispersion. Figure 10.34: (c) BER versus chromatic dispersion after 2375-km transmission and with 13tap equalizers T0 /2-spaced, no filtering T0 /2spaced, 7-GHz filter T0 -spaced, 7-GHz filter. The lower performance of a T0 -spaced equalizer can be somewhat alleviated with strong electrical filtering in the receiver [443]. Low-pass electrical filtering increases the ISI and spreads therefore the energy of the received signal to the T0 -spaced sampling points. In addition it removes the aliasing induced through baud-rate sampling. The equalizer must in turn compensate for both the additional ISI resulting from the low-pass filtering, as well as the channel distortions. To illustrate the feasibility of a T0 -spaced equalizer, we determine the OSNR requirement as a function of low-pass filter bandwidth in the presence of chromatic dispersion. This is achieved by low-pass filtering the input samples with an electrical 5th order Bessel filter. Afterwards, the samples are re-quantized using 5 bit resolution to ensure that subsequent signal processing using floating point arithmetic does not reverse the low-pass filtering. Subsequently, the digital signal algorithms as described in Section 10.3 are applied, but with the difference that now T0 -spaced FIR filters are used. Note that the sampling time instant has a large impact when using only 1 sample/symbol. This implies that for such a digital coherent receiver the clock recovery implementation is much more critical. Here, the sample time instant is optimized to give the lowest mean-square error at the output of the equalizer. Figures 10.33a and 10.33b shows the required OSNR with 0, -250 and -500 ps/nm of chromatic dispersion for T0 /2-spaced and T0 -spaced signal processing, respectively, where a 13-tap FIR is used in all measurements. It is evident that for 2 sample/symbol signal processing, the chromatic dispersion tolerance is independent of the electrical low-pass filtering bandwidth. The required OSNR increases only when the filtering 3-dB bandwidth is below 10 GHz as the lowpass filtering starts to incurs a significant penalty. For 1 sample/symbol signal processing, on the other hand, the chromatic dispersion tolerance improves significantly as the electrical low-pass filtering bandwidth is reduced. For a 7-GHz low-pass filtering bandwidth, there is a ∼0.7 dB 235 Chapter 10. Digital coherent receivers back-to-back penalty from the low-pass filtering. For -500 ps/nm of chromatic dispersion, the additional OSNR penalty is less than 1 dB. For a low-pass filtering bandwidth below 6 GHz, the performance is limited by the filtering, both back-to-back and with chromatic dispersion. 0 Transmittance (dB) -5 -10 -15 -20 0 5 5 -order Bessel f 3dB = 7 GHz th 5th-order Gauss f 3dB = 13 GHz 10 15 Frequency (GHz) 20 Figure 10.35: Transmittance spectrum of a 7-GHz Bessel and 13-GHz Gauss filter. The measured optical filter tolerance (as depicted in Figure 10.20) shows a 1-dB OSNR penalty for a ∼27 GHz filtering bandwidth, which is a factor of four difference with the 7-GHz optimal electrical filter bandwidth. In theory, there should be equivalence between the optical and electrical filtering after coherent detection. A factor of two is accounted for by noting that the optical filter is defined as a band-pass, double-sided, bandwidth. On the other hand, the electrical filter bandwidth is defined as a low-pass, single-sided, bandwidth. The other factor of two results from the Bessel filter shape, as the narrowband filtering tolerance is not only defined through the 3-dB bandwidth but strongly dependent on the exact filter curve. A Bessel filter has a very flat roll-off, whereas a Gauss-shaped filter has a steeper roll-off with frequency. When a Gauss-shaped electrical filter is used in the receiver, the filter bandwidth for a 1-dB penalty increases to 13-GHz, a factor of two difference with the (Gauss-shaped) optical filter bandwidth of 27-GHz. This is illustrated in Figure 10.35, which depicts the filters curves of a 5th order Bessel and Gauss filter, with a 7-GHz and 13-GHz 3-dB bandwidth, respectively Next, the T0 -spaced equalizer with 7-GHz 5th order Bessel filtering is used to process the data obtained after long-haul transmission. For both T0 - and T0 /2-spaced FIR filters, this results in ∼0.5dB penalty. When using a T0 -spaced FIR filter, a chromatic dispersion window of ∼1000 ps/nm is obtained without a significant penalty, as shown in Figure 10.34. Hence, we can conclude that a 111-Gb/s digital coherent receiver can be realized using only 27.75-Gbaud ADCs. The tolerance towards chromatic dispersion is sufficient to enable the use of 111-Gb/s transponders on network infrastructure that has been designed for 10-Gb/s systems, without the use of tunable dispersion. The compensation of PMD using T0 -spaced equalizers is not determined here, but in [351, 444] it is shown that it is not possible to compensate for an arbitrarily high PMD. An alternative might be to sample at a slightly higher sample rate, for example with 1.5 sample/symbol, and re-time the samples through signal processing. In [444], Ip and Kahn show that this allows for the compensation of arbitrarily high DGD. In addition, this shows that a 111-Gb/s digital coherent receiver can be realized using an electrical component with a ∼15 GHz bandwidth, which significantly reduces the cost and complexity of the transmitter and receiver. 236 10.8. Summary & conclusions 10.8 Summary & conclusions The digital coherent receiver architecture discussed in this chapter clearly shows the potential of signal processing in optical communication systems. It allows for high bit-rate transmission systems where the system design complexity is shifted more to the electrical domain instead of the optical domain, as is the case for convention transmission systems. The main benefits of a digital coherent receiver can be summarized as: → A digital coherent detection translated the full optical field into the digital domain. This enables efficient signal processing that can theoretically compensate for any (linear) distortion accumulated along the transmission link. → The optical front-end of a digital coherent receiver consists of a LO, PBS and two 90o hybrids, it is therefore much simpler in comparison to a direct detection POLMUX-DQPSK receiver. The four signal components (in-phase & quadrature on both polarizations) are detected with single-ended photodiodes. The resulting direct detection impairments are reduced through a high ∼18-dB LO to signal ratio. → For both 43-Gb/s an 111-Gb/s POLMUX-DQPSK modulation we have shown the effective compensation of linear transmission impairments, i.e. chromatic dispersion, DGD and SOPMD. This confirms that as long as a large enough number of FIR filter taps is used, any linear signal distortion can be compensated. → The impact of PDL results in a penalty for a digital coherent receiver, either due to a OSNR difference between the tributaries or a loss of orthogonality. However, 3 dB of PDL can be