MIMO-(英文文献)

424IEEETRANSACTIONSONCOMMUNICATIONS,VOL.56,NO.3,MARCH2008MIMOMultichannelBeamforming:SERandOutageUsingNewEigenvalueDistributionsofComplexNoncentralWishartMatricesShiJin,Member,IEEE,MatthewR.McKay,Member,IEEE,XiqiGao,SeniorMember,IEEE,andIainB.Collings,SeniorMember,IEEEAbstract—ThispaperanalyzesMIMOsystemswithmulti-channelbeamforminginRiceanfading.OurresultsapplytoawideclassofmultichannelsystemswhichtransmitontheeigenmodesoftheMIMOchannel.Wefirstpresentnewclosed-formexpressionsforthemarginalorderedeigenvaluedistribu-tionsofcomplexnoncentralWishartmatrices.Theseareusedtocharacterizethestatisticsofthesignaltonoiseratio(SNR)oneacheigenmode.Basedonthis,wepresentexactsymbolerrorrate(SER)expressions.Wealsoderiveclosed-formexpressionsforthediversityorder,arraygain,andoutageprobability.WeshowthattheglobalSERperformanceisdominatedbythesubchannelcorrespondingtotheminimumchannelsingularvalue.Wealsoshowthat,atlowoutagelevels,theoutageprobabilityvariesinverselywiththeRiceanK-factorforcaseswheretransmissionisonlyonthemostdominantsubchannel(i.e.asinglechannelbeamformingsystem).Numericalresultsarepresentedtovalidatethetheoreticalanalysis.IndexTerms—Multiple-inputmultiple-outputsystems,Riceanfading,Wishartmatrices,multichannelbeamforming.I.INTRODUCTIONMULTIPLE-INPUTmultiple-output(MIMO)communi-cationsystemshavereceivedconsiderableattentioninrecentyearsastheyoffersubstantialcapacityimprovementsoverconventionalsingle-inputsingle-output(SISO)systems[1,2],withnopenaltyineitherpowerorbandwidth.Whenperfectchannelstateinformation(CSI)isavailableatboththetransmitterandreceiver,itiswellknown[1]thatthecapacity-achievingstrategyistotransmitontheeigenmodesoftheMIMOchannelusinglineartransmit-receiveprocessing(here-afterreferredtoasmultichannelbeamforming(MB)),uponwhichindependentGaussiancodeswithwater-fillingpowerallocationareemployed.Inpractice,thehighcomplexityrequirementsofGaussian-likecodesareoftenprohibitive,andeithersuboptimally-codedoruncodedtransmissionisused.PaperapprovedbyN.C.Beaulieu,theEditorforWirelessCommunicationTheoryoftheIEEECommunicationsSociety.ManuscriptreceivedFebruary23,2006;revisedAugust1,2006.ThisworkwassupportedbyNationalNaturalScienceFoundationofChinaunderGrants60572072and60496311,theChinaHigh-Tech863PlanunderGrant2006AA01Z264,NationalBasicResearchProgramofChinaunderGrant2007CB310603,andtheDoctorSubjectFoundationofChinaunderGrant20060286016.S.JinandX.GaoarewiththeNationalMobileCommunicationsRe-searchLaboratory,SoutheastUniversity,Nanjing,210096,P.R.China(e-mail:{jinshi,xqgao}@seu.edu.cn).M.R.McKayiswiththeDepartmentofElectronicandComputerEngi-neering,HongKongUniversityofScienceandTechnology,ClearWaterBay,Kowloon,HongKong.(email:[e-mail]).I.B.CollingsiswiththeWirelessTechnologiesLab.,ICTCentre,CSIRO,Australia(e-mail:[e-mail]).DigitalObjectIdentifier10.1109/TCOMM.2008.060115.Interestingly,forthesesuboptimalsystems,ithasbeenshownthatundermostperformancecriteriaofpracticalinterest(e.g.symbolerrorrate(SER),mean-squareerror(MSE),amongothers),MBstillcorrespondstotheoptimalchoiceoflineartransmit-receiveprocessing(insomecasesuptoarotationmatrix)[3].InthispaperweprovideananalyticalinvestigationoftheperformanceofuncodedMBMIMOsystemsinRiceanfadingchannels.Althoughthesesystemsareparticularlyappealingfromapracticalpointofview,therearecurrentlyveryfewre-latedanalyticalperformanceresultsavailableintheliterature.In[4],theglobalSER(i.e.SERaveragedoverallsubchannels)wasderivedforRayleighandRiceanfadingchannelsundertheassumptionthatallavailablesubchannelswereusedfortransmission,withequalpower,andwiththesame(BPSK)modulation.Itwasshownin[5]however(viaMonteCarlosimulations),thattheperformanceissignificantlyimprovedbytransmittingononlyasubsetoftheavailablesubchannels,andalsobyusingdifferentpowersandconstellationsoneachofthese.TheglobalSERresultsof[4]cannotbeeasilygeneralizedtotheseimportantscenarios.In[6],globalandper-subchannelSERexpressionswerepresentedforMBMIMOsystemsinRayleighfadinginthehighsignaltonoiseratio(SNR)regime,allowingfortransmissiononasetofarbitrarilyselectedsubchannels.InthispaperweconsiderthemoregeneralclassofRiceanfadingchannels,andseekperformancemeasuresforallSNRs.ThemaindifficultyinobtaininganalyticalperformanceresultsforMBMIMOsystemsinRiceanfadingisthatitrequiresthemarginalstatisticaldistributionsoftheorderedeigenvaluesofcomplexnoncentralWishartmatrices.AlthoughmanyresultsareavailablefortheeigenvaluestatisticsofcomplexcentralWishartmatrices(see[7–13],andreferencestherein),thereareveryfewresultsforthenoncentralcase.In[14],thejointprobabilitydensityfunction(p.d.f.)oftheseorderedeigenvalueswasobtainedforthespecialcaseoffull-ranknon-centralitymatrices.Thisjointp.d.f.wasusedin[15]toderivetheexactp.d.f.andcumulativedistributionfunction(c.d.f.)ofthedual-antennaMIMOcapacityinRiceanchannelswithrank-1meanmatrices.Unfortunatelythejointp.d.f.involvesahypergeometricfunctionofmatrixargumentsandVandermondedeterminants,andisnoteasilymarginalized.In[16],thep.d.f.andc.d.f.forthemaximumeigenvaluewasobtainedforthespecia