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SPREAD Sm PECTRUMCOMMUNICATIONSM Y TH S A ND REALITIES

Andrew J. ViterbiCoding is always beneficial and sometimes crucial for thesuppression of interference in spread spectrum communications

INTRODUCTIONSpread pectrum o mm unicat ion echniquesdateba ck to the early fifties. Since the ea rliest app lications,system mprovem entshavebeenmore volutionarythan evolutionary. Like mo st mpro vem ents in elec-t ronic sys tems, these are duerimarily to th e vailabilityof ever higher spee d nteg rated circuit com pon ents,which translate in this c a se to wider sp read spec tra. Inthree decades the achievable spreading factor has grownby about three ordersf magnitude to the point thatweare now limited more by bandwidthallocations hanby technolog y limitations. Before wexamine the quanti-tative effectsof spreadin g, let u s cata log briefly t he multi-ple purpose s of spread spectrum communicat ions .First , we note that spreading here referso expans ionof the bandwidth well beyond what is required to trans-mit digital data. Thu s, a system transm itting data at a rateR ) f 100Mbits/s using approximately 00MHz of band-width ( W ) is not spread atll, while system transm ittinga t 100 bi ts /s spread over a spect rumof about 100 MHzhas a factorW/R = 106, or 60 dB of so-cal ledprocess inggain.

The author s with the Linkabit Corporation, SanDiego, CA92121.Which parallels the evolution of data rate capabilities of digitalcommunications.

PURPOSESThe purpose andpplicability of spread spectrum tech-Interference Suppressionnergy Density ReductionRanging or Time Delay Me asurem entForemos t among these s the suppress ion of interfer-ence.which may be character ized as any combinat ionfth e following:1) Ot he r Us ers : intentional (hostile or unintentional),2) Multiple Acc ess: pectrum haring by coo rdi-

3 Multipath: self-jamm ing by delaye d signal.Protection gainstn-bandnterference is usuallycalled anti- jamming (A/J) . Thiss the single most exten-sive application of spread spectrum communicat ion. Asimilar application is that of multiple ac ces s by num erou susers who share the same spectrum in a coordinatedma nne r, in that each employsignaling char acteristic s orparameters (of ten refer red to as codes)hich a re distin-guishable from those of all other users. One reason orusing this shared spectrum , so-calledode-division m ulti-ple access (CDMA), is tha t by distinguishing signals inthis way, separation in the more com mon dime nsionsff requency or t ime is not required, and hence the usualtransmission tolerances need not be imposed on these

niques is threefold:

nated users,

parameters .

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The thi rd formof interference suppressed by sprea dspectrum techniques is the self interference caused bymultipath in which delaye d versions f he signal, arrivingvia alternate paths, interfere with the direct path trans-mission.While thesecondand hi rd orms of interferencewould appear morebenign than thatof a hostile emitter,the t echn ique and ff ec t a r e the s ame. Wha t makes theintentiona l nterferenc e more challenging is the gameaspect of the problem and the fact that the inter fer ings o u r c e is general ly granted much more power than thecommunicator, which is usually not the caseor cooper-ating users and even less so for multipath interference.The second class of applications centers about thereduct ion of the energy dens i tyf the transm itted ignal.This, too, has a threefold purpose:1) o m eet international allocations regulations,2) to m inimize detectability,

3 for privacy.Downlink transm issions rom atellitesmustmeetinternational regulations on the spectral density of thesignals received on earth.y spreading this energy overawider bandwidth, otal ransmittedpowercanbeincreased , and hence per fo rmance improved . Spread ingalso decreases the detectabili tyf a signal by a regulatorybody whichemploys spectral analysiso monitor or regu-late emissions. (It is not known w hether bootleg radioamateur sare using pread pectrummodulat ion toeva de FC C regulations.) Even mo re promising is thepotential orachievingprivacy in com mun ication bysprea ding one.s signal sufficiently to hid e n the bac k-ground noise.T he application of sprea d spec trum for ranging orposition location is rapidly gaining in importance. In sim-plest terms, position location consists of measuring thedelay of a pulse or pulses. Errorn delay measurem ent isinversely proportion al to th e bandwidth of the signalpulse. This is most easily see n by the simple exampleofFig. 1.The accuracy f t he measurement t is obviouslyproportional to th e ise t imeof the pulse, whichs inver-sely proport ional o the bandw idthf the puls e ignal. Ofcourse, a one-shot measu remen t o n single pulse is not

