typicaluk2

CompressedChannelEstimationforHigh-MobilityOFDMSystems:PilotSymbolandPilotPatternDesignXiangRen,XiaofeiShao,MeixiaTao,andWenChenDepartmentofElectronicEngineering,ShanghaiJiaoTongUniversity,ChinaSchoolofElectronicEngineeringandAutomation,GuilinUniversityofElectronicTechnology,ChinaEmail:{renx;simonsho;mxtao;wenchen}@sjtu.
edu.
cnAbstract—Orthogonalfrequency-divisionmultiplexing(OFD-M)hasbeenwidelyadoptedforbroadbandwirelesscommuni-cationsduetoitshighspectralefciency.
However,itissensitivetothetimeselectivitycausedbythehigh-mobility,whichlargelydegradestheaccurateofestimatingthechannelstateinformation(CSI).
Therefore,thechannelestimationinhigh-mobilityOFDMsystemshasbeenalong-standingchallenge.
Recently,numerousexperimentalstudieshaveshownthathigh-mobilitybroadbandwirelesschannelstendtohavesomeinherentsparsity.
Inthispaper,weintroducethecompressedsensing(CS)toutilizetheinherentchannelsparsityandestimatethehigh-mobilitychannel.
BasedontheCSminimizationcriterion,weproposetwooff-linepilotdesignalgorithmstoimprovetheestimationperformance.
Oneistodesignthepilotsymbolonlyandtheotheristojointlydesignthepilotsymbolandthepilotpattern.
Simulationresultsshowthattheproposedmethodsachievebetterestimationperformancesthanconventionallinearmethodsinhigh-mobilityenvironments.
IndexTerms—Channelestimation,High-mobility,Compressedsensing,OFDM,Pilotdesign.
I.
INTRODUCTIONOrthogonalfrequencydivisionmultiplexing(OFDM)hasbeenadoptedwidelyforbroadbandwirelesscommunicationsystemsduetothehighspectralefciency.
However,thetheo-reticalbenetsofOFDMsystemsmaynotbefullyachievedinbroadbandhigh-mobilityenvironmentssincethechannelsarebothrapidlytime-varyingandfrequency-selective.
InOFDMsystems,eachsubcarrierhasanarrowbandwidthtoensurethesignalrobustagainstthefrequencyselectivitycausedbythemultipathdelayspread.
Inhigh-mobilityenvironments,thechannelmayvarysignicantlyduringoneOFDMsymbolduration,whichbreaksdowntheorthogonalitybetweensub-carriersandintroducesinter-carrierinterference(ICI).
Channelestimationoverhigh-mobilityenvironmentshasbeenconsid-eredinanumberofrecentpapers[1]-[3].
Inwork[1],theDopplerinformationisusedtodesignthebasisforthebasisexpansionmodels(BEM).
Inwork[2],theDopplerspreadinformationisutilizedforcomputingthechannelcorrelations.
ThisworkissupportedbytheNational973Project#2012CB316106,byNSFChina#61328101and#61329101,bytheSTCSMScienceandTechnologyInnovationProgram#13510711200,andbytheSEUNationalKeyLabonMobileCommunications#2013D11.
Inwork[3],additionalpilotswithDopplershiftisdesignedforhigh-mobilityuserstoimprovethechannelestimation.
However,thesemethodsarebasedontheimplicitassumptionofarichunderlyingmultipathenvironment.
Recently,numerousexperimentalstudiesshowthatthechannelsinbroadbandwirelesscommunicationsystemstendtoexhibitasparsestructure,andcanbecharacterizedwithfewparameters.
Toutilizetheinherentsparsityofthehigh-mobilitychannel,manyresearchershavestudiedtheappli-cationofcompressedsensing(CS)methodsin[4]-[6].
Thework[4]proposedaCS-basedsparsechannelestimatorwithadesignedthresholdforOFDMsystems.
Thework[5]proposedapilotdesignschemebasedonthecross-entropyoptimizationmethodforOFDMsystems.
Thework[6]gaveaCS-basedchannelestimationmethodinultrawide-bandcommunicationsystems.
However,theseworksseldomconsideredthecoher-enceofCS,whichinuencestheCSreconstructionperfor-mancedirectly.
Thefundamentalwork[7]concludedthatasystemwithlowCScoherenceleadstoagoodperformance.
Inourpreviouswork[8],wedesignedthepilotsymboltominimizetheCScoherenceforMIMO-OFDMsystemsoverhigh-mobilitychannels.
