Characterizing Digitally Modulated Signals Width CCDF Curves Agilent Application Note 5968-6875E

Characterizing Digitally Modulated Signals with CCDF CurvesApplication Note Table of Contents 1. Introduction When are CCDF curves used? 2. What are CCDF curves? Statistical origin of CCDF curves Why not crest factor? 3. CCDF in communications Modulation formats Modulation filtering Multiple-frequency signals Phases affect multi-tone signals Spread-spectrum systems Number of active codes in spread spectrum Orthogonal coding effects Multi-carrier signals 4. CCDF in component design Compression of signal by nonlinear components Correlating the amplifier curves with the CCDF plot Compression affects other key measurements Applications 5. Summary 6. References 7. Symbols and acronyms 2 modulation formats. resulting in a peak-to-average ratio that is dependent upon not only the number of channels being combined. amplified. Similarly. amplifiers). Analog FM systems operate at a fixed power level: analog double-sideband large-carrier (DSB-LC) AM systems cannot modulate over 100% (a peak value 6 dB above the unmodulated carrier) without distortion. Outside of cellular communications. This application note examines the main factors that affect power CCDF curves. the broadcast industry is also moving into the era of digital modulation. Today. baseband DSP signal designers can completely specify the power characteristics of signals to the RF designers by using CCDF curves.Introduction Digital modulation has created a revolution in RF and microwave communications. Power Complementary Cumulative Distribution Function (CCDF) curves provide critical information about the signals encountered in CCDF curves apply to many 3G systems. Cellular systems have moved from the old analog AMPS and TACS systems to second generation NADC. This signal characteristic can lead to higher distortion unless the peak power levels are accounted for in the design of system components. • Evaluating spread-spectrum systems. Third generation systems. These curves also design applications. system manufacturers can avoid ambiguity by completely specifying the test signal parameters to their amplifier suppliers. but also which specific channels are used. The move to 3G systems will yield signals with higher peak-to-average power ratios (crest factors) than previously encountered. and describes how CCDF curves are used to help design systems and components. on the other hand. 3 . and GSM standards. Some of provide the peak-to-average power these applications are: data needed by component • Visualizing the effects of designers. High Definition Television (HDTV) systems will use 8-level Vestigial Side Band (8VSB) and Coded Orthogonal Frequency Division Multiplexing (COFDM) digital modulation formats in various parts of the world. the cellular industry talks of moving to third generation (3G) digital systems such as W-CDMA and cdma2000. • Designing and testing RF components. • Combining multiple signals via systems components (for example. CDMA. and decoded in communication systems. When are CCDF curves used? Perhaps the most important application of power CCDF curves is to specify completely and without ambiguity the power characteristics of the signals that will be mixed. such as amplifiers and mixers. This helps avoid costly errors at system integration time. combine multiple channels. For example. the signal in the form shown in Figure 1A is difficult to quantify because of its inherent randomness and inconsistencies. This means the signal power exceeds the average by at least 7. each of the lines across the waveform shown in Figure 1A represents a specific power level above the average.5 dB for 1 percent of the time.What are CCDF curves? A. Figure 1B displays the CCDF curve of the same 9-channel cdmaOne signal captured on the E4406A VSA.0010% 0. 