Modulation Schemes

UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONGUNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Contents ECTE465 Lecture 4 Assoc. Prof. Tadeusz A Wysocki (Tad) [email protected] tel: (02) 4221 3413 • Digital Modulation Schemes – PSK – QAM – MSK – GMSK • Spread Spectrum Communications ECTE465 L.4 ECTE465 L.4 10/3/2006 Dr Tad Wysocki ECTE465 L.4 ECTE465 L.4 2 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Introduction • A digital modulator is a device that maps digital information onto analog waveforms. • This is done to: – minimize the effect of channel – minimize the energy per transmitted symbol – minimize the bandwidth – facilitate distinction between different symbols. Digital Modulation Schemes • Factors influencing the choice of a modulation scheme: – power efficiency (sometimes referred to as energy energy per bit to noise power spectral density Eb/N0 error (e.g. 10-6), – bandwidth efficiency ηB describing the ability of a modulation scheme to accommodate data within the given bandwidth; if R is data rate, and B is the bandwidth occupied by the modulated signal, then ηB = R/B bps/Hz. efficiency) ηP, often expressed as the ratio of the signal required at the receiver input for a certain probability of 10/3/2006 Dr Tad Wysocki ECTE465 L.4 ECTE465 L.4 3 10/3/2006 Dr Tad Wysocki ECTE465 L.4 ECTE465 L.4 4 the two phases are separated by 180o.4 ECTE465 L. caused by timevarying channels. Examples of Modulation Schemes • Example of digital modulation schemes used in wireless communication systems: Digital Modulation Schemes Linear CPM Spread Spectrum BPSK FSK Frequency Hopping Direct Sequence QPSK GMSK mQAM 10/3/2006 Dr Tad Wysocki ECTE465 L. 10/3/2006 Dr Tad Wysocki ECTE465 L. – performance of a modulation scheme in an interference environment.4 ECTE465 L.4 ECTE465 L.4 5 10/3/2006 Dr Tad Wysocki ECTE465 L. – sensitivity to detection of timing jitter. – For the sinusoidal carrier of the amplitude Ac. multipath propagation (resulting in time dispersion). like Rayleigh and Rician fading.5Ac2Tb.4 6 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG BPSK (1) • Binary Phase Shift Keying (BPSK) – The phase of a constant amplitude carrier is switched between two values according to the modulating data m1 and m2 corresponding to binary 1 and 0 or +1 and -1.4 ECTE465 L.4 8 .UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Digital Modulation Schemes • Factors influencing the choice of a modulation scheme (ctd. – sensitivity to Doppler spread (due to movements of mobile terminals). – To obtain the best error performance. or 2 Eb Tb cos(2πf c + θ c ) 0 ≤ t < Tb s BPSK (t ) = =− 2 Eb Tb cos(2πf c + π + θ c ) cos(2πf c + θ c ) 0 ≤ t < Tb 2 Eb Eb = 0. – performance of a modulation scheme under mobile channel impairments.): – cost and complexity of mobile terminal. which gives 10/3/2006 Dr Tad Wysocki Ac = 2 Eb Tb Tb 7 for binary -1.4 ECTE465 L. the energy per bit is given by: BPSK (2) • The transmitted BPSK signal is either: s BPSK (t ) = for binary +1. given a particular implementation of the demodulator. 2 -3 t/Tb 10/3/2006 Dr Tad Wysocki ECTE465 L. 0 Data 1 0 -2 Normalized PSD [dB] -1 0 1 2 3 4 5 6 -1 0 2 1 -2 0 BPS K -3 0 0 -1 -2 -4 0 0 1 2 3 4 5 t/Tb 6 -5 0 -6 0 Example plots for BPSK signalling. 1 . • The QPSK signal. 3π/2.2 0 k = 1.2 1 0 .4 -0 . such as 0. has twice the bandwidth efficiency of BPSK.4 ECTE465 L.8 Magnitude 0 . π. it is convenient to introduce pulse shaping.4 ECTE465 L.5. can be expressed as s BPSK (t ) = ± m(t ) 2 Eb Tb cos(ω c + θ c ) where the pulse m(t) is chosen to have a raised cosine spectrum with the rolloff factor α = 0.4 sQPSK (t ) = 2 E s Ts cos[ω c t + 0.4 -7 0 -3 -2 -1 0 1 2 3 (f .4 ECTE465 L. • To minimize the error probability. as 2 bits are transmitted in a single modulation symbol.4 11 10/3/2006 Dr Tad Wysocki 12 . 