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

A p p l i c a t i o n N o t e

C h a r a c t e r i z i n g D i g i t a l l y M o d u l a t e d S i g n a l s w i t h C C D F C u r v e s

2

1. Introduction

When are CCDF curves used?

2. What are CCDF curves?

Statistical origin of CCDF curvesWhy not crest factor?

3. CCDF in communications

Modulation formatsModulation filtering

Multiple-frequency signalsPhases affect multi-tone signals

Spread-spectrum systemsNumber of active codes in spread spectrumOrthogonal coding effectsMulti-carrier signals

4. CCDF in component design

Compression of signal by nonlinear componentsCorrelating the amplifier curves with the CCDF plotCompression affects other key measurementsApplications

5. Summary

6. References

7. Symbols and acronyms

Table of Contents

3

Digital modulation has created arevolution in RF and microwavecommunications. Cellular systemshave moved from the old analogAMPS and TACS systems to secondgeneration NADC, CDMA, and GSMstandards. Today, the cellularindustry talks of moving to thirdgeneration (3G) digital systemssuch as W-CDMA and cdma2000.Outside of cellular communications,the broadcast industry is alsomoving into the era of digitalmodulation. High DefinitionTelevision (HDTV) systems willuse 8-level Vestigial Side Band(8VSB) and Coded OrthogonalFrequency Division Multiplexing(COFDM) digital modulation for-mats in various parts of the world.

The move to 3G systems will yieldsignals with higher peak-to-averagepower ratios (crest factors) thanpreviously encountered. AnalogFM systems operate at a fixedpower level: analog double-side-band large-carrier (DSB-LC) AMsystems cannot modulate over100% (a peak value 6 dB above the unmodulated carrier) withoutdistortion. Third generation systems,on the other hand, combine multiple channels, resulting in apeak-to-average ratio that isdependent upon not only the number of channels being com-bined, but also which specificchannels are used. This signalcharacteristic can lead to higherdistortion unless the peak powerlevels are accounted for in thedesign of system components,such as amplifiers and mixers.

Power Complementary CumulativeDistribution Function (CCDF)curves provide critical informationabout the signals encountered in3G systems. These curves alsoprovide the peak-to-average powerdata needed by componentdesigners.

Introduction This application note examines the main factors that affect power CCDF curves, and describes how CCDF curves are used to help design systems and components.

When are CCDF curves used? Perhaps the most important appli-cation of power CCDF curves is to specify completely and withoutambiguity the power character-istics of the signals that will be mixed, amplified, and decoded in communication systems. For example, baseband DSP signaldesigners can completely specify the power characteristics of signals to the RF designers by using CCDF curves. This helps avoid costly errors at system integration time. Similarly, systemmanufacturers can avoid ambiguity by completely specify-ing the test signal parameters to their amplifier suppliers.

CCDF curves apply to many design applications. Some of these applications are:

• Visualizing the effects of modulation formats.

• Combining multiple signals via systems components (for example, amplifiers).

• Evaluating spread-spectrum systems.

• Designing and testing RF components.

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Figure 1A shows the power versustime plot of a 9-channel cdmaOnesignal. This plot represents theinstantaneous envelope powerdefined by the equation:

Power = I2 + Q2

where I and Q are the in-phaseand quadrature components ofthe waveform.

Unfortunately, the signal in theform shown in Figure 1A is difficult to quantify because of its inherent randomness andinconsistencies. In order toextract useful information fromthis noise-like signal, we need a statistical description of thepower levels in this signal, and a CCDF curve gives just that.

A CCDF curve shows how muchtime the signal spends at or abovea given power level. The powerlevel is expressed in dB relative tothe average power. For example,each of the lines across the wave-form shown in Figure 1A repre-sents a specific power level abovethe average. The percentage oftime the signal spends at or above each line defines theprobability for that particularpower level. A CCDF curve is aplot of relative power levels ver-sus probability.

Figure 1B displays the CCDFcurve of the same 9-channelcdmaOne signal captured on theE4406A VSA. Here, the x-axis isscaled to dB above the averagesignal power, which means we areactually measuring the peak-to-average ratios as opposed toabsolute power levels. The y-axisis the percent of time the signalspends at or above the powerlevel specified by the x-axis. Forexample, at t = 1% on the y-axis,the corresponding peak-to-averageratio is 7.5 dB on the x-axis. Thismeans the signal power exceedsthe average by at least 7.5 dB for1 percent of the time. The posi-tion of the CCDF curve indicatesthe degree of peak-to-averagedeviation, with more stressful signals further to the right.