Inthispaper,weproposetwooff-linelowcoherencepilotdesignalgorithmsforthecompressedchannelestimationinthehigh-mobilityOFDMsystems.
BasedontheCScoher-enceminimizationcriterion,wedesignthepilotsymbolandjointlydesignthepilotpatternandthepilotsymbolwithtwoalgorithmstoimprovetheestimationperformance.
Simula-tionresultsshowthatthebothoftheproposedalgorithmsachievebetterperformancesthantheconventionalpilotinhigh-mobilityenvironmentswithoutneedingextracomplexity.
II.
HIGHMOBILITYCHANNELMODELA.
PhysicalModelInthehigh-mobilityenvironment,channelschangerapidlyandcauselargeDopplerfrequencyshift,whichmeansthattheDopplerspreadvmaxisverylargeandcausetimeselectivefading.
Frequencyselectivefadingisalsounavoidableinhigh-mobilitysystem,forthedelayspreadτmaxcausesmultipatheffect.
Therefore,wecanconsiderthehigh-mobilitychannelasatimeandfrequencydoubly-selectivechannel[9].
IEEEICC2015-SignalProcessingforCommunicationsSymposium978-1-4673-6432-4/15/$31.
002015IEEE4553Atypicalphysicalmultipathwirelesschannelmodelofthetime-selectiveandfrequency-selectivechannelcanbeaccuratelymodeledas[9]:H(n,f)=NPp=1βpaR(θR,p)aHT(θT,p)ej2πvptej2πτpf,(1)whichrepresentssignalpropagationoverNPpaths,hereβpdenotesthecomplexpathgain,θR,pistheangleofarrival(AoA)atthereceiver,θT,pistheangleofdeparture(AoD)atthetransmitter,τpisthe(relative)delay,andvpistheDopplershiftassociatedwiththepthpath.
TheNT*1vectoraT(θT)andtheNR*1vectoraR(θR)denotethearraysteeringandresponsevectors,respectively.
Weassumethatτp∈[0,τmax]andvp∈vmax2,vmax2,whereτmaxdenotesthemaximumdelayspreadandvmaxthemaximumDopplerspreadofthechannel.
B.
ParameterModelLetTdbethepacketduration,Wbethebandwidth,T0betheOFDMsymbolduration,W0bethebandwidthofeachsubcarrier,Nt=Td/T0andNf=W/W0bethenumberofthesymbolandthesubcarrier,respectively.
Thehigh-mobilitychannelbetweenthetransmitterandthereceiverinthedelay-DopplerdomaincanbemodeledasH(n,f)=L1l=0Mm=Mβl,mej2πmNtnej2πlNff,(2)whereL=Wτmax+1representsthemaximumnumberoftheresolvabledelaysandM=TdvmaxrepresentsthemaximumnumberoftheresolvableDopplerspreadsofthehigh-mobilitychannel,fisthesubcarrierfrequencyandnisthetimeslot.
Forthesakeofwritingconvenience,wedenetwovectorsuf=1,ej2π1Nff,.
.
.
,ej2π(L1)Nffandun=ej2πMNtn,ej2π(M+1)Ntn,.
.
.
,ej2πMNtn.
Thenthechannelmodelcanberewrittenasamatrixform:H(n,f)=ufBuTn=(unuf)b,(3)whereBisanL*(2M+1)channelcoefcientmatrixinthedelay-Dopplerdomainofthehigh-mobilitychannel,i.
e.
,B=β0,M···β0,M.
.
.
.
.
.
.
.
.
βL1,M···βL1,M.
(4)Denebvec(B)isthestackingvectorofthechannelcoefcientmatrix,i.
e.
,b=[β0,MβL1,Mβ0,MβL1,M]T,(5)whereeachcoefcientβl,misthesumofthecomplexgainsofallphysicalpathslyingintheunitsamplingsubspaceinthedelay-Dopplerdomain.
ThecoefcientsareconsideredconstantineachOFDMsymbolanddifferentbetweentwosymbols.
Thus,thetotalhigh-mobilitychannelmodeleffec-tivelycapturestheunderlyingmultipathenvironmentthroughD=L(2M+1)resolvablepaths.
Notethatsinceourfocusistodiscusstheperformanceofthechannelestimator,thechannelmodelerrorisomittedinthispaperforconvenience.
