Channel

    JournalofHarbinInstituteofTechnolo(NewSeries),Vo1.15,No.6,2008 ;ChannelestimationforMIMO-OFDMsystemsinmobilewirelesschannels ;wuYun,LUOHan—wen,SONGWen—tao

    ;吴赘,罗汉文,宋文涛

    ;CollegeofInformationScience&Technology,DonghuaUniversity,Shanghai201620,China,E—mail:wuyun—

    ;hit@dhu.edu.cn;

    ;2.Dept.ofElectronicEngineering,ShanghaiJiaotnngUniversity,Shanghai200240,China)

    ;Abstract:Achannelestimationmethodisproposedforrnuhiple—inputmultiple—output

    oahogonal~equencydi—

    ;visionmuhiplexing(MIMO—OFDM)systemsintime—varyingfadingchannels.Inthis

    method,adecision—direct—

    ;edspace—alternatinggeneralizedexpectation—maximization(SAGE)algorithmisintr

    oducedtothetrackingof

    ;time—varyingfading.InordertoimprovetheestimationperformanceoftheSAGEalgorithm,alowrankapproxi—

    ;mationmethodispresentedbyusingthesignalsubspaceofthechannelfrequencyautocorrelationmatrix.The

    ;studyrevealsthatthismethodcanbeincorporatedintotheSAGEalgorithm.Furthermore.amodifiedfastsub—

    ;spacetrackingalgorithmisgiventoadaptivelyestimatethesignalsubspacebyutilizingtrainingOFDMblocks

    ;sentatregularinterva1.Simulationresultsdemonstratetheconsiderablebenefitsoftheproposedchannelestima—

    ;tionmethod.

    ;Keywords:MIM0一OFDM;channclestimation:SAGE:subspacetracking

    ;CLCnumber:TN929.5Documentcode:AArticleID:1005-9113(2008)06-084I-05 ;Sinceorthogonalfrequencydivisionmultiplexing

    ;(OFDM)splitsbroadbandwithintoanumberofnar-

    ;rowbandwidthsandtransmitsthemsimultaneously.it

    ;hasastrongimmunityagainstinter—symbolinterference

    ;(ISI)duetomuhipathpropagationandrequiressimple

    ;complexityforequalization.Ontheotherhand.muhi

    ;inputmultioutput(MIMO)techniqueisenvisagedto

    ;improvethecapacityandthereliabilityofthelink.

    ;Therefore.MIM0.0FDMisagoodcandidatesforfuture

    ;generationwirelesssystemsE2].

    ;InMIM0—0FDMsystems.coherentdecodingre.

;quireschannelstateinformationfCSI)betweenmulti—

    ;pietransmitantennasandreceiveantennas.whichisu—

    ;suallydifficulttoobtain,especiallyfortime—varying

    ;dispersivefadingchannelssincethereceivedsignalis ;thesuperpositionofthesignalstransmittedfromdiffer. ;enttransmitantennassimultaneously.Intypiealchan.

    0FDMsystems.the ;HelestimationalgorithmsforMIM0—

    ;channelsareestimatedutilizingpilotsymbolsortraining ;sequences-6』.

    ;InRef.『3],atwo.dimensional

    ;MMSE(minimummeansquareerror)channelestima. ;torisproposedforMIMO一0FDMsystems.makinguse

    ;ofthechannelstatisticssuchasthechannelpowerde—

    ;layprofile(PDP)andtheDopplerfrequencyshift. ;However.thisestimatorhasahighcomplexity.AFre. ;quencydomainchannelestimatorisproposediflRef. ;[4]relayingontimedivisionmultiplexpilotsymbols. ;InRef.j5】,atimedomainLS(1eastsquare)channeJ ;estimationschemefor0FDMwithmultipletransmitan—

    ;tennasbasedondiscreteFouriertransformfDFT)is ;proposedandoptimaltrainingsequencesaredesigned ;tosimplifythechannelestimation.Moreover.itturns ;outthatchannelestimatorinthetimedomainhasabet—

    ;terperformancecomparedtothatinthefrequencydo—

    ;mainsincetheformerrequireslessunknownparameters ;toestimate.