100% 10% 1% 0. at t = 1% on the y-axis. The power level is expressed in dB relative to the average power.00 ms Figure 1A: Construction of a CCDF curve The signal power exceeds the average by at least 7. For example. Here. Y-axis is the percent of time the signal power is at OR ABOVE the power specified by the x-axis. For example.00 ms 1. The position of the CCDF curve indicates the degree of peak-to-average deviation.5 dB on the x-axis.00 dB/ RF Envelope 3 2 1 Avg 0.00 Res BW 5.1% 0. X-axis is dB above average power Figure 1B: CCDF curve of a typical cdmaOne signal Figure 1A shows the power versus time plot of a 9-channel cdmaOne signal. Ref–10. we need a statistical description of the power levels in this signal.00000 MHz 15. A CCDF curve is a plot of relative power levels versus probability.00010% 0.00 dB A CCDF curve shows how much time the signal spends at or above a given power level. which means we are actually measuring the peak-toaverage ratios as opposed to absolute power levels.010% 0. The percentage of time the signal spends at or above each line defines the probability for that particular power level. with more stressful signals further to the right. the x-axis is scaled to dB above the average signal power. In order to extract useful information from this noise-like signal. Unfortunately.5dB for 1% of the time. 1 2 3 Band-limited Gaussian noise CCDF reference line. This plot represents the instantaneous envelope power defined by the equation: Power = I 2 + Q 2 where I and Q are the in-phase and quadrature components of the waveform. and a CCDF curve gives just that. the corresponding peak-to-average ratio is 7. 4 . The y-axis is the percent of time the signal spends at or above the power level specified by the x-axis.00 dBm 3. B. Let’s start with a set of data that has the Probability Density Function (PDF) shown in Figure 2. Crest factor is the ratio of the peak voltage to its root-mean-square value. a common measure of stress for a stimulating signal has been the crest factor. which makes repeatable measurements difficult. the use of a single level (such as 0.Statistical origin of CCDF curves Rotate -1 0 1 2 dB above average Ref–10. and reliable measurement to meet this need. 5 . To mitigate this.0 RF Envelope PDF 50 40 30 20 10 0 -3 -2 -1 0 1 2 dB above average 3 %Probability 3 50 ab 10 20 Pr 30 ili ty 0 -3 ob -2 % d B -1 ab o 40 ve 0 av e ra 1 ge 2 Avg ExtHt 0. Why not crest factor? As the need for characterizing noise-like signals becomes greater.00dBm 3. let’s briefly investigate the mathematics of CCDF curves. %Probability CCDF CDF 120 100 80 60 40 20 0 120 100 80 60 40 20 0 -3 -2 -1 0 1 2 dB above average 3 In short. • The highest peak value that occurs for true noise depends on the length of the measurement time. crest factor places too much emphasis on a signal’s instantaneous peak value. To generate the CCDF curve in the form shown in Figure 1A. A logarithmic y-axis provides better resolution for low-probability events. To obtain the Cumulative Distribution Function (CDF). the CCDF is the complement of the CDF (CCDF = 1 – CDF). Finally. • A peak that occurs infre quently causes little spectral regrowth.00 ms 1.000 kHz Guassian Samples 1365points @733. While this lessens the emphasis on a single point of a waveform.00 ms -3 -2 3 Now that we’ve seen a practical CCDF curve (Figure 1A). Traditionally.0 Trig Free Res BW 100. convert the y-axis to logarithmic form and begin the x-axis at 0 dB. • A single peak that is much higher than the prevailing signal level sometimes is treated as an anomalous condition and ignored. inverting the CDF results in the CCDF. we search for the most convenient. useful.2 percent of the waveform is above it. That is. while CDF emphasizes minimum values. the peak value is sometimes considered to be the level where 99. CCDF gives us more complete information about the high signal levels than does crest factor [1].8 percent of the waveform is below the peak value.33 ns 50 40 30 20 10 0 %Probability 0. The reason we plot CCDF instead of CDF is that CCDF emphasizes peak amplitude excursions.00 dB/ MaxP -9. and 0.2 percent) is still rather arbitrary. we compute the integral of the PDF. CDF PDF 50 40 30 20 10 0 -3 -2 -1 0 1 2 dB above average 3 dP = 120 100 80 60 40 20 0 -3 -2 -1 0 1 2 dB above average 3 Cumulative Probability 1– = -3 -2 -1 0 1 2 dB above average 3 1- Cumulative Probability Cumulative Probability Figure 2: Mathematical origin of CCDF This measurement is of questionable value for several reasons: • Error-correction coding will often remove the effect of a single error-causing peak in the system. 59 deg I-Q 8 mV/div -40 mV -52. we can fully characterize the power statistics of different modulation formats.01% 0. QPSK signal TRACE A: Ch1 Main Time A Mkr 40 mV 0.) 16QAM signal Figure 4: CCDF curves of a QPSK signal and a 16QAM signal Modulation formats The modulation format of a signal affects its power characteristics. We can quickly verify that the 16QAM signal has a more stressful CCDF curve than that of the QPSK signal.CCDF in communications A. Therefore. the bit rate of a 16QAM signal is twice that of a QPSK signal for a given symbol rate. it also produces greater peak-to-average ratios than does QPSK.144 mV -145.2875833511 mV B.) QPSK signal and (B. the vector plot of a Quadrature Phase Shift Keying (QPSK) signal is compared to that of a 16-Quadrature Amplitude Modulation (16QAM) signal. 