. . . . ~ . . I - . . - I _-- . L

Uncertainty At = Rtse Time of Pulse=-.. I . : ~ . . W l

Fig. 1. Time delay measurement .

very reliable. Ra ther, the sprea d spec trumignal used forranging is a long sequence of polarity changes (binaryPSK-m odulated signal). Upon reception, this is corre-lated against a local replica an d lined up to perform anaccurate range ordelay measurement.BASIC TECHNIQUES

Havingoutlined themultiple uses of spectrum spread-ing, we must examine ateast a superficial description ofthe concept beforew e c a n p r o c e e d t oispel myths andunco ver realities abou t this increasingly popula r tech-nique . Fig. 2 is an all-purpose diagramo descr ibe spreadspectrum mod ulation. Multiplication of two unrelate dsignals produces aignal whose spectrums th e convolu-tion of t he spec t r af the two component s ignals . Thus ,fthe digital data (bina ry)signal is relatively narrow-bandcompared to the sp read ingignal, the pr od uc t ignal willhave near ly the spectrumf the wider (spre adin g) signal.So muc h for the mod ulator. At th e demo dulator, thereceived signal is multiplied by exac tly the sam e sprea d-ing signal. Now if the spreadingsignal, locally generatedat the eceiver, is l ined up synchron ized) with thereceived spread signal, the resul t is the original signalplus, possibly, so me spurio us higher frequency compo-nen ts outsid e the ban d f the original s ignal, and hen ceeasily filtered to reproduce the original data essentiallyundistorted. If there is anyundesired signal at hereceiv er, on the other han d, the sprea ding signa l willaffect it just as it did th e original signal at the tran sm itter .Thus , even if it is a narrow-band signal in the middle ofthe bandof interes t ,t will be spre ad to the ban dw idthfthe sprea ding signal.Th e result is that the undes i red ( jamming)signal willhave a bandwidthof at least W f its power is J watts , itsaverage density, which is essentially uniform and can betreated as wide-band noise,will be

N O= J/W watts/Hz.Let the desired component of the received signal havepo we rs wat t s. Thus ,f the data rate isR bits/second, thereceived energy per bit is

Eb = S / R watts . second.Now it is generally recogn ized that digital com mun ica-tion system bit error rate perform ance is a direct func-tion of the d imen sionless ra tio Eb/No, which for spr eadspectrum s ignals may thus b e expressed as

Eb - s wNo J R

and hence, the jamming power-to-signal power ratiois

This establishes that fEb/No is the minimum bit energy -to-noise dens i ty rat io needed to suppor t aiven bit erro rr a t e , a n d W/R is the ratio of spread bandwidth to the12 IEEE Co m m u n i c a t i o n s M a g a z i n e

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Dataignal Rate R

SpreadingSignalSpreading

SignalMultiplication ONCE Spreads Signal BandwidthMultiplication TWICE Followedby Filtering Recovers Original SignalDESIREDSignalMultipliedTWICE,UndesiredONCE

I .. .. ,______.__ - . .____ _ .- _---____. _.I . _IFig. 2. Bas ic spread-spec t rum techniques .

Reality is, in fac t, ust the oppo site. o see that codingdo es not reduce he effective processinggain, let usrewrite jamming margin(1) n terms of the symbof ra teR, and thesymbol energy,. These are re la tedo the bitra te and thebit energy through the code rate r,efineda s t h e n u m b e rf data bi ts per t ransmitted symbol, or theinverse of the coding expansion factor. (For exam ple,ra te 1 /2 coded system t ransmi ts two code symbols foreach data bit.) t follows that

R , =R/ rn d E, = Ebr.

