无线通信论文

MotorolaLabs

CommunicationsSystemsResearchLab

Schaumburg,Illinois,USA

ABSTRACT

Ahighpeak-to-average-powerratio(PAPR)isaprimarydraw-backoforthogonalfrequency-divisionmultiplexing(OFDM).ManymethodshavebeenproposedtoreducetheOFDMPAPRforsingle-antennaandforMIMOsystems.Somesys-tems,however,usemultipleantennasforfrequency-selectivetransmitbeamformingeithertoasingleormultiplesimulta-neousreceivers.ThispaperpresentsanewmethodforPAPRreductionthatminimizesthepeakpoweracrossallantennaswhilepreservingthemaximalratiotransmission(MRT)gainandzero-crosstalkcriteriaatthereceivers.Becausethegainandzerocrosstalkispreservedatthereceivers,noperfor-mancelossisseenbythereceiverswhenusingthePAPR-reducedtransmitvector.Witheighttransmitantennas,thealgorithmdemonstratesanaverageof5.5dBPAPRreduc-tionforsingle-userbeamformingandabout4.5dBPAPRre-ductionforfour-usertransmitspatialdivisionmultipleaccess(Tx-SDMA).

1.INTRODUCTION

Communicationssystemsbasedonorthogonalfrequencydi-visionmultiplexing(OFDM)canachievehighperformanceintermsofdatarate,spectralefficiency,andtolerancetochannelimpairmentsatmoderateimplementationcomplexity.TheseadvantageshaveledtotheadoptionofOFDMinmanymod-ernwirelesscommunicationsstandards,including802.11a,g(Wi-Fi),802.16(WiMAX),andtheEuropeanterrestrialdig-italaudioandvideobroadcaststandards,andmakeOFDMaprimecontenderformanynewstandards.

PerhapsthegreatestdrawbackofOFDM,however,isarelativelyhighpeak-to-average-power(PAPR)ratio,whichincreasestheback-offrequiredinthetransmitterpoweram-plifierandtherebygreatlyreducesthetransmitterefficiency.ManymethodshavebeenintroducedforreducingthePAPRofOFDM,assummarizedin[1];approachesincludesettingasidesomechannelsforpeakcancellationsignals,variouscodingmethods,andselectivephasemanipulation.Practicalpeakreductionintherangeof3-4dBhasbeenreportedusingthesemethods.However,thesemethodsentailareductionindatarateduetothereservedchannels,thecodingredun-

DouglasL.Jones

UniversityofIllinoisatUrbana-ChampaignElectricalandComputerEngineering

Urbana,Illinois,USA

dancy,orthetransmissionofsideinformation,respectively.Atechniquecalledactiveconstellationextension(ACE)mod-ifiesdata-bearingchannelsinawaythatmaintainsdatarate,margins,andbiterrorratewhilereducingthePAPRbyupto4dB[1],[2].ACEcanalsobemadecompatiblewithmoststandardOFDMreceiverswhileretainingvirtuallyallofitsPAPRreduction[3].

Multipleantennascansignificantlyimprovetheperfor-manceandcapacityofwirelesscommunicationsystems.Themainapproachesincludeexploitingdiversitytoreducetheprobabilityofdeepfadesanddropouts,multi-inputmulti-output(MIMO)signalingtoincreasetheoveralldataratebe-yondthatpossiblewithasingleantenna,andbeamformingoneithertransmitorreceive.Beamformingcansteerthetrans-mitenergymoreefficientlyinthedirectionoftheintendeduser,canoptimallycombinemultiplereceivedversionsofthesignal,orcanreduceinterferencebysteeringnullsinthedi-rectionofothersourcesorreceivers.Mostemergingwire-lessstandardsalloworrequiretheuseofmultipleantennas,andothersystemscanapplybeamforminginwaysthatcom-plywithsingle-channelstandards.PAPRreductionmeth-odsfordiversityandMIMOmulti-antennaOFDMsystemshaverecentlybeendeveloped[4][5],includinggeneraliza-tionsofACEforbothdiversityandMIMOOFDMsignaling[5].Asinthesingle-channelcase,MIMOACEmaintainsdatarateandperformanceandremainscompatiblewithstan-dardMIMOreceivers;comparablepeakpowerreductionsofupto3-4dBarealsoobserved.

