Parallel Interference Cancellation in Multicarrier DS-CDMA Systems

K.R.ShankarkumarandA.Chockalingam

DepartmentofECE,IndianInstituteofScience,Bangalore560012,INDIA

Abstract—Inthispaper,wepresentandanalyzetheperfor-manceofaparallelinterferencecancellation(PIC)schemeformulticarrier(MC)direct-sequencecode-divisionmultiple-access(DS-CDMA)systems.AteachcancellationstageintheproposedPICscheme,oneachsubcarrier,aweightedsumofthesoftoutputsoftheotherusersinthecurrentstageiscancelledfromthesoftoutputofthedesireduser(ratherthanmakinghardbitdecisionsoftheotherusersandregeneratingandcancelingtheinterferingsignals)toformtheinputtothenextstage.Atthelaststage,theinterferencecancelledoutputsfromallthesubcarriersaremaximalratiocombined(MRC)toformthedecisionstatistic.Theschemehastheadvantageofnotrequiringtheamplitudeestimatesoftheotherusers.Wederiveanalyticalexpressionsforthebiterrorrate(BER)atdifferentstagesintheproposedPICschemeonRayleighfadingchannels.Analyticalresultsarefoundtoagreewellwiththesimulationresults.TheresultsshowthattheproposedPICschemeoffersbetterinterferencesuppressioncapabilitythantheconventionalmatchedfilterreceiver.WealsoobtainboundsonthecodedBERoftheproposedPICschemeforaconvolutionallycodedmulticarrierDS-CDMAsystemwherethePIC-MRCoutputfeedsasoftdecisionViterbidecoder.

Keywords–Parallelinterferencecancellation,multicarrierDS-CDMA,

fadingchannels.

I.INTRODUCTION

Multicarrier(MC)approachoffersseveraladvantagesin-cludingrobustnessinfadingandinterference,operationatlowerchipratesandnon-contiguousbandwidthoperation.Severalstudieshaveanalyzedtheperformanceofmulticar-rierDS-CDMAsystems[1]-[2].Inthispaper,weconsiderparallelinterferencecancellation(PIC)formulticarrierDS-CDMA.PICschemesformulticarrierDS-CDMAhavebeenstudiedin[4]-[5].ThesestudiesconsiderharddecisionPICreceivers,wherehardbitdecisionsaremadeontheoutputofthematchedfilters(MF),whicharethenisusedtoregenerateandcancelthemultipleaccessinterference(MAI)inparallel.OurcontributioninthispaperisthatweproposeandanalyzeaPICschemewhichdirectlyusesthesoftoutputoftheMFs(ratherthanthehardbitdecisions)forcancellationanddoesnotrequiretheestimationoftheamplitudesoftheusers.IntheproposedPICscheme,ateachcancellationstage,oneachsubcarrier,aweightedsumofthesoftoutputsoftheotherusersinthecurrentstageissubtractedfromthesoftoutputofthedesireduser(ratherthanmakinghardbitdecisionsoftheotherusersandregeneratingandcancelingtheMAI)toformtheinputtothenextstage.Atthelaststage,theinterferencecancelledoutputsfromallthesubcarriers

aremaximalratiocombined(MRC)toformthedecisionstatistic.Wederiveanalyticalexpressionsforthebiterrorrate(BER)forthefirstandsecondstagesintheproposedPICschemeonRayleighfadingchannels.Analyticalresultsarefoundtoagreewellwiththesimulationresults.TheproposedPICschemeisshowntoofferbetterperformancethantheconventionalMFreceiver.WealsoobtainboundsonthecodedBERoftheproposedPICschemeforaconvolutionallycodedmulticarrierDS-CDMAsystemwherethePIC-MRCoutputfeedsasoftdecisionViterbidecoder.

II.SYSTEMMODEL

Weconsidera-usersynchronousDS-CDMAsystem.Eachuseremploysamulticarriermodulator,wherethetransmitdatasequencemultipliedbyaspreadingsequencemodulatessubcarriers,asshowninFig.1.Thetransmittedsignalforthethuserisgivenby

cos

,is

givenby

cos

(6)

,andandarerespec-tively,andafterpassingthroughthethbandpass

filter.Thepowerspectraldensityofis.

Withoutanylossofgenerality,inthefollowingweanalyzethesystemdecisionforthethbitofthethuser.Letdenotethesoftoutputofthethbitofthethuser(

)onthethsubcarrierofthe(PICreceiver.The)softof

thethstage()outputofthethbitofthethuseronthethsubcarrierofthe1ststage,,isgivenby

(9)

(13)

andthevarianceof

is

.