original da ta ban dwidth, also called the processing gain,then J/S is the maximum tolerable jamming power-to-signal pow er rat io, also known as the jammingmargin.W e have com e this far without even specifying thecharacterist ics of the spreading ignal . Th ere are ,n fact,two distinct classes of spreading techniques. Th e first iscal leddi rec t sequence or pseudonoisePN)spread spec-t rum. Here the spreadings achieve d by multiplication bya binary pseudora ndom sequence whoseymbol (switch-ing) rate is many imes he binary data bit rate. Th espreading sequence symbol rates sometim es called thechip ra te .The seco nd class t il izes afrequency hopping carrier.H e r e the spre adin g signal remains at a given frequencyfor each bit or eve n or seve ral bits. Thu s, locally it is nowider tha n the data signal, but when it hop s to a newfrequency, i t may be anywhere within the spreadingbandwidth W.One fundam enta l d i fference between the two tech-n iques is tha t d i rec t sequence PN spreadignals can becoherently demo dulated. With frequency hopped sig-na l s , on t he o the r hand , phase cohe rences difficult tomaintain when the signal freq uen cy is hopped over awide range ; hence, this mo dulation is usually dem odu-lated noncoherently.We are ow ready to explore several irmly ent ren che ditems of com m on wisdom regarding he relative desirabil-i ty of various eatures of spreadspec t rumsystems.Often these at t itudes are misguided, a s we shall pres-ently sho w. In all cas es, the ide asold for both classe s fspread spect rum techniques , bu tor all but the last co n-cept he argu me nts are som ewh at simpler for directsequen ce sp reading, w hich we shall therefore consider.We are ready now to reveal the first of four myths.First Myth:Error-correct ing coding requires redundancy, wnichsp reads bandw id th andhus reduces auailable process-ing gain for the available bandw idth.Coding does not reduce theeffective process-

ing gain in a spread spectrum system.

May 1979

Now if we repeat the previous dimensional argum entreplacing bits by symbols everyw here, we haveWIR,J / S = ,/No

but substituting the precedingefinitions for symbol r ateand energy, we obtain for the maximum tolerable J / SratioW No - W / RJ / S = /r Ebr&/No

which gets us back to (1).This m ay s ee m like sleight ofhan d, but t really is not. Mor eover, although t will takesome further reading to be convinced, we a re reallyahead of the gam e. For i th coding , the requi red &/NOfor agiven level of performance (bi t error rate)s actuallyred uce d. Th us, for a given processing gain (W/R) thejamming margin is further increased by coding.For those who are a t i sf ied tha t spect rum spreading(especially direct sequence PN) t echniques make henoise look white while the signal energy, without orwith coding, can be fully rec over ed by the receiverscorrelating multiplier, the dispelling of the First Mythwill com e as no sur pris e.et it is often this sophisticatedgroup who will fall prey to theSec ond Myth:form interference.Error-correct ing coding is effectiue only against uni-

2Symbol rate refers to hecode sym ol of theerror-correctingcode-not that of the PN spreading code, which is usually called chiprate.

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In particular , hemyth ont inues ; oding is noteffective against pulsed interferenc e. Yet, this is evenmore dramatically false than heFirstMyth.Letusconsider what theffect of pulsed interferenc e can be foran uncoded sys tem. Suppose the j amming is presentonly a fraction p < 1 of the time, but that during thistime, the noise density level is increased to a level No/pwatts . This assumes spectrum spreadinghich turns thejamming signal into broad-band noise and an averagep o w e r a t h e r h a n a peakpow er limitation on hejamm er. (Wh ile this may be slightly pessimistic for thecommunica to r ,anyotheras sumpt ion is a risky betagainst techn ologica l progress.) Now it is well knownthat wi th coherentdemodula t ionanuncoded BPSKmodulated sys tem produces bit er ror rate b elated to&/No as

whereQ(x)= e-""* du.1 "

But if the noise is intermittent, and hence onlywithprobability p corrupts a given transmitted bit3 with thehigher noise density No/p, the resulting bit erro r rat ebecomes3We assume for simplicity that a given interference pulse corrupt s an ,integral number of bits. This is a reasonable assumption if the pulsewidth is many times the bit duration. Otherwise, he situation is actuallyless favorable to the jammer.