WepresenthereamethodforPAPRreductionthatisap-plicabletobothmaximalratiotransmission(MRT)andtrans-mitspatialdivisionmultipleaccess(Tx-SDMA)[6].NotethatMRTisdesignedfortransmissiontoasinglereceiver(mobile)andTx-SDMAsimultaneouslytransmitstomultiplereceivers(intheversionofTx-SDMAconsideredinthispa-per,azero-crosstalkcriterionisemployed).ThePAPRreduc-tionmethodoperatesonthetransmitvectoroneachsubcarrierwherethetransmitvectorisaproductofthetransmitsymbolvectortimesthetransmitweightmatrix.Themethodisde-signedtoreducethePAPRwhileconstrainingthereceivedsignalateachmobiletobeidenticaltothenon-PAPRre-ducedtransmitvector.Thismeansthatboththegainandzero-

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crosstalkismaintainedbythePAPR-reducedtransmitvector.ThePAPR-reducedtransmitvectorisabletoaccomplishthisbyrequiringaslightlyincreasedtransmitpower(e.g.,insim-ulationresults,around0.2dBmorepowerisneededonaver-ageoverthenon-PAPRreducedtransmitvector).However,thesubstantialimprovementinPAPRmorethanmakesupforthissmallincreaseintransmitpower.Witheightbaseanten-nas,PAPRreductionofabout5.5dBisobservedwithMRTtransmissionandabout4.5dBwithTx-SDMAtransmissionwithfourmobiles.

2.TRANSMITBEAMFORMERSFOROFDM

SYSTEMSOFDMisanidealmodulationmethodforbeamformingbe-causethechannelvectorseenbythemobile(assumingasin-glereceiveantenna)onagivensubcarrierisflatfaded.ThismeansthatanybeamformingmethoddesignedforflatfadingcanbeeasilyappliedtoOFDMoneachsubcarrieraslongaschannelstateinformationisavailableatthebase.Assumingthattherearetransmitantennasatthebaseandbeams

signal(oneforeachmobile)aretobetransmitted,the

sentfromthebaseisgivenas(whereisthetransmitvectoronsubcarrier):

3.PEAKPOWERREDUCTIONFORMRTAND

TX-SDMABEAMFORMERSMRTandTx-SDMAbeamformerweights[6]minimizethetotalradiatedtransmitenergyrequiredtoachieveacertainsignallevelatthereceiverwhilemaintainingazero(orlow)crosstalkbetweeneachreceiver.InOFDM,thesebeamform-ingmethodsoperateonaper-subcarrierbasisandthusthere-sultingtransmitvectorwillstillhaveahighPAPRsimilartothatofregularOFDM.Sincetheenergyconsumedbytypicalpoweramplifiersismostlyafunctionofthepeakpower,theMRT/Tx-SDMAweightswillgenerallynotminimizetheen-ergyconsumedbyapracticaltransmittercircuit.Weinsteadmustsolvethefollowingoptimizationproblem:minimizethe

,whereisthetransmitwave-peakpower

formonantenna,overanalog(continuous)time.Thecontinuouswaveformisinterpolated(perhapswithashapingfilter)fromthefrequency-domaintransmitsig-transmitantenna,(istheelementnalforthe

ofthetransmitvector,):

interpIFFT

(5)

(1)

isthetransmitweightforuseronsubcar-where

isthetransmittedsymbolforuseronsubcar-rierand

rier.Inmatrixform,(1)canbewrittenas:

(2)