A.2ndStageOutputStatisticsofthe

-thSubcarrier

Thesoftoutputsfromthe1ststage,,arefedasinputtothe2ndstagewherecancellationisperformed.TheobjectiveoftheinterferencecancellationistoestimatetheMAIoftheuser’sthtotaluserinsignal.parallelItisandnotedcancelthat,thefromestimate(10),fromthethwecancomputetheMAIaslongaswehavetheknowledgeof

and.Giventheknowledgeofthespreading

sequencesofalltheusers,canbedetermined.ThustheproblemtoestimatetheMAIofthethuseristofindanaccurateenoughestimateof.Anestimateof

,thoughimperfect,maybeobtainedbymultiplyingbyafactor,i.e.,

(14)

where

isgivenby

(17)

where

Forlarge,canbeapproximatedasaGaussianr.v.withzeromeanandvariance

(19)

Therefore,thevarianceoftheinterferenceandnoiseatthe

2ndstageoutputforthethuser,

,canbeobtainedas(20)

B.3rdStageOutputStatisticsofthe

-thSubcarrier

Inthe3rdstage,weessentiallytrytocanceltheinterferencecausedbythe’imperfect’cancellationinthe2ndstage.Aswedidinthe2ndstagecancellation,herealsoweobtainanimperfectestimateoftheinterferencetermanduseitinthecancellation.Further,inthe3rdstagecancellationthisestimatemustbeadded(notsubtracted)tothepreviousstageoutputinordertothecancelthenegativeimperfectcancellationtermintroducedinthe2ndstagecancellation.Accordingly,theinterferencecancelledoutputofthethuseratthe3rdstage,,canbewrittenas

(21)

(23)

Theaveragebit-errorprobabilityisthengivenby

istheaverageSNRpersubcarrier.

D.CodedPICScheme

Now,weextendtheproposedPICschemetoaconvo-lutionallycodedmulticarrierDS-CDMAsystemandstudy

itsperformance.Weconsideraconvolutionallycodedmul-ticarrierDS-CDMAsystem,wheretheuserdatabitsareinputtoarate-convolutionalencoderwhichgenerates

codedsymbolsforeachdatabit.Theoutputcodesymbolsareinterleavedandserial-to-parallelconvertedsuchthattheparallelcodesymbolsmaybetransmittedsimultaneously.Then,eachofthecodesymbolsmultipliedbytheuser-specificspreadingsequencemodulatessubcarriers,whichresultsinsubcarriers.

ThePICreceiverfortheabovecodedmulticarriersystememploysabankofPICdemodulatorsNotethatremappedinthesymboldemapper,atotalofsubcarriersareintosubcarriergroups,andeachgroupconsistsofsubcarrierswhichcarriesthesamecodesymbol.Inthedemapper,theoutputsfromsubcarrierswhichcarrythesamecodesymbolarecombined.Theoutputofthedemapperisparallel-to-serialconverted,anddeinterleaved.TheoutputofthedeinterleaveristhenfedtothesoftdecisionViterbidecoder.

Thecancellationprocessinthe-stagePICdemodulatoristhesameasthatfortheuncodedsystemshowninFigs.2(a),(b),exceptthatcodesymbolsareconsideredhereinsteadofuncodeddatabits.Also,theMRCandhardbitdecisionasshowninFig.2(c)arenotperformedhere.Instead,the

softoutputscorrespondingtothesubcarriersatthelastcancellationstageisfedtothedemapper,wheretheoutputsfromsubcarrierswhichcarrythesamecodesymbolarecombinedasfollows:

(26)

where,,isthedemapperoutputcorre-spondingtothethconvolutionallycodedsymbol,

representsthesetofsubcarriers

whichcarrythethcodedsymbol.Letthedatablocklengthbebits.Thesoftoutputsfromthedemapper/deinterleaver,,

arefedasinputtothesoftdecisionViterbidecoder.

Supposethedecoderchoosesthatpathwhichhasthemaxi-mumpathmetric,wherethebranchmetrics,,andpathmetricsofthethpath,,respectively,aredefinedas

and

(27)

whererepresentsthethcodedsymbolofthethtrellispathattimeindex,then,withsufficientinterleavingofthecodedsymbols,anupperboundonthecodedBERperformancecanbeobtainedusingthetransferfunctionoftheconvolutionalcodeused,as[2]

,and

isthe

transferfunctionoftheconvolutionalcodeused.