tolerated with less than a 2-dB OSNR penalty. We further analyzed the transmission performance of 43-Gb/s and 111-Gb/s POLMUX-DQPSK modulation when combined with a digital coherent receiver: → For 43-Gb/s POLMUX-NRZ-DQPSK, a 2375 km reach is feasible using EDFA-only amplification and an optimal input power of -3 dBm per channel. → A significant drawback for POLMUX-DQPSK modulation is the severe XPM and XPolM penalty incurred through co-propagating NRZ-OOK channels, which reduces the feasible transmission reach. This penalty can be reduced by optimizing the number of symbols used for CPE. However, it remains desirable to increase the channel spacing to ≥100 GHz between 43-Gb/s and 10.7-Gb/s modulated channels. → For 111-Gb/s POLMUX-RZ-DQPSK, a transmission reach of 2375 km is measured using hybrid EDFA/Raman amplification. The optimum input power per channel is approximately -5 dBm. → With 111-Gb/s POLMUX-RZ-DQPSK modulation, a spectral efficiency of 2.0-b/s/Hz is feasible while maintaining a sound tolerance towards narrowband filtering. In a long-haul 237 Chapter 10. Digital coherent receivers transmission experiment, 5 add/drop nodes on a 50-GHz grid are passed. This results in a 32-GHz spectral width after transmission, which does not incur a noticeable penalty. → The higher sampling rate of the ADCs in a 111-Gb/s transponder can be reduced through 1-sample/symbol quantization and subsequent T-spaced signal processing. This requires electrical low-pass filtering with a 7-GHz Bessel filter to spread the energy to the T-spaced sampling points. A >1000-ps/nm chromatic dispersion tolerance with only 0.7-dB OSNR penalty is obtained using a T-spaced 13-tap equalizer. On the basis of these results we can concludes that long-haul transmission with a 43-Gb/s and 111-Gb/s bit rate can be realized using POLMUX-DQPSK modulation and digital coherent receivers. The feasibility of upgrading an existing transmission systems that already carries 10.7Gb/s NRZ-OOK modulation remains a question for further research. The results discussed in this chapter are all based on off-line processing, and the step to realtime processing is a critical one to determine the feasibility of such transmission systems. For example, in [428], Sun et. al. reported the first real-time ASIC implementation of a digital coherent receiver at 43-Gb/s. The described ASIC requires 20 million transistors and has a power dissipation of 21 Watts, which underlines the state-of-the-art nature of this technology. However, the advantages of digital coherent detection are such that it is likely that this technology will be broadly adapted in the upcoming years. 238 This is even more true for POLMUX signaling. (4) chromatic dispersion tolerance. But when digital coherent detection provided a practical alternative to optical polarization de-multiplexing.11 Outlook & recommendations In upcoming years. In this section we aim to compare the various options that can be considered for such transmission systems based on the results described in the thesis. (2) OSNR requirement. many people in the fiber-optic industry considered it only suitable for transmission experiments and never stable enough for commercial deployment. Table 11. 11. It should also be stressed here that technology changes constantly. (5) PMD tolerance and (6) transponder complexity. DQPSK modulation went from the first experimental demonstration at 43-Gb/s to commercial products [309]. In the little over three years that have been covered by the work in this thesis. The comparison in this section is therefore based on the current state-of-the-art and bound to be soon outdated. (3) nonlinear tolerance. Until recently. a field trail has now already demonstrated its feasibility in a deployed network [310]. 239 .1 shows a summary of the advantages and disadvantages of the different modulation formats. And whereas 100-Gb/s DQPSK was not even on the horizon three years ago.1 Robust optical modulation formats The choice of the optical modulation format is a trade-off between a number of different requirements: (1) spectral efficiency and optical filter tolerance. this technology went in the course of less than two years from the first lab demonstrations to commercial deployment [428]. the steady growth in Internet bandwidth will fuel the need to develop and deploy 40-Gb/s and 100-Gb/s optical transmission systems. For 100-Gb/s transponders. DQPSK modulation seems therefore the better choice for PMD-limited transmission links and/or systems with multiple OAMD/PXC nodes. In this case. 1 We 240 . both duobinary and DPSK are difficult to realize due the high symbol rate. This combination of a limited spectral efficiency and feasible transmission distance.000 km 1. either partial DPSK or DQPSK modulation is a better choice because of their higher narrowband filtering tolerance. At the same time. but it is insufficient to negate the need for tunable dispersion compensation (generally 500 ps/nm for a 1-dB OSNR penalty). Outlook & recommendations The importance of each of these requirements differs depending on the optical transmission system. the higher PMD tolerance is a definite advantage of DQPSK modulation. on the other hand. SSMF fiber with a 21-dB span loss. at least for long-haul transmission.8-b/s/Hz and a reach in excess of 500-km. Only those options are discussed that are likely to have a spectral efficiency of >0. which determine the transmission reach. However. It therefore requires both tunable dispersion compensation as well as PMD compensation for transmission over high-PMD fiber. the differences are significant and particulary poor for duobinary modulation. But it is likely that. DQPSK modulation has a better chromatic dispersion tolerance. More likely.0-b/s/Hz spectral efficiency as well as a reduction in the electrical assume here EDFA-only amplification. In comparison. the higher transponder complexity of a DQPSK transponder in comparison to DPSK might negate these advantages. A further concern for DPSK modulation is the smaller chromatic dispersion and PMD tolerance. This makes it difficult to use POLMUX signaling as the interaction between PMD-related impairments and other transmission impairments complicates system design too much.Chapter 11. is a much more attractive option as it allows for a 1. in particular when a transmission link contains multiple OADM/PXC.000 km. Hence. fiber type. with only a 1-dB advantage for DPSK. the higher OSNR requirement will limit the feasible transmission distance. the choice is reduced to duobinary. Duobinary is currently (beginning of 2008) the most widely deployed modulation format for 40-Gb/s transmission. it will be replaced by other options as soon as they become available. (partial-)DPSK or DQPSK modulation1 . is likely to stall the deployment of such formats. DQPSK modulation. We first consider the modulation formats of interest in the absence of electronic equalization. the optimal choice of the modulation format will depend on such factors as the bit rate. However. But