    ;AnEM—typespace-alternatinggeneralizedexpecta—

    ;tion—maximization(SAGE)algorithmisintroducedto ;estimateandtracktheOFDMchannelswithtransmitter ;diversityinRef.[7],whichhasafastconvergence ;ratecomparedtothetraditionalEMalgorithm.Ateach ;iterationandforevery0FDMlink,theSAGEalgorithm ;pa~itionstheproblemofestimatingamulti—?inputchan--

    ;nelintoindependentchannelestimationsforeachtrans—

    ;mits.receiveantennapair.TheSAGEalgorithmcanbe ;viewedasaniterativeLSestimatorofRef.I51.Com—

    ;paredtotheestimationestimatorinRef.J5J,noma—

    ;trixinversionisrequiredinthetrackmode. ;Inthispaper,weproposeanewchannelestima—

    ;tionmethodforMIM0一OFDMsystemsintime—varying

    ;fadingchannels.Atthetrainingblocks,optimaltrain—

    ;ingsequencesbasedtimedomainLSestimatorisused ;forchannelestimation.Atthedatablocks,adecision—

    ;directedSAGEalgorithmisintroducedtotracktime—va.

    ;ryingfading.Forpracticalwirelesschannelsinlarge ;cells,themultipathpropagationisaptlymodeledbya ;fewdominantspecularpaths,typicallytwotosix. ;Therefore.aparametricchannelmodeIandcorrespond—

    18. ;Received20H06一l0—

    ;SponsoredbytheNationalNaturalScienceFoundationofChina(GrantNo.60572157)and

    theNationalHighTechnologyResearchandDevelopmentPro? ;gram(863)(GrantNo.2003AA12331007).

    ;?

    ;841?

    ;JournalofHarbinInstituteofTechnology(NewSeries),Vo1.15,No.6,2008

    ;ingchannelestimatorareproposedtoimprovetheesti—

    ;mationperformanceinRef.[8].However,thatmeth—

    ;odhasahighcomputationcomplexityfortheexplicit ;estimationandtrackingofthechanneldelays.Here, ;weovercometheseproblemsbyavoidingtheexplicit ;estimateofthechanneldelays.Instead,werelyon ;low—rankchannelapproximationtoimprovetheestima—

    ;tionperformancebyselectingthefewsignificantsingu—

    ;larvaluesofthechannelfrequencyautocorrelationas ;thesignalsubspace.Thesignalsubspacereflectsthe ;propertyofmultipathdelays,henceforthreferredtoas ;thedelay—subspace.Ourstudyrevealsthismethodcan ;beincorporatedintoSAGEalgorithmreasonable.Since ;themultipathdelaysvaryslowlyinmobileenviron—

    ;ment,wepresentamodifiedfastsubspacetracking ;algorithmtoadaptivelyestimatethedelay—subspaceby

    ;usingtrainingOFDMblockssentatregularinterva1. ;Thecomputationsimulationsshowthattheproposed ;delaysubspacetrackingbasedSAGEalgorithm(ST+ ;SAGE)canimprovethechannelestimationperform—

    ;anceconsiderablycomparedtothetraditionalSAGEal—

    ;gorithm.

    ;1SystemDescription

    ;1.1MIMO-0FDMSystems

    ;ConsideraMIMO—OFDMsystemwithNtransmit

    ;antennasandNreceiveantennas.Attimen,adata ;blocku=[u(0),u(1),…,H,(K一1)]iscoded

    ;intoNdifferentsymbolblocks,=[x(0),(1), ;…

    ;,t(K一1)]’,fori=1,…N,accordingtoanap—

    ;propriatecodingscheme.Thecodedvectorismodu—

    ;latedbyaninversediscreteFouriertransform(IDVF) ;intoanOFDMsymbolsequence.Acyclicprefix(CP)

    ;oflengthGisaddedtotheOFDMsymbolsequenceand ;theresultingsignalistransmittedfromtheithtransmit ;antenna.