IV.PERFORMANCE

RESULTS

Inthissection,wepresentthenumericalresultsofthebiterrorrateperformanceoftheproposedPICreceiverformulticarrierDS-CDMA,bothfortheuncodedaswellascodedschemes.Wehaveassumedperfectchannelestimationatthereceiver.WecomparetheBERperformanceatvariousstagesofthePIC(i.e.,).Fig.4showstheBERperformanceofthePICreceiverasafunctionofthenumberofusers(),atvariousstagesofthePIC()fortheuncodedsystem.ThefigureshowstheplotscorrespondingtoboththeanalyticalresultsevaluatedthroughEqn.(25),aswellastheresultsobtainedthroughbiterrorsimulations.Inthesimulations,randombinarysequencesareusedforspreading.FromFig.4,weobservethattheproposedPICreceiverwith2stages()givessignificantimprovementintheBERperformancecomparedtotheconventionalMF-MRCreceiver(i.e.,).Thisimprovementisfurtherenhancedwhenonemoreadditionalstageofcancellation()isused.

Fig.5comparestheBERperformanceoftheuncodedsystemfordifferentvaluesofthenumberofsubcarriers(the2nd()andprocessinggains(),at)and3rd()stagesofthePIC.Asexpected,foragivennumberofPICstages,theperformanceimprovesasthenumberofsubcarriersisincreased,becauseofthefrequencydiversitybenefitofferedbythemulticarrierapproach.

TheBERperformanceofthePICfortheconvolutionallycodedsystemisshowninFigs.6and7.InFig.6,upperboundsonthecodedBERevaluatedfromEqn.(28)areplottedforrateandconvolutionalcodes(i.e.,

)anddifferentnumberofsubcarriers(

).Threedifferentsystemsallhavingsamesystembandwidthwithatotalnumberof8subcarriers(i.e,),butwithdifferentcombinationsofand,namely

(

),()and(

),areconsidered.Forallthesethreesystems,theBERperformanceatvariousstagesofthePIC()arealsoshown.Itisobservedthatforallthethreecodedsystems,theproposedPICreceiverprovidessignificantlyimprovedBERperformancecomparedtotheconventionalMF-MRC()receiver.Also,foragivennumberofPICstages,theperformanceofthe(),()and()systemsaresimilar,withthelowestratecode()systemperformingslightlybetter.Alargerimpliesasmallertokeepthesystembandwidthconstant,wherethefrequencydiversitybenefitismore(duetolarge)butthetimediversitybenefitduetoahighratecode(i.e.,small)isless.Ontheotherhand,alowratecode(large)impliesmoretimediversitybenefitandlessfrequencygain(duetosmall).Thus,toachieveadesiredperformanceinagivensystembandwidth,Fig.6pointstoapossiblecomplexitytradeoffbetweensystemshavingdifferentvaluesofand.

InFig.7,thetheoreticalupperboundsoncodedBERarecomparedwithsimulationBERresultsforvariousstagesofcancellationfor,,,and

dB.Theanalyticalresultsarefoundtoreasonablyagreewiththesimulationresults.Thus,theproposedPICreceivereffec-tivelycancelstheMAIandimprovestheBERperformancebothinuncodedandcodedsystems.V.CONCLUSION

Wepresentedandanalyzedtheperformanceofaparallelinterferencecancellation(PIC)schemeformulticarrierDS-CDMAsystems.Theschemehastheadvantageofnotrequir-ingtheamplitudeestimatesoftheotherusers.Wederivedanalyticalexpressionsforthebiterrorrate(BER)atdifferentstagesintheproposedPICschemeonRayleighfadingchannels,bothforuncodedaswellasconvolutionallycodedsystems.Analyticalresultswereshowntoagreewellwiththesimulationresults.TheproposedPICreceiverwasshowntoeffectivelycanceltheMAIandsignificantlyimprovetheBERperformancecomparedtoconventionalMF-MRCreceiver,bothforuncodedaswellascodedsystems.

REFERENCES

[1]S.KondoandL.B.Milstein,“PerformanceofmulticarrierDS-CDMA

systems,”IEEETrans.Commun.,vol.44,no.2,pp.238-246,Feb.1996.