2.6Rb. for this set of phases. 3.6 0 . the phase of the carrier takes on 1 of 4 equally spaced values. ECTE465 L. π/2. with each phase value corresponding to a unique pair of message symbols.4 ECTE465 L.UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG BPSK (3) 2 BPSK (4) • The 90% of the BPSK signal energy is contained within a bandwidth of approximately 1. and such a generalized BPSK signal can be expressed as: QPSK (1) • Quaternary PSK (QPSK) sometimes referred to as Quadrature PSK. 4 Ts = 2Tb ECTE465 L.4 10 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG BPSK (5) • To improve spectral performance of BPSK.5π (k − 1)] 0 ≤ t < Ts -2 -1 0 1 2 3 0 .fc)Tb 9 10/3/2006 Dr Tad Wysocki 10/3/2006 Dr Tad Wysocki ECTE465 L. • Contrary to PSK.4 ECTE465 L. 10/3/2006 Dr Tad Wysocki ECTE465 L. 3π/4. it allows for both phase and amplitude modulation. 3. or more often as a pair of two amplitudes Ik and Qk.Ts).5π (k − 1)]sin(ω c t ) Q Q • Assuming two orthogonal basis functions: are defined over the interval [0. 5π/4. and phase θk. right-.5π (k − 1)]cos(ω c t ) − 2 E s Ts sin [0. 4 10/3/2006 Dr Tad Wysocki QPSK constellations: ECTE465 L.4 ECTE465 L.4 ECTE465 L.5π (k − 1)]φ 2 (t ) k = 1. π.the carrier phases are: π/4.4 left -.5π (k − 1)]φ1 (t ) − E s sin[0.the carrier phases are: 0. 2.4 ECTE465 L. 13 10/3/2006 Dr Tad Wysocki 14 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG BER for Coherent BPSK and QPSK From QPSK to QAM (1) • Quadrature Amplitude Modulation (QAM) is a generalization of QPSK signalling. we can write: QPSK (3) • The latest formula leads to the graphical representation of QPSK signals sQPSK (t ) = 2 E s Ts cos[0. 3π/2. 7π/4.4 ECTE465 L. φ 2 (t ) = 2 Ts sin(ω c t ) sQPSK (t ) = E s cos[0. then we can write sQPSK(t) in a form: Es I I φ1 (t ) = 2 Ts cos(ω c t ).UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG QPSK (2) • Using a simple trigonometric identity.4 16 .4 15 10/3/2006 Dr Tad Wysocki ECTE465 L. π/2. • Each modulated signal symbol is characterized by a pair of amplitude Ak. 4 ECTE465 L. 19 10/3/2006 Dr Tad Wysocki 10/3/2006 Dr Tad Wysocki ECTE465 L.4 20 . and is therefore more affected by noise. • 16QAM has the largest distance between points. and phase θk. but more susceptible to noise.4 18 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Example • Example constellations for 8-QAM and 16-QAM.ary schemes are more bandwidth efficient.4 Qk = Ak sin(θ k ) Ik = Ak cos(θ k ) 17 10/3/2006 Dr Tad Wysocki 10/3/2006 Dr Tad Wysocki ECTE465 L. and Qk = Ak sin(θ k ) ECTE465 L. • M. φ1 (t ) = 2 Ts cos(ω c t ). Types of QAM Q Q I I • Amplitude and phase shift keying can be combined to transmit several bits per symbol ( in this case M= 4) .4 ECTE465 L.4 ECTE465 L.UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG From QPSK to QAM (2) • Using the previously two orthogonal basis functions. but requires very linear amplification. φ 2 (t ) = 2 Ts sin(ω c t ) Q Qk Ak we can represent any modulated signal symbol having an amplitude Ak. They all require linear amplification. 16PSK has less stringent linearity requirements.4 ECTE465 L.4 ECTE465 L. 0<t<Ts : From QPSK to QAM (3) • Graphical illustration of a QAM principle. as: where: sQAM (t ) = I k cos(ω c t ) − Qk sin(ω c t ) θk Ik I I k = Ak cos(θ k ). but has less spacing between constellation points. 4 24 .4 ECTE465 L. In Offset QPSK.OQPSK – π/4 QPSK Differential π/4 QPSK Q Bit sequence 11 01 00 10 Phase difference π/4 3π/4 -3π/4 . Highly linear amplifier required.4 ECTE465 L. several modifications to BPSK and QPSK have been proposed.UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Other Digital Phase Modulation Schemes • In order to improve performance of digital modulation used in wireless communication systems. and successfully applied.DBPSK – Offset QPSK -.4 21 10/3/2006 Dr Tad Wysocki ECTE465 L. the transitions on the I and Q channels are staggered. so transitions through zero cannot occur.4 ECTE465 L. In π/4. Phase transitions are therefore limited to 90o. This scheme produces the lowest envelope variations. 