more importantly. due to its low transponder complexity 40-Gb/s duobinary might be the best choice for regional networks (300 km . transmission distance and network architecture. which might be useful for PMD-limited transmission links. When we consider the OSNR requirement and nonlinear tolerance. However.500 km). this 1-dB advantage combined with a 2-3 dB advantage in nonlinear tolerance makes DPSK the more suitable choice for long-haul transmission (1. multiple cascaded OADM/PXC in the link and a 3-dB margin with respect to the FEC limit.800 km). the feasible transmission distance of 40-Gb/s DQPSK modulation is not likely to exceed 1. binary modulation formats do not provide a (significant) increase in spectral efficiency when the bit rate is increased from 40-Gb/s to 100-Gb/s. However. This puts stringent requirements on the bandwidth of the electrical components in the transponder. It is therefore unlikely that a ’standard’ modulation format will be the best choice for a wide range of transmission systems. DPSK and DQPSK both have a significantly lower OSNR requirement. The poor filter tolerance of 40-Gb/s DPSK when used on a 50-GHz wavelength grid is its most significant drawback. For a digital coherent receiver. A transmission reach of ∼1000 km seems feasible with POLMUX241 . the nonlinear tolerance can be improved through digital signal processing. DQPSK plus MSPE/MLSE can be an option in transmission links where it is desirable to have a polarization-insensitive receiver. the chromatic dispersion and PMD tolerance depend only on the signal processing and can therefore be nearly arbitrarily high. 11. The OSNR requirement is close to optimum in all three cases with a slight exception for DQPSK. which makes it the most suitable choice with respect to transmission reach. On the other hand. However. However. it requires the most complex transmitter structure of all three modulation formats. POLMUX-BPSK is therefore likely to have the highest nonlinear tolerance. the chromatic dispersion compensation is somewhat limited as the signal processing cannot compensate for arbitrary large distortions without penalty. on the other hand. But. For 100-Gb/s DQPSK. for example in the presence of co-propagating 10-Gb/s NRZ-OOK channels. For 40-Gb/s transponders all three modulation formats seem to be a suitable choice. The same is true for the PMD tolerance as no polarization-diversity receiver is used. which results from both multi-level modulation as well as the required electronic signal processing. POLMUX-BPSK might be the best choice for long-haul transmission as the higher nonlinear tolerance improves transmission reach. For all three formats. Robust electronic equalization bandwidth of the transponder components.11. it is not likely to exceed ∼600 km in commercial systems.2 Robust electronic equalization We now consider the impact of electronic equalization on the choice of the modulation format. the limited speed of state-of-the-art ADCs restrict the symbol rate to <30-Gbaud. the limited nonlinear tolerance and high OSNR requirement will restrict the feasible transmission distance. This disqualifies the use of binary modulation formats for electronic equalization at either 40-Gb/s or 100-Gb/s bit rates. (POLMUX-)DQPSK modulation is more vulnerable to phase perturbations as it has a more dense signal constellation. both the chromatic dispersion and PMD tolerance can be sufficiently high such that no tunable optical compensation is required in the receiver. We therefore consider the following options: direct detection DQPSK modulation combined with MSPE/MLSE and POLMUX-BPSK or POLMUX-QPSK modulation combined with a digital coherent receiver. only POLMUX-QPSK seems to be a viable option as the symbol rate of both DQPSK and POLMUX-BPSK is too high to combine with digital signal processing. POLMUXQPSK has the advantage of a lower symbol rate. When the difference in symbol rate is less significant. which reduces the requirements on the ADCs. 100-Gb/s DQPSK modulation is not directly compatible with the 50-GHz channel spacing of most deployed long-haul transmission systems.2. The main drawback of all three formats is the high transponder complexity. For a 100-Gb/s transponders. With a direct detection receiver. as differential detection is required. The improvement in chromatic dispersion and PMD tolerance is one of the main benefits of electronic equalization. In addition. On the other hand. The main difference with the previously discussed modulation formats is that electronic equalization makes it feasible to use POLMUX signaling. similar as observed for 40-Gb/s transmission. In summary. This could be alleviated through a higher level of optical integration. MSPE/MLSE POLMUX-BPSK. DPSK is the state-of-the-art binary modulation format for 40-Gb/s transmission. However. Spectral Efficiency OOK duobinary RZ-DPSK partial DPSK DQPSK DQPSK. can enable robust and cost-effective optical transmission systems with the capacity to transport the data required for tomorrow’s Internet applications. 3 The nonlinear tolerance depends strongly on the bit rate and dispersion map. 4 The transponder complexity denoted in the table does not include either optical dispersion or PMD compensation. digital signal processing and photonic integration. for example using InP photonic integrated circuits. Outlook & recommendations Table 11. We therefore conclude that the combination of multi-level modulation. and is therefore used here as the reference. it becomes challenging to realize long-haul transmission even when the best possible solution is considered. This in turn indicates that for a 100-Gb/s data rate per wavelength. the combination of multi-level modulation formats and digital signal processing has very advantageous properties to realize robust high-capacity transmission. as this is different for each transmission link and not strictly determined by the choice in modulation format. coherent POLMUX-QPSK. This can either be realized through nonlinear signal processing. A further improvement in transmission reach is only possible through an improvement in nonlinear tolerance.Chapter 11. this combination comes also at the cost of a higher transponder complexity. coherent OSNR requirement Nonlinear tolerance3 CD tolerance PMD tolerance Transponder Complexity4 - QPSK modulation and a digital coherent receiver. in the transmitter and receiver. or through optical compensation along the link. 2 Partial 242 . for example with optical phase conjugation.1: C OMPARISON OF MODULATION FORMATS2 . It is therefore likely that the compensation of nonlinear transmission impairments will become one of the most significant fields of research in the upcoming years. the denoted comparison is an estimation at a 40-Gb/s bit rate. 1 List of symbols · var(·) ∇ α βn γ ˆ γ ∆τ ε0 θ λ λ0 µ µ0 ρ σ τ φ φSPM χ (n) ψ Ensemble average Ensemble variance Vector differential operator Fiber attenuation Group velocity of the nth order Fiber nonlinearly Path-averaged fiber