    ;Atthereceiver,thereceivedsignalvectorfirst ;hastheCPremovedandisthendemodulatedbyaDFT ;toyieldthedemodulatedsignalvectors.Thereceived ;signalafterOFDMdemodulationcanbeexpressedas ;Y=X,H+

    [,:,…,],isaK×Kdiagonal ;whereX,,垒

    ;matrixwith:(k,k)=(k);日垒[H,日:,…,-

    ;Nr]and垒[,,…,],isaK×1

    ;vectorwith(后)denotingthefrequencyresponseof ;channe1atsubcarrierfromtransmitantennaitore—

    ;ceiveantennaj;WisanK×Ni.i.d.Gaussianma—

    ;trixwithzeromeanandvariance,

    ;.Throughoutthe

    ;paper,itisassumedthattheISIiscompletelyelimina—

    ;tedbyinsertingtheCPandtimeandfrequencysyn—

    ;chronizationisperfect.

    ;1.2ChannelModel

    ;Thecomplexbasebandrepresentationofthemo一

    ;?

    ;842?

    ;bilewirelesschannelimpulseresponse(CIR)canbe ;describedbv[]

    ;L1

    ;hji(,r)=?()(r—T1)

    ;wherethe{(t)}denotesthepossiblytime—variant

    ;attenuationfactorfortheLmuhipathpropagationpaths ;and{t『f}arethecorrespondingtimedelays.Thechan—

    ;nelscorrespondingtodifferenttransmitandreceivean—

    ;tennasinMIMOsystemsusuallyhavethesame ;PDP.Therefore.thedelaycharacteristicisassumed ;tobesameforallavailablechannelsinthispaper. ;Eachpathgainiswide—sensestationary(WSS)nar-

    ;row—bandcomplexGaussianprocesses.Fordifferent1, ;iandj,0If(t)areindependent.TheCIRisassumedto ;beconstantduringoneOFDMsymbols.

    ;ThechannelfrequencyresponseforOFDMsystem ;withpropercyclicextensionandsampletimingcanbe ;expressedas

    ;()垒//’(nr,,,kaf):

    ;L一1

    ;?,=0

;(Z)exp(一J(2wkl/K))(1)

    ;where(z)垒h(n,lT,);=(K+G)isthe

    ;OFDMsymboldurationincludingguardintervaland ;isthesampleinterval;?厂=1/KT,isthesubearrier

    ;spacingoftheOFDMsystem.Theaveragepowerof ;(1)’sdependsonthePDPofthewirelesschannels.

    ;Leth;i:[|}l(0),…,(L一1)]’and=

    ;[:(0),…,(K一1)],Eq.(1)bewrittenina

    ;matrixformas

    ;=F

    ;whereFisamatrixwithF(,)=exp(一wkl/K)for

    ;=

    ;0,1,…,K一1andl=0,1,…,L一1.

    ;2ChannelEstimation

    ;Z.1LSEstimator

    ;Atthetrainingblocks,weintroducetheLSesti—

    ;mator[jt0estimatetheM1MOchanne1.Thisestimat0r ;isaDFTbasedtimedomainchannelestimation ;scheme.Let

    ;垒[F,XiF,…,xF]

    ;h垒[(),(),…,(JII)]

    ;h垒[h,h,…,]

    ;ThereceiversignalY,j

    ;canbeexpressedas

    ;Yn

    ;=Th+

    ;ThentheLSestimateofthechannelis

    ;五:(THT)一THY

    ;InRef.[5],optimaltrainingsequencesarepres—

    ;entedtoreducethecomplexityofchannelparameter ;estimation.Furthermore,itshowsthatthechanneles—

    ;timatorwiththeoptimaltrainingsequencescanachieve ;thebestestinmtionperformance.Selectedaconstant—

    ;umgnitudetrainingsequence,Ib(七)=1Iforthe

    ;JournalofHarbinInstituteofTechnology(NewSeries),Vo1.15,No.6,2008

    ;firsttransmitantenna,thetrainingsequencesusedfor ;theothertransmitantennasareconstructedby ;b(k)=b()exp(j2盯Ko(i一1)k/K),i=2,…?