Herewedenethedominantnon-zerocoefcientsinbasthosecontributingsignicantchannelcoefcients,i.
e.
|βl,m|2>γ,whereγisanappropriatelychosenthresholdwhosevaluedependsuponthedesignaccuracy.
Foranap-propriatelychosenthresholdγ≥0,thechannelissaidtobeS-sparse,if|βl,m|2>γandb0=SL(2M+1).
Theworks[9]and[10]haveshownthatthethedoubly-selectivechannelscanbemodeledaccuratelywithsparsebinthedelay-Dopplerdomain.
Inthisway,CSisintroducedinthefollowingsectiontoutilizethesparsityofhigh-mobilitychannels.
III.
SYSTEMMODELLetusconsideranOFDMsystemwithKsubcarriersinahigh-mobilityenvironment.
InthenthOFDMsymbol,theinformationsignalsXn(k)areinputinthefrequencydomainatKsubcarriers,inwhichn=0,.
.
.
,N1andk=0,.
.
.
,K1.
TheOFDMmodulationisthenimplementedatthetransmitantennabyperformingtheinversediscreteFouriertransform(IDFT).
AftertheIDFTmoduleandparalleltoserialmodule,Xn(k)aretransformedfromthefrequencydomainintothetimedomain.
Cyclicprex(CP)isinsertedintotransmitsignalstoavoidtheintersymbolinterference(ISI).
Then,theemittedsignalspassthehigh-mobilitywirelesschannelsandarrivethereceiveantenna.
Toensuretheestimationaccuracy,inthispaper,wesendpilotsignalsinthefrequencydomain.
AssumethattherearePpilotswhichareplacedatsubcarriersk1,k2,.
.
.
,kP,andP≤K.
ThereceivedpilotvectoratthereceivercanberepresentedasamatrixformYn=XnHn+HnICIXnvec+Wn,(6)=XnHn+Nn,(7)whereYn=[Yn(k1),Yn(k2),.
.
.
,Yn(kP)]Tisthereceivedpilotvectoratthereceiveroverallpilotssubcarriers,Xn=diag([Xn(k1),Xn(k2),.
.
.
,Xn(kP)]T)isadiagonalmatrixofthetransmittedpilotmatrixatpilotsubcarriers,XnvecdenotesthevectorobtainedbystackingthediagonalofXn,Wn=[Wn(k1),Wn(k2),.
.
.
,Wn(kP)]Tisthenoisevector,Hn=[Hn(k1),Hn(k2),.
.
.
,Hn(kP)]TistheICI-freehigh-mobilitychannelmatrixinthefrequencydomain,andHnICIisthechannelmatrixwithzerodiagonalentriesandwhoseoff-diagonalentriesrepresenttheICIcausedbytime-variantchannels.
Inthispaper,wefocusonthechannelestimationanddeneNn=HnICIXnvec+Wn.
Substituting(3)into(7),andthenwecangetthematrixform:Yn=XnUnb+Nn,(8)whereUn=[unuk1,unuk2unukP]TisaP*L(2M+1)channelmodeldictionarymatrixofthehigh-mobilitychannelofthenthsymbol,andukp=uf|f=kp.
Foranappropriatethresholdγ>0,thechannelisS-sparseifb0=SL(2M+1).
Inthisway,weconvertthetaskofestimatingthehigh-mobilitychannelHninthefrequencydomaintoestimatingthechannelcoefcientsbinthedelay-Dopplerdomain,whichfortunatelyaresparseinpractice[10].
IEEEICC2015-SignalProcessingforCommunicationsSymposium4554IV.
LOWCOHERENCECOMPRESSEDCHANNELESTIMATIONCSisaninnovativeandrevolutionaryideathatcanutilizetheinherentsparsityofthewirelesschannel,whichisknownasthecompressedchannelestimation[9].
NowwebrieyintroducesCStheoryforbetterexplanation.
Letsignalx∈Rmbeanm*1vectorandhasthesparsityofSunderthedictionarybasisD∈Rm*U(m0.
FromTheorem1,wecanndthatoncePisdesignedwithaxedDsuchthat{PD}isassmallaspossible,thenalargenumberofcandidatesignalsareabletoresideundertheumbrellaofsuccessfulCSbehaviorwhichleadstobetterCSperformance.
B.
ProblemStatementAswehavealreadyknownthatalowerleadstoabetterCSperformance,wearegoingtoreducethecoherenceinoursystemtoimprovetheestimationperformance.