Clearly, the amm er would choo se the duty factor pwhich pessim izes perform ance-th at is, maxim izes biterror rate.n term s of the approx imation ,which is a strictupper bound,- this occurs when1P=- &/No provided ,/NO > I

at which value

(Note that a l thoughwe worked with the approximationfor ts simplicity, ha dw eused heexact Q-er ror -funct ion) express ion, the wors t casep would be nearlythe s ame and themaximum bit error rate would not besignificantly lowe r.)The result is quite drama tic. Puls e jamming-withspread spectrum but without coding-changes n ex po-nential relation into n inverse-lin ear one. Num erically,fwe des i re bit er ror rate per forman ce on the order ofP b io- , stationarynoise or amm ing) equires only&,/No = 10 dB, while with pulse jammingwe must haveEb/No = 45 dB, an increase n required s ignal powerofover three ordersof magnitudeAmazingly, coding can almostully resto re this dep lor-able situation, but before we can explain why, we m ustbriefly explo re a sum ma ry of the gene ral capa bilities ofcoded sys tems.

Coding Fundamentals~~ ~

When a binary data streammust be transmitted over anoisy channel with a troublesome bit error rate , oding can beused to significantlyreduce the error rate ncurred by the message.Inblock coding chemes, themessage bit stream ispartitioned into blocksf k bits, where ks the block length.Each such message blockis replaced with ann bit code word (n is bigger tha nk) which is transmitted in its place. Thus, every n bit transmitted contains onlyk messagebits so that the rate r of the code is k/n bits per code symbol.A common noisy channel model is the so-called Gaussian channel where each bit, viewed as a square pulse of amplitude k 1, isindependently subjected to additive noise and an error occurswhen the noise alters the pulse polarity.As a resultof erro rs, the eceived n-bit block can be any of 2" possible words. Since here areonly k different code words that could havebeen transmitted (one for each k-bit gnessage block) and Zk is typically much less than 2". the number of possible received words 2 is muchgreater than the numberf code words 2 k .For each received code word, the decoderdecides what was the most likely code word that wastransmitted, and the receiver then identifies the corresponding k-bit message block. In this way error correction can be achieved.A notablydifferent approach is convolutional coding. ere the ncoming message bit stream isapplied to aK-s tage hift register which isshifted b bits at a time. For eachK messageits stored in the register, ther e aren inear logic circuits which operate on the register content s toproduce n code bits of the encoded output stream. For eachhiftof the register, bnew message bits are inserted and n code bits are delivered,so that the rates b/n information bits per code symbol. In this case, a particular code bit depends on K message bits where is called theconstraint lengthof the code.Note also hat a particular messagebit remains in the register for K/b hifts, and thus nfluences the value ofnK/b cod e bits.Unlike block coding, the optimal decoding operation for convolutional codes requires memory hat stores,n effect, a function of the entirepast history of the received bit stream. The performance (as measured by error rate) of a convolutional coding system improves as t hecomplexity (Le., memory) allowed for the decoder s increased. Several methods of decoding convolutional codes have been developed. Theoptimal (maximum ikelihood) scheme isgenerally known as theViterbi algorithm. Viterbi decoding for reasonably short constra int engths isfeasible to implement and high decoding speeds are chievable. For extremely low error probabilities, a large constraint IengthK is required.The computational complexityof Viterbi decoding for large K makes this approach impractical. Another approach , sequential decoding,then becomes more attractive. third echnique,feedback decoding,hough inferior in performance against random errors,s particularlywell suited to correcting systematic error bursts which may occur in fading channels.Both fading and pulse jamming introduce memory n the channel and furthermodify the channel statistics.Yet the same oding techniquesas used for the Gaussian channel are at least as effective here, provided interleaving is employed to reduce oreliminate this memory.

14 I E E E C o m m u n i c a t i o n sa g a z i n e

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ISCRAMBLER UNSCRAMBLER

INTERLEAVER DEINTERLEAVERCODER OROR j> DECODER iI ~~ iL-. . _____....___. _.._ _._._.__. ._I____^.-I . . .

