Introduction to CDMA Technology

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Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread SpectrumChapter 2Introduction to Spread SpectrumCommunicationsAs discussed in Chapter 0, a spread spectrum modulation produces a transmitted spectrum much widerthan the minimum bandwidth required. There are many ways to generate spread spectrum signals. Weare going to introduce some of the most common spread spectrum techniques such as direct sequence(DS), frequency hop (FH), time hop (TH), and multicarrier (MC). Of course, one can also mix thesespread spectrum techniques to form hybrids which have the advantages of different techniques.Spread spectrum originates from military needs and finds most applications in hostile communi-cation environments. We will start by briefly looking at the advantage of spreading the spectrum inthe presence of a Gaussian jammer as our motivation to study spread spectrum communications. To-ward the end of the chapter, we will also state some common spread spectrum applications. Detailedtreatments of some of these applications are left for the coming chapters.

2.1 Motivationa jamming analysisConsider the transmission of a bit stream1212 (12) through an AWGN channel. We employBSPK modulation at the carrier frequency. The channel is also corrupted by an intentional jammer.The received signal , in complex envelope representation, is given by

2.1(2.1)Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrum@ t=(k+1)T+ r(t)=s(t)+j(t)+n(t)p Tc (T-t)r k = sk + jk + nk^bksgn(Re[ ])Figure 2.1: Matched filter receiver for BPSK data with jammerwhere

34 12


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12

is the transmitted signal, is the AWGN with power spectrum (2.2)14 , and is the jammingsignal. In (2.2), is the symbol duration, is the symbol pulse width, and is the average transmittedpower. From Section 1.7, we know that the spectrum of the transmitted signal isgiven by if we model the bits as iid random variables and 34 34 3434(2.3) as a uniform random variable on 14 . By exam-ining the spectrum of the transmitted signal, a reasonable jamming strategy is to put all the jamming

power into the band coincides with the main lobe of the signal spectrum, i.e., from3434to is a zero-mean WSS Gaussian random process with34 , and 14 otherwise. Moreover, and rad/sec. For simplicity, we assume thatpower spectrum

forare independent.Neglecting the jamming signal, the ML receiver is the matched filter receiver developed in Sec-tion 1.2. We redraw the matched filter receiver in Figure 2.1 here for convenience. Let us considerthe performance of the matched filter when the jamming signal is present. Conditioning on1, thesampled output of the matched filter corresponding to the th symbol is

(2.4)where112 12


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We will see that the conditional error probability does not depend on(averaged over) is the same as the conditional error probability.2.2.Hence the unconditional error probabilityTan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrum 34 1212and(2.5)

12

12

(2.6) (2.7)and are independent zero-mean Gaussian randomFrom the assumptions above, we know thatvariables. It remains to determine their variances. The variance of is123434

For 14 (2.8), we note that its variance is equal to the value of the autocorrelation function of the matched filteroutput component due to at 14.Using the Fourier relationship between autocorrelation functionand power spectral density, we have3412

34123412 34 34 3412


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3434 3414 1434 34 34 34(2.9)Now, we can calculate the symbol (bit) error probability of the communication system describedabove. By symmetry, we know that the average symbol error probability is equal to the conditional12. Under the condition thatRe[ ] is a Gaussian random variable with mean 34 and variancesymbol error probability given that, say,symbol error probability is14

34 12

3434 1434 14 12 14 1434where

of3412, the decision statistic34 . Therefore, the12 14(2.10) is the symbol energy. Comparing (2.10) to (1.22), we suffer a loss in SNR by a factor12 14 1434

14 with respect to the case where the jammer is not present.2.3Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread SpectrumThere are two ways to reduce the loss in SNR. For a bandwidth limited channel, we can increasethe transmitted power of the signal. If power is the main constraint, we can reduce the pulse width. This corresponds to spreading the spectrum of the transmitted signal. In mili