[2]D.N.RowitchandL.B.Milstein,“Convolutionallycodedmulticarrier

DSCDMAsystemsinamultipathfadingchannel-PartI:Performanceanalysis,”IEEETrans.Commun.,vol.47,pp.1570-1582,Oct.1999.[3]J.Proakis,DigitalCommunications,NewYork:McGraw-Hill,19.[4]H.K.Park,E.Kim,Y.LeeandK.H.Tchah,“MulticarrierCDMA

systemwithParallelInterferenceCancellationforMultipathFadingChannels,”Proc.IEEEPIMRC’98vol.2,pp.513-517,Sept.1998.[5]A.Nahler,R.Irmer,andG.P.Fettweis,“Parallelinterferencecan-cellationwithreducedcomplexityformulticarrierspreadspectrumFCDMA,”Proc.IEEE6thISSSTA,pp.353-357,Sept.2000.

2Cos(ω1t+ θκ,1 )

Chip wave

shaping filter

||

S k(t)

bi

k

.

I.M.h(t)

||(n)

I.M.: Impulse Modulator Ck

Energy/Chip = Eck

||

2Cos(ωΜ t+ θκ,Μ)

Fig.1.

MulticarrierDS-CDMATransmitterofthuser

L(t)

(i+1)T+nTc

N-1

Z(1)(2)

LPF

1,m1,m

(i)Z1,m(i)

Z(L-1)

1,m(i)

Z(L)

1,m(i)

n=02Cos(ωmt + θ’)1

( n)

1,m

NC1

MF on mth subcarrier for user 1

Interference

MF for user 2 onZ(1)(i)

(2)

(L-1)InterferenceCancellation

Z2,m(i)

Z2,m(i)

Z(L) r(t)

H*(f - fm)r’m(t) mth subcarrier

2,mCancellation

2,m(i)

+ H*(f + fm)

MF for user K onZ(1)Z(2)

(L-1)

(L)

K,m

(i)K,m(i)

ZK,m(i)

ZK,m(i)

mth subcarrier

Stage 1

Stage 2

Stage L

Fig.2.

-stagePICdemodulatoronthe

thsubcarrier

Z(L)

k,1(i)Z(L)

k,2(i)

MaximalZk(i)bk(i)

RatioCombiner

Z(L)

k,M(i)

Fig.3.

MRCandbitdecisionforthethuser

10−11st stage (L=1), Simulation1st stage (L=1), Analysis2nd stage (L=2), Simulation2nd stage (L=2), Analysis3rd stage (L=3), Simulation3rd stage (L=3), Analysisrorr10−2e tib fo ytilibabor EPb/η0 = 15 dB M = 2, N = 3210−310−451015202530Number of users, KFig.4.Probabilityofbiterror,,versusnumberofusers,stagesofthePICreceiverfortheuncodedsystem.Analysisand,atsimulationdifferentplots.,,dB.

10−110−2rorre tib f10−3o ytilibaborP10−4M = 1, N = , 2nd stageM = 2, N = 32, 2nd stageM = 4, N = 16, 2nd stageM = 1, N = , 3rd stageM = 2, N = 32, 3rd stageM = 4, N = 16, 3rd stage10−5 Eb/η0 = 15 dB10−651015202530Number of users, KFig.5.Probabilityofbiterror,,versusnumberofusers,stagesofthePICfortheuncodedsystemwithdifferentvaluesof,atdifferent).Analysisplots(

only.

dB.

R = 2, M = 4, 1st stage (L=1)10−2R = 4, M = 2, 1st stage (L=1)R = 8, M = 1, 1st stage (L=1)R = 2, M = 4, 2nd stage (L=2)R = 4, M = 2, 2nd stage (L=2)10−4R = 8, M = 1, 2nd stage (L=2)R = 2, M = 4, 3rd stage (L=3)R = 4, M = 2, 3rd stage (L=3)R = 8, M = 1, 3rd stage (L=3)rorr10−6e tib fo ytili10−8baborP10−1010−1210−14N = 32, Eb/η0 = 15 dB10−1651015202530Number of users, KFig.6.UpperboundonthecodedBERversusnumberofusers,atdifferentPICstagesoftheconvolutionallycodedsystemwithdifferent,combinationsofcoderate()andnumberofsubcarriers().,

dB.

10−11st stage (L=1), Simulation1st stage (L=1), Analysis2nd stage (L=2), Simulation2nd stage (L=2), Analysis3rd stage (L=3), Simulation3rd stage (L=3), Analysis10−2rorre tib fo ytiliba10−3borP10−4N = 32, Eb/η0 = 15 dBR = 2, M = 110−51012141618202224262830Number of users, KFig.7.ComparisonoftheanalyticalboundsonthecodedBERversusthe

simulatedBERatdifferentPICstagesoftheconvolutionallycodedsystem.

,,,dB.