6 .287583351 mV 52.00 dB Figure 3: Vector plots of (A.287583351 mV 52. 16QAM signal TRACE B: Ch1 Main Time 40 mV 100% 10% 1% QPSK signal I-Q 0. and compare the results of choosing one modulation format over another.00000 MHz 10.1% 16QAM signal 8 mV/div 0. The 16QAM signal appears to have higher peak-toaverage power ratios. A QPSK signal transfers only two bits per symbol.0000 s 28. Using CCDF curves. While 16QAM is capable of transmitting more bits per state than QPSK for a given symbol rate. Figure 4 shows the power CCDF curves of both a 16QAM and QPSK signal obtained by the HP E4406A VSA.0001% -40 mV -52.00 Res BW 5. but it is difficult to make quantitative observations from this plot.2875833511 mV 0. while a 16QAM signal transfers four bits per symbol.001% 0. In Figure 3. 00 dB Figure 5: CCDF curves of a QPSK signal and a OCQPSK signal. Similarly. Low-alpha rootraised-cosine filter (b) This implies that the amplifiers and components used for a 16QAM signal will have different design needs than those for QPSK signals because of the higher peak-to-average statistics. 7 .01% 0.High-alpha rootraised-cosine filter (a) 100% 10% QPSK signal 1% 0.00000 MHz 10.0001% 5 10 0.00 Res BW 5.001% OCQPSK signal 0 0. we can use CCDF curves to compare between QPSK and Orthogonal Complex QPSK (OCQPSK). 0 5 10 Figure 6: Impluse response of a high-alpha and a low-alpha filter. This is one of the reasons why 3G cellular systems will use OCQPSK in the mobile stations. The CCDF curves in Figure 5 immediately tell us that OCQPSK is less stressful than QPSK.1% 0. 287583351 mV 52. Signal A clearly looks more spread out in the vector plot due to the lower filter alpha.055 mV 79.2875833511 mV Signal B: Filter alpha at 0. Although low-alpha (low-a) filters require less bandwidth than high-alpha filters.1% 0.001% 0.403 mV -19. Also shown (Figures 7a and 7b) are the vector diagrams of the two signals. Figure 7c shows the CCDF plots of QPSK signals with different filtering a factors. This timedomain ringing results in the addition of more symbols. 8 . captured on an E4406A VSA.0001% -40 mV -52. For example.287583351 mV 52. Modulation filtering The filtering parameters for a particular modulation format can significantly affect the CCDF curves of the signal.91518 us 40 mV 20. as mentioned above.01% A Signal B I-Q 8 mV /div B 0. The CCDF curve can be used to troubleshoot signals. However.470 deg 1% 0. The magnitude of the time-trace vector plot squared would represent the power of the signals.22 Root-raised-cosine filter (c) -52. they have a longer response time and more severe ringing (Figure 6).552 deg Signal A I-Q 8 mV /div Signal A: Filter alpha at 0.91518 us 40 mV 24. Higher or lower CCDF curves give an indication of the filtering present on the signal.75 Root-raised-cosine filter -40 mV 100% 10% (b) TRACE B: Ch 1 Main Time B Mkr 5.(a) TRACE A: Ch 1 Main Time A Mkr 5. An incorrect curve could identify incorrectly coded baseband signals. The CCDF plot confirms that the low-a filter produces higher peak-power events than the high-a filter. high-a filters also require a larger bandwidth.2875833511 mV Figure 7: CCDF curve and vector plots of high-alpha filter and low-alpha filter. which causes higher peak-power events. 00 dB The same effect applies to multiple digitally modulated signals at different frequencies sent through a single amplifier or antenna. The CCDF curve allows us to easily determine how closely the multi-tone signal matches a true AWGN signal. A single Continuous Wave (CW) signal has a substantially constant envelope power.00 Res BW 5. creating problems for the overall system. an amplifier designed for multiple GSM signals at different frequencies will need to handle signals with significantly more stressful CCDF curve power statistics.0001% A B C 0. As we saw in Figure 10. Theoretically. the CCDF curves begin to resemble the Additive White Gaussian Noise (AWGN) curve. as the number of tones increases.Set A: 4-tone signals Set B: 64-tone signals Set C: 1000-tone signals 100% 10% 1% 0. notice that as the number of tones increases. which is why the number of tones is somewhat ambiguous when specifying the power characteristics of multi-tone signals (see phases affect multi-tone signals. However. The CCDF curve of a two-CW signal differs significantly from that of the single CW signal. Many of today’s schemes to achieve multi-carrier signals must consider such effects. similar to an AM signal. The NPR test requires a Gaussian noise stimulus with a notch located in the center of the band. an amplifier designed for a GSM signal only transmits a constant envelope signal during a time slot. the CCDF curve of this signal should be a point at 0 dB and 100%.5 dB. which means that its peak envelope power nearly equals its average power. 