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tary applications, oneconsideration is that we do not want our enemies to intercept or detect our transmission. The higher thetransmission power the more susceptible is the transmission being intercepted. Therefore, we usuallyresort to spreading the spectrum of the transmitted signal instead of raising the transmission power.This is the reason why spread spectrum is originally considered for military communications.In terms of jamming immunity, the spreading method described above is far from desirable. Simplyreducing is effective only for the continuous Gaussian jammer assumed above. Since the continuousGaussian jammer spreads its power across the whole symbol period, for a small , we only need tointegrate a small fraction of the symbol duration and, hence, pick up a small jamming energy. However,because of the regularity of the transmitted signal, it is easy for the enemiesto determine when thepulses are sent. Hence, they can switch to a pulse jammer which outputs high power jamming pulsescoincide with our transmission pulses. By doing so, the jammer can cause maximumdegradation to

our transmission without increasing the average jamming power. In this case, reducing will nothelp to combat the pulse jammer. To tackle the pulse jammer, we can randomize the transmissiontime of the pulse within the symbol duration to make the detection of the transmission times of thepulses difficult. Without the knowledge of the transmission times of the pulses,the pulse jammerbecomes ineffective. We once again force our enemies to spread the jamming powerboth in time andin frequency. As a result, we arrive back at the case of continuous Gaussian jammer, and we can spread

the spectrum to combat the jammer. The spreading technique just described is known as time hopping.The discussion above brings out an important characteristic of spread spectrum communications.In order for the receiver to perform properly, it has to know the transmission times of the pulses. Thismeans that the transmission times cannot be truely random. Instead, a sequence of pseudo-randomtransmission times is pre-assigned to both the transmitter and the receiver. This sequence is generallyreferred to as a code. We will see that all spread spectrum techniques contain some forms of pseudo-random codes. In fact, we usually do not classify a spectral spreading technique

, which does notemploy any form of codes (like the one in (2.2)), as a spread spectrum modulation.2.4Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrum2.2 Direct sequence spread spectrumOne non-trivial way of spreading the spectrum of the transmitted signal is to modulate the data signalby a high rate pseudo-random sequence of phase-modulated pulses before mixing th


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e signal up to thecarrier frequency for transmission. This spreading method is called direct sequence spread spectrum(DS-SS). More precisely, suppose the data signal is12where1234 12(2.11)12 is the symbol sequence and is the symbol duration. Note that all the signalshereare complex envelopes unless otherwise indicated. We modulate the data signalsignalwhere which is given by12

limited to

12

12

by a spreading(2.12) is called the chip waveform, which is time-12 is called the signature sequence and14 . We impose that condition that

, where , which is usually referred to asthe processing gain or the spreading gain, is the number of chips in a symbol and is the separationbetween consecutive chips. For convenience, we normalize the energy of the chipwaveforms to .The spread spectrum signal is given by 34

12

12

(2.13)where is the largest integer which is smaller than or equal to . This general model fo


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r DS-SScontains many different modulation and spreading schemes. Some of the common examples are listedin Table 2.1. For example, a pictorial description of the BPSK modulation with BPSK spreadingscheme is given in Figure 2.2.To obtain the power spectrum of the spread spectrum signal, we model the spreading elements

as iid zero-mean random variables with

3412, and the propagation delay as a uniform randomvariable as described in Section 1.7. Moreover, we also normalize the average symbol energy to ,i.e.,3412. Then the power spectrum of the spread spectrum signal is 2.5 34(2.14)Tan F. Wong: Spread Spectrum & CDMA

2. Intro. Spread SpectrumBPSK modulation QPSK modulationBPSKspreadingQPSKspreading

34 12

34 12

34 12

1212

34 34 34

34 1234 1234

34 12

34 1234 1234

34 12 Table 2.1: Common spreading schemesb(t)

a(t)s(t)Figure 2.2: BPSK modulation and BPSK spreading scheme2.6Tan F. Wong: Spread Spectrum & CDMAr(t)2. Intro. Spread Spectrum@ t=(k+1)T+zk


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h k(t)decisiondevice^bkFigure 2.3: Matched filter receiver for the th symbol of the DS-SS signalwhere is the Fourier transform of the chip waveform .The power spectra of the spreadsignals for the four schemes shown in Table 2.1 are all given by 34 34 3434(2.15)Comparing this to the power spectrum of the original data signal 34 34 3434(2.16)we see that the spectrum is spread times wider by the direct sequence technique

in (2.13). Inpractice, the spreading sequences are pseudo-random. We will discuss, in Chapter3, different ways togenerate sequences which have properties close to those of random sequences.In an AWGN channel, the ML receiver for the spread spectrum signal is the matched filter receivershown in Figure 2.3. We note that the matched filter is time-varying unless thespreading sequence12