Inthefrequencydomainandasgivenin(3),thesignalre-coveredatreceiverisafterpassingthroughtheMISOchannel,whereandarethetransmitbeam-formerandtheMISOchannelfromthetransmitarraytothesinglereceiverantennaatmobile.Sincethereceiverre-quiresaconsistentgainandphaseineachchannelasmea-,thesuredfrompilotsymbolstoequalizeandrecover

frequency-domainbeamformercoefficientsformobilemustbeconstrainedtoalwaysproducethesameoverallcomplex

givenin(4))gain(with

whereisthevectorofsymbolsforeachmobileon

subcarrierandisamatrixwhoserowis.Thereceivedsignalonsubcarrieratmobileisgivenas:

(6)

(3)

isthechannelvectoronsubcarrierforuserwhere

.Notethatforthispaperitisassumedthatthetransmitterhasperfectchannelknowledge.

)orTx-SDMAthetransmitForeitherMRT(i.e.,

weightmatrixcanbeexpressedas:

(4)

whereisamatrixwhosecolumnis.Notethattheterminthedenominatorispresentsothattheaveragetransmitpowerisone.AlsonotethatforTx-SDMA,thenu-meratorenforcesazero-crosstalkconstraintonthedifferentbeams.

Notethat(6)enforcesthezero-crosstalkcriteriaandthatsatis-fyingthisrequirementusesuponlyonedegreeoffreedompermobileleavingampleopportunityforadjustingtheremaining

).AlsodegreesoffreedomtoreducePAPR(aslongas

notethatwemakethestandardbeamformingassumptionsthatthetransmitterhasaccesstoaccuratechannelstatefeed-backandthatthechannelisessentiallystationarybetweenupdates.

Sincetheconstraintsthatthepeakislessthanathresh-old,retentionoftheMRTreception,andnullsinthedirectionofotherreceiversareallconvex,projectionontoconvexsets(POCS)theorytellsusthataniterativealgorithmbasedonsuccessiveprojections(clippingandbeamformerconstraintrestoration)convergestowardasolutionifoneexists.Further-more,sinceasmallcliprepresentsagradientstepintermsofpeakreduction[2],analgorithmthatsuccessivelyreducesthepeaktoaminimumachievablevaluewithbeamformercon-straintrestorationisthereforeagradient-projectalgorithm.Theseobservationsplacethefollowingiterativealgorithmon

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asolidtheoreticalfoundationandconfirmitsconvergenceto-wardanoptimalsolution.

Theiterativealgorithmperformsthefollowingsteps:1.Assignfrequency-domainconstellationpointsforallmobiles,,accordingtotheinputdataandsettheit-.erationnumber,

2.Createtheprojectionmatrixoneachsubcarrieras

.

3.Createthetransmitvectoroneachsubcarrier,

(2)usingthetransmitweightsin(4)andset

,from

.

4.Reconstructthetime-domainsignalspaddedinverseFFTaccordingto:

withazero-

Whenapplicable,thisapproachofferssubstantiallymorede-),sothepeakre-greesoffreedomthanACE(for

ductionmaybeexpectedtobegreater.ThisapproachcouldalsobecombinedwithactiveconstellationextensionoftheOFDMsymbolstopotentiallyreducethepeaksevenfurther.

approachestherecouldbeasignificantbenefitofAs

combiningtheACEalgorithmwiththeproposedmethod.Notethatthestepofenforcingthegainandzero-forcingconstraintsresultinasmallincreaseinthetransmitpoweroverthenon-PAPRreducedMRTweights(e.g.,simulationsshowedarounda0.2dBincreaseinpoweronaverage).How-ever,thefactthatthePAPRisgreatlyreducedusingthePAPR-reducedweightsenablesthepoweramplifiertooperatemoreefficientlyandthusthetrivialpowerincreaseisareasonabletradeoff.

interpIFFT

4.SIMULATIONRESULTS

whereistheelementof;anoversamplingfactoroffourfortheIFFThasexperimentallybeenfoundtobeample.

toapredeterminedlevel(e.g.,alevelof3dB5.Clip

abovetheaveragepowerwasusedinthesimulations).

canbeclippedseparatelyoneachNotethateither

antennaorcanbeclippedtoalevelrelativetotheaveragepoweracrossallantennas.Thesecondoptionmaybeusefulwhenthepowertransmittedfromeachantennavariesandanabsolutemaximumpowerinputtothepoweramplifierisdesired.