180o phase transition) . All QPSK schemes require linear power amplifiers.QPSK the set of constellation points are toggled each symbol. S/P Converter 90o Phase Shifter -Asin(ωct) Σ sQAM(t) Pulse Generator Q(t) 10/3/2006 Dr Tad Wysocki ECTE465 L. • Some of these schemes are: – Differential BPSK -.4 22 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Types of QPSK General QAM Modulator Pulse Generator I(t) Acos(ωct) Carrier Generator Data • • • • Conventional QPSK has transitions through zero ( ie.4 ECTE465 L.4 23 10/3/2006 Dr Tad Wysocki ECTE465 L.π/4 I 10/3/2006 Dr Tad Wysocki ECTE465 L. 4 26 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Break GMSK (1) • Gaussian Minimum Shift Keying (GMSK) is a derivative of MSK. the sidelobe levels of the spectrum are significantly reduced. MSK (2) • MSK is spectrally efficient modulation scheme. – characterized with good BER performance (because of the orthogonality).4 27 10/3/2006 Dr Tad Wysocki ECTE465 L. • The premodulation Gaussian filtering introduces inter-symbol interference (ISI) but it is not severe for the 3-dB bandwidth-bit duration product (BTb) of the filter not lower than 0. 10/3/2006 Dr Tad Wysocki ECTE465 L. 10/3/2006 Dr Tad Wysocki ECTE465 L. in which the peak frequency deviation is equal to the half of bit rate. • MSK can be regarded as a special form of OQPSK where the rectangular baseband pulses are replaced with half-sinusoidal pulses.5. compared with MSK. MSK is: – a constant envelope signalling. • By passing the modulating NRZ data waveform through a premodulation Gaussian pulse-shaping filter. and therefore it is attractive for wireless and mobile applications. corresponds to the minimum frequency spacing between upper and lower frequencies in FSK.4 28 . • GMSK with BTb = 0.4 ECTE465 L. Here. – a self-synchronizing signal.4 ECTE465 L. 2∆f is the peak-to-peak frequency shift.5.4 25 10/3/2006 Dr Tad Wysocki ECTE465 L.UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG MSK (1) • Minimum Shift Keying (MSK) is a special type of Continuous Phase-Frequency Shift Keying (CP-FSK). • A modulation index hFSK= 0.5.4 ECTE465 L. • MSK is equivalent to CP-FSK with a modulation index hFSK= (2∆f)/Rb equal to 0.4 ECTE465 L. required for two FSK signals to be orthogonal. • In addition.3 is used in GSM. 4 ECTE465 L. 31 10/3/2006 Dr Tad Wysocki 10/3/2006 ECTE465 L.2 0 .3 2 ln 2 B • In MSK .0 5  π  π exp − 2 t 2 . In GMSK. Magnitude • -2 -1 0 N o r m a liz e d t im e t / T 1 2 3 0 -3 10/3/2006 Dr Tad Wysocki ECTE465 L.4 0 .4 ECTE465 L.3 5 0 .4 ECTE465 L.4 29 10/3/2006 Dr Tad Wysocki ECTE465 L.3. the BT is infinity and this allows the square bit transients to directly modulate the VCO. • The bandwidth of SS signal is relatively insensitive to the data signal.4 ECTE465 L. Dr Tad Wysocki A spread spectrum transmitter. In the diagram.3 0 .  α  α   2 α= BT=0. GMSK generally achieves a bandwidth efficiency less than 0.4 ECTE465 L.6 bits per second per Hz) .4 30 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG GMSK Spectra UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Spread Spectrum (SS) . resulting in transmitted signal having bandwidth being much larger than the data signal. low values of BT create significant intersymbol interference ( ISI) . the portion of the symbol energy α acts as ISI for adjacent symbols.4 32 . • • GMSK has a main lobe 1. If BT is less than 0.1 5 0 . some form of combating the ISI is required.5 times that of QPSK.UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG GMSK (2) • The GMSK filter has an impulse response given by: GMSK (3) • hG (t ) = 0 .7 bits per second per Hz ( QPSK can be as high as 1.1 0 .4 5 0 .