12 is periodic with period . For the th symbol, the impulse response of the matched filter is given by

12

14

For BPSK modulation, the decision device gives decisionthe decision device gives decision12 sgn Re

34 (2.17)sgn Re . For QPSK modulation,12 sgn Im . The general case is left as34an exercise. Alternatively, we can implement (see Homework 2) the matched filter


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receiver as shownin Figure 2.4.The spreading method described in (2.13) is by no mean the only possible DS-SS technique. Forexample, one can spread the in-phase and quadrature channels independently instead of spreading thecomplex channel as in (2.13). Suppose the complex data signal is 2.7(2.18)Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrum@ t=(l+1)T +c(k+1)N-1 (Tc -t)*r(t)zkl=kNdecision

device^bka*lFigure 2.4: Equivalent implementation of the matched filter receiver in Figure 2.3where 12

121212 (2.19) (2.20) are the (real-valued) in-phase and quadrature data signals. The in-phase and quadrature data signalsare spread respectively by the (real-valued) in-phase spreading signal and quadr

ature spreadingsignature , where 12

12


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12

12

(2.21)

(2.22)

and and are the in-phase and quadrature chip waveforms (both are time-limited t14 ),respectively. The resulting spread spectrum signal is given by 14 14 (2.23)With the same model for the data symbols and spreading sequences we have before2, the power spectraldensity of the spread spectrum signal in (2.23) is given by 34 34 34

where and are the Fourier transforms of the chip waveforms and , respetively.2(2.24)In this case, is still modeled as uniformly distributed on 14 and 14 is assumed to be a constant.2.8Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrum@ t=(l+1)T +

crx (t) decision ^

device b xk decision ^

device b yk(k+1)N-1x(Tc -t)l=kNa xl@ t=(l+1)T +T + c0

ry (t)

(Tc -t)r(t) = rx (t) + j ry (t)(k+1)N-1l=kNa ylFigure 2.5: Matched filter receiver for independent-channel-spreading DS-SSThis DS-SS model includes offset QPSK spreading and serial-MSK spreading, whichwe are notgoing to discuss in detail. The matched filter receiver for this form of DS-SS i


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s shown in Figure 2.5.We note that the two different forms of DS-SS described in (2.13) and (2.23) overlap, but they are notsubsets of each other.In order to implement the matched filter receivers shown above, we need to achieve timing andphase synchronization which will be discussed in Chapter 5.2.3 Frequency hop spread spectrumAnother common method to spread the transmission spectrum of a data signal is to(pseudo) randomlyhop the data signal over different carrier frequencies. This spreading method iscalled frequency hopspread spectrum (FH-SS). Usually, the available band is divided into non-overlapping frequency bins.The data signal occupies one and only one bin for a duration and hops to another bin afterward.When the hopping rate is faster than the symbol rate (i.e., ), the FH scheme is referred toas fast hopping. Otherwise, it is referred to as slow hopping. A typical FH-SS transmitter and thecorresponding receiver are shown in Figures 2.6 and 2.7, respectively.Because it is practically difficult to build coherent frequency synthesizers, modulation schemes,

2.9Tan F. Wong: Spread Spectrum & CDMAdata2. Intro. Spread Spectrumb(t)DataModulatorHighpassFilters(t)a(t)FrequencySynthesizer

FH codeclockCodeGeneratorFigure 2.6: Transmitter for FH-SSImageRejectionFilterBandpassFiltera(t)FrequencySynthesizer

FH codeclockCodeGeneratorFigure 2.7: Receiver for FH-SS2.10DataDemodulatorestimateddata


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Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrumsuch as -ary FSK, which allow noncoherent detection are usually employed for thedata signal. For -ary FSK, the data signal3 can be expressed as3434where1412 1234

14

1212 (2.25). The frequency synthesizer outputs a hopping signal

34where 1412

1212

12 14 14

(2.26). This means that there are frequency bins in the FH-SS system.We impose the constraint that for fast hopping, or for slow hopping. The FH-SSsignal is given by34 12