Inthispaper,bothofthepilotsymbolandthepilotpatternarediscussed.
SinceweonlyconsidertheestimationprocessinoneOFDMsymbol,thesuperscriptsnintherestofthepaperareomittedforcompactness.
Therefore,ourobjectiveistoAlgorithm1:PilotSymbolDesign1:SetX∈RP*P,theshrinkfactorλandthemaximumiterationtimeIter.
2:NormalizethecolumnsinthematrixXUandobtaintheeffectivedictionaryD.
3:ComputeGramMatrix:G=DTD.
4:UpdatetheGrammatrixandobtainGwithgij=λgij,λδ·sign(gij),gij,|gij|≥δ,δ≥|gij|≥λδ,λδ≥|gij|,wheresign(x)=1,x≥01,xI[m+1,v]then22:Xm+1Xm+1;vu;23:else24:Xm+1Xm;25:endif26:endfor(k)27:endfor(n)D.
JointPilotSymbolandPilotPatternDesignInthissubsection,followthespiritofthediscretestochasticoptimization[16],weproposeajointpilotsymbolandpilotpatterndesignalgorithmtoreduce{XU},whichjointlyconsider|X|andp.
Thekeyideaofthisalgorithmistogenerateasequenceofpilotsets,whereeachnewsetisobtainedfromthepreviousonebytakingasteptowardstheglobaloptimum.
Inthispaper,weassumethattherearetwopilotsymbolpowerE1andE2.
Denepm,pmandpmasdifferentpilotplacementsetsatthemthiteration.
Iterdenotestheiterationtimes,andNxdenotesthenumberoftotalpilotsets.
ThepilotplacementsetoccupationprobabilityvectorI[m]=[I[m,1],I[m,2],.
.
.
,I[m,Nx]]Tindicatestheoccupationprobabilityofeachpilotplacementsetatthemthiteration,inwhichI[m,i]∈[0,1]andiI[m,i]=1.
ThedetailsaregiveninAlgorithm2.
Accordingto[15],thisprocesscanquicklyconvergetotheglobaloptimalsolution.
Furthermore,asUcanbeobtainedbefore,Algorithm2isalsooff-line,thusitscomplexitycanbeignoredinthepracticalsystems.
E.
PracticalApplicabilityInpracticalhigh-mobilitysystems,thesystemparameters(suchasτmax,vmax,andetc.
)canbeestimatedinadvance.
Thus,wecanpre-calculatethechannelmodeldictionaryU,whichreectsthepropertiesofthehigh-mobilitychannel.
Inthisway,theoptimalpilotcanbepre-designedbythegivenalgorithmsandpre-storedatthetransmitterandthereceiver,whichisanoff-lineprocess.
Whenthesystemruns,thetransmittersendsXtoestimatethechannel.
Afterpassingthehigh-mobilitychannel,atthereceiver,CSreconstructionalgorithms(suchasBPandOGA)canreconstructtheesti-matedcoefcientsbinthedelay-Dopplerdomain.
Afterthat,theCSIisrecoveredbyH=Ub.
Finally,theestimatedCSIHisusedtorecoverthereceivedsymbol.
Moveover,exceptforthesystemparametersneededbyconventionalpilot-assistedchannelestimationmethods,theonlynecessarilyprioriinformationoftheproposedschemeisthemaximumDopplerfrequencyspreadvmax.
Inpractical,vmaxisavailableinsomesystems.
Forexample,inahighspeedtrain(HST)communicationsystem,astheHSTmovesalongtherailwayanditsmaximumspeedisknown,itiseasytogetvmax.
Therefore,theproposedschemesarefeasibletoimplementinthecurrentOFDMcommunicationsystems.
V.
SIMULATIONRESULTSInthissection,inthehigh-mobilityenvironment,wecom-paretheMSEperformanceofthecompressedchanneles-timationBPwiththeproposedpilotdesignalgorithmsandwiththeconventionalequidistantpilot.
Theconventionalleastsquare(LS)andlinearminimummeansquareerror(LMMSE)estimatorsarealsoincluded.
HereweconsideranOFDMsysteminthehigh-mobilityenvironment.
Assumedthatthereare512subcarriersinOFD-M,and120arepilotsubcarriers.
Thebandwidthis5MHz,thepacketdurationisT=40ms,andcarrierfrequencyisoperatedatfc=2.
5GHz.
TheadditivenoiseisaGaussianandwhiterandomprocess.
Thehigh-mobilitychannelismodeledas(3).
