ANTENNA SYSTEMS AND PROPAGATION FOR FUTURE WIRELESS COMMUNICATIONS Simple correlated channel - PDF document

ANTENNASYSTEMSANDPROPAGATIONFORFUTUREWIRELESSCOMMUNICATIONSSimplecorrelatedchannelmodelforultrawidebandmultiple-inputmultiple-outputsystemsJ.Adeane,W.Q.Malik,I.J.WassellandD.J.EdwardsAbstract:Asimplecorrelatedchannelmodelforultrawideband(UWB)multiple-antennasystemsisproposed.TheauthorsshowthatasinglenumericalvalueofthespatialcorrelationcoefÞcientissufÞcienttoaccuratelymodeltheperformanceofUWBspatialmultiplexingsystemsinanindoorenvironment.TheappropriatevalueofthecorrelationcoefÞcientisselectedbyensuringaclosematchbetweenthebiterrorrateresultsachievedontheproposedcorrelatedchannelandthoseonthemeasuredindoorchannel.TheauthorsalsoexperimentallyconÞrmthattheperformancesub-stantiallydegradesinthepresenceofhighvaluesofspatialcorrelationforarangeofspatialmulti- # operatingintheLOSenvironment.Itcanbeseenthatforasmallarray,theÞxedcorrelationmodelcloselyapproxi-matestheperformanceachievedinthemeasuredchannelanddoesnotdifferappreciablyfromtheperformanceofthedistance-basedmodel.ToseetheeffectofhighcorrelationontheBERperform-ance,wesimulatetheCM1modelwithcorrelationcoefÞ-0.8.ItcanbeseenfromFig.6althoughthespatialcorrelationdoesnotsigniÞcantlyaffectthediversityorder,itintroducesalargeSNRpenalty,asisexpectedfromwidebandantennadiversityrsity.WenotethattheZFreceiverisparticularlysen-sitivetospatialcorrelation,andacorrelationcoefÞcientof0.8degradesitsperformancebyapproximately12dB.Ontheotherhand,theMLreceiversuffersapenaltyof7.5dB.TheseresultsdemonstratethatitisessentialtotakespatialcorrelationintoaccountwhendeterminingtheperformanceofMIMOUWBsystems,asitdrasticallyimpactstheachievableperformancelevels.Fig.7,theproposedcorrelationmodelisappliedtoa3asymmetricalarrayconÞguration.Onceagain,itcanbeseenthattheproposedmodelprovidesanaccurateapproximationofthemeasurementresults.ComparingFigs.3,itcanbeconcludedthatincreasingthenumberofreceiveantennasinSMsystemswhilekeepingthenumberoftransmitantennasÞxedincreasesdiversity,thusimprovingBERperformance.Ontheotherhand,Figs.5showthatincreasingthenumberoftransmitantennas(upto,thenumberofreceiveantennas)whilekeepingthenumberofreceiveantennasÞxedincreasesthedatarateattheexpenseofhighermulti-streaminterfer-ence,thusdegradingtheBERperformance.Finally,Fig.8examinesthecaseofalargerarraysize,thatis88.Itcanbeseenthatevenforareasonablylargearraysize,thedifferencebetweentheÞxedanddistance-dependentcorrelationmodelsislessthan2dBathighSNR.Thus,theperformancepredictionaccuracyoftheÞxedspatialcorrelationmodelismaintainedatlargearraysizes.For0.4,thereisa7.5dBdifferencebetweentheBERresultsontheÞxedcorrelatedchannelmodelandthoseontheindependentchannel.Thisobser-vationemphasisestheimportanceoftakingcorrelationintoaccountindevisingaUWBspatialchannelmodel. Fig.3BERperformanceof22MIMO-UWBsystemsforvariousdetectionalgorithmsintheLOSindoorchannelmodel(CM1)withr0.4andforthemeasuredLOSchannel Fig.4BERperformanceof22MIMO-UWBsystemsforvariousdetectionalgorithmsintheNLOSindoorchannelmodel(CM2)withr0.4andforthemeasuredNLOSchannel Fig.6ComparisonbetweenBERperformanceof2MIMO-UWBsystemsforvariousdetectionalgorithmsintheLOSindoorchannelmodel(CM1)withr0(independentchan-nels)andr0.8(highlycorrelatedchannels) Fig.5ComparisonbetweenBERperformanceof3MIMO-UWBsystemsforvariousdetectionalgorithmsintheLOSindoorchannelmodel(CM1)withr0.4andforthemeasuredLOSchannelIETMicrow.AntennasPropag.,Vol.1,No.6,December2007 