12

for the case of fast hopping (


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123412

14

14(2.27)

), or for the case of slow hopping (

14 14

(2.28)). The orthogonality requirement for the FSK signals forces theseparation between adjacent FSK symbol frequencies be at least34for fast hopping, or3434slow hopping. Hence, the minimum separation between adjacent hopping frequenciesis 34fast hopping, or

3434, 34).34),hopping bins (), and34 hops per symbolTo obtain the power spectrum of the -ary FH-SS signal, we model the phasesrandom variables uniformly distributed on 14 34 .random variables taking values from the set14symbol frequencies

for for slow hopping. For example, Figure 2.8 depicts the operation of a fastFH-SS system with -FSK modulation (( forThe hopping frequencies

14 are modelled as iid

12

12


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with equal probabilities. The FSKare iid random variables taking values from the setequal probabilities. The delayand 14 as iid1412 12with is assumed to be uniformly distributed on 14 for fast hopping, or14 for slow hopping. We also assume that all the random variables mentioned aboveare indepen-dent. With these assumptions, we can show (see Homework 2) that the power spectrum of the FH-SS3All the signals in this section are real bandpass signals2.11Tan F. Wong: Spread Spectrum & CDMAdata sequencecode sequencehop bin2. Intro. Spread Spectrum01

10+1+1-1 -1+1-1 +1-1-1 -1-1-1 +1+1+1 -1-1+1 -1+1+1 +1-1+11537064276

543210Transmitted frequency patternTTc1/TcDehopped frequency patternFigure 2.8: Fast FH-SS system with 2-FSK modulation, 8 hopping bins, and 2 hopsper symbol

2.12Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrumsignal is given by 12 12 34

14


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14 34 34

34

34

3434(2.29)for fast hopping, or

34 34

34 34 34 (2.30)

34

34

14 14for slow hopping. Therefore, the spectrum of the original data signal is approximately spread by 12 12a factor of for fast hopping, or by a factor of for slow hopping.2.4 Time hop spread spectrumIn time hop spread spectrum (TH-SS), we spread the spectrum by modulating the data signal by apseudo-random pulse-position-modulated spreading signal. We have described the general idea inSection 2.1. Here, we give the precise definition. Suppose the data signal

1234 is 12(2.31)We modulate the data signal by the spreading signalwhere34 1412

12and 1212


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(2.32) . The resulting spread spectrum signal is given by 34 1212

To obtain the power spectrum of the TH-SS signal , we model the data symbols

as iid zero-12. The pulse location indices are assumed to be iid randomvariables taking values from 14 12 12 with equal probabilities. The propagation delay ismodelled as a uniform random variable on 14 as usual. It can be shown (see Homework 2) that thepower spectral density of the spread spectrum signal is the same as the one obtained in Section 2.1,mean random variables withi.e.,34(2.33) 34

34 3434

2.13(2.34)Tan F. Wong: Spread Spectrum & CDMAr(t)2. Intro. Spread SpectrumdecisiondevicepTc(T-t)^

bk@ t=(k+1)T+akTc + TimingCircuitCodeGeneratorTH codeclockFigure 2.9: Matched filter receiver for TH-SSThe matched filter receiver for this spreading method is shown in Figure 2.9. It


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is the same as thereceiver in Figure 2.1 except that the sampler is controlled by a timing circuitwhich is in turn drivenby the pseudo-random pulse-location code.We note that there are other types of TH-SS techniques. For example, one can usepulse-positionmodulation for the data signal. As a result, the spread spectrum signal will bepurely pulse-positionmodulated. The hopping scheme is similar to the -ary FSK FH-SS system describedin Figure 2.8with frequency bins replaced by time bins.2.5 Multicarrier spread spectrumIn FH-SS, only one of many possible frequencies is transmitted at a time. The other extreme is thatwe transmit all the possible frequencies simultaneously. The resulting spreadingmethod is calledmulticarrier spread spectrum (MC-SS). More precisely, suppose the data signal3412122.14

is given by(2.35)Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread SpectrumWe modulate the data signal by the spreading signal 12The resulting spread spectrum signal is 12 14

121234 121212 14(2.36)