64-CW. To simulate a notch in the multi-tone signal. two CW signals at different frequencies create a time-domain waveform with fluctuating amplitude. one of the 1000-tone signals (the one in the middle) closely approximates the AWGN up to about 9. Looking at Figure 8 again. On the other hand. we expect the peak-power events to also increase. is an arbitrary waveform signal generator capable of generating a multi-tone CW signal. tones are omitted at the frequencies where the notch is desired. Figure 8: CCDF curves of multiple frequency signals. which can reduce costs and maximize workspace. This becomes an important application in Noise Power Ratio (NPR) measurements.001% 0. For instance. NPR is a common characterization for nonlinear performance in communications circuits.01% 0. These tones all have random phase relationships. The stimulus is generated using large filters and components. However.00000 MHz 10. 9 .1% Tones have random phase relationships AWGN 0. Figure 8 shows the sets of CCDF curves of 4-CW. Multiple-frequency signals Combining multiple signals of different frequencies increases the power in the resulting multi-tone signal. and 1000-CW signals displayed on the E4406A VSA. An alternative NPR test stimulus. below). 001% 0. Figure 10 shows two spectrally identical 8-tone signals. Figure 9 shows that a 4-tone signal with all phases aligned is slightly more stressful than one particular 64-tone signal with random phase relationships. … . 315 degrees). Signal A has initial phases aligned at 0 degrees.00000 MHz 15. For instance. A multi-tone signal in which the phases of all tones are aligned yields the maximum CCDF curve possible.1% 0.00000 MHz 15.00 Res BW 5. Signal A: 8 tones have phases all alighed Signal B: 8-tones have phases offset by 45 degrees 100% A 10% 1% 0. 45.0001% B 0. while Signal B has phases offset by 45 degrees (that is. The aligned phase signal (Signal A) has a significantly more stressful CCDF curve.01% 0. 0. 100% 4 tones 10% 1% 0. the phase relationships of multi-tone signals can either significantly reduce or increase the power statistics.00 dB Figure 10: CCDF curves of 8-tone signals 10 .00 Res BW 5.01% 0.0001% 64 tones AWGN 0.001% 0. We saw above that a signal with more tones is likely to have more stressful power characteristics.00 dB Figure 9: CCDF curves for a phase-aligned 4-tone signal and a 64-tone signal with random phases. 90. it is possible to generate a signal with fewer tones that is as stressful or sometimes more stressful than a signal with more tones. However.Phases affect multi-tone signals As mentioned in the previous section.1% 0. 5 1.5 1 0.5 -0. at the receiver end. (cdmaOne spread-spectrum systems send each bit to both I and Q.5 -0.5 Summed QPSK Vectors B. A "1" information bit sends all 64 bits of the appropriate Walsh code. 11 .5 -1 -0. the system relies on orthogonal coding in order to separate the information for different users. Since these user channels are all transmitted together in the same frequency band.5 1 0.5 -0.5 -1 -0. the vectors sometimes add up (when in the same direction).5 1 1.5 1 1. QPSK 1.5 -0.5 -1 -1.5 1 0.5 -1 -1.5 1. while 3G systems send every other bit to I or Q. the Walsh-coded information translates into a QPSK vector.5 1 1.5 -1 -0.5 -1.5 -1.5 -1 -1.5 -1 -1.5 -1 -0.) The vectors associated with all the active codes then superimpose upon one another to form a spread-spectrum signal. IS-95 cdmaOne format uses Walsh codes.5 -1. With the presence of more codes. QPSK 1.5 -1.5 0. most systems apply a known scrambling code in order to distinguish and to retrieve the desired user information.5 0.5 -1 -0.5 -1.5 1.A. Orthogonal codes allow spreading of the information bits from each user. The CCDF curve of a signal reflects this fact.5 1 0. Finally.5 1 1.5 1 1.5 -1 -1.5 -0. and sometimes cancel each other out (when in opposing directions).5 -1.5 0.5 1 0.5 1 1. A "0" information bit sends the inverse 64 bits of the appropriate Walsh code.5 -1 -0.5 Summed QPSK Vectors Figure 11: (A) Addition and (B) cancellation of vectors in spread-spectrum systems.5 -1 -1. As displayed in Figure 11. Spread-spectrum systems We can view spread-spectrum signals as multiple QPSK signals summed together at baseband. the potential peak power of the signal rises. Next.5 -0. Adding up the QPSK vectors of multiple codes defines the peak power for a symbol at any given time.5 0.5 0.5 0.5 1 0.5 1. Each QPSK signal represents a unique user channel or information stream. 