Fig. 4. In t ro duc t ion of in ter leav ing for d is pos ing bu rs t s .appear at the receiver as wide-band noisef den sity level (9) .This says that ifros sm all en oug h, n o p h l t y is paidJ

N o / p , but for a educe dduty actor p . Suppose , asbefore, with little loss of reality, tha t a n ntegral num berof code symb ols are affected by jamming. We canno tquite apply what we just learned about coding becausethe jamming pulses ffect many contiguous symbols; owe cpn hardlycall the channel memorylessas required.But his 'is eas ily remed ied. Suppo se we cons t ruct adevice which random ly cramb les heord er of th esymbols prior o transmission, but after coding, and putsthem back in the r ight order after reception, but beforedecoding (Fig. 4) . (Scram blers and unscram blers aremore commonlycalled interleavers and deinterleavers.)But heunscrambler which res tores he ransmit tedsymbols to their right place in order actually scramblesthe egular amm ingpulses nto andompatterns?Scramblingor nterleaving husmakesour ystemmemorylessagainand we canapplyournew-foundcoding know ledge.Withoutbelaboring heexactdetails,arguing ntu-itively an d believingly on the basis of (2) and 2 ' ) , let USreplace e-E,/Nny pe-pE5'N''n ll the orm ula s of theprevious (uniform noise) section. Thus,7)is replace d by

ro = 1 - 10 I + pe-pE,'No]. (7')Combining (7') with 6 )and 8), e get

whichobviously reduces to (9) for uniform amming(P = 1).This is maxim ized by a jam mer with duty cycle

= (21-r"- 1 e (10)provided ro > 1 - og, (1 + e- )= 0.548 for which

Eb ae-'-m a x -= for ro > 0.548.O+

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U

zI

n

z

I

1ro ar- _- -Fig. 6. * / N o equ i rem ent i n pu ls ed no is e w i thou t i n te r leav ing .For a s dec reases, t he numberof symbols per bit an d,for a constant duration interferenc e pulse, the num berf

symbols per pulse B ) ncreases . Thus, keepingB f ixed ,a s is don e for conve nience in Fig. 6 , gives misleadinglyfavorable results.O ur final "myth" happens fortuitously to coincideithreality. We call it, there fore , a Folk The orem ." Itconce rns an in teres ting comparison of di rec t sequenc e(coh erent) sprea ding i th frequency hopping (noncoher-ent) spreading:Fourth Folk Theorem: (Myth = Reality)Pe r fo rmance offrequency-hoppedspreadspectrum s3 dB worse than tha t of di rec t sequence P N ) s p r e a dspect rum.Th e commonly invoked "mythical" argum ent is thatnoncoherent ys temscan utilize atbestor thogonalsignals (e.g., binary SK mo dulation ) insteadof antipodalsignals (binary PSK modulation) an d this acco unts fort he 3 dB. The t roubleith this argu me nt is tha t it igno resthe possiblity of higher signaling alph abe ts suc h asMFSK ) and , wo rse till, the real possibility that frequen cy-hopped sy s t emsmay be morevulnerable t o nonuniforminterference.We note, in fact , that in frequency-h opped systems ,t he j ammer need no tay the cost f a higher peak powersignal, for if he jams just a fraction of the band,6p < 1,with power density N o / p , he will ap pe ar to the eceiverjust a s a partial time jammer. ote also that if the hoppingra te is at leas t as grea t as theymbol rate, nterleaving isunnecessary .Fo r a lphabe t sf s i zeq , (4) and (5)must bemodified tobecome

p b< -K(h--') block codes (4 )and

6Possibly varying hisbyhoppinghimself in order to defeat theobvious communicator strategy of determining the jammed region andstaying out of it

p b < (9 - W K O[1 4 1 convolutional codes (5')which reduce to (4) and5)w h e n q = 2. There is nothingto gain by using multiple signal alphab ets for coh ere nt,d i rec t sequence systems, bu t with frequency-hoppedsystems, we can show 2] that for the wor st case artial-band jammer