nonlinearly mean DGD Permittivity of vacuum Optical polarization angle Optical wavelength Zero-dispersion wavelength Statistical mean Permeability of vacuum Nonlinear phase noise Statistical variance PMD vector Optical phase SPM-induced phase shift Susceptibility of the nth order Optical polarization phase 243 .A List of symbols & abbreviations A. Appendix A.t) f f0 F gR G h I n n0 n2 nsp N0 Nspan P P0 PDλ L LD Le f f Lspan LW Q S t. List of symbols & abbreviations ω ω0 Ae f f B0 c D Dlocal E(z. T T0 vp Vπ Vpp z Angular frequency Optical carrier frequency Effective area of a fibers core Signal bandwidth (B0 = 1/T0 ) Speed of light (c = 2.99792 ·108 m/s) Dispersion parameter Local dispersion Optical field as a function of time and distance Optical frequency Optical carrier frequency Noise figure (optical amplifier) Raman gain coefficient Gain (optical amplifier) Planck’s constant (h = 6.626068 ·10−34 m2 kg/s) In-phase tributary Refractive index Linear refractive index Nonlinear refractive index Spontaneous emission factor Noise power spectral density Number of spans in the transmission link Optical power Optical input power Polarization dependent wavelength shift Fiber length Normalized dispersion length Effective fiber length Fiber span length Walk-off length Quadrature tributary Dispersion slope parameter Time Symbol time Phase velocity Characteristic voltage of a modulator Peak-to-peak voltage Transmission distance 244 . 2 List of abbreviations ADC AGC Al2 O3 AM APol ASE ASIC AWG BER BERT BPF BSF BPSK CDR CMA CPE CR CRZ CSF CSRZ CW DD DCF DCM DFB DFF DFG DGD DGE DML DPSK DOP DQPSK DSF DSL DSO EAM ECL EDFA EO EOP Analog-to-digital converter Automatic gain control Aluminium Oxide Amplitude modulation Alternating polarization modulation Amplitude spontaneous emission Application specific integrated circuit Arrayed waveguide grating Bit-error-rate Bit-error-rate tester Band pass filter Band selection filter Binary phase shift keying Clock and data recovery Constant modulus algorithm Carrier phase estimation Clock recovery Chirped return-to-zero Channel selection filter Carrier-suppressed return-to-zero Continuous wave Decision-directed Dispersion compensated fiber Dispersion compensation unit Distributed feedback Data flip-flop Difference frequency generation Differential Group Delay Dynamic gain equalizer Directly modulated laser Differential phase shift keying Degree of polarization Differential quadrature phase shift keying Dispersion shifted fiber Digital subscriber line Digital Storage Oscilloscope Electro-absorption modulator External cavity laser Erbium doped fiber amplifier Eye opening Eye opening penalty 245 .A.2. List of abbreviations A. List of symbols & abbreviations Er3+ FBG FEC FIR FFT FWM GaAs GDR GeO2 GVD IFWM InP INT ISI ITU IXPM JD LiNbO3 LMS LSPS MEMS MLSE MSPE MZM MZDI NRZ NZDSF OADM OH− OPC OOK OSNR OTN PBF PBS PC PCD PDF PDL PDM PM PMD POLMUX POLSK Erbium Fiber Bragg grating Forward error correction Finite impulse response Fast Fourier transform Four wave mixing Gallium Arsenide Group delay ripple Germanium Oxide Group velocity dispersion Intra-channel four wave mixing Indium Phosphite Interleaver Inter symbol interference International telecommunication union Intra-channel cross polarization modulation Joint decision Lithium Niobate Least mean square Loop-synchronous polarization scrambler Micro electro-mechanical system Maximum likelihood sequence estimation Multi-symbol phase estimation Mach-zehnder modulator Mach-Zehnder delay interferometer Non-return-to-zero Non-zero dispersion shifted fiber Optical add-drop multiplexer Hydroxyl Optical phase conjugation On-off keying Optical signal-to-noise ratio Optical transport network Pump block filter Polarization beam splitter Polarization controller Polarization chromatic dispersion Probability density function Polarization dependent loss Polarization division multiplexing Phase modulator Polarization mode dispersion Polarization multiplexing Polarization shift keying 246 .Appendix A. A. List of abbreviations PPLN PRBS PRQS PSBT PSD PSK PSP PXC QPM QPSK RIN RX RZ SBS SHG SiO2 SOP SOPMD SPM SRS SSMF TDC TX VOA WDM WSS XPIC XPM XPolM Periodically-poled lithium Niobate Pseudo random bit sequence Pseudo random quaternary sequence Phase shaped binary transmission Power spectral density Phase shift keying Principle state of polarization Photonic cross connect Quasi phase matching Quadrature phase shift keying Relative intensity noise Receiver Return-to-zero Stimulated Brillouin scattering Second harmonic generation Silicon Oxide State of polarization Second order polarization mode dispersion Self phase modulation Stimulated Raman scattering Standard single mode fiber Tunable dispersion compensator Transmitter Variable optical attenuator Wavelength division multiplexing Wavelength selective switch Cross polarization interference canceler Cross phase modulation Cross Polarization modulation 247 .2. Appendix A. List of symbols & abbreviations 248 . However. The impact of isolated transmission impairments. The BER is normally measured as a function of the OSNR. The more accurate measurement is to take the average of the noise power at a slightly higher and lower wavelengths. as this corrects for a (linear) tilt in the spectrum. K(∆T ) (B. with co-propagating WDM channels it is difficult to quantify the noise level. the OSNR cannot easily be measured with high accuracy using this method. As a result. The OSNR is normally determined by dividing signal and ASE power.B Definition of the Q-factor and eye opening penalty The experimental results discussed in this thesis use the bit-error-ratio (BER) to quantify transmission impairments and pulse degradations. We therefore use the BER/Q-factor to quantify the performance in the long-haul WDM transmission experiments. where the ASE power is measured at a wavelength close to the signal. according to. such as chromatic dispersion or DGD.1) where k(∆T ) are the bit errors counted during the time interval ∆T and K(∆T ) is the total number of received bits during this interval. The BER quantifies the fraction of errors that occurred in a given time interval ∆T . 