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CARRIER

    CARRIER

    July2007V01.24No.4JOURNALOFELECTRONICS(CHINA

    CARRIERFREQUENCYOFFSETESTIMATION

    OFDMAUPLINKBASEDONSUBSPACE

    FORINTERLEAVED

    PROCESSING

    FanDaCaoZhigang

    fStateKeyLaboratoryonMicrowaveandDigitalCommunications,DepartmentofElectronic

    Engineering,TsinghuaUniversity,Beijing100084,China)

    AbstractThispaperinvestigatesCarrierFrequencyOffset(CFO).estimationintheuplinkofthe

    OrthogonalFrequency

    DivisionMultipleAccess(OFDMA)systemswiththeinterleavedsubcarrier assignment.CFOsbetweenthetransmittersandtheuplinkreceiverwilldestroyorthogonalityamong

    differentsubcarriers,henceresultingininter

    carrierinterferenceandmultiuserinterference.A

    two-stagefrequencyoffsetestimationalgorithmbasedonsubspaceprocessingisproposed.Themain

    advantageoftheproposedmethodisthatitcanobtaintheCFOsofalluserssimultaneouslyusingonly

    oneOFDMAblock.Comparedwiththepreviouslyknownmethods,itnotonlyhasarelativelylow

    implementationcomplexitybutisalsosuitableforrandomsubchanne1assignment. KeywordsOrthogonalFrequency

    DivisionMultipleAccess(OFDMA);CarrierFrequencyOffset

fCFO);Subspaceprocessing;NormalizedRootMeanSquareError(NRMSE)

    CLCindexTN911.7

    DOI10.1007/81176700600927

    I.Introduction

    Broadbandwirelessmultipleaccesshasat

    tractedmuchattentionrecently.IntheIEEE 802.16/WiMAXfamilyofstandards[1,2J,Orthogonal FrequencyDivisionMultiplexingAccess(OFDMA) isselectedasthephysicallayertechnology.

    OFDMAisalsobeingpursuedasapotentialcan

    didateforfuturemobilecommunicationsystems. InOFDMA.thesubcarriersareassignedto

    differentusersforparalle1signaltransmission.and frequencyguardbandisnotemployedbetween

    adjacentusers,therebyhavinghighfrequencyeffi

    ciency.IntheAdditiveWhiteGaussianNoise fAWGN)channel,theorthogonalityofsubcarriers wil1preventInterCarrierInterferences(ICI)and

    MultiUserInterferences(MUI)amongusersin OFDMAsystems.ButOFDMAinheritsthe

    weaknessofOFDM.i.e..beingsensitivetoCarrier FrequencyOf~et(CFO)inducedbyDopplereffects and/orpooroscillatoralignments.Insuchcases.it wil1destroyorthogonalityamongdifferentsubcar

    Manuscriptreceiveddate:May15,2006;reviseddate: November6,2006.

    SupportedbytheSpecializedResearchFundforthe DoctoralProgramofHigherEducation.ChinaMinistryof Education(No.20030003039).

    Communicationauthor:FanDa.bornin1978.male,Ph.D

    candidate.DepartmentofElectronicEngineering, .

    TsinghuaUniversity,Beijing100084,China. Email:~nd03@mails.tsinghua.edu.cn.

    riers.resultinginICIandMUI[.Toachieveade

    sirableperformance.ithasastrictrequirementon thefrequencysvnchronizationbetweentheSub

    scriberStationfSS)andtheBaseStation(BS)in theOFDMAuplink.Thus.CFOestimationisa majortaskinsuchasystem.

    ItisknownthatCFOestimationforOFDMhas beenextensivelystudiedinthe1astdecade.and severa1solutionsareavailablet4-61.Unfortunately, aUofthemaresuitedforthebroadcast(downlink) scenarioandcouldnotbedirectlyusedintheup

    1inkofthemultiuserOFDMsystem.Themain reasonisthateachuser'ssignalatBSmustbe separatedfromtheothersbeforehissynchroniza

    tionparametersareobtained.Ontheotherhand, eachuserhashisownCFO.whichmeansthatthe CFOestimationintheOFDMAuplinkbecomesa multipleparameterestimationproblemandis closelyrelatedtothesubcarrierassignmentscheme

    adopted.

    Onthesubcarrierassignment,therearetwo schemes.blockandinterleaved[3J.Theformeras

    signssomeconsecutivesubcarrierstoeachuser.In the1atter.thesubcarriersofdifferentusersare interleavedoverthewholebandwidth.InRefs.17l and[8],theauthorsproposedabankofbandpass

filterstoseparatedifferentusers'signalsandes

    timatethecorrespondingCFOsintheOFDMA uplinkwiththeblocksubcarrierassignment.