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Band-limited Gaussian noiseCCDF reference line.

X-axis is dB above average power

Figure 1A: Construction of a CCDF curve

Figure 1B: CCDF curve of a typical cdmaOne signal

What are CCDF curves?

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This measurement is of question-able value for several reasons:

• Error-correction coding will often remove the effect of a single error-causing peak in the system.

• A single peak that is much higher than the prevailing signal level sometimes is treated as an anomalous condition and ignored.

• A peak that occurs infrequently causes little spectral regrowth, which makes repeatable measurements difficult.

• The highest peak value that occurs for true noise depends on the length of the measurement time.

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In short, crest factor places toomuch emphasis on a signal’sinstantaneous peak value. To mitigate this, the peak value issometimes considered to be thelevel where 99.8 percent of thewaveform is below the peak value,and 0.2 percent of the waveform is above it. While this lessens theemphasis on a single point of awaveform, the use of a singlelevel (such as 0.2 percent) is stillrather arbitrary. CCDF gives usmore complete information aboutthe high signal levels than doescrest factor [1].

Figure 2: Mathematical origin of CCDF

Now that we’ve seen a practicalCCDF curve (Figure 1A), let’sbriefly investigate the mathematicsof CCDF curves. Let’s start with aset of data that has the ProbabilityDensity Function (PDF) shown inFigure 2. To obtain the CumulativeDistribution Function (CDF), wecompute the integral of the PDF.Finally, inverting the CDF resultsin the CCDF. That is, the CCDF is the complement of the CDF(CCDF = 1 – CDF). To generatethe CCDF curve in the formshown in Figure 1A, convert they-axis to logarithmic form andbegin the x-axis at 0 dB. A logarith-mic y-axis provides better resolu-tion for low-probability events.The reason we plot CCDF insteadof CDF is that CCDF emphasizespeak amplitude excursions, whileCDF emphasizes minimum values.

Why not crest factor?

As the need for characterizingnoise-like signals becomesgreater, we search for the mostconvenient, useful, and reliablemeasurement to meet this need.Traditionally, a common measureof stress for a stimulating signalhas been the crest factor. Crestfactor is the ratio of the peakvoltage to its root-mean-squarevalue.

Statistical

origin of

CCDF

curves

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Modulation formats

The modulation format of a signalaffects its power characteristics.Using CCDF curves, we can fullycharacterize the power statisticsof different modulation formats,and compare the results of choosing one modulation formatover another.

In Figure 3, the vector plot of aQuadrature Phase Shift Keying(QPSK) signal is compared to that

CCDF in communications

of a 16-Quadrature AmplitudeModulation (16QAM) signal. AQPSK signal transfers only twobits per symbol, while a 16QAMsignal transfers four bits per symbol. Therefore, the bit rate of a 16QAM signal is twice that of a QPSK signal for a given symbol rate. The 16QAM signalappears to have higher peak-to-average power ratios, but it is difficult to make quantitativeobservations from this plot.

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Figure 3: Vector plots of (A.) QPSK signal and (B.) 16QAM signal

Figure 4: CCDF curves of a QPSK signal and a 16QAM signal

Figure 4 shows the power CCDFcurves of both a 16QAM andQPSK signal obtained by the HPE4406A VSA. We can quickly verifythat the 16QAM signal has a morestressful CCDF curve than that ofthe QPSK signal. While 16QAM iscapable of transmitting more bitsper state than QPSK for a givensymbol rate, it also producesgreater peak-to-average ratiosthan does QPSK.

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Figure 6: Impluse response of a high-alpha and a low-alpha filter.

(a)

0 5 10

High-alpha root-raised-cosine filter

(b)

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Low-alpha root-raised-cosine filterFigure 5: CCDF curves of a QPSK signal and a OCQPSK signal.

This implies that the amplifiers and components used for a16QAM signal will have differentdesign needs than those for QPSKsignals because of the higherpeak-to-average statistics.