001% 0.00 Res BW 5.3594791889 mV 0.0001% B 10 mV /div -50 mV -65. 12 .359479189 mV 65. Number of active codes in spread spectrum The number of active codes in a spread-spectrum system affects the power statistics of the signal.359479189 mV 65. thus incurring higher stress on system components. In Figure 12c. Signal A (pilot channel) has a significantly lower statistical power ratio than does Signal B (pilot plus 8 other randomly chosen channels) as indicated by the CCDF curves and the vector plots.1% 0.00 dB Figure 12: CCDF curves and vector plots of a single-channel cdmaOne signal and a nine-channel cdmaOne signal. Increasing the number of channels in a spread-spectrum system increases the power peaks.00000 MHz 15. we compare the CCDF curves of two cdmaOne signals.01% 0.3594791889 mV -50 mV (c) 100% 10% (b) TRACE B: D 1 Main Time 50 mV A Signal B I-Q 1% 0. the signal with higher channel usage has a more stressful power CCDF curve. As expected.(a) TRACE A: D 1 Main Time 50 mV Signal A I-Q 10 mV /div Signal A: cdmaOne signal–Pilot Signal B: cdmaOne signal–Pilot plus eight other channels -65. Signal A consists of randomly chosen codes. 39. There is a significant difference between the CCDF curves of the two signals. These code combinations are also deterministic.1% 0. Signal A and Signal B each have nine active codes. In Figure 13. 9. the peakto-average power ratios of a signal depend on the specific selection of the channels used. The symmetric properties are the main reason that certain code combinations have more stressful CCDF curves than others.01% 0. 13 . while Signal B consists of one of the worst (most stressful) 9-code combinations possible. we compare the CCDF curves of two cdmaOne signals. 11.0001% B A ~2. 63 100% 10% 1% 0. 15. 12. 47.001% 0. 55. 22. 10.00 dB Orthogonal coding effects Given a fixed number of active CDMA code channels.3 dB difference 0. This is a consequence of orthogonal coding effects.00000 MHz Figure 13: Effect of code selection on CCDF curves.Signal A (9 cdmaOne codes): Pilot: code 0 Sync: code 32 Paging: code 1 Traffic: codes 8. The deterministic construction process for Walsh codes gives the codes some symmetric properties.00 Res BW 5. However. 13 Signal B (9 worst spacing codes): Pilot: code 0 Sync: code 32 Paging: code 7 Traffic: codes 15. 65 dBm 10.29 -67.76 -70.74 -66.00 kHz 1.86 -42.18 -69.52 Upper dBc dBm -45.11 -72.00 MHz 10.3 dB more range for Signal B.00 kHz 30.00000 GHz Total Pwr Ref: ACPR Offset Freq 750. the amplifier designer would encounter ambiguity in the design specifications.7 ExtAt 0. 14 . the designer would have to design the amplifier with about 2.24 -71.43 Upper dBc dBm -44.00 MHz Lower dBc dBm -45.00 kHz 30.7 ExtAt 0. ACPR Ref 3. ACPR Ref 3. If the CCDF curve of the signal was not defined.62 dBm 10.00 kHz 1.00 dB/ MaxP 3.0 Center 1.98 Mhz IS-95A Averages: 19 PASS Spectrum (Total Pwr Ref) Span 10.00 kHz Signal B (9 worst spacing codes): Output signal of amplifier fails ACPR test Suppose an amplifier designer was asked to design an amplifier with certain ACPR characteristics for a 9-channel CDMA signal.00 MHz 10. CCDF curves can help amplifier designers avoid ambiguity in design specifications.08 -66.00000 GHz Total Pwr Ref: ACPR Offset Freq 750. From the CCDF curve.13 -68.Signal A (9 cdmaOne codes): Output signal of amplifier passes ACPR test.98 Mhz IS-95A Averages: 19 FAIL Spectrum (Total Pwr Ref) Span 10.83 F -41.10 3.0 Center 1. but the customer might test the amplifier with Signal B and fail the amplifier (Figure 14).00 kHz Figure 14: ACPR measurements of amplified signals.67 3. The designer could design the amplifier to work with Signal A.00 dB/ MaxP 2.62 dBm/ Integ Bw 30.40 F -40.73 -42.00 MHz Lower dBc dBm -44.65 dBm/ Integ Bw 30. 0001% A 0. 