    JOURNALOFELECTRONICS(CHINA),Vo1.24No.4,July2007 However.itmayintroduceMUIduetotheim perfectdesignofthefilterbank.Anotherdisad

    vantageoftheblockmethodisthatitprevents channeldiversity,i.e.,adeepfademighthita numberofsubcarriersofagivenuser,resultingin performancedegradationofthesystem.

    Onthecontrary,theinterleavedmethod

    maximizesthe~equencydiversityforeachuser. However,itcomplicatestheCFOestimationinthe OFDMAuplinkbecauseitminimizesthedistances betweensubcarriersassignedtodifferentusers.In Ref.9],Cao,eta1.studiedtheCFOestimationfor theuplinkoftheinterleavedOFDMAsystem,and proposedaCFO_estimationalgorithmbasedonthe signa1structure.Themainadvantageoftheesti mationalgorithminRef.91isthatitcanestimate

    al1theCFOsoftheuserssimultaneouslyusingonly oneOFDMAblock.However,itrequiresapriori informationsuchasthenumberofactiveusersand theircorrespondingoccupiedsubchannels,which limitsitsapplication.Throughoutthispaper,we wil1refertothealgorithminRef.9]astheCa0_

    Tureli-YaofCTY1scheme.

    ThispaperinvestigatestheCFOestimationin theuplinkofinterleavedOFDMAsystems.We

proposeatwo-stageCFOestimationalgorithm

    basedonsubspaceprocessing,whichkeepsthe advantageofestimatingtheCFOsofal1userssi- multaneouslyusingonlyoneOFDMAblockand doesnotrequireanyaprior/information.There- ceivedsignalscanbearrangedintoamatrixform similartothedatamode1oftheMUltipleSignal ClassificationfMUSIC1algorithminthemulti

    antennasreceivingsystem[01.Thenumberofusers canbedetectedbytheAICInortheMDL[.cri-

    terion.Afterthecoarse-tofineCFOestimation stages.theCFOsofal1involveduserscanbees- timatedbyusingthesubspacebasedMUSIClike

    algorithm.Sincethenumberofusersandtheoc- cupiedsubchannelscanbeestimated,theproposed algorithmcanbeeasilyextendedtotherandom subchannelassignment.

    Therestofthispaperisorganizedasfollows. ThesystemmodeloftheinterleavedOFDMAup- linkisintroducedinSectionII.InSectionIII,the proposedCFOestimationalgorithmisderived. SimulationresultsaregiveninSectionIV,and conclusions3,redrawninSectionV.

    II.SystemModel

    Inthissection.weintroducethesigna1mode1of theinterleavedOFDMAuplink[.

    Consideran

    OFDMAsystemwithNsubcarriersandMusers. whereeachSScommunicateswiththeBSthrough anindependentmultipathchanne1.SupposetheN

    subcarriersaredividedintoQsubchannels,and eachsubchannelhasP=N|QsubcarriersFor theinterleavedsubcarrierassignment,theq-th subchanneliscomposedofsubcarrierswithindex set(q,Q+q,,(P1)Q+q),q=0,1,,Q1.

    Thesuperscriptf.1')denotesthemthuser.

    Fig.1depictsthetransmitterstructureofthe mthuser,wheres=[5I)s]isthe

    informationblockthatthemthuserwilltransmit

    duringoneOFDMAblock.whichisfirstmapped intoasetofNmodulationsymbols{),ac- cordingto

    =

    ?

    whereP=0,1,,P1,andq()denotesthesub

    channe1indexofuserm.

    Forsimplicity,weassumethatbothtimesyn- chronizationandsampling3,reideallyperformedat theuplinkreceiver.AftertheremovalofCyclic PrefLx(CP),theremainingNsamplesofone OFDMAblock,{rnN-1,canbearrangedintoa

    QxPmatrix

    y=

    ×P

    =

    vs+=v{uo())+

    whereorepresentsSchurproduct,V=

    

    t,'M]isaQxMVandermondematrixwith

    (q,m)thentryexp(j21rqO(~)),S=Uo(B) withU=[(')('.)('M)]PandB=

    [(6')(6'.)(6'M)P,andisaPxPin-

    versefastFouriertransformmatrixwith[= exp(21rnk/P1.isaQxPAWGNmatrix.Each elementofWisaGaussianrandomvariablewith zeromeanandvariance..