Similarly, we can use CCDF curves to compare between QPSKand Orthogonal Complex QPSK(OCQPSK). The CCDF curves inFigure 5 immediately tell us thatOCQPSK is less stressful thanQPSK. This is one of the reasonswhy 3G cellular systems will useOCQPSK in the mobile stations.

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Figure 7: CCDF curve and vector plots of high-alpha filter and low-alpha filter.

Modulation filtering

The filtering parameters for aparticular modulation format cansignificantly affect the CCDFcurves of the signal. Althoughlow-alpha (low-a) filters requireless bandwidth than high-alphafilters, they have a longerresponse time and more severeringing (Figure 6). This time-domain ringing results in theaddition of more symbols, whichcauses higher peak-power events.

For example, Figure 7c showsthe CCDF plots of QPSK signalswith different filtering a factors,captured on an E4406A VSA. Also shown (Figures 7a and 7b)are the vector diagrams of thetwo signals. The magnitude of the

time-trace vector plot squaredwould represent the power ofthe signals. Signal A clearlylooks more spread out in thevector plot due to the lower filter alpha. The CCDF plotconfirms that the low-a filterproduces higher peak-powerevents than the high-a filter.However, as mentioned above,high-a filters also require alarger bandwidth.

The CCDF curve can be used to troubleshoot signals. Higheror lower CCDF curves give anindication of the filtering pres-ent on the signal. An incorrectcurve could identify incorrectlycoded baseband signals.

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Signal B:Filter alpha at 0.75Root-raised-cosine filter

(c)

9

Multiple-frequency signals

Combining multiple signals of different frequencies increases thepower in the resulting multi-tonesignal, creating problems for theoverall system.

A single Continuous Wave (CW)signal has a substantially constantenvelope power, which meansthat its peak envelope powernearly equals its average power.Theoretically, the CCDF curve of this signal should be a point at 0 dB and 100%. On the otherhand, two CW signals at differentfrequencies create a time-domain

waveform with fluctuating ampli-tude, similar to an AM signal. TheCCDF curve of a two-CW signaldiffers significantly from that ofthe single CW signal.

Figure 8 shows the sets of CCDF curves of 4-CW, 64-CW, and1000-CW signals displayed on the E4406A VSA. These tones allhave random phase relationships,which is why the number of tonesis somewhat ambiguous whenspecifying the power characteris-tics of multi-tone signals (seephases affect multi-tone signals,below). However, as the numberof tones increases, we expect thepeak-power events to also increase.

Figure 8: CCDF curves of multiple frequency signals.

The same effect applies to multipledigitally modulated signals at different frequencies sentthrough a single amplifier orantenna. Many of today’sschemes to achieve multi-carriersignals must consider sucheffects. For instance, an amplifierdesigned for a GSM signal onlytransmits a constant envelope signal during a time slot. However,an amplifier designed for multipleGSM signals at different frequen-cies will need to handle signalswith significantly more stressfulCCDF curve power statistics.

Looking at Figure 8 again, noticethat as the number of tonesincreases, the CCDF curves beginto resemble the Additive WhiteGaussian Noise (AWGN) curve.This becomes an important appli-cation in Noise Power Ratio(NPR) measurements.

NPR is a common characterizationfor nonlinear performance incommunications circuits. TheNPR test requires a Gaussiannoise stimulus with a notch locatedin the center of the band. Thestimulus is generated using largefilters and components. An alter-native NPR test stimulus, whichcan reduce costs and maximizeworkspace, is an arbitrary wave-form signal generator capable of generating a multi-tone CW signal. To simulate a notch in themulti-tone signal, tones are omittedat the frequencies where thenotch is desired. As we saw inFigure 10, one of the 1000-tonesignals (the one in the middle)closely approximates the AWGNup to about 9.5 dB. The CCDFcurve allows us to easily deter-mine how closely the multi-tonesignal matches a true AWGN signal.

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Set A:4-tone signals

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10

it is possible to generate a signalwith fewer tones that is as stress-ful or sometimes more stressfulthan a signal with more tones. Forinstance, Figure 9 shows that a 4-tone signal with all phasesaligned is slightly more stressfulthan one particular 64-tone signalwith random phase relationships.