provided

For asymptotically large q , this approachesE bNo_ - 4 In 2 a

which is exactly a factorf 2 3 dB) above the inimum ofFig. 3 which occ urs as .ro -0. This comparison issho wn in Fig. 7 , which also shows theiminishing retu rnsof using alphabet size q> 8.Th e asymptotic minimum isvirtually rea che d for q > 32.Not ice tha t noncoherent f requency-hopped systemsexhibitminimum, while coh eren td i rec t equencesystem s impro ve monotonically as l /ro incr eases . Theexplanation of this behavior is bet ter unders tood byexamining Fig. 8 which is a more detai led and morerealistic ex amination of performance for an octal alpha-bet . Her e th e a ssum ptions are mo re' real ist ic. Specific-ally, chan ne l quality information is limited t o tw o bits(four levels)out of each of t he q m atc hed filters. This alsoallows for apracticalautom atic gain contr ol AGC)technique, which has not been men tioned up o hispoint.

The cu rve fo r p = 1 is, of course, for uniform noise.The i nc rease a t igh ra t e s ( r ando close to 1) is d u e t othe lack of coding redundancy. The increase a tow ratesis du e to the higher loss, characteristic of noncoherentcombining of symbols in high diversity (here low rate)noncoherent communication systems.As p , the fractionof the interference bandwidth decreases, performancegets increasingly worse at high rates since theiversity islacking toovercom e he trong amm er. But a s rodec rea ses , diversity beco m es sufficient to fully defeat th elow p jammer, as show n by the family of cu rves of Fig. 8.

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i1 2 3 4 5 6 7 . 8 91 i. . I . .. 1 . I - . 1. I _ i i _i.~Il_i

- .

1 1ro a r_ = _Fig. 7 r equ i rem ent f o ronc oheren trequenc yo p p e d

systems.SUMMARY

Beyond cataloging the many uses of spread spec t rumcommunicat ion, we have made no at tempt to b eniformin our treatm entof this extensive and many-facetedield.We hav e concentrated rather on its application for thesuppress ion of in ter ference, and have made three mainpoints:Coding is alwaysuseful, and it may be critical toadequateperformance of spreadspec t rumsys tems,particularly when the na tureof the interferences partial-t ime,or in th ecase of f requency-hoppedspreading,partial ba nd . Pro pe r interfacing of the decoder to thede mo du lato r, in utilizing quality (soft decision) informa-

tion, is i m p o r t a n t to ensure m a x i m u m benefit f r o mcoding.Interleaving or scrambling may be equally essentialnthe presence of burst interference.Direct sequen ce spread spectrum fficiency is aboutdouble that or frequency hopping. Thiss t an tamount todoubling the processing gain W/R.However, frequency-hopping technologymay have an edgen achievable band

L- __ L I ___ . . J 1 i . A.- L L. ,...J1 2 3 4 5 6 7 8 9 1 01 1ru a r-_ -

Fig. 8. / N o r equ i rem ent f o r oc ta ln o n c o h e r e n t r e q u e n c yh o p p e d y s t e mn par t ia l band nter ferencewi th eceiverquan t i z a t i on ( p = i n te r fe renc e f r ac t i ona l bandw id th ) .

spreading ofone o r more o rder sf magnitude over directseque nce pread ing technology w hich greatly ver-shadows the system edgeof the latter.Although the efficiency of direct sequence

spread spectrum i s about double that offrequency hopping, this advantage i s over-shadowed by the greater band spreading

achievable with frequency hoppingtechnology.REFERENCES[11 A. J. Viterbi and J . K . Omura,PrinciplesofDigital Communicationand Coding. New York: McGraw-Hill, 1979.[2] A. J . Viterbi and I. M. Jacobs, Advances in coding and modula-tion for noncoherent channelsaffected by fading, partial-band and multiple-access nterference, in Advances in Communication Systems,

VO I 4. New York: Academic. 1975

Whats Your Reaction?Now that you heard what Andrew Viterbi has to say,

what do you have to say?Praise, criticism, corrections, disagreements, and

other comments are always welcome and appreciated.(Please indicate if we may publish your remarks in

the Packets to the Editor column.)-Editor

8 IEEE Communicat ions Magaz ine