    ;where:L?fJ?.Letx=b,itfollowsthat

    ;T=HencetheLSestimatorissimplifedto ;磊=J_TH

    ;fL

    ;Thenthefrequencychannelestimateisob—

    ;tainedbyperformingDFTon.

;2.2SAGEAlgorithm

    ;Thedecision--directedSAGEalgorithmisintro?- ;ducedinRef.[7]totrackthetime—varyingchannel

    ;forOFDMwithtransmitterdiversity.IntheSAGEalgo- ;rithmofRef.[7],thechannelfrequencyresponseis ;firstobtained.Inordertoimprovetheestimationper- ;formancebyutilizingtheinformationofPDP,thechan—

    ;nelistransformedintotimedomainbyusingtheIDFT.

     ;Finallythechannelfrequencyresponseisobtaineda—

    ;gainusingDUF.WeextendthismethodfortheMIMO—

    ;OFDMchanneltracking.Aftersomemanipulations, ;theprocedureoftheSAGEalgorithmcanbedescribed ;asfollows.

    ;Considerthereceiveddatayasincompletedata, ;anddefinethecompletedataRas

    ;R=X日+W,i=1,2,…/V

    ;whereH:A[日,’,…,],=?=

    ;1

    ;,

    ;thus

    ;R,theiterativeprocessisasfollows.

    ;Initialization:For1?i?

    ;2.=X觎.

    ;Atthekthiteration(:0,1,2,…):

    ;Fori:1+[kmodN],compute

    ;=

    ;2+[Y一

    ;=J7()(2)

    ;n

    ;=

    ;X:钟n’

    ;For1???andj?i,compute

    ;:

    ;ThesuperscriptdenotesthekthiterationandH ;?FF”.ThematrixFisformedaccordingtotheinfor—

    ;mationofPDP,thereforeitcanbereferredasthede—

    ;lay—subspace.Thennisthecorrespondingsubspace ;projectmatrix.

    ;TheSAGEalgorithmdescribedaboveusesprior ;informationofPDP.However.itisusuallydifficultto ;obtaintheexactinformationofPDPinpractice.In ;mostchannelestimationmethods.thelengthofchannel ;isassumedtobethesameasthatofCPinordertore—

    ;ducetheMSE(mean.squareerror)ofthechanneles—

    ;timate.Consideringthenumberofmuhipathusuallyis ;2—6forpracticalwirelesschannels,wegiveanim—

    ;plicitmethodforestimatingthemuhipathdelaystoim—

    ;provethechannelestimateperformance.Sinceitisas—

    ;sumedthatallthechannelsbearthesamePDP,the ;superscriptsjandiwillbeneglectedinthelaterdiscus—

    ;sionaboutthedelay—subspace.Introducingthesingular ;valuedecompositionF=UA,weget

    ;J7=FF:UA/Iu=U

    ;whereUdenotesthedelay—subspacebasis,whichcan

    ;beestimatedasthespanoftherlargesteigenvectorsof ;thesamplecorrelate

    ;channelestimateofmultiplesymbolblocksmustbe ;pre—obtained.Moreover,thismethodhasahighCOB—

    ;putationcomplexitywhenthemuhipathdelaysvary. ;Therefore,wewillgiveanultrafastsubspacetracking ;algorithmtoestimatethedelay.subspace. ;2.3TrackingtheDelay-subspaceviaFastSub- ;spaceTrackingAlgorithm

    ;Sincethedelayvariationisslowandoftencon. ;stantoveralargenumberof0FDMsymbols.Weuti. ;1izesubspacetrackingalgorithmtoadaptivelyestimate ;thedelay—subspacebyusingthechannelestimationob. ;tainedbyLSalgorithmattheregulartraining0FDM ;blocks.Subspacetrackinghasbeenintroducedina—

    ;daptivefilteringwhenthesignalunderconsideration ;hasasubspacewithadimension1essthanthenumber ;ofthedatasnapshotsl.