A multi-tone signal in which thephases of all tones are alignedyields the maximum CCDF curvepossible. Figure 10 shows twospectrally identical 8-tone signals.Signal A has initial phases alignedat 0 degrees, while Signal B hasphases offset by 45 degrees (thatis, 0, 45, 90, … , 315 degrees). The aligned phase signal (Signal A)has a significantly more stressfulCCDF curve.

Figure 9: CCDF curves for a phase-aligned 4-tone signal and a 64-tone signal with random phases.

Figure 10: CCDF curves of 8-tone signals

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Phases affect multi-tone signals

As mentioned in the previous section, the phase relationships of multi-tone signals can eithersignificantly reduce or increase thepower statistics. We saw abovethat a signal with more tones islikely to have more stressfulpower characteristics. However,

11

Spread-spectrum systems

We can view spread-spectrum signals as multiple QPSK signalssummed together at baseband.Each QPSK signal represents aunique user channel or informa-tion stream. Since these userchannels are all transmittedtogether in the same frequencyband, the system relies on orthog-onal coding in order to separatethe information for different users.

Orthogonal codes allow spreadingof the information bits from eachuser. IS-95 cdmaOne format usesWalsh codes. A "1" information bitsends all 64 bits of the appropri-ate Walsh code. A "0" informationbit sends the inverse 64 bits ofthe appropriate Walsh code. Next,the Walsh-coded informationtranslates into a QPSK vector.(cdmaOne spread-spectrum

Figure 11: (A) Addition and (B) cancellation of vectors in spread-spectrum systems.

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systems send each bit to both I and Q, while 3G systems sendevery other bit to I or Q.) Thevectors associated with all theactive codes then superimposeupon one another to form aspread-spectrum signal. Finally, at the receiver end, most systemsapply a known scrambling codein order to distinguish and toretrieve the desired user information.

Adding up the QPSK vectors ofmultiple codes defines the peakpower for a symbol at any giventime. As displayed in Figure 11,the vectors sometimes add up(when in the same direction), andsometimes cancel each other out(when in opposing directions).With the presence of more codes,the potential peak power of the signal rises. The CCDF curve of a signal reflects this fact.

12

Figure 12: CCDF curves and vector plots of a single-channel cdmaOne signal and a nine-channel cdmaOne signal.

Number of active codes

in spread spectrum

The number of active codes in aspread-spectrum system affectsthe power statistics of the signal.Increasing the number of channelsin a spread-spectrum systemincreases the power peaks, thusincurring higher stress on systemcomponents.

In Figure 12c, we compare theCCDF curves of two cdmaOnesignals. Signal A (pilot channel)has a significantly lower statisticalpower ratio than does Signal B(pilot plus 8 other randomly chosen channels) as indicated bythe CCDF curves and the vectorplots. As expected, the signalwith higher channel usage has amore stressful power CCDF curve.

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Orthogonal coding effects

Given a fixed number of activeCDMA code channels, the peak-to-average power ratios of a signaldepend on the specific selectionof the channels used. This is aconsequence of orthogonal codingeffects. The deterministic con-struction process for Walsh codesgives the codes some symmetricproperties. The symmetric prop-erties are the main reason thatcertain code combinations havemore stressful CCDF curves thanothers. These code combinationsare also deterministic.

Figure 13: Effect of code selection on CCDF curves.

In Figure 13, we compare theCCDF curves of two cdmaOnesignals. Signal A and Signal Beach have nine active codes.However, Signal A consists of randomly chosen codes, whileSignal B consists of one of theworst (most stressful) 9-codecombinations possible. There is asignificant difference between theCCDF curves of the two signals.

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Signal A (9 cdmaOne codes):Pilot: code 0Sync: code 32Paging: code 1Traffic: codes 8, 9, 10, 11, 12, 13

Signal B (9 worst spacing codes):Pilot: code 0Sync: code 32Paging: code 7Traffic: codes 15, 22, 39, 47, 55, 63

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Figure 14: ACPR measurements of amplified signals.