(2.37)The data and spreading sequences are phase-modulated as in the case of DS-SS. The carrier frequenciesshould be chosen so that signals at different frequencies do not interfere eachother. The minimum


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frequency separation is34 . To obtain the power spectrum of the spread spectrum signal, we modelthe spreading elements as iid zero-mean random variables with3412, and the propagation14 . Moreover, we also normalize the average symbol energy34 12. Then the power spectrum of the spread spectrum signal is (seedelay as a uniform random variable onto by settingHomework 2) 34 34 12 1434(2.38)34The matched filter receiver for MC-SS is shown in Figure 2.10. When , the operationof the correlator branches in Figure 2.10 can be approximately performed by a si

ngle FFT. Hence thematched filter receiver can be implemented very efficiently. To see this, consider the output of the thcorrelator for the th symbol in Figure 2.10 and denote it by . Then, 12 34 12

1234 14

In above, we divide the intervalsub-interval, for

1412(2.39) 12 into sub-intervals of length . In the th12, we approximate4 the integral

12

Hence,34 12


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34

34

(2.40)(2.41)

144Better approximations can be made, say, by using the trapezoidal and Simpsons methods instead. We still get similarFFT implementation of the correlator branches by using these approximations.2.15Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrum(k+1)T+

( ) dtkT+ e-jw0 t+a*0,k(k+1)T+ ( ) dtkT+ r(t)e-jw 1t+a*1,k

(k+1)T+ ( ) dtkT+ -jwN-1 t+ ea*N-1,kFigure 2.10: Matched filter receiver for MC-SS2.16decisiondevice^

bkTan F. Wong: Spread Spectrum & CDMA2. Intro. Spread SpectrumWe note that (2.41) says that for each , the sequence 12 14is approximately the DFT (scaled)

12. Therefore, we can implement the correlator branches ap-14


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proximately by sampling at the chip rate and passing the samples through an FFT circuit. Similarof the sequence approximations can also be applied on the transmitter side.2.6 ApplicationsAs discussed in Section 2.1, anti-jamming is an important application for spreadspectrum modula-tions. In addition to anti-jamming, we will briefly introduce several other spread spectrum applica-tions in this section. In describing these applications, we focus on DS-SS systems. One should notethat other spread spectrum techniques also have similar applications since the main idea behind theseapplications is the spreading of the spectrum.2.6.1 Anti-jammingWe know that we can combat a wide-band Gaussian jammer by spreading the spectrumof the datasignal. Here we consider another kind of jammersthe continuous wave (CW) jammers.Supposethe spread spectrum signal is given by (2.13) and it is jammed by a sinusoidal signal with frequency

14 and power . The received signal is given by

34 14 (2.42)where represents the AWGN. When one of the four DS-SS schemes in Table 2.1 is used, we can

34 3434 14 14easily see that the power spectrum of the received signal is given by 34 (2.43)We consider the matched filter receiver in Figure 2.3. For convenience, we redraw the receiver inthe equivalent correlator form in Figure 2.11. At the output of the despreader,the signal can be

expressed as 34 34


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14142.17(2.44)Tan F. Wong: Spread Spectrum & CDMAz(t)r(t)2. Intro. Spread Spectrum(k+1)T+ ( ) dtkT+ decisiondevice^bka* (t- )Figure 2.11: Matched filter receiver (correlator form) for DS-SSIt can be shown (see Homework 2) that the power spectrum of the despread signal is 34 34 1434 34 3434

14 1434(2.45)Now the anti-jamming property of the spread spectrum modulation can be explainedby comparingthe spectra of the signals before and after despreading in Figure 2.12. Before despreading, the jam-mer power is concentrated at frequency 14 and the signal power is spread across awide frequency3434 ). The despreader spreads the jammer power into a wide frequency band

( 34 34 ) while concentrates the signal power into a much narrower band ( 34 34 ).band (The integrator acts like a low-pass filter to collect power of the despread signal over the frequencyband3434 . As a result, almost all of the signal power is collected, but only

12 th of thejammer power is collected. The effective power of the jammer is reduced by a factor of . This is thereason why is called the spreading gain.2.6.2 Low probability of detectionAnother military-oriented application for spread spectrum is low probability ofdetection (LPD), whichmeans that it is hard for an unintentional receiver to detect the presence of the signal. The idea behindthis can be readily seen from Figure 2.12. When the processing gain is large eno