15 . Figure 15 compares the CCDF curve of a 9-code cdmaOne signal to that of three 9-code cdmaOne signals combined (in adjacent frequency channels).00 dB Figure 15: CCDF curves for a multi-carrier cdmaOne signal and a single-carrier cdmaOne signal Multi-carrier signals As discussed earlier. since multi-carrier signals use distinct frequency bands. Using CCDF curves.Signal A: One 9-active-code cdmaOne signal Signal B: Three 9-active-code cdmaOne signals 100% 10% 1% 0. Clearly. the multi-carrier signal B has the more stressful CCDF curve. This effect also applies to multicarrier signals in spread-spectrum systems. multi-tone signals cause greater stress on components such as amplifiers and mixers than single-tone signals.001% 0. power amplifier designers know exactly how stressful a signal the amplifier will need to handle. Systems developers also need to consider this power increase to ensure proper operation of the system.00000 MHz 15. Many companies are now creating amplifier designs that can handle combined multi-carrier cdmaOne signals.01% 0.1% B 0. measured with the E4406A VSA.00 Res BW 5. 2 24 23.6 2: 24.6 2 2 1: 2 0 -2 1 -4 Log Mag 0.40 dB m Meas1: Mkr1 Meas2: Mkr2 -13.40 dB dBm 12 10 8 6 2 1: Power 2: Off Log Mag 2.000 MHz Stop -13. The right display shows the same information portrayed as a plot of output power versus input power. then the output would be a linear amplification of the input signal. an amplifier compresses a signal when the signal exceeds the amplifier power limitations.0 dB/Ref 4. Consider a noise-like signal passing through this amplifier. If both the input and output signals remain within the power constraints of the amplifier. 16 . To avoid compression.000 MHz Stop -13.00 dBm CW 1 000.00 dBm Start -28.8 1 24.8 23.52 dBm 23.CCDF in component design 1: Off 2: S21 Fwd Trans dB 25.2 dB/Ref 24. For instance.00 dBm (a) Gain versus input power (b) Output power versus input power Figure 16: Characterization of power amplifier Compression of signal by nonlinear components In nonlinear components. an engineer needs to know the [optimum] input power level for the amplifier.2 25 24. The left display shows the amplifier gain versus input power.00 dBm CW 1 000.187 dBm 1 Start -28. if either the input or output signal exceeds the power limitations of the amplifier.934dB -27. However. compression of signals may occur. Figure 16 shows two characterizations of the same amplifier. the signal undergoes compression.98 dBm -3. We will see how CCDF curves can be used to determine input power levels and serve as a guide for RF power amplifier designers and systems engineers. 000 KHz Gaussian Samples 1365 points (b) Output power versus input power Ref 10.0 Trig Free 0.33ns Figure 17: Power-versus-time plots for input and output signals of an amplifier.(a) Amplifier input signal Ref–15. Even if we were able to perceive some clipping.00 ms Res BW 100.0 RF Envelope ExtAt 0. we have no convenient way of describing the compression quantitatively in the time domain.00 ms @733.00 dB/ MaxP 4.000 KHz Gaussian Samples 1365 points 1.00 dBm 4. 1.00 dB/ MaxP -9. we can easily detect compression of a signal by comparing the power CCDF curves of the input signal and the amplified output signal. However.00 dBm 4.0 Unfortunately.00 ms @733.0 RF Envelope ExtAt 0.33ns Trig Free 0. it is difficult to see compression effects in the time domain (Figure 17).00 ms Res BW 100. because we cannot see appreciable amounts of clipping. 17 . If a signal passing through an amplifier were perfectly (linearly) amplified.00 dB Figure 18: Compression effects displayed by CCDF curves. The CCDF curve of the clipped signal decreases and no longer matches the original input signal. peaks will occur above –15 dBm 3% of the time. The power axes of the CCDF curve and the gain curve have the same scale.00000 MHz 15. For example. allowing us to line up the two curves. Therefore.001% 0. This effect makes the CCDF a good indicator of compression. the output waveform no longer resembles an amplified version of the input waveform. As seen from the CCDF curve comparisons. and the peak-to-average ratios change. By definition. the input signal spends 3% of its time at or above 6 dB relative to the average power (from the CCDF curve). Therefore. CCDF curves are clearly an excellent tool for displaying compression effects.001% 0. clipping occurs.100% 10% 1% 0. Both the average and envelope power of the amplified signal would increase by a common factor. we can correlate the two graphs.01% 0.1% 0.00 Res BW 5. the output signal has significantly distorted peakpower events. and the two CCDF curves would appear identical. the CCDF curve can be a good tool for determining the optimum signal level for a particular amplifier. At –15 dBm on the gain curve.1% 0. will spend at least 3% of the time compressed by 0. CCDF curves measure how far and how often a signal exceeds the average power.5 21 -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 Input Power (dBM) 0.0001% 25.5 22 21. the signal is compressed about 0.0001% 0. By viewing these curves. This distortion will affect the Bit Error Rate (BER) or Frame Error Rate (FER) of the system.5 25 24.5 24 23. when the output signal exceeds the power limitations of the amplifier.00 Res BW 5. We have shifted the graph to line up the 0 dB point of the CCDF curve with the average power of the input signal on the gain curve. an amplifier designer can easily check the amplifier power performances against the desired specifications.5 Amplifier Gain vs Input Power (with 1GHz CW signal) Input signal Amplified signal 23 22. 100% As seen in Figure 18.01% 0. Therefore. with a gain in power.00000 MHz 15. Since the average power of the signal equals –21 dBm. the output waveform of the signal in the time domain would perfectly resemble the input waveform. the signal Figure 19: Correlation of amplifier gain and input signal CCDF curve. However. 10% Input signal CCDF 1% 0.00dB Correlating the amplifier curves with the CCDF plot Figure 19 correlates the input signal CCDF curve to the amplifier gain versus input power plot. Now.6 dB. the peak-to-average power ratio would not change.6 dB or more. 18 . 00 -92.00 kHz 1. Measurements such as ACPR and CDP are well complemented by CCDF curves.00 kHz 30.98 MHz -21.20 -74. The compression has caused approximately 15 dB degradation in the ACPR of the signal.00 dB/ MaxP 3.80 Figure 20: ACPR increases as the signal passes through the amplifier.05 -95.23 MHz Upper dBc dBm -71.57 -74.38 -92.0 Center 1. Figure 21 (page 20) shows the CDP plots of the input and output signal of the amplifier.47 dBm 10.00000 GHz Total Pwr Ref: ACPR Offset Freq 750.96 -67.50 IS-95A Averages: 20 PASS Bar Graph (Total Pwr Ref) Lower dBc dBm -45. Figure 20 shows two ACPR measurements comparing the input and output signals of an amplifier.27 -67.00 kHz 30.28 -41.82 -70.7 ExtAt 0. (b) Amplifier output signal ACPR Ref 3.00 kHz 1.(a) Amplifier input signal ACPR Ref–21.00 kHz 1.47 dBm/ Integ Bw 30.95 -71.00 dB/ MaxP -12.19 dBm 10.00 kHz 1.19 dBm/ Integ Bw 30. While ACPR and CDP give us information regarding overall average power and individual channel power. The amplified signal (with compression) has significantly reduced the Signal-to-Noise Ratio (SNR) of the active channels versus the inactive channels.0 Center 1. CCDF tells us the more detailed information about the peaks of a signal. 19 .00000 GHz Total Pwr Ref: ACPR Offset Freq 750.24 Compression affects other key measurements The result of this compression will also affect key amplifier and transmitter system specifications such as Adjacent Channel Power Ratio (ACPR) and code-domain power (CDP).41 IS-95A Averages: 20 PASS Bar Graph (Total Pwr Ref) Lower dBc dBm -71.3 ExtAt 0.23 MHz Upper dBc dBm -45.22 -95.42 -41.98 MHz 3. 01 dB Paging: -7. circuit components or subsystems can be tested for linearity non-intrusively. if the amplifier compresses the signal.25 dB 63 Act Set Th -20.70 dB IS-95A Averages: 10 Bar Graph (Total Pwr Ref) Applications CCDF curves can help to confirm whether or not a component design performs as specified. For example. The amplifier designer would need to increase the range of the amplifier to account for the power peaks. If the design is correct.25 dB Sync: -13.00 dB/ Sync Esec 0 Time Ofs: Freq Error: 1. which means the CCDF curve decreases.98 MHz -11755.00 dB 5.48 us 7.18 dB IS-95A Averages: 10 Bar Graph (Total Pwr Ref) (b) Amplifier output signal Code Domain Ref 0. the curves will coincide.12 dB Avg IT: -43. Figure 21: CDP increases as the signal passes through the amplifier.98 MHz 9917.(a) Amplifier input signal Code Domain Ref 0.00 dB 5.58 dB Max IT: -47.13 dB 32 Pilot: -7.01 dB Paging: -7. Similarly.00 dB Avg AT: -10.39 us 8. a power amplifier designer can compare the CCDF curve of a signal at the input and output of an RF amplifier.53 dB 32 Pilot: -7. also.00 dB/ Sync Esec 0 Time Ofs: Freq Error: 1. However. or the system designers could lower the average power of the signal to meet the power limitations of the amplifier. Making CCDF measurements at several points in the system allows system engineers to verify performance of individual subsystems and components. CCDF curves can also be used to troubleshoot a system or subsystem design.33 dB 63 Act Set Th -20.27 dB Sync: -13.28 dB Avg IT: -49.59 dB Max IT: -37.00 dB Avg AT: -10.24 Hz -30. 