Suppose an amplifier designerwas asked to design an amplifierwith certain ACPR characteristicsfor a 9-channel CDMA signal. Ifthe CCDF curve of the signal wasnot defined, the amplifier designerwould encounter ambiguity in thedesign specifications. The designercould design the amplifier to workwith Signal A, but the customermight test the amplifier withSignal B and fail the amplifier(Figure 14). From the CCDFcurve, the designer would have todesign the amplifier with about2.3 dB more range for Signal B.CCDF curves can help amplifierdesigners avoid ambiguity indesign specifications.

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Signal A (9 cdmaOne codes):Output signal of amplifier passes ACPR test.

Signal B (9 worst spacing codes):Output signal of amplifier fails ACPR test

15

Multi-carrier signals

As discussed earlier, multi-tone signals cause greater stress oncomponents such as amplifiersand mixers than single-tone signals.This effect also applies to multi-carrier signals in spread-spectrumsystems, since multi-carrier signalsuse distinct frequency bands. Manycompanies are now creatingamplifier designs that can handlecombined multi-carrier cdmaOnesignals.

Figure 15: CCDF curves for a multi-carrier cdmaOne signal and a single-carrier cdmaOne signal

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Signal A:One 9-active-code cdmaOne signal

Signal B:Three 9-active-code cdmaOne signals

Figure 15 compares the CCDFcurve of a 9-code cdmaOne signalto that of three 9-code cdmaOnesignals combined (in adjacent frequency channels), measuredwith the E4406A VSA. Clearly, the multi-carrier signal B has the more stressful CCDF curve. Using CCDF curves, power amplifier designers know exactlyhow stressful a signal the amplifierwill need to handle. Systemsdevelopers also need to considerthis power increase to ensureproper operation of the system.

16

Figure 16: Characterization of power amplifier

Compression of signal by

nonlinear components

In nonlinear components, com-pression of signals may occur. Forinstance, an amplifier compressesa signal when the signal exceedsthe amplifier power limitations. Toavoid compression, an engineerneeds to know the [optimum]input power level for the amplifier.We will see how CCDF curves canbe used to determine input power levels and serve as a guide for RFpower amplifier designers and systems engineers.

Figure 16 shows two characteri-zations of the same amplifier. Theleft display shows the amplifiergain versus input power. Theright display shows the sameinformation portrayed as a plot of output power versus inputpower. Consider a noise-like signalpassing through this amplifier. Ifboth the input and output signalsremain within the power con-straints of the amplifier, then the output would be a linearamplification of the input signal.However, if either the input oroutput signal exceeds the powerlimitations of the amplifier, the signal undergoes compression.

CCDF in component design

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Figure 17: Power-versus-time plots for input and output signals of an amplifier.

Unfortunately, it is difficult to seecompression effects in the timedomain (Figure 17), because wecannot see appreciable amountsof clipping. Even if we were ableto perceive some clipping, we haveno convenient way of describingthe compression quantitatively inthe time domain. However, wecan easily detect compression of a signal by comparing the powerCCDF curves of the input signaland the amplified output signal.

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Correlating the amplifier

curves with the CCDF plot

Figure 19 correlates the input signal CCDF curve to the amplifiergain versus input power plot. Thepower axes of the CCDF curveand the gain curve have the samescale, allowing us to line up thetwo curves. We have shifted thegraph to line up the 0 dB point ofthe CCDF curve with the averagepower of the input signal on thegain curve. Now, we can correlatethe two graphs.

For example, the input signalspends 3% of its time at or above 6 dB relative to the averagepower (from the CCDF curve).Since the average power of thesignal equals –21 dBm, peaks willoccur above –15 dBm 3% of thetime. At –15 dBm on the gaincurve, the signal is compressedabout 0.6 dB. Therefore, the signal

Figure 18: Compression effects displayed by CCDF curves.

Figure 19: Correlation of amplifier gain and input signal CCDF curve.

As seen in Figure 18, CCDFcurves are clearly an excellenttool for displaying compressioneffects. By definition, CCDFcurves measure how far and how often a signal exceeds theaverage power. If a signal passingthrough an amplifier were per-fectly (linearly) amplified, theoutput waveform of the signal inthe time domain would perfectlyresemble the input waveform,with a gain in power. Both theaverage and envelope power of the amplified signal wouldincrease by a common factor.Therefore, the peak-to-averagepower ratio would not change,and the two CCDF curves wouldappear identical. However, whenthe output signal exceeds thepower limitations of the amplifier,clipping occurs; the output wave-form no longer resembles anamplified version of the inputwaveform, and the peak-to-aver-age ratios change. The CCDFcurve of the clipped signaldecreases and no longer matchesthe original input signal. Thiseffect makes the CCDF a goodindicator of compression.

will spend at least 3% of the timecompressed by 0.6 dB or more. Byviewing these curves, an amplifierdesigner can easily check theamplifier power performancesagainst the desired specifications.

As seen from the CCDF curve comparisons, the output signalhas significantly distorted peak-power events. This distortion willaffect the Bit Error Rate (BER) orFrame Error Rate (FER) of thesystem. Therefore, the CCDFcurve can be a good tool fordetermining the optimum signallevel for a particular amplifier.

100%

10%

1%

0.1%

0.01%

0.001%

0.0001%0.00 15.00 dBRes BW 5.00000 MHz

Input signal

Amplified signal

19

Figure 20: ACPR increases as the signal passes through the amplifier.

Compression affects

other key measurements

The result of this compressionwill also affect key amplifier andtransmitter system specificationssuch as Adjacent Channel PowerRatio (ACPR) and code-domainpower (CDP). Figure 20 showstwo ACPR measurements com-paring the input and output sig-nals of an amplifier. The com-pression has caused approximate-ly 15 dB degradation in the ACPRof the signal.

Figure 21 (page 20) shows theCDP plots of the input and outputsignal of the amplifier. The ampli-fied signal (with compression) has significantly reduced theSignal-to-Noise Ratio (SNR) ofthe active channels versus theinactive channels.

Measurements such as ACPR andCDP are well complemented byCCDF curves. While ACPR andCDP give us information regard-ing overall average power andindividual channel power, CCDFtells us the more detailed infor-mation about the peaks of a signal.


Ref–21.19 dBm Bar Graph (Total Pwr Ref)10.00

dB/

MaxP-12.3

ExtAt0.0

Center 1.00000 GHz

Total Pwr Ref: -21.19 dBm/ 1.23 MHzACPR


750.00 kHz 30.00 kHz -71.00 -92.20 -71.38 -92.571.98 MHz 30.00 kHz -74.05 -95.24 -74.22 -95.41


Ref 3.47 dBm Bar Graph (Total Pwr Ref)10.00

dB/

MaxP3.7

ExtAt0.0

Center 1.00000 GHz



750.00 kHz 30.00 kHz -45.42 -41.95 -45.28 -41.821.98 MHz 30.00 kHz -71.27 -67.80 -70.96 -67.50


(b) Amplifier output signal

20

Code Domain IS-95A Averages: 10

Ref 0.00 dB Bar Graph (Total Pwr Ref)5.00dB/

Sync Esec

0 32 Act Set Th -20.00 dB

Time Ofs: -11755.48 us Pilot: -7.01 dB Avg AT: -10.58 dBFreq Error: 7.24 Hz Paging: -7.27 dB Max IT: -47.28 dB1.98 MHz -30.13 dB Sync: -13.25 dB Avg IT: -49.18 dB


(b) Amplifier output signal

63

Code Domain IS-95A Averages: 10

Ref 0.00 dB Bar Graph (Total Pwr Ref)5.00dB/

Sync Esec

0 32 Act Set Th -20.00 dB

Time Ofs: 9917.39 us Pilot: -7.01 dB Avg AT: -10.59 dBFreq Error: 8.21 Hz Paging: -7.25 dB Max IT: -37.12 dB1.98 MHz -27.53 dB Sync: -13.33 dB Avg IT: -43.70 dB

63

Figure 21: CDP increases as the signal passes through the amplifier.

Applications

CCDF curves can help to confirmwhether or not a componentdesign performs as specified. For example, a power amplifierdesigner can compare the CCDFcurve of a signal at the input andoutput of an RF amplifier. If thedesign is correct, the curves willcoincide. However, if the amplifiercompresses the signal, the peak-to-average ratio of the signal islower at the output of the amplifier,which means the CCDF curvedecreases. The amplifier designerwould need to increase the rangeof the amplifier to account for the power peaks, or the systemdesigners could lower the averagepower of the signal to meet thepower limitations of the amplifier.