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ugh, the spreadspectrum signal hides below the white noise level. Without knowledge of the signature sequences, anunintentional receiver cannot despread the received signal. Therefore, it is hard for the unintentionalreceiver to detect the presence of the spread spectrum. We are not going to treat the subject of LPDany further than the intuition just given. A more detailed treatment can be found in [1, Ch. 10].2.18Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread SpectrumBefore despreadingj ()PJn ()NoPTc-2 /Tcs ()2/Tc0After despreadingPT

NoP J Tc-2 /Tc-2 /T2 /T igure 2.12: Spectra of signals before and after despreading2.192 /TcTan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrum2.6.3 Multipath combiningAnother advantage of spreading the spectrum is frequency diversity, which is a desirable property

when the channel is fading. Fading is caused by destructive interference betweentime-delayed replicaof the transmitted signal arise from different transmission paths (multipaths).The wider the transmittedspectrum, the finer are we able to resolve multipaths at the receiver. Loosely speaking, we can resolvemultipaths with path-delay differences larger than12 seconds when the transmission bandwidth is Hz. Therefore, spreading the spectrum helps to resolve multipaths and, hence, combats fading.The best way to explain multipath fading is to go through the following simple example. Suppose

the transmitter sends a bit with the value 12 in the BPSK format, i.e., the transmitted signal envelopeis , where is the symbol duration. Assume that there are two transmission paths eading fromthe transmitter to the receiver. The first path is the direct line-of-sight pathwhich arrives at a delay14 seconds and has a unity gain. The second path is a reflected path which arrives at a delay of 34seconds and has a gain of 14 , where


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1214 is the chip duration of the DS-SS system we areofgoing to introduce in a moment. The overall received signal can be written as 14 34 (2.46)where is AWGN. To demodulate the received signal, we employ the matched filter receiver,which is matched to the direct line-of-sight signal, i.e., . The output of the matched filter is plotted in Figure 2.13. We can see from the figure that the contribution from the second pathpartially cancels that from the first path. We sample the matched filter outputat time signal contribution in the sample is14

. The and the noise contribution is a zero-mean Gaussian randomvariable with variance 14 . Compared to the case where only the direct line-of-sight path is present,, while the noise energy is the same.the signal energy is reduced byTherefore, the bit errorprobability is greatly increased.Now, let us spread the spectrum by the spreading signalwhere14 12

14 12 12 12 12 12 12 12 12 12 12(2.47). The received signal for thisDS-SS system is 14 34

2.20(2.48)Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrum11st path0.80.60.40.2


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overall00.20.42nd path0.60.8100.511.52time (T sec)Figure 2.13: Matched filter output for the two-path channel without spreading2.212.5Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrum11st path2nd pathoverall0.8

0.60.40.200.20.40.60.8100.511.5

22.5time (T sec)Figure 2.14: Matched filter output for the two-path channel with spreadingAgain, we consider using the matched filter receiver, which is matched to.The output of thematched filter is shown in Figure 2.14. We can clearly see from the figure thatthe contributions fromthe two paths are separated since the resolution of the spread system is ten times finer than that ofthe unspread system. If we sample at , we get a signal contribution of , which is the same as

what we would get if there was only a single path. Hence, unlike what we saw inthe unspread system,multipath fading does not have a detrimental effect on the error probability. Infact, we will show inChapter 4 that we can do better by taking one more sample at 34to collect the energy of thesecond path. If we know the channel gain of the second path, we can combine thepaths coherently.