Wetakethemaximumdelayspreadasτmax=50sandthemaximumDopplerfrequencyisvmax=1.
389KHz,whichmeansthemaximumvelocityofthemobileuseris600km/h.
Thepilotsandsymbolsaremodulatedbythestar16-QAMwithtwosymbolpowers.
Inourexperiment,weassumedthatthereareonly10%ofthechannelcoefcientsarenonzero.
Thesimulationssetupcorrespondingtorealizingthechannelmatrixbyrstrandomlyselectingthelocationsof10%non-zeroschannelcoefcientsandthengeneratingtheirvaluesindependently.
Hereweconsidertwodesignedpilotsets.
OneiswiththeequidistantpilotpatternandthepilotsymboldesignedbyAlgorithm1.
TheotherisconsideredwiththepilotpatternandpilotsymboldesignedbyAlgorithm2.
Fig.
1presentsthecomparisonoftheMSEperformancesofdifferentpilotsetswiththeBP,theLS,andtheLMMSEestimatorsversustheSNRat600km/h.
Algorithm1andAl-gorithm2aresetasIter=200.
TheLSandtheLMMSEarebothequippedwiththe"equidistant"pilotin[17]withrandomsymbols,whichisclaimedastheoptimalpilotplacementtothedoublyselectivechannels.
ItisseenthattheCSchannelestimatorsimprovetheMSEperformancesfortakinguseofthesparsefeature.
Ascanbeseen,120pilotsarenotenoughforlinearestimatorstogetsufcientchannelinformationandreconstructthechannelexactly.
Asexpected,bothBPwiththeproposedpilotdesignalgorithmsgetbetterperformancesthantheonewiththeequidistantpatternandrandomsymbols.
Itmeansthat,withtheproposedalgorithms,thecoherencebetweenthepilotandthehigh-mobilitychanneliseffectivelyreducedandhenceimprovetheestimationperformance.
IEEEICC2015-SignalProcessingforCommunicationsSymposium4556Fig.
1.
MSEperformancesofdifferentchannelestimatorsinanOFDMsystemwith512subcarriersat600km/h,inwhichthereare120pilotsubcarriers.
Fig.
2presentsthecomparisonoftheMSEperformancesofthesystemat300km/hwith120pilotsubcarriers.
Ascanbeseen,comparingwithFig.
1,allestimatorsgetbetterperformancesatlowerspeedforsufferinglessDopplerspread.
However,theLSandLMMSEstillneedmorepilotstogettheaccurateCSI,whiletheBPmethodsperformwellwiththesamenumberofpilots.
Simulationresultsshowthattheproposedalgorithmscanalwaysimprovethechannelestimateperformanceinhigh-mobilityenvironments.
Inaddition,fromFig.
1andFig.
2,wendthatAlgorithm2ismoreeffectivethanAlgorithm1foralsoconsideringthepilotpattern.
More-over,astheproposedalgorithmsareoff-line,theoptimalpilotscanbepre-designedinthepracticesystems,whichmakestheproposedschemescanbeeasilyusedinthecurrentOFDMsystems.
VI.
CONCLUSIONInthispaper,twooff-linelowcoherencepilotdesignalgorithmsareproposedforthecompressedchannelestimationinhigh-mobilityOFDMsystems,inwhichthepilotsymbolandthepilotpatternarebothstudied.
Simulationresultsdemonstratedthattheproposedalgorithmsefcientlyimprovethesystemperformanceinthehigh-mobilityenvironments.
Furthermore,exceptforthesystemparametersneededbyconventionalpilot-assistedchannelestimationmethods,theonlynecessarilyprioriinformationoftheproposedschemesisthemaximumDopplerfrequencyvmax.
ThismakestheproposedmethodsarefeasiblefortheimplementationinthecurrentwirelessOFDMcommunicationsystems.
REFERENCES[1]E.
Panayirci,H.
Senol,andH.
V.
Poor,"Jointchannelestimation,equalizationanddatadetectionforOFDMsystemsinthepresenceofveryhighmobility,"IEEETrans.
SignalProcess.
,vol.
58,no.
8,pp.
4225-4238,Aug.
2010.
[2]T.
Y.
Al-Naffouri,K.
M.
Z.
Islam,N.
Al-Dhahir,andS.
Lu,"Amodelreductionapproachforofdmchannelestimationunderhighmobilityconditions,"IEEETrans.
SignalProcess.
,vol.