transmitantennas,receiveantennasandfrequencycom-ponents,respectively,followingtheapproachinin.H(UWB)canbeseenasafrequency-domainrowvector,eachofwhoseelementsistheßat-channel(i.e.nar-rowband)MIMOmatrix,,atfrequencyyffl,...,fhg,whereflandfhdeÞnethelower-andupper-endfrequenciesofthechanneltransferfunction,consideringadiscretefre-quencyrepresentation.Byapplyingtheconceptofmulticar-rierMIMOsystems,alsowidelyknownasMIMO-OFDM,wecanreducetheUWBchannelintoasetofparallelßatchannels,eachcenteredatagivenfrequencycomponent.Usingthisapproach,foragiven,thesystemcanbewrittenasarethetransmittedandreceivedsignalvectorsatrespectively,ively,n(f)1,n(f)2,...,n(f)N]isthezero-meancomplexGaussiannoisevectorwithunitvariance,andisthespatialchannelmatrixcomprisingtheßat-fadingcoefÞcients.Thechannelintheaboveexpressionisnormal-isedsothateachunderlyingßatSISOchannelhasunitunit.AlsonotethatinthisSMsystem,,arethedatabitsoriginatingfromthetransmitantennas.Tomakethecomparisonfair,wekeepthetotaltransmitpowerthesameinallthecasesconsidered.3SpatialcorrelationmodelWemodelthecorrelationbetweenMIMOsub-channelswithintheframeworkoftheseparablecorrelationmodel,thatiswiththeassumptionthatthecorrelationamongthereceiveantennasisindependentofthecorrelationbetweenthetransmitantennas.ThiscanbejustiÞedbyconsideringthatonlytheimmediatesurroundingsoftheantennaarraycontributetothecorrelationbetweenarrayelements,andhavenoimpactoncorrelationsobservedbetweentheelementsofthearrayattheotherendofthelink,whichisareasonableassumptionforanindoorpropagationenviron-ment.Inourtreatment,theeffectofantennacouplingisneg-lected,andwefocusonlyonthespatialcorrelation.WecanincludethecorrelationintotheMIMOUWBchannelmodelbyintroducingÞxedtransmitandreceivecorrelationmatricesfollowingthewell-knownKroneckermodel,sosoH(f)¼R1=2rxHfwR1=2tx(2)whereHw(f)isastochasticmatrixwithindependent,identicallydistributedcomplexGaussianentrieswithzeromeanandunitvariance.Thematricesarethetransmitandreceivecorrelationmatriceswithdimensions,respectively.Withdenotingtherowofthcolumnof,thecorrelationmatricesin(2)canbeevaluatedas,forOnewaytocomputespatialcorrelationisbygatheringalargeamountofMIMOmeasurementdatainthetargetpropagationenvironment.Adisadvantageofthisapproach,besidethefactthatitmaybeverytime-consuming,isthatitmaybenecessarytoestimatealargenumberofcorrelationcoefÞcients:inanMIMOsystems,therearespatialsub-channels,andcorrelatingeachpairofthemwouldgiveriseto(correlationvalues.Henceinthispaper,weproposeasimplermodellingapproachthatisshowntobesufÞcientlyrealistictoreßecttheUWBMIMOchannelstatistics.Tosatisfytheserequire-ments,weproposeaÞxedcorrelationmatrixfortheUWBMIMOchannelsimilartothatproposedfortheÞxedbroad-bandwirelesschannelchannel.Underthismodel,thecorre-lationmatricesin(2)aregivenbywhere(denotestheconjugateoperation.AnalternativetotheÞxedcorrelationmatricesistousethedistance-dependantcorrelationfunctionasisproposedinininthecontextofnarrowbandMIMOsystems.Usinganapproximationfunctiontocalculatethefadingcorrelationbetweentwoadjacentantennaelements,itcanbeshownthatthecorrelationcoefÞcientsdecayexponentiallywiththesquareoftheinter-elementdistancee.Thecorre-lationmatricesunderthedistance-dependentmodelaredevisedasfollowsfollowsRtx¼1(rtx12)4TheÞxedcorrelationmatricesappropriateforaparticularenvironmentcanbedeterminedbyselectingthenumericalvaluesof,suchthataclosematchisobtainedtotheBERresultsachievedwhenconductingthesystemsimulationusingthemeasuredindoorchannel.TheadvantageoftheÞxedcorrelationmodelisitssimplicityanditsimmediateapplicationtotheexistingIEEE802.15.3astandard,whichspeciÞesamodiÞedSaleh-ValenzuelaSISOchannelmodelmodel.NotethatourproposedmodelisconsiderablysimplