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Channel

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Channel

    Channel

    JournalofHarbinInstituteofTechnolo(NewSeries),Vo1.15,No.6,2008 ;ChannelestimationforMIMO-OFDMsystemsinmobilewirelesschannels ;wuYun,LUOHanwen,SONGWentao

    ;吴赘,罗汉文,宋文涛

    ;CollegeofInformationScience&Technology,DonghuaUniversity,Shanghai201620,China,Email:wuyun

    ;hit@dhu.edu.cn;

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

    ;Abstract:Achannelestimationmethodisproposedforrnuhipleinputmultipleoutput

    oahogonal~equencydi

    ;visionmuhiplexing(MIMOOFDM)systemsintimevaryingfadingchannels.Inthis

    method,adecisiondirect

    ;edspacealternatinggeneralizedexpectationmaximization(SAGE)algorithmisintr

    oducedtothetrackingof

    ;timevaryingfading.InordertoimprovetheestimationperformanceoftheSAGEalgorithm,alowrankapproxi

    ;mationmethodispresentedbyusingthesignalsubspaceofthechannelfrequencyautocorrelationmatrix.The

    ;studyrevealsthatthismethodcanbeincorporatedintotheSAGEalgorithm.Furthermore.amodifiedfastsub

    ;spacetrackingalgorithmisgiventoadaptivelyestimatethesignalsubspacebyutilizingtrainingOFDMblocks

    ;sentatregularinterva1.Simulationresultsdemonstratetheconsiderablebenefitsoftheproposedchannelestima

    ;tionmethod.

    ;Keywords:MIM0OFDM;channclestimation:SAGE:subspacetracking

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

    ;(OFDM)splitsbroadbandwithintoanumberofnar-

    ;rowbandwidthsandtransmitsthemsimultaneously.it

    ;hasastrongimmunityagainstintersymbolinterference

    ;(ISI)duetomuhipathpropagationandrequiressimple

    ;complexityforequalization.Ontheotherhand.muhi

    ;inputmultioutput(MIMO)techniqueisenvisagedto

    ;improvethecapacityandthereliabilityofthelink.

    ;Therefore.MIM0.0FDMisagoodcandidatesforfuture

    ;generationwirelesssystemsE2].

    ;InMIM00FDMsystems.coherentdecodingre.

;quireschannelstateinformationfCSI)betweenmulti

    ;pietransmitantennasandreceiveantennas.whichisu

    ;suallydifficulttoobtain,especiallyfortimevarying

    ;dispersivefadingchannelssincethereceivedsignalis ;thesuperpositionofthesignalstransmittedfromdiffer. ;enttransmitantennassimultaneously.Intypiealchan.

    0FDMsystems.the ;HelestimationalgorithmsforMIM0

    ;channelsareestimatedutilizingpilotsymbolsortraining ;sequences-6.

    ;InRef.3],atwo.dimensional

    ;MMSE(minimummeansquareerror)channelestima. ;torisproposedforMIMO0FDMsystems.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.

    ;AnEMtypespace-alternatinggeneralizedexpecta

    ;tionmaximization(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

    ;tionmethodforMIM0OFDMsystemsintimevarying

    ;fadingchannels.Atthetrainingblocks,optimaltrain

    ;ingsequencesbasedtimedomainLSestimatorisused ;forchannelestimation.Atthedatablocks,adecision

    ;directedSAGEalgorithmisintroducedtotracktimeva.

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

    18. ;Received20H06l0

    ;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 ;lowrankchannelapproximationtoimprovetheestima

    ;tionperformancebyselectingthefewsignificantsingu

    ;larvaluesofthechannelfrequencyautocorrelationas ;thesignalsubspace.Thesignalsubspacereflectsthe ;propertyofmultipathdelays,henceforthreferredtoas ;thedelaysubspace.Ourstudyrevealsthismethodcan ;beincorporatedintoSAGEalgorithmreasonable.Since ;themultipathdelaysvaryslowlyinmobileenviron

    ;ment,wepresentamodifiedfastsubspacetracking ;algorithmtoadaptivelyestimatethedelaysubspaceby

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

    ;anceconsiderablycomparedtothetraditionalSAGEal

    ;gorithm.

    ;1SystemDescription

    ;1.1MIMO-0FDMSystems

    ;ConsideraMIMOOFDMsystemwithNtransmit

    ;antennasandNreceiveantennas.Attimen,adata ;blocku=[u(0),u(1),…,H,(K1)]iscoded

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

    ;,t(K1)]’,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,,

    ;matrixwith:(k,k)=(k);日垒[H,:,…,-

    ;Nr]and[,,…,],isaK×1

    ;vectorwith()denotingthefrequencyresponseof ;channe1atsubcarrierfromtransmitantennaitore

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

    ;trixwithzeromeanandvariance,

    ;.Throughoutthe

    ;paper,itisassumedthattheISIiscompletelyelimina

    ;tedbyinsertingtheCPandtimeandfrequencysyn

    ;chronizationisperfect.

    ;1.2ChannelModel

    ;Thecomplexbasebandrepresentationofthemo

    ;?

    ;842?

    ;bilewirelesschannelimpulseresponse(CIR)canbe ;describedbv[]

    ;L1

    ;hji(,r)=?()(r—T1)

    ;wherethe{(t)}denotesthepossiblytimevariant

    ;attenuationfactorfortheLmuhipathpropagationpaths ;and{tf}arethecorrespondingtimedelays.Thechan

    ;nelscorrespondingtodifferenttransmitandreceivean

    ;tennasinMIMOsystemsusuallyhavethesame ;PDP.Therefore.thedelaycharacteristicisassumed ;tobesameforallavailablechannelsinthispaper. ;Eachpathgainiswidesensestationary(WSS)nar-

    ;rowbandcomplexGaussianprocesses.Fordifferent1, ;iandj,0If(t)areindependent.TheCIRisassumedto ;beconstantduringoneOFDMsymbols.