249 . BER = k(∆T ) . The impact of isolated transmission impairments in a long-haul WDM transmission system is more difficult to quantify. in order to define the required OSNR for a certain BER. can then be quantified as a function of the required OSNR for a chosen BER. e. as shown by Bergano et. the optimum decision threshold ID is defined as. When a hard-decision threshold receiver takes a binary decision on a signal degraded by ASE. The Q-factor can then be used to approximate the BER. σ0 + σ 1 (B. in [445].1 Q-factor The Q-factor is related to the signal-to-noise ratio at the decision circuit expressed in terms of the photocurrent [445].1a. This approximation is valid under certain conditions.6) where er f c(·) is the complementary error function and the approximation is valid for a BER lower than 10−2 .3) which is visualized in Figure B.4) This can be written independently of the optimum threshold ID by combining Equations B. (B. 2 2 2πQ 2 (B. Q0 = Q1 = µ0 − I σ0 µ1 − I σ1 (B. respectively.Appendix B. This is valid independently of the specific distribution of the noise probability density functions.4. Definition of the Q-factor and eye opening penalty B. For direct detected phase modulated formats. µ 1 − µ0 Q= .5) σ0 + σ 1 The photocurrent of an ideal photodiode has a Chi-square distribution when the amplitude of the ASE noise is Gaussian distributed. This results from 250 . σ1 σ0 (B. 1 Q Q2 1 √ )≈ √ BER ≡ er f c( exp(− ). This is a result of the quadratic relation between photocurrent and incident optical power. However. al. for a direct detected OOK modulated signal the Chi-square distribution can be approximated with a Gaussian distribution.3 and B. The Q-factor can then be defined as.2) where µ0 and µ1 are the mean photocurrents of the marks (’1’s) and spaces (’0’s) level. and σ0 / σ1 is the standard deviation. Bosco and Poggiolini showed in [446] that a Gaussian approximation of the Chi-square distributed photocurrent is not accurate. Q= µ1 − ID ID − µ0 = .g. It is defined as the distance from the decision threshold to the mean photocurrent divided through the standard deviation. such as a high enough OSNR (>10 dB) and low ISI. ID = σ0 µ1 + σ1 µ0 . the eye opening penalty (EOP) is used as a measure besides the BER to qualify signal impairments. We note that Equation B. It has therefore the advantage that it can be computed 251 . which gives an indication of the system margin.2. this implies that either the Q(dB) or OSNR can be lowered by 3 dB before the FEC limit is reached. (B. Alternatively.6 is still valid for phase modulated formats. The Q-factor is often defined in logarithmic units. Figure B. and can be used to compute the Q-factor based on a known BER. a 1 dB increase in OSNR will result in a ∼1 dB increase in Q(dB). The EOP is not dependent on the OSNR but it is computed only from the shape of the eye diagram. Eye opening penalty the phase demodulation with an MZDI and subsequent balanced detection.6. This is used in this thesis to compute Q(dB) for D(Q)PSK modulation. BER estimation for phase modulated formats is possible through the Eigenfunction Expansion Method [288] or using the Karhunen–Lo´ ve approximation [299].1: (a) Definition of the optimum decision threshold and (b) relation between Q and BER.2 Eye opening penalty In the analytical simulations. B. I0 Probability ID I1 18 16 Q(dB) ‘0’s ‘1’s 14 12 10 8 Photocurrent (mA) (a) 6 -12 -10 -8 -7 -6 -5 -4 -3 -2 log(BER) (b) Figure B. which affects the probability density distribution of the noise. Q(dB) = 20 · log10 (Q). but it is not accurate to compute the BER using Equation B.7) Using Q(dB) as an indication of transmission performance has the advantage that it is proportional to the OSNR. When a transmission operates at a 3 dB margin with respect to the FEC limit. Hence.1b visualizes the relation between log(BER) and Q(dB). This property is used to express the system margin in long-haul transmission systems. We note that the Q-factor can still be defined for phase modulated formats.B. Both BER estimae tion approaches have been used in the analytical simulations of this thesis. Definition of the Q-factor and eye opening penalty with relatively low computational effort. (B. The 20% eye opening width is used here to account for signal jitter.2: Definition of the EOP and its relation to the shape of the (electrical) eye diagram.9) The EOP(dB) is zero for an ideal NRZ-OOK eye diagram. the necessity to include balanced detection limits the EOP computation to the electrical eye diagram. In the comparison between modulation formats. The definition of the eye opening is the largest square box with a width equal to 20% of the symbol period that fits into the eye diagram. the EOP is therefore normalized with respect to the EOP in the absence of transmission impairments We note that the EOP can be computed either from the optical eye diagram (before the photodiode) or the electrical eye diagram. The EOP is usually defined in logarithmic units as. In particular RZ pulse carving lowers the EOP below zero. it can be a factor of 2-3 smaller than the OSNR penalty [330]. 2 · mean .1 graphically depicts the definition of the EOP. In particular in the presence of ISI. such as chromatic dispersion or PMD. Figure B. The EOP based on the electrical eye diagram is a more realistic definition as it includes the impact of narrowband electrical filtering. (B. Several definitions of the EOP exist in literature.2T0 Signal amplitude (mA) T0 mean Eye opening (EO) Time (ps) Figure B.8) EOP = EO where mean defines the average value of all lines in the eye diagram and EO is the eye opening. The EOP is not always a good approximation of the OSNR penalty. where T0 is the bit interval.Appendix B. but it can be lower than zero for other modulation formats. 0. 252 . such as for example in Chapter 8. EOP(dB) = 10 · log10 (EOP). For phase modulated formats. but in this thesis we defined it as. 1.1: Coherent receiver using an asymmetric 3x3 coupler with 2:2:1 output ratio The input vector x can thus be defined as.1) where we assume that the information is carried in the optical phase ϕ(t) and both the received signal and local oscillator have the same carrier frequency ω0 . The configuration of a coherent receiver using an asymmetric fiber coupler is depicted. x(t ) 1:2:2 LO coupler y1 (t ) PD y2 (t ) i1 (t ) i2 (t ) Figure C.C Asymmetric 3 x 3 coupler for coherent detection As discussed in Chapter 10. in C. The output vector y of the asym253 . a coherent receiver requires a 90o hybrid for detection of the in-phase and quadrature components. for a single polarization. (C. √ P exp( j[ω0t + ϕ(t)]) x(t) = √ s PLO exp( j[ω0t + ϕLO ]) . In this appendix we will give the proof that an asymmetric 3x3 fiber coupler can be used as a 90o Hybrid. In this thesis this has been realized using an asymmetric 3x3 fiber coupler. The two inputs signals of the fiber coupler consist of the received optical signal and the LO laser. φ11 = φ22 = φ33 = 0 . (C. √ √ ⎛ ⎞ 2exp( j π ) 2exp( j π ) 1 4 2 ⎟ √ 1 ⎜ √ ⎟. The elements of S can be written as.6) ⎞ ⎟ ⎟ ⎟ . (C.4 0. k=1 ∑ s2 = ∑ s2 = 1. We now follow this derivation to compute the scattering matrix of an asymmetric coupler with a 1 : 2 : 2 output ratio. Sik = sik e jφik . Using the normalization of the scattering matrix given in [447].2 0.3) The amplitude coefficients of S are therefore directly defined by the output ratio.4) 0. this results in.5) The remaining amplitude coefficients of S can be computed directly out of the amplitude coefficients.4 0.4 ⎠ .2) where i and k are the matrix indexes. For a 1 : 2 : 2 output ratio we then find. (C.8) ⎟ ⎠ .2 0. we assume the coupler to be lossless. Solving this set of equations for a 1 : 2 : 2 output ratio results in the following scattering matrix S.. The scattering matrix derivation for a generalized 3x3 coupler has been analyzed by Pietzsch in [447].4 0. φ12 = φ21 .7) 1 2 4 ⎝ ⎠ 5 √ √ 2 1 − 2 The output vector y(t) follows now out of y(t) = Sx(t). (C. For simplicity. ⎛ √ √ Ps exp( j[ω0 (t) + ϕ(t)]) + 2PLO exp( j[ω0 (t) + ϕLO + π ]) 4 ⎜ √ 1 ⎜ √ PLO exp( j([ω0 (t) + ϕLO ]) y(t) = √ ⎜ 2Ps exp( j[ω0 (t) + ϕ(t) + π ]) + 4 5⎜ ⎝ √ √ 2Ps exp( j[ω0 (t) + ϕ(t) + π]) + 2PLO exp( j[(ω0 (t) + ϕLO ]) 254 s2 s2 − s2 s2 − s2 s2 ml mk jl jk il ik 2sil sik s jl s jk . ⎛ ⎞ 0.4 s2 = ⎝ 0. φ23 = φ32 . S = √ ⎜ 2exp( j π ) (C. Asymmetric 3 x 3 coupler for coherent detection metric 3x3 coupler is now defined by multiplication of the input vector with a 3x3 scattering matrix S. In this case the dissipated power is zero and the scattering matrix has to be unitary.e.4 0.2 By variation of the optical path lengths in and out of the fiber coupler it can be shown that five of the nine angle coefficients can be chosen arbitrarily (see for example also [448]). ik ik i=1 3 3 (C. cos(φik − φil − φ jk + φ jl ) = where i = j = m and l = k. i. (C.Appendix C. (C.The third fiber output of the coupler can be detected with a third photodiode and used to cancel √ out the DC term Ps .9) Ps i(t) = 5 1 2 PLO + 5 2 1 √ 2 2PLO Ps + 5 sin(ϕ(t)) cos(ϕ(t)) . The current after an ideal photodiode is then given by i(t) = |y(t)y∗ (t)|. This we can rewrite as. But in the work described in this thesis the third output is not used and the √ DC term Ps is canceled out using a high LO to signal ratio PLO /Ps .10) Equation C. √ π π 1 Ps + 2PLO + 2PLO Ps [exp( j[ϕ(t) − ϕLO − 4 ]) + exp(− j[ϕ(t) − ϕLO − 4 ])] .10 is equal to the photocurrents described in [449] 255 . 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Khoe. ”Inter-channel Depolarization Impairments in 21. J. Belgium. and H. Gottwald. D. G. Germany. Leisching. 129-132. pp. M. ”Fiber Bragg Gratings for In line Dispersion Compensation in Cost effective 10. 2006. D. Gottwald. pp. D. Spinnler. pp. H. Veljanovski. in Proc. Khoe. Jansen. D. Dec.4-Gbit/s POLMUX OOK and DPSK Transmission”. J. Zeng. de Waardt. P. B. D. 285 . 2005. 2006. D. van den Boom. Dec. c53. and A. Apr. S. P. ”Performance of Maximum Likelihood Sequence Estimation in 10 Gb/s Transmission Systems with Polymer Optical Fiber”. S. and H. S. Jansen. L. List of publications 286 .Appendix C. 8-b/s/Hz. WDM) optische langeafstandstransmissiesystemen. WDM is een aantrekkelijke technologie omdat het een hoge spectrale effici¨ ntie mogelijk maakt.Samenvatting Sinds de introductie van de eerste glasvezelcommunicatiesystemen is de transmissiecapaciteit voortdurend toegenomen en zijn de kosten per verzonden bit continue verlaagd. op basis van de voorspelde toename van het dataverkeer e zal het binnen niet al te lange tijd nodig zijn om een volgende generatie van transmissiesystemen te ontwikkelen.2 tot 0. i. DPSK). namelijk chromatische dispersie en polarisatiemode dispersie (polarization mode dispersion. Voor de volgende generatie van transmissiesystemen is intensiteitsmodulatie echter ongeschikt.0-b/s/Hz. genereert DPSK minder niet-lineaire verstoringen en voldoet een lagere OSNR in de ontvanger.g. PMD). nog steeds beperkt. De transmissiesystemen die momenteel worden ontwikkeld. Het eerste gedeelte van deze dissertatie behandelt modulatieformaten die het mogelijk maken om de capaciteit en transmissieafstand van optische transmissiesystemen verder te verbeteren. Deze formaten zijn dispersie bestendig en gaan daarnaast zuinig om met optische bandbreedte (en maken daardoor een hogere spectrale effici¨ ntie mogelijk). Echter.e. Zo kunnen niet-binaire modulatieformaten met meer dan twee signaalniveaus worden gebruikt. De kern van het wereldwijde telecommunicatienetwerk bestaat tegenwoordig uit golflengte gestapelde (wavelength division multiplexed. Deze systemen zullen naar verwachting 40 Gb/s of 100 Gb/s per kanaal transporteren met een spectrale effici¨ ntie tussen 0. maken daarom meestal gebruik van differenti¨ le fasemodulatie (differential phase-shift keying. DQPSK) wordt e uitgebreid besproken in deze dissertatie. Daarnaast is het een vereiste dat e de tolerantie ten opzichte van signaalverstoringen vergelijkbaar is met de huidige generatie van transmissiesystemen. de efe fici¨ ntie waarmee de beschikbare bandbreedte van een fiber wordt benut. Commerci¨ le WDM e e transmissiesystemen gebruiken tegenwoordig maximaal 80 kanalen met een 50-GHz kanaalafstand en 10-Gb/s of soms 40-Gb/s per golflengte kanaal.8 tot 2. 40 Gbaud) is de robuustheid ten opzichte van de belangrijkste lineaire verstoringen. Dit vertaalt zich in een spectrale effici¨ ntie van 0. Maar door de hoge symboolsnelheid (e. 40-Gb/s DQPSK moduleert 2 bits per symbool en ben287 . Vergeleken met e intensiteitsmodulatie. OSNR) nodig en genereert sterke niet-lineaire verstoringen op de transmissielijn. Van oudsher maken optische transmissiesystemen gebruik van intensiteit gemoduleerde signalen. heeft een hoge signaal-ruis verhouding (optical signal-to-noise ratio. Het vereist doorgaans een te grote kanaalafstand. In het bijzonder 40-Gb/s dife ferenti¨ le kwadratuur fasemodulatie (differential quadrature phase shift keying. Elektrische compensatie is echter bijzonder effectief wanneer het wordt gecombineerd met een coherente ontvanger. Gecombineerd met optische fase omkering (optical phase conjue gation) kan dit verder worden verbeterd en is het mogelijk om een transmissieafstand van 4. waardoor modulatie met 4 bits per symbool wordt gerealiseerd. zoals de concentratie van dispersie compensatie op slechte enkele punten langs de transmissielijn en dispersie compenserende fiber-Bragg gratings. een verhoging van de benodigde OSNR en een lagere tolerantie ten opzichte van niet-lineaire verstoringen. Voor incoherente ontvangers kan multi-symbol phase estimation (MSPE) worden gebruikt om zowel de OSNR als de niet-lineaire tolerantie van D(Q)PSK modulatie te verbeteren.0-b/s/Hz spectrale effici¨ ntie. Deze techniek moduleert de beide orthogonale polarisaties in een fiber onafhankelijk van elkaar. Hierdoor kan de spectrale effici¨ ntie worden verdubbeld en de symboolsnelheid worden e gehalveerd in vergelijking tot niet-polarisatie gestapelde signalen.6-b/s/Hz. Daardoor kunnen bijna onbeperkt hoge chromatische dispersie en PMD waardes worden gecompenseerd en tegelijkertijd kan een polarisatie gestapeld signaal worden opgesplitst in de beide polarisatiecomponenten.Appendix C. Om de spectrale effici¨ ntie e verder te verhogen.375 km met e 2.700 km en een spectrale effici¨ ntie van 1.als nadelen. fase en polarisatie) overgezet naar het elektrische domein. We beschrijven daarnaast de combinatie van 40-Gb/s DQPSK modulatie met verschillende dispersie compensatie technieken. Het verbetert de tolerantie ten opzichte van chromatische dispersie en PMD. We bespreken de mogelijkheid om langeafstandstransmissie te realiseren met 40-Gb/s DQPSK modulatie en laten zien dat een maximale afstand van 2. We bespreken de benodigde systeemarchitectuur voor een digitale coherente ontvanger en behandelen daarnaast een 100-Gb/s POLMUX-DQPSK transmissie experiment over 2. de wisselwerking tussen PMD en andere