    Moreover,v(m)

    ,

    ()and6()aredefinedre_

    spectivelyas

FANeta1.CarrierFrequencyOffsetEstimationforInterleavedOFDMAUplinkBasedonSu

    bspaceProcessing435

    ej2~r0()

    eJ20()/P

    eJ2(QrJ

    .ej2~r(1)/|P1J

    b=I…矽)i

    whereHisthechannelfrequencyresponseon thefq'+pQ)thsubcarrierduringoneOFDMA block,(?)denotestranspose.Em'?(0.5,0.5)is

    thenormalizedCFOofthemthuser.Let

    {?,')M:0representtheCFOsbetweenusersand theuplinkreceiverandAfdenotethesubcarrier spacing,thenE'isdefinedasE=Af''/Af.

    ()isdefinedastheeffectiveCFOofthemth

    user,whichisgivenby

    0'=(g'+E')

    x(m)

(3)

    Cycfic''

    prlr=:rr

    m)

    P/sr

    IFFT''

    ?

    .

    (

    羔盟.

    ?

    5

    Fig.1Interleaved-OFDMAuplinktransmitterstructureofthe

    m-thuser

    III.CFOEstimation

    Inthissection,wefirstdefinetheCFOspec- trumandthenproposeatwo-stageCF0estima-

    tionalgorithmbasedonsubspaceprocessingto estimatetheCFOsofal1userssimultaneouslyin theuplinkofinterleavedOFDMAsystemsusing

    onlyoneOFDMAblock.

    1.DefinitionoftheCFOspectrum

    FromEq.f21,yissimilartothedatamode1of theMUSICalgorithminthemulti-antennasre

    ceivingsystem.andv(,hasthesamestructureas thearraysteeringvector[.LetYf,sf,wfdenotethe /-thcolumnofS,respectively,where =

    1,2,,P,wehavef+wf.Thecovariance

    matrixofYfisgivenby

=

    E[="+0.2

    where]meanstheexpectationvalue,(?)" representstheHermitianoperation,=E[8fsis

    thecovarianceof8fjand/isaQ×Qidentitymatrix

    FromEq.(4),itisknownthatisaHermitian matrix,anditseigenvaluesareallpositivereal numbers.Let,denotetheQei

    genvaluesofindescendingorder. Basedonthesubspaceprocessingtechnology[, wefindthat)McorrespondtotheMlargest valuesofPcFo(),whichisgivenby Pc.()=lJaH().((5)

    wherea(0)=[1eej2~r(Q-1)o],isaQ×(Q

    M)matrixcomposedoftheQMeigenvectors

    correspondingtol】…,andthesubspace

    spannedbyisthenoisesubspaceof. AsPI)()isafunctionoftheeffectiveCFO, wedefineo()astheCFOspectrumaccording tothedefinitionofDirectionOf-Arrival(DOA)

    spectrumintheMUSICalgorithm[. Withalargenumberofcolumnsintheco- variancematrixcanbeestimatedby :

    1yy"

    P:

    1?P

    f=1

    (6)

    Then,U,theestimationofU,,canbederived

    byintroducingeigendecompositionto. 2.Two-stageCFO-estimationalgorithm FromEq.(5),theestimationsof{m'):1cor

    respondtotheMlargestpeaksofPcFO().Cao,et a1.proposedaCFOestimationalgorithmbasedon thesignalstructure[.Themainadvantageofthe estimationalgorithminRef.91isthatitcanesti-

    mateal1theCFOsoftheuserssimultaneously usingonlyoneOFDMAblock.However.itrequires apr/or/informationsuchasthenumberofusers andtheoccupiedsubchannels,whichlimitsits application.Inthecaseofrandomsubchannelas

    signment,thenumberofusersandtheoccupied subchannelsareunknowntotheuplinkreceiver, thusanaccuratepeaksearchintheCFOspectrum

    overtherange0?[(00.5)/Q,(Ql+0.5)/Q]is

    requiredintheCTYmethod[.whichiscomputa- tionallyveryexpensive.Tosolvethisproblem,we proposeatwo-stageCFOestimationalgorithm

    basedonsubspaceprocessinginthispaper.The flowchartofthealgorithmisshowninFig.2.

    JOURNALOFELECTRONICS(CHINA),Vo1.24No.4,July2007 coarse

    stage

    n)

    Fig.2Flowchartoftheproposedtwo-stageCFOestimationalgo- rithmbasedonsubspaceprocessing

    f1)CoarseestimationFirst,weintroduce SVDoreigendecompositionto.Thenthehum-

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