    ;ThechannelfrequencyresponseforOFDMsystem ;withpropercyclicextensionandsampletimingcanbe ;expressedas

    ;()//’(nr,,,kaf):

    ;L1

    ;?,=0

;(Z)exp(J(2wkl/K))(1)

    ;where(z)h(n,lT,);=(K+G)isthe

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

    ;spacingoftheOFDMsystem.Theaveragepowerof ;(1)’sdependsonthePDPofthewirelesschannels.

    ;Leth;i:[|}l(0),…,(L1)]’and=

    ;[:(0),…,(K1)],Eq.(1)bewrittenina

    ;matrixformas

    ;=F

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

    ;=

    ;0,1,…,K1andl=0,1,…,L1.

    ;2ChannelEstimation

    ;Z.1LSEstimator

    ;Atthetrainingblocks,weintroducetheLSesti

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

    ;[F,XiF,…,xF]

    ;h[(),(),…,(JII)]

    ;h[h,h,…,]

    ;ThereceiversignalY,j

    ;canbeexpressedas

    ;Yn

    ;=Th+

    ;ThentheLSestimateofthechannelis

    ;:(THT)THY

    ;InRef.[5],optimaltrainingsequencesarepres

    ;entedtoreducethecomplexityofchannelparameter ;estimation.Furthermore,itshowsthatthechanneles

    ;timatorwiththeoptimaltrainingsequencescanachieve ;thebestestinmtionperformance.Selectedaconstant

    ;umgnitudetrainingsequence,Ib()=1Iforthe

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

    ;firsttransmitantenna,thetrainingsequencesusedfor ;theothertransmitantennasareconstructedby ;b(k)=b()exp(j2Ko(i1)k/K),i=2,…?

    ;where:L?fJ?.Letx=b,itfollowsthat

    ;T=HencetheLSestimatorissimplifedto ;=J_TH

    ;fL

    ;Thenthefrequencychannelestimateisob

    ;tainedbyperformingDFTon.

;2.2SAGEAlgorithm

    ;Thedecision--directedSAGEalgorithmisintro?- ;ducedinRef.[7]totrackthetimevaryingchannel

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

    ;nelistransformedintotimedomainbyusingtheIDFT.

     ;Finallythechannelfrequencyresponseisobtaineda

    ;gainusingDUF.WeextendthismethodfortheMIMO

    ;OFDMchanneltracking.Aftersomemanipulations, ;theprocedureoftheSAGEalgorithmcanbedescribed ;asfollows.

    ;Considerthereceiveddatayasincompletedata, ;anddefinethecompletedataRas

    ;R=X+W,i=1,2,…/V

    ;whereH:A[,’,…,],=?=

    ;1

    ;,

    ;thus

    ;R,theiterativeprocessisasfollows.

    ;Initialization:For1?i?

    ;2.=X.

    ;Atthekthiteration(:0,1,2,…):

    ;Fori:1+[kmodN],compute

    ;=

    ;2+[Y

    ;=J7()(2)

    ;n

    ;=

    ;X:n’

    ;For1???andj?i,compute

    ;:

    ;ThesuperscriptdenotesthekthiterationandH ;?FF”.ThematrixFisformedaccordingtotheinfor—

    ;mationofPDP,thereforeitcanbereferredasthede

    ;laysubspace.Thennisthecorrespondingsubspace ;projectmatrix.

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

    ;ducetheMSE(mean.squareerror)ofthechanneles

    ;timate.Consideringthenumberofmuhipathusuallyis ;26forpracticalwirelesschannels,wegiveanim

    ;plicitmethodforestimatingthemuhipathdelaystoim

    ;provethechannelestimateperformance.Sinceitisas

    ;sumedthatallthechannelsbearthesamePDP,the ;superscriptsjandiwillbeneglectedinthelaterdiscus

    ;sionaboutthedelaysubspace.Introducingthesingular ;valuedecompositionF=UA,weget

    ;J7=FF:UA/Iu=U

    ;whereUdenotesthedelaysubspacebasis,whichcan

    ;beestimatedasthespanoftherlargesteigenvectorsof ;thesamplecorrelate

    ;channelestimateofmultiplesymbolblocksmustbe ;preobtained.Moreover,thismethodhasahighCOB

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

    ;Sincethedelayvariationisslowandoftencon. ;stantoveralargenumberof0FDMsymbols.Weuti. ;1izesubspacetrackingalgorithmtoadaptivelyestimate ;thedelaysubspacebyusingthechannelestimationob. ;tainedbyLSalgorithmattheregulartraining0FDM ;blocks.Subspacetrackinghasbeenintroducedina

    ;daptivefilteringwhenthesignalunderconsideration ;hasasubspacewithadimension1essthanthenumber ;ofthedatasnapshotsl.

    ;Thelow.rankestimatorneedstobeperformedfor ;allthechannelsbetweentransmitterandreceiveran

    ;tennas.However.sinceitisassumedthatallthechan

    ;nelsbearthesamePDP.thenthedelaysubspacewill

    ;besameforallthechannels.Therefore,thecalcula. ;tionandtrackingofthedelaysubspaceforoneofthe

    ;availablechannelissufficient.

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

    ;gorithmforthisspecificproblemisthenasfolloimators(fo ;=100Hz)

    ;4Conclusion

    ;AchannelestimationmethodforMIMO.0FDM ;systemsintime-?varyingfadingchannelshasbeenpro-

;posed.ThedecisiondirectedSAGEalgorithmisintro

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

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    ;845?

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