signaalverstoringen e maakt het problematisch om deze techniek toe te passen zonder de compensatie van PMD. Op basis van de resultaten in dit proefschrift kunnen we concluderen dat met behulp van nietbinaire modulatieformaten het mogelijk is om langeafstandstransmissie te realiseren met zowel 40-Gb/s als 100-Gb/s per golflengte kanaal en een 50-GHz kanaalafstand. Niet-binaire modulatie heeft echter zowel voor. kan POLMUX signalering worden gecombineerd met DQPSK. Echter. maar het volledige optische basisband veld (amplitude.8-b/s/Hz spectrale effici¨ ntie.800-km kan worden overbrugd met 0. In een coherente ontvanger wordt niet alleen de amplitude.500km te overbruggen. We bespreken een transmissie experiment met 80-Gb/s POLMUX-RZ-DQPSK over een transmissie afstand van 1. Elektronische compensatie versimpelt daarnaast het systeemontwerp en maakt deze modulatieformaten robuust tegen signaalverstoringen. In het tweede deel van deze dissertatie komen polarisatie gestapelde (POLMUX) signalen aan de orde. In het derde deel van deze dissertatie behandelen we elektrische compensatie methoden. 288 . Deze kunnen worden ingezet om de nadelige eigenschappen van DQPSK modulatie en POLMUX signalen te verminderen. maar resulteert ook in een meer complexe zender en ontvanger structuur. Daarnaast kan Maximum likelihood sequence estimation (MLSE) worden gebruikt om de chromatische dispersie en PMD tolerantie te verhogen. Samenvatting odigd daardoor slechts een symboolsnelheid van 20-Gbaud. Stefano Calabr` and Dr.D. As well. It is an interesting observation. Palle Jeppesen.D.D.Acknowledgement ”A dwarf standing on the shoulders of a giant may see farther than the giant himself. In particular. for supervising my graduation project within Siemens and. project. As well. I also received support from many other co-workers and students within Nokia Siemens Networks throughout the Ph. for offering me the possibility to pursue my Ph.D. that together we discussed all aspects of a Ph. Jos van der Tol for the time they invested in reading this thesis and providing me with feedback. The research project we pursued together have redefined my definition of teamwork.” (Didacus Stella) The end of a Ph. that we celebrated together during these years. in all corners of the world. I would like to thank Claus-J¨ rg Weiske. for supervising my Ph. I also would like to thank Dr. Erich Gottwald. he was always only a phone call away when I need advice or a trusted opinion. I would further like to express my thanks to Prof. Doing so. I am very grateful to Prof.D. Huug de Waardt for being my supervisor during all these years. project as well as his flexibility in the cooperation with Nokia Siemens Networks (previously Siemens Communications) have been of great value to me. Dr. Despite the challenge posed by the distance between Eindhoven and Munich. Ton Koonen. Peter Krummrich.D. Sander Jansen. I am as well indebted to Dr. on fiber-optic transmission systems while using exactly such systems. I would like to thank Dr. His ”let’s get this working” mentality was instrumental in building up the highly complicated transmission experiments of which some are described in this thesis. He offered me a chance to pursue research in fiber-optic transmission by arranging for me to go to Munich for my graduation project. I am also greatly indebted to Dr. I will fondly remember the many parties. The most intensive and rewarding cooperation during my Ph. has without doubt been with Dr.D. there. Djan Khoe for his support during these years. both professionally as well as in private life. later on. Prof. I can wholeheartedly conclude that the past three and a half years have been an exciting time. Robert Killey and Dr. In a time when engineering positions where hard to come by this provided me with the best possible choice I could have made. Vladimir Veljanovski and Mohammad Alfiad for reading parts of this thesis and helping me to improve this work through their comments. This would not have been possible without the support of many. project is a very suitable moment in time to look back and reflect on the years past. Antonio Napoli. Prof. Nancy Hecker-Denschlag. o 289 . to whom I would like to express my sincere gratitude here. His continuing support throughout my Ph. project within o Nokia Siemens Networks and for all the stimulating technical discussions we had over the years. I would like to thank Dr. Dr. Johan van Zantvoort. which covers most of the results in Section 9. Stefan Sp¨ lter for the effort he put into keeping me at Nokia Siemens Networks after a finishing my Ph. Carl Paquet and Yves Painchaud of Teraxion for supplying me with FBG samples to measure the impact of phase ripple on DQPSK modulation. without the intention to forget someone. From Eindhoven University of Technology I would further like to thank. Dr. Alessandro Bianciotto. Bas Huiszoon. to finish with the words of Moliere. I particulary would like to thank Murat Serbay from the University of Kiel for his work during our first long-haul RZ-DQPSK transmission experiment. Dr. Dr. I would like to thank Iveth for her support. Juraj Slovak. Dr. Torsten Wuth.2. Dr. Susan de Leeuw. for his excellent master thesis work. Achim Autenrieth. Without their help on all things electrical. Els Gerittsen and Jos´ Hakkens for their great e help with the administrative work. Nicola Calabretta. Chris Fludger. Dr. Christoph Schulien of CoreOptics for our cooperation on the transmission experiments with a digital coherent receiver. without the intention to forget someone. Arne Striegler. As well. I am very grateful to my parents Walter and Antoinette. Wolfgang Schairer. Dr. Bernt Satorius and Carsten Bornholdt from the Heinrich-Herz Institute for our cooperation on DPSK regeneration and the Enterprise Services group from T-Systems for their support during our DQPSK field-trail. Dr. I am indebted to the secretaries of the department. Maria Garc´a Larrod´ . Dr. because to live without loving is not really to live. David Stahl. project at Nokia Siemens Networks will be as successful as your master thesis. Furthermore. the many trips to D¨ sseldorf u airport when I was coming from or going to Munich are very much appreciated. Dr. Dr. I also very much enjoyed working together with Ernst-Dieter Schmidt. But most of all I would like to thank her. As well. Dr. Acknowledgement Andreas Sch¨ pflin and Erik de Man. And finally. Gottfried Lehmann. Lutz Rapp. Dr. patience. A word of encouragement and thanks here also to Mohammad Alfiad. it would not have o been possible to build up many of the optical transmission experiments covered in this thesis. I hope that your Ph.D. Harm Dorren. Dario Setti. my sister Marieke. I want to express my thanks to. I further would like to thank Vladimir Veljanovski for his everlasting good mood and our after-work parties in ’Dilingers’. Dr. her husband Dolf and my brother Gijs for supporting me throughout these years. Eduard Tangdiongga and Dr. Christian Sanabria von Walter. ı e Prof. As well. Sebastian Randel is gratefully acknowledged for his work on the DPSK receiver software and our many technical discussions. and I’m grateful for the effort he put into organizing the various cooperations. project. Bernhard Spinnler. Maxim Kuschnerov of the Federal Armed Forces University Munich for our fruitful discussions on signal processing algorithms. Ulrich Gaubatz for the helpful advice he has given over the years.Appendix C.D.D. Thomas Duthel and Dr. Fabian Hauske of the Federal Armed Forces University Munich for his work on MLSE receivers. Finally. as well as for reading and correcting large parts of this thesis. Dr. I’m grateful to Dr. I also would like to thank my mother for correcting the Dutch summary in this thesis. 