58,no.
4,pp.
2181-2193,April2010.
Fig.
2.
MSEperformancesofdifferentchannelestimatorsinanOFDMsystemwith512subcarriersat300km/h,inwhichthereare120pilotsubcarriers.
[3]N.
Aboutora,W.
Hardjawana,andB.
Vucetic,"Anewiterativedoppler-assistedchannelestimationjointwithparallelICIcancellationforhigh-mobilityMIMO-OFDMsystems,"IEEETrans.
Veh.
Technol.
,vol.
61,no.
4,pp.
1577-1589,May2012.
[4]H.
Xie,G.
Andrieux,Y.
Wang,J.
F.
Diouris,andS.
Feng,"AnoveleffectivecompressedsensingbasedsparsechannelestimationinOFDMsystem,"IEEEInternationalConferenceonSignalProcessing,Commu-nicationandComputing(ICSPCC),2013.
[5]J.
C.
Chen,C.
K.
Wen,andP.
Ting,"AnefcientpilotdesignschemeforsparsechannelestimationinOFDMsystems,"IEEECommunicationsLetters,vol.
17,pp.
1352-1355,2013.
[6]M.
K.
Cohen,I.
I.
Technion,I.
Haifa,C.
Attias,andB.
Farbman,"ChannelestimationinUWBchannelsusingcompressedsensing,"IEEEInternationalConferenceonAcoustics,SpeechandSignalProcessing(ICASSP),2014.
[7]J.
C.
EmmanuelandB.
W.
Michael,"Anintroductiontocompressivesampling,"IEEESignalProcessingMag.
,vol.
25,no.
2,Mar.
2008.
[8]X.
Ren,W.
Chen,andZ.
Wang,"LowcoherencecompressedchannelestimationforhighmobilityMIMOOFDMsystems,"GlobalCommu-nicationsConference(GLOBECOM),Dec.
2013.
[9]W.
U.
Bajwa,J.
Haupt,A.
M.
Sayeed,andR.
Nowak,"Compressedchannelsensing:anewapprocahtoestimationsaprsemultipathchan-nels,"IEEESignalProcessingMag.
,vol.
98,no.
6,pp.
1058-1076,June2010.
[10]W.
U.
Bajwa,A.
M.
Sayeed,andR.
Nowak,"Learningsparsedoubly-selectivechannels,"ConferenceonCommunicationControlandCom-puting,46th,pp.
575-582.
Sept.
2008.
[11]S.
S.
Chen,D.
L.
Donoho,andM.
A.
Saunders,"Atomicdecompostiionbybasispursuit,"SIAMReview,vol.
43,pp.
129-159,2001.
[12]M.
Elad,"Optimizedprojectionsforcompressedsensing,"IEEETran-scationonSignalProcessing,vol.
55,no.
12,pp.
5695-5702,Dec.
2007.
[13]E.
J.
Candes,J.
K.
Romberg,andT.
Tao,"Stablesignalrecoveryfromincompleteandinaccuratemeasurements,"CommunicationsonPureandAppliedMathematics,vol.
59,no.
8,pp.
1207-1223,2006.
[14]Y.
C.
Pati,R.
Rezaiifar,andP.
S.
Krishnaprasad,"Orthogonalmatchingpursuit:recursivefunctionapproximationwithapplicationstowaveletdecomposition,"Proceedingsofthe27thAnnualAsilomarConferenceonSignals,Systems,andComputers,1993.
[15]P.
Cheng,Z.
Chen,Y.
Rui,Y.
Guo,L.
Gui,M.
Tao,andQ.
T.
Zhang,"ChannelestimationforOFDMsystemsoverdoublyselectivechannels:adistributedcompressivesensingbasedapproach,"IEEETransactiononCommunications,vol.
61,no.
10,pp.
4173-4185,Oct.
2013.
[16]I.
Berenguer,X.
Wang,andV.
Krishnamurthy,"AdaptiveMIMOantennaselectionviadiscretestochasticoptimization,"IEEETrans.
SignalProcessing,vol.
53,no.
11,pp.
4315-4329,Nov.
2005.
[17]X.
Ma,G.
Giannakis,andS.
Ohno,"Optimaltrainingforblocktrans-missionsoverdoubly-selectivewirelessfadingchannels,"IEEETrans.
SignalProcess,vol.
51,no.
5,pp.
1351-1366,May2003.
IEEEICC2015-SignalProcessingforCommunicationsSymposium4557