MIMO检测2

ATMIMODetectionIIAT2Outline1.List-BasedDetection2.LR-BasedDetectionAT31.List-BasedDetection•SICdetectorssufferfromerrorpropagation;•List-basedapproachescanbeemployedtomitigateerrorpropagationbyselectingmultiplecandidatesymbolstobuildupalistforthefinalharddecision.KKsyHsnHsh+nTT[]=[]KKsHHhssyHsnATAlgorithm:•GeneratealistofQcandidatevaluesfor,say.denotestheq-thclosestsymbolto.Hereandrepresentsthelinearfilter;•Bycancelingthecontributionofthesymbolvectorto,usingeachcandidateofinthelist,asetofQresidualvectorsisgeneratedas;41.List-BasedDetectionKs(1)(2)(Q){,,...,}yyyLinear-listdetection(q)2(q)Initialization:for1toargmin||\endforKKKsKqQssysSSSSS(1)(2)(){,,...}KKKQsss()KqsyHKywy1K[,...,]W=wwKsyKs(q)(q)KKsyyhAT•Applyanindependentsub-detectortoeach,andobtaindecisionoftheremainingsymbols.Let.Asaresult,theQcandidateharddecisionvectorscanbeobtained;•Fromthecandidates,obtainthefinalharddecisionvectorthatbestrepresentstheobservationvectorinthesenseofthesumofsquarederror(SSE)as51.List-BasedDetections(1)(2)(Q){,,...,}sssLinear-listdetection(q)(q)(q)Ksssy(q)y(1)(2)(Q){,,...,}sss()(1)()()2{,...}argmin||||qQqssssyHsAT61.List-BasedDetectionSIC-listdetectionH+x=Qy=Rsn,0...0KKKKKrxsnAcxsn+Msx=As+cnATAlgorithm:•GeneratealistofQcandidatevaluesfor,say.denotestheq-thclosestsymbolto.Here;•Bycancelingthecontributionofthesymbolvectortousingeachcandidateofinthelist,asetofQresidualvectorsisgenerated;•Applyanindependentsub-detectortoeachandobtaindecisionoftheremainingsymbols.LetAsaresult,theQcandidateharddecisionvectorscanbeobtained;71.List-BasedDetectionKs(1)(2)(Q){,,...,}xxxSIC-listdetection(1)(2)(){,,...}KKKQsss()KqsKx1K,KKKxrxxKsKs(q)x(1)(2)(Q){,,...,}sss(q)(q)(q)KsssAT•Fromthecandidates,obtainthefinalharddecisionvectorthatbestrepresentstheobservationvectorinthesenseofSSEas81.List-BasedDetections(1)(2)(Q){,,...,}sss()(1)()()2{,...}argmin||||qQqssssxRsSIC-listdetectionAT•Forlinear-listandSIC-listdetection,thesub-detectorsareappliedtoeachvectorand,respectively.Theq-thsub-systemcanbewrittenas91.List-BasedDetectionqyforlinear-listdetectionforSIC-listdetectionqqyHsnxAsnSub-detectorsqxSincethelinearsub-detectorprovidesless-impressiveperformance,forthetrade-offbetweentheMLandlinearschemes,theSICsub-detectorispreferred.ATE.g.(ZF-list)Considera3x3MIMOsystemwith4-QAMmodulation,wherethechannelmatrixandthenoisevectoraregivenbyand,respectively.Supposethatthe4-QAMisusedforsignalingandthetransmitsignalvectorisgivenbyThenthereceivedsignalbecomes101.List-BasedDetection0.511.41.4iiyHsn=01110iiiiiH0.50.41.4in111iiisATWehave.LettingQ=2andq=1,2,whiledenotestheq-thclosetsymbolto,wehaveThelinearfilterofHusingtheZFisgivenby111.List-BasedDetectionH3ˆ=-0.25-0.15iywyH-10.50.500.50.5()0.50.510.50.50.50.510.50.5iiiiiiW=HHH(1)3(2)311sisi3()qsˆyUsingtheZFasthesub-detectortodetectthesub-vectorand,wehave(1)s(1)11iis(2)11iis(2)sATAsaresult,thetwocandidateharddecisionvectorsaregivenby121.List-BasedDetection(2)ˆssUsing,thefinalharddecisionisobtainedas.(1)111iiis(2)111iiis()(1)()()2{,...}argmin||||qQqssssyHsATE.g.(SIC-list)Considera3x3MIMOsystemwith4-QAMmodulation,wherethechannelmatrixandthenoisevectoraregivenbyand,respectively.Supposethatthe4-QAMisusedforsignalingandthetransmitsignalvectorisgivenbyThenthereceivedsignalbecomes131.List-BasedDetectionyQRsn01110iiiiiH0.50.41.4in111iiisATLetting,wehavewhere141.List-BasedDetectionHxQy1.410.711.4101.220.820.82000.82iiRDenotingbythe(3,3)-thentryofR,wehave3,3r133,33ˆ0.250.15xrxi0.991.70.571.390.200.12iiixRsn=ATWithQ=2,wehave151.List-BasedDetection(1)3(2)311sisiUsingtheSICasthesub-detectortodetectthesub-vectorand,wehave(1)s(1)11iis(2)11iis(2)sATAsaresult,thetwocandidateharddecisionvectorsaregivenby161.List-BasedDetection(2)ˆssUsing,thefinalharddecisionisobtainedas.(1)111iiis(2)111iiis()(1)()()2{,...}argmin||||qQqssssyHsATSimulationresults:171.List-BasedDetection16-QAM2x2MIMOATSimulationresults:181.List-BasedDetection16-QAM4x4MIMOAT19Outline1.List-BasedDetection2.LR-BasedDetectionAT202.LR-BasedDetection•Latticereduction(LR)canbeusedtodecodelatticecodedsignals.•ThisapproachhasbeenappliedtoMIMOdetectionbyYaoin2002.•Wubbenet.alextendedthisLRbaseddetectionfurtherin2004.•IthasbeenreportedthattheLRbasedMIMOdetectioncanachieveafullreceivediversity.–ItmeansthattheBERperformancewillbethesameastheMLperformanceexceptforanoffsetAT21Distortionduetofadingchannels:SignalvectorinorthogonalspacenHsrTiltedduetochannelmatrix:Basisvectorsarenotorthogonal2.LR-BasedDetectionAT22LatticeReductionFindanewsetofbasisvectorsthatare(nearly)orthogonaloverlattice2.LR-BasedDetectionAT23LLLalgorithm2.LR-BasedDetection•Inordertofindamatrixwhosecolumnvectorsarenearlyorthogonaltogeneratethesamelattice,theLLLalgorith