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Otherwise we can perform equal-gain noncoherent combining. This ability of the spread spectrum2.22Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrummodulation to collect energies from different paths is called multipath combining.2.6.4 Code division multiple accessWe end our survey of spread spectrum applications by introducing the most investigated applicationof spread spectrum techniquescode division multiple access (CDMA). For simplicity, let us focus onDS-SS. We can allow different users to use the channel simultaneously by assigning different spread-ing code sequences to them. Thus there is no physical separation in time or in frequency betweensignals from different users. The physical channel is divided into many logicalchannels by the spread-ing codes. Different from TDMA and FDMA, spread signals from different users dointerfere eachother unless the transmissions from all users are perfectly synchronized and orthogonal codes are used.The interference from other users is known as mulitple access intereference (MAI). In general, syn-

chronization across users is hard to achieve in the uplinks of most practical wireless systems. In somesituations, we may not want to restrict ourselves to orthogonal codes. Therefore, we are interested ininvestigating how MAI affect the performance of the system and how we can eliminate the effect ofMAI. Detailed discussions on these two issues will be provided in Chapters 6 and7. Here we presenta crude analysis on how MAI affect the bit error probability performance of thesystem.Suppose we employ DS-SS with BPSK modulation and BPSK spreading. There are simul-taneous users, each having a distinct pseudo-random sequence, in the system. We

select one of theusers, call it the desired user, and try to determine the bit error probabilityfor this user. We assumethat the desired user employs the correlator receiver, which is matched to the spreading code of thedesired user. To simplify the discussion, we assume that the received powers ofsignals from all theusers are identical. Recall from the discussion in Section 2.6.1 that the despreader removes the effectof spreading from the desired signal. Since the despreader is not matched to thesignals from otherusers, it cannot remove the effect of spreading for those signals. As a result,the signals from other

users remain wideband after despreading, while the despread desired signal is the same as the originalunspread narrowband data signal. Since the integrator following the despreader acts like a lowpassfilter collecting power from the passband of the data signal, a crude but reasonable approximation is toassume the signals from other users are independent and identical white Gaussianrandom processes2.23Tan F. Wong: Spread Spectrum & CDMA


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2. Intro. Spread Spectrumwith power spectral density 5 , where is the received power and is the chip duration. Thusthe combined effect of the MAI and AWGN is the same as that of the AWGN with power spectral 12 14.density raised from 14 to error probability is given bywhere 34 12 14 121434 14 12 12 14

is the symbol duration andby a factor of12 12Substituting this back into (1.22), we see that the bit(2.49) is the symbol energy. We suffer a loss in SNR 14 with respect to the single-user system. If the number of users in thesystem is fixed, we can reduce the loss in SNR by increasing the processing gain, i.e., the bandwidthof the system. Unlike the case of anti-jamming, we cannot reduce the loss by merely increasing thesignal power.Using (2.49), we can have a preliminary estimate on the capacity of a DS-SS CDMA

system. First,14 is large in most practical situations. Hence,we note that the signal-energy-to-white-noise ratiowe can further approximate the error probability byFor example, a bit error probability of1434 1212(2.50)1214 is considered sufficient in voice communications. Using

the result in (2.50), we see that the CDMA system with processing gain can accommodate aboutusers without using any error-correcting code. With a powerful error-correctingcode, we expectthis number to increase.2.7 References[1] R. L. Peterson, R. E. Ziemer, and D. E. Borth, Introduction to Spread Spectrum Communications,Prentice Hall, Inc., 1995.


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5The reason we set the power spectral density to is that the power spectra of the DS-SS signals are squared sincfunctions which peak at14 with the value .2.24Tan F. Wong: Spread Spectrum & CDMA2. Intro. Spread Spectrum[2] M. B. Pursley, Performance evaluation for phase-coded spread-spectrum multiple-access com-munication Part I: System analysis, IEEE Trans. Commun., vol. 25, no. 8, pp. 795799,Aug. 1977.[3] R. A. Scholtz, Multiple access with time-hopping impulse modulation, Proc. MILCOM 93,pp. 11-14, Boston, MA, Oct. 1993.[4] N. Yee, J. M. G. Linnartz, and G. Fettweis, Multi-carrier CDMA in indoor wireless radionetworks, IEICE Trans. Commun., vol. E77-B, no. 7, pp. 900904, Jul. 1994.[5] S. Kondo and L. B. Milstein, Performance of multicarrier DS CDMA systems, IEEETrans.Commun., vol. 44, no. 2, pp. 238246, Feb. 1996.[6] R. L. Pickholtz, L. B. Milstein, and D. L. Schilling, Spread spectrum for mob

ile communica-tions, IEEE Trans. Veh. Technol., vol. 40, no. 2, pp. 313321, May 1991.2.25

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Introduction to CDMA Technology

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