(1) • A spread spectrum (SS) signal is generated by modulating a data signal onto a wideband carrier.5 0 .2 5 0 . UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Spread Spectrum (SS) .4 ECTE465 L.4 ECTE465 L. – Frequency Hopping (FH) Signal with hop time Th: » fast hopping Th < Tb.(2) • The most widely applied SS signals are as follows: – Direct Sequence (DS) Signal with chip time Tc. Signal 35 10/3/2006 Receiver Input Dr Tad Wysocki ECTE465 L. – under some conditions can share the same frequency band (as an “overlay”) with other users. because of its noiselike signal characteristics.an important feature for mobile communications.4 34 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Spread Spectrum (SS) . which can be a big obstacle in urban communication.4 36 . usually expressed in dB.(3) • The main advantages of SS signals (from the viewpoint of mobile communications) are: – resists intentional and non-intentional interference -. Spread Spectrum (SS) . – has the ability to eliminate or alleviate the effect of multipath propagation. » slow hopping Th > Tb.4 ECTE465 L. 10/3/2006 Dr Tad Wysocki ECTE465 L.4 33 10/3/2006 Dr Tad Wysocki ECTE465 L. – It is defined as a ratio of the spread spectrum bandwidth WSS to the baseband bandwidth required for data Wd: Gp = WSS/Wd ISI and Interference Rejection • Narrowband Interference Rejection (1/K) S(f) I(f) S(f) I(f)*Sc(f) Receiver Input Despread Signal S(f)*Sc(f) Info. Signal • Multipath Rejection (Autocorrelation r(t)) S(f) S(f)*Sc(f)[αδ(t)+β(t-τ)] αS(f) βρS’(f) Despread Signal – Value of the Gp.4 ECTE465 L.4 ECTE465 L.(4) • Processing gain: – One of the most important parameters of the SS systems is the processing gain Gp. – Chirp Signals (CS). – it is permitted to operate unlicensed SS systems with limited RF-power in the ISM frequency bands. 10/3/2006 Dr Tad Wysocki Info. determines the interference rejection capabilities of the SS system. – Time Hopping (TH). physical implementation of a spreading sequence b(t) . 10/3/2006 Dr Tad Wysocki ECTE465 L.4 38 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Spread Spectrum (SS) .4 ECTE465 L. Block diagram of DS BPSK transmitter. 10/3/2006 Dr Tad Wysocki ECTE465 L.4 ECTE465 L. s(t) = Ag(t)b(t)cos(ω0t + ηc) Baseband spreading DS BPSK transmitter. {gn(j )} = (0.4 39 10/3/2006 Dr Tad Wysocki ECTE465 L.(6) • Example signals for the DS BPSK transmitter with baseband spreading. Spread Spectrum (SS) . the received signal can be expressed as: θ(t) = s(t-τ) + n(t) =Ab(t-τ)g(t-τ)cos[ω0(t-τ) + η0] + n(t) where n(t) is the noise from the channel and the frontend of the receiver. 1. 1) Spread Spectrum (SS) . 1.UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Spread Spectrum (SS) .(5) • • Direct Sequence (DS) SS combined with BPSK as a data modulation is one of the most commonly considered SS scheme. and finally. The transmitted DS BPSK signal is given by: g(t) . 1.4 ECTE465 L.4 37 10/3/2006 Dr Tad Wysocki ECTE465 L.(6) • Alternative transmitter for DS BPSK SS allows for performing spreading in the baseband. 0.4 ECTE465 L.4 40 . • Because of the propagation delay τ.(7) • DS BPSK demodulator recovers the data signal b(t). 0. the sequence of data symbols {bk} from the received signal θ(t).physical representation of bipolar data. the carrier frequency.4 42 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG DS QPSK • Apart from BPSK.UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Spread Spectrum (SS) . 10/3/2006 Dr Tad Wysocki ECTE465 L. 43 10/3/2006 Dr Tad Wysocki 10/3/2006 Dr Tad Wysocki ECTE465 L.4 44 .4 Example signals for DS BPSK receiver. • To perform a successful demodulation.