Similarly, CCDF curves can alsobe used to troubleshoot a systemor subsystem design. MakingCCDF measurements at severalpoints in the system allows systemengineers to verify performanceof individual subsystems andcomponents; also, circuit compo-nents or subsystems can be testedfor linearity non-intrusively.

21

CCDF measurements are becominga valuable tool in the communica-tions industry. The need for CCDFarises primarily when dealingwith digitally modulated signals inspread-spectrum systems such ascdmaOne, cdma2000, and W-CDMA.Because these types of signals arenoise-like, CCDF curves provide auseful characterization of the signalpower peaks. CCDF is a statisticalmethod that shows the amount oftime the signal spends above anygiven power level. The mathemat-ical origins of CCDF curves arethe familiar PDF and CDF curvesthat most engineering studentshave seen in an introductoryprobability and statistics course.

The CCDF measurement is anexcellent way to fully characterizethe power statistics of a digitallymodulated signal. Modulation for-mats can be compared via CCDFin terms of how stressful a signalis on a component such as anamplifier. The CCDF curve can alsobe used to determine the impactof filtering on a signal. From theCCDF curves of multi-tone signals,amplifier designers know exactlyhow much headroom to allow forthe peak power excursions toavoid compression. Offsetting thephases of a multi-tone signal canminimize unwanted power peaks.CCDF curves are a powerful wayto view and to characterize howvarious factors affect the peakamplitude excursions of a digitallymodulated signal.

Summary In particular, CCDF curves are a valuable measurement tool for spread-spectrum systems. For instance, the number ofactive codes in a CDMA signalsignificantly affects the powerstatistics. Furthermore, differentcombinations of active codes yielddifferent power CCDF curves, dueto orthogonal coding effects.Multi-carrier signals also cause a significant change in CCDFcurves, similar to the effect ofmulti-tone signals. CCDF isbecoming a necessary design andtesting tool in 3G communicationssystems.

Perhaps the most important contribution of CCDF curves is insetting the signal power specifica-tions for mixers, filters, amplifiers,and other components. The CCDFmeasurement can help determinethe optimum operation point forcomponents. As this new toolbecomes more prevalent, we canexpect to see correlation studiesbetween CCDF curve degradationand digital radio system parameterssuch as BER, FER, CDP, and ACPR.

22

1. Nick Kuhn, Bob Matreci, and Peter Thysell, Proper Stimulus Ensures Accurate Tests of CDMA Power,

(article reprint) Microwaves & RF, January 1998,literature number 5966-4786E.

2. Digital Modulation in Communications Systems

– An Introduction,

Application Note 1298, literature number 5965-7160E.

3. Testing and Troubleshooting RF Communications

Transmitter Designs,


4. Performing cdma2000 Measurements Today,


5. Understanding CDMA measurements for Base Stations

and Their Components,


References

23

3G—Third Generation8VSB—8-level Vestigial Side BandACPR—Adjacent Channel Power RatioAM—Amplitude ModulationAMPS—Advanced Mobile Phone SystemAWGN—Additive White Gaussian NoiseBER—Bit Error RateCCDF—Complementary Cumulative Distribution FunctionCDF—Cumulative Distribution FunctionCDMA (cdmaOne, cdma2000)—Code Division Multiple AccessCDP—Code Domain PowerCOFDM—Coded Orthogonal Frequency Division MultiplexingCW—Continuous WavedB—DecibeldBm—Decibels relative to 1 milliwatt. (10log(power/1mW))DSB-LC—Double-SideBand Large-CarrierDSP—Digital Signal ProcessingEDGE—Enhanced Data for GSM EvolutionFER—Frame Error RateFM—Frequency ModulationGSM—Global System for Mobile communicationsHDTV—High Definition TeleVisionHPSK—Hybrid Phase Shift KeyingI and Q—In-phase and QuadratureNADC—North American Digital CellularNPR—Noise Power RatioOCQPSK—Orthogonal Complex Quadrature Phase Shift KeyingPDF—Probability Density FunctionQAM—Quadrature Amplitude ModulationQPSK—Quadrature Phase Shift KeyingRF—Radio FrequencySNR—Signal to Noise RatioTACS—Total Access Communications SystemVSA—Vector Signal AnalyzerW-CDMA—Wideband-Code Division Multiple Access

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