20 . the peakto-average ratio of the signal is lower at the output of the amplifier.21 Hz -27. and W-CDMA. Offsetting the phases of a multi-tone signal can minimize unwanted power peaks. The CCDF measurement can help determine the optimum operation point for components. 21 . The CCDF curve can also be used to determine the impact of filtering on a signal. The mathematical origins of CCDF curves are the familiar PDF and CDF curves that most engineering students have seen in an introductory probability and statistics course. FER. we can expect to see correlation studies between CCDF curve degradation and digital radio system parameters such as BER. The need for CCDF arises primarily when dealing with digitally modulated signals in spread-spectrum systems such as cdmaOne. and other components. Because these types of signals are noise-like.Summary CCDF measurements are becoming a valuable tool in the communications industry. and ACPR. As this new tool becomes more prevalent. filters. cdma2000. Multi-carrier signals also cause a significant change in CCDF curves. CCDF is becoming a necessary design and testing tool in 3G communications systems. CCDF curves are a valuable measurement tool for spread-spectrum systems. due to orthogonal coding effects. In particular. amplifiers. different combinations of active codes yield different power CCDF curves. Perhaps the most important contribution of CCDF curves is in setting the signal power specifications for mixers. The CCDF measurement is an excellent way to fully characterize the power statistics of a digitally modulated signal. the number of active codes in a CDMA signal significantly affects the power statistics. amplifier designers know exactly how much headroom to allow for the peak power excursions to avoid compression. CDP. Furthermore. Modulation formats can be compared via CCDF in terms of how stressful a signal is on a component such as an amplifier. CCDF curves are a powerful way to view and to characterize how various factors affect the peak amplitude excursions of a digitally modulated signal. CCDF curves provide a useful characterization of the signal power peaks. CCDF is a statistical method that shows the amount of time the signal spends above any given power level. From the CCDF curves of multi-tone signals. similar to the effect of multi-tone signals. For instance. Application Note 1325. 22 . (article reprint) Microwaves & RF. Nick Kuhn. January 1998. Application Note 1298. 2. Digital Modulation in Communications Systems – An Introduction. literature number 5968-0953E. 4. Application Note 1313. Performing cdma2000 Measurements Today. 3. Understanding CDMA measurements for Base Stations and Their Components. Bob Matreci. 5. literature number 5968-3578E. and Peter Thysell. literature number 5968-5858E. literature number 5966-4786E.References 1. Application Note 1311. Testing and Troubleshooting RF Communications Transmitter Designs. Proper Stimulus Ensures Accurate Tests of CDMA Power. literature number 5965-7160E. (10log(power/1mW)) DSB-LC—Double-SideBand Large-Carrier DSP—Digital Signal Processing EDGE—Enhanced Data for GSM Evolution FER—Frame Error Rate FM—Frequency Modulation GSM—Global System for Mobile communications HDTV—High Definition TeleVision HPSK—Hybrid Phase Shift Keying I and Q—In-phase and Quadrature NADC—North American Digital Cellular NPR—Noise Power Ratio OCQPSK—Orthogonal Complex Quadrature Phase Shift Keying PDF—Probability Density Function QAM—Quadrature Amplitude Modulation QPSK—Quadrature Phase Shift Keying RF—Radio Frequency SNR—Signal to Noise Ratio TACS—Total Access Communications System VSA—Vector Signal Analyzer W-CDMA—Wideband-Code Division Multiple Access 23 .Symbols and Acronyms 3G—Third Generation 8VSB—8-level Vestigial Side Band ACPR—Adjacent Channel Power Ratio AM—Amplitude Modulation AMPS—Advanced Mobile Phone System AWGN—Additive White Gaussian Noise BER—Bit Error Rate CCDF—Complementary Cumulative Distribution Function CDF—Cumulative Distribution Function CDMA (cdmaOne. cdma2000)—Code Division Multiple Access CDP—Code Domain Power COFDM—Coded Orthogonal Frequency Division Multiplexing CW—Continuous Wave dB—Decibel dBm—Decibels relative to 1 milliwatt. 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