(8) Spread Spectrum (SS) .4 ECTE465 L.4 ECTE465 L. The block diagram of a conventional DS BPSK receiver. only Quadrature Phase-Shift Keying (QPSK) is a modulation scheme commonly discussed in conjunction with DS SS systems. the resulting narrowband signal w(t) is then demodulated using a conventional BPSK demodulator.(2) Functional diagram of a DS QPSK transmitter.(9) • After despreading.4 ECTE465 L. 41 10/3/2006 Dr Tad Wysocki ECTE465 L. DS QPSK .4 ECTE465 L. Functional diagram of a DS QPSK receiver. as well as the beginning of each bit. and its differential form DBPSK. the receiver needs to know the phase ϖ’. ζ0.4 ECTE465 L. a DS QPSK system can transmit twice as much data as a DS BPSK sys-tem that uses the same bandwidth and has the same processing gain and signal to noise ratio.Disadvantages • A disadvantage of a DS QPSK system is a higher complexity than that of a DS BPSK system.4 ECTE465 L. the bandwidth occupied by a DS QPSK signal equals to the half of the bandwidth occupied by an equivalent DS BPSK signal. • In addition. DS QPSK . and therefore equal to the bandwidth of the aggregate signal s(t).4 ECTE465 L.4 45 10/3/2006 Dr Tad Wysocki ECTE465 L. Walsh-Chirp sequences. 16-chip Walsh Sequences 10/3/2006 Dr Tad Wysocki ECTE465 L. FZC sequences.4 46 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Spread Spectrum (SS) .4 ECTE465 L. • Alternatively. • Some examples: – – – – – – m-sequences. • The sequences should possess low mutual crosscorrelation for any relative delay. Walsh sequences. the data rates of bI(t) and bQ(t) are equal to half the rate of b(t).UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG DS QPSK . • Because. Gold codes.4 47 10/3/2006 Dr Tad Wysocki ECTE465 L. also known as pseudo-noise (PN) codes.4 48 . 10/3/2006 Dr Tad Wysocki ECTE465 L.4 ECTE465 L. which can significantly impair the system performance.(9) • There are many families of spreading sequences. Kassami sequences.Advantages • The bandwidth of modulated signals sI(t) and sQ(t) are the same. if the two carriers used for demodulation at the receiver are not truly orthogonal. then there will be a cross talk between the in-phase and quadrature channels. 1 Dj(f-fc) 4 2 3 10/3/2006 Dr Tad Wysocki ECTE465 L. MAI users collide on some hops. • The actual spreading sequences are bipolar sequences.4 50 UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Spectral Properties Slow vs.4 ECTE465 L. Channel introduces noise. ISI. 1} FH Modulator FH Demodulator Spreading codes used to generate a (slow or fast) “hopping” carrier frequency for d(t).4 ECTE465 L.4 ECTE465 L.4 ECTE465 L.MSK) Frequency Hopping Mixer d(t) s(t) Channel Mixer Nonlinear Demod. Narrowband interference affects certain hops. – Correct using error-control coding 1 Di(f-fc) 3 2 4 • Slow Hopping . narrowband and MAI interference. but channel nulls affect certain hops.bandwidth need not be continuous. – Correct using error-control coding and interleaving.UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG 15-chip Gold-like Sequences • There are 16 Gold-like sequences of length 15. Sci(t) • • VCO VCO Sci(t) ˆ g n = (−1) gn ∈ {+1 − 1} .hop on every symbol – NB interference.4 51 10/3/2006 Dr Tad Wysocki ECTE465 L. MAI interference. Channel bandwidth determined by hopping range . • g n ∈ {0.4 49 10/3/2006 ECTE465 L. Dr Tad Wysocki 10/3/2006 Dr Tad Wysocki ECTE465 L. MAI interference. and channel nulls affect just one symbol.hop after several symbols – NB interference. Fast Hopping • Fast Hopping . obtained using the formula: Nonlinear Modulation. – – – – Hopping has no effect on AWGN No ISI if d(t) narrowband.4 52 . (FSK. and channel nulls affect many symbols. 4 ECTE465 L.4 53 .UNIVERSITY OF WOLLONGONG UNIVERSITY OF WOLLONGONG Questions & Comments 10/3/2006 Dr Tad Wysocki ECTE465 L. 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