290 . Hans-Joerg Thiele. During my Ph. I have been in the privileged position to cooperate with many people from other universities and companies. Dr. Cornelius Cremer. although he never convinced me of his theory on group velocity dispersion. Christian Palm and Carlos Climent. Dr. Jeffrey Lee. Patrick Leisching. Uwe Feiste. encouragement. he wrote 5 patents related to fiber-optic communications.Curriculum Vitae Dirk van den Borne was born in Bladel. he has authored and co-authored more than 50 peer-reviewed journal papers and conference contributions. In June 2004. Germany. Germany.D. degree in electrical engineering at the Eindhoven University of Technology. cum laude.Sc. at the Fujitsu laboratories Ltd. In 2007 he received the telecommunication award from the Royal Institution of Engineers in the Netherlands (KIVI-NIRIA) and the IEEE Laser & Electro-Optics Society (LEOS) graduate student fellowship. of which 10 were invited contributions. 1979. on October 7. Japan. His Ph. He received his M. programm. The Netherlands. working on super-continuum generation and pulse compression. In 2002-2003 he spend 4 months. Germany. The research was carried out in the long-haul optical transmission R&D department of Nokia Siemens Networks (previously Siemens AG) in Munich. After completing the VWO (secondary school) at the PIUS-X college in Bladel in 1998. alternative dispersion compensation schemes and electronic impairment mitigation.D.Sc. During his Ph. he performed his Master’s thesis work at Siemens AG in Munich. In addition. studies. Dirk is with Nokia Siemens Networks in Munich. in Kawasaki. he started working towards the Ph. Since March 2008. Later on. in 2004.D. as part of the M. 291 . work focused on improvements in long-haul optical transmission systems using robust modulation formats. degree. he started studying electrical engineering at the Eindhoven University of Technology. working on polarization-mode dispersion related impairments in polarization-multiplexed transmission. Appendix C. Curriculum Vitae 292 . 215 LMS. 48 OPC. 228 OSNR requirement. 173 equalization. 234 carrier recovery. 106. 52 lumped. 203 analog. 82 OSNR requirement. 223. 113 in-line. 218 direct detection. 39 AMI. 69 CSRZ. 19 digital coherent receiver.Index AGC. 227 DGD. 210 baud-rate. 83 single-ended detection. 215 polarization de-multiplexing. 205 homodyne. 41 hybrid EDFA/Raman. 50 inline under-compensation. 62. 221 digital signal processing. 49 system penalty. 207 baud-rate equalizers. 212 dispersion compensation. 121 tunable. 220. 234 ASE. 44 analog-to-digital converters. 52 pre-compensation. 212 FFT. 219. 207 hetrodyne. 77 chromatic dispersion. 218 DCF. 175 performance monitoring. 109 post-compensation. 51 accumulated dispersion. 44 Raman. 204 digital. 43 C-band. 227 long-haul transmission. 69 CWDM. 54. 79 partial. 48 DCF. 7. 111 optimization of. 209. 82 demodulation. 205 intra-dyne. 225 polarization dependent loss. 49 differential group delay. 234 chromatic dispersion. 77 293 . 76 DGD. 25. 55. 14 cycle slips. 214 MLSE. 51 dispersion maps. 15 DPSK. 49 attenuation. 49 index profile. 14 coherent receivers. 207 CRZ. 206 polarization diversity. 7. 77 amplification EDFA. 52 dispersion slope. 211 CMA. 212 coherent. 74 balanced detection. 184 MSPE. 38. 207 differential decoding. 216 clock recovery. 49 FBG. 87 MZDI. 82. 88 duobinary. 92 precoder. 197 OOK. 36 Mach-Zehnder. 36 meshed networks. 83. 72 OSNR requirement. 73 electrical. 93 polarization dependence. 15 Kerr effect. 76 amplitude imbalance. 47 noise figure. 230 nonlinear phase noise. 36 direct. 106 narrowband filtering. 33 XPM. 81 colorless. 15 group velocity dispersion. 73 DGD. 117 DQPSK. 16 duobinary. 176 multi-level modulation. 99 OSNR requirement. 41 amplifier structure. 138 NLSE. 22 FWM. 23 nonlinear impairments. 69. 188 partial DPSK. 67 POLMUX. 69 EDFA. 75 DQPSK. 182 . 184 DPSK. 94 nonlinear tolerance. 28. 89 PRQS. 186 modulation. 150 XPolM. 76 destructive port. 175 laser linewidth. 57 tunable. 30 laser linewidth. 31 SPM. 25. 113 GDR. 189 Gaussian model method. 186 joint-symbol. 27. 76 differential delay. 145 SRS. 63. 180 nonlinear phase noise. 150. 5. 97 long-haul transmission. 71 polybinary. 29 IFWM. 77. 134 POLMUX-DQPSK. 55 cascading of. 70 electro-absorption. 31 compensation. 47 stimulated emission. 40 group velocity. 116 FEC. 101 DSF. 178 priciple of. 42 FBG.Index DQPSK. 73 PSBT. 191. 36 DPSK. 43 ASE. 1 Mach-Zehnder modulator. 194 trellis decoding. 14. 77 constructive port. 187 histogram method. 58 294 MLSE. 30 IXPM. 180 long-haul transmission. 97 demodulation. 36 OOK. 23 L-band. 30 nonlinear phase noise. 93 phase offset. 76 chromatic dispersion. 71 optical. 56 phase ripple. 158 MSPE. 57 wavelenght de-tuning. 87 chromatic dispersion. 89 DGD. 182 OSNR requirement. 25 PRQS. 20 POLMUX. 19 state of. 21 distribution. 142 nonlinear tolerance. 28 Jones vector. 16 OADM. 143 polarization interleaving. 12 transponder. 4. 23 nonlinearity. 221 interleaving. 143. 67 NZDSF. 3 WSS. 150 dispersion tolerance. 228 narrowband filtering. 58 OOK. 38 polarization degree of. 11 birefringence. 20 depolarization. 4 spectral efficiency. 131 POLMUX. 21 polarization multiplexing. 60 partial DPSK. 137 PMD tolerance. 152 principle. 45 amplifier structure. 14 effective length. 22. 37 Raman amplification. 131 depolarization. 59 conversion efficiency. 101 pulse carving.Index nonlinear Schr¨ dinger equation. 58 295 . 17 Poincar´ sphere. 138 second order. 207 direct detection. 18 chromatic dispersion. 63 polarization dependence. 61 PPLN. 150 POLMUX-DQPSK. 5. 18 e principle states of. 83. 62 DQPSK. 18 dependent loss. 20 optical compensation. 4 WDM. 162. 169 SSMF. 121 nonlinear phase noise. 226 nonlinear tolerance. 138 polarization dependent loss. 159 long-haul transmission. 25 insertion loss. 46 re-circulating loop. 44 effective noise figure. 207 polarization interleaving. 121 dispersion compensation. 22 polarization. 46 backward pumping. 165 power map. 16 optical phase conjugation. 132 XPolM. 17 polarization diversity. 145 OSNR requirement. 45 safety. 57 outage. 44 all-Raman. 162. 16 Stokes parameters. 194 photodiode. 12 nonlinear coefficient. 23 o NRZ-OOK. 12 manufacturing. 106 robustness. 160 PMD. 157 coherent detection. 45 forward pumping. 164 polarization mode dispersion. 67 optical fiber. 166 OSNR requirement.