    ;Thelow.rankestimatorneedstobeperformedfor ;allthechannelsbetweentransmitterandreceiveran—

    ;tennas.However.sinceitisassumedthatallthechan—

    ;nelsbearthesamePDP.thenthedelay—subspacewill

    ;besameforallthechannels.Therefore,thecalcula. ;tionandtrackingofthedelay—subspaceforoneofthe

    ;availablechannelissufficient.

    ;WemodifytheLORAF3inRef.1llltotrackthe ;delay.subspace.TheLORAF3algorithmisanultrafast ;subspacealgorithmwiththeorderofO(Kr),risthe ;rankofthedelay—subspace.ThemodifiedLORAF3al—

    ;gorithmforthisspecificproblemisthenasfolloimators(fo ;=100Hz)

    ;4Conclusion

    ;AchannelestimationmethodforMIMO.0FDM ;systemsintime-?varyingfadingchannelshasbeenpro—-

;posed.Thedecision—directedSAGEalgorithmisintro—

    ;ducedtotrackthechannelvariation.Consideringthe ;muhipathpropagationinpracticalwirelesschannelsis ;aptlymodeledbyafewdominantspecularpaths,we ;proposeaschemetoimprovethechanne1estimation ;performanceofSAGEalgorithmbyusingalowrank ;approximation.Bythenusingsubspacetracking,itis ;observedthatourproposedchannelestimationmethod ;forMIMO—OFDMsystemscanbefeasible.Simulation ;resultsdemonstrateourproposedchannelestimation ;methodcaneffectivelyreducechannelestimationerror ;andthusimprovesystemsperformancecomparedtothe ;methodbasedonthetraditionalSAGEalgorithm. ;References:

    ;[1]GoldsmithA,JafarSA,JindalN,eta1.Capacitylimitsof ;MIMOchannels.IEEEJSelAreasCommun.2003.21 ;(5):684—702.

    generationMIMO—OFDM ;[2]SampathH,TalwarS.Afourth—

    ;broad—bandwirelesssystem:design,performance,and ;fieldtrialresults.IEEECommunMag,2002,40(9): ;143—149.

    ;f3lJeonWG,PaikKH,ChoYS.Two—dimensionalMMSE

    ;channelestimatorforOFDMsystemswithtransmitterdiver- ;sity.IEEEProcVTC.AtlanticCity:IEEE,2001.1682—

    ;1685.

    ;[4]LeeKF,WilliamsDB.Amuhiratepilot—symbol—assisted

    ;channelestimatorfor0FDMtransmitterdiversitysystems. ;IEEEProcICASSP.SaltLake:IEEE,2o01.2409—

    ;2412.

    ;i5lLiY.SimpifiedchannelestimationforOFDMsystemswith ;multipletransmitantennas.IEEETransCommun,2002,1 ;(1):65—75.

    ;[6]MaX,0hM,GiannakisGB,eta1.Hoppingpilotsfores—

    ;timationof~equency—offsetandmuhiantennachannelsin ;MIMO—OFDM.IEEETransCommun,2005,53(1):

    ;162—172.

    ;[7]XieY,GeorghiadesCN.TwoEM—typechannelestimation

    ;algori—thinsfor0FDMwithtransmitterdiversity.IEEE ;TransCommun,2003.5l(1):106—115.

    ;J8lYangBG.LetaiefKB.ChannelestimationforOFDM ;transmissioninmuhipathfadingchannelsbasedonpara—

    ;metricchannelmodeling.IEEETransCommun.2001.49 ;(3):467—479.

    ;[9]ProakisJ.DigitalCommunications.NewYork:McGraw

;HillPress.2001.12一l2.

    ;[1O]LiY,WintersJH,SollenbergerNR.MIM0—0FDMf叫

    ;wirelesscommunications,signaldetectionwithenhanced ;channelestimation.IEEETransCommun,2002,50(9): ;1471—1477.

    ;1】1lStrobachP.Low.rankadaptivefilters.IEEETransSignal ;Processing,1996,44(12):2932—2947.

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