6.Returntothefrequencydomainforallantennasvia

;zeroallfrequenciesnotcorrespond-FFTstoobtain

ingtodata-bearingchannels.

7.Foreachtion:

computetheTx-SDMA-restoringprojec-8.

,returntoStep4anditerateuntilthedesired

peaklevelisachievedforalltimesamples,thealgo-rithmconverges,orthemaximumallowednumberofiterationsisexceeded.

atThesignaltransmittedfromthebaseisgivenby

thefinaliteration.Notethatthecomputationalcomplexityofapplyingtheprojectionmatrixcanbemadelowerbytakingadvantageofthestructureoftheprojectionmatrix.Forex-ample,inthesingle-usercase,theprojectionmatrixisrankoneandcanbeexpressedasaproductofavectortimestheHermitianofthesamevector.Thusamatrix-vectormultiplyissavedinStep7.

Thisiterativealgorithmissimilarinspirittothatfirstin-troducedin[2]fortheACEalgorithm,butinthiscasethetransmitvectoritself,ratherthantheconstellationpoints,aremodifiedwithinconstraintsguaranteeingreceiverinvariance.

Simulationresultsarenowpresentedforan802.16-likeOFDMsystemwithasystembandwidthof5.0MHz,asub-carrierspacingof11.2kHz,anFFTsizeof512,and432sub-transmitcarriersusedfordata.Thebasestationhas

antennas(withanantennaspacingof5.0)andthemobileshaveonlyasinglereceiveantenna.Thedownlinkchannel

secRMSdelayspreadwithawassimulatedwitha

angularspreadatthebaseand64-QAMmodulationwasused.ThePAPRwasmeasuredonaper-antennabasisbytakingan

IFFTtosimulateacontinuoustimesignal.ThePAPRwascalculatedonaperOFDMsymbolbasis(i.e.,onlythemaximumpeakperOFDMsymbolwasusedincalculatingtheCDF)andthePAPRwasaveragedoveralltransmitanten-nas.ThePAPRreductionalgorithmusedaclippingvalueof3dBabovetheaveragepowerandtheclippingwasdonesep-aratelyoneachtransmitantenna.Forcalculatingthesignalto

IFFT.beclipped,thePAPRreductionalgorithmuseda

Figure1showstheCDFofthePAPRforthePAPRre-ductionalgorithmforavaryingnumberofmobiles(users)forafixednumberofiterations(nine).Ascanbeseen,asthenumberofusersincreases,lessPAPRreductionisobtainedforafixednumberofiterations.InfacttheeightuserCDFisidenticaltothenon-PAPRreducedbeamformerCDFforanynumberofusers.Theseresultsareexpectedsincethedegreesoffreedom(whichareusedforPAPRreduction)inthetrans-mitweightsdecreaseasthenumberofusersincreases.Notethatabout5.5dBofreduction(measuredatthe95%proba-bilitypoint)isseenforthePAPRreducedMRTweights(oneuser)andthePAPRreducedTx-SDMAweightsforfourusersseesabout4.5dBofreduction.

Figure2showsthePAPRimprovementasafunctionofthenumberofiterationsforTx-SDMAwithfourmobiles.NotethatmostofthePAPRimprovementcanbeobtainedwithjustafewiterations,anddiminishingreturnsareseenafteraboutfiveiterations.

RecallthatthePAPR-reducedweightspresentedinthis

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ProbabilitypaperaredesignedtoprovidethesamegainandzerocrosstalkastheoriginalweightsbyallowingthePAPRre-ducedweightstotransmitwithmorepower.Theframeerrorrate(FER)performanceofthePAPRreducedweightsisthusidenticaltothenon-PAPRreducedweights,butthisisforapower-unfaircomparison.Toassessthelevelofpowerin-creaseneeded,apower-fairFERcomparisonismadewherethePAPR-reducedtransmissionisnormalizedtounittrans-mitpowerlikethenon-PAPRreducedweights.Thesimula-tionresultslookedattheSNRlossata0.01FER(forrate3/4turbo-coded64-QAM)forthetransmitweightswithPAPRreductionversusnoPAPRreduction.ThesimulationresultsshowedthatthePAPR-reducedMRTandTx-SDMAweightsneededabout0.2dBmorepoweronaverageregardlessofthenumberofusers(onetosevenuserswassimulated)tomatchthesamegainasthenon-PAPRreducedweightswhennineiterationsofthealgorithmwereused.This0.2dBincreasedtransmitpoweristrivialwhencomparedagainstthesubstan-tialPAPRreductionpossiblewiththealgorithm.

5.CONCLUSIONS

ThispaperpresentsanewmethodofPAPRreductionfortransmit-beamformedOFDMsystems.ThemethodoperatesonthetransmitvectoroneachOFDMsubcarrier(asopposedtothetransmitweights)toreducethePAPRofper-subcarrierMRT/Tx-SDMAtransmissionwhilepreservingtheMRTgainandzerocrosstalkateachreceiver.Becausethegainandzerocrosstalkispreservedatthereceivers,noperformancelossisseenbythereceiverswhenusingthePAPR-reducedtransmitvector.Insimulationresultsforan802.16-likesystemwitheighttransmitantennas,significantPAPRreductionwasseen(e.g.,abouta5.5dBreductionforthePAPR-reducedMRTweightsandabouta4.5dBreductionforthePAPR-reducedTx-SDMAweightsforfourreceivers).

6.REFERENCES

[1]B.S.KrongoldandD.L.Jones,“PeakPowerReduction

viaActiveConstellationExtension,”IEEETransactionsonBroadcasting,Vol.49,No.3,September2003,pp.258–268.[2]D.L.Jones,“PeakPowerReductioninOFDMandDMT

viaActiveChannelModification,”Proc.33stAsilomarConferenceonSignals,Systems,andComputers,1999,pp.1076–1079.[3]T.E.DetwilerandD.L.Jones,“OFDMReceiverDesign

forActiveConstellationExtension,”Proc.39thAsilomarConferenceonSignals,Systems,andComputers,2005.[4]H.-C.Lee,D.N.Liu,W.-J.Zhu,andM.P.Fitz,“Peak

powerreductionusingaunitaryrotationinmultipletrans-

mitantennas,”IEEEInternationalConferenceonCom-munications,2005,pp.2407–2411.

[5]G.WooandD.L.Jones,“PeakPowerReductionin

MIMOOFDMviaActiveChannelExtension,”IEEEIn-ternationalConferenceonCommunications,2005.[6]J.K.Cavers,“Single-UserandMultiuserAdaptiveMaxi-malRatioTransmissionforRayleighChannels,”inIEEETransactionsonVehicularTechnology,Vol.49,No.6,November2000.

10.90.80.70.60.50.40.30.20.101 user2 users3 users4 users5 users6 users7 users8 users45678PAPR (dB)91011Fig.1.CDFofPAPRforvaryingnumberofbeams/usersfor9iterationsofthePAPRreductionalgorithm.

10.90.80.70.6Probability0.50.40.30.20.100 iters.1 iter.2 iters.3 iters.4 iters.5 iters.6 iters.7 iters.8 iters.9 iters.10 iters.45678PAPR (dB)91011Fig.2.CDFofPAPRforvaryingnumberofiterationsofthePAPRreductionalgorithmforTx-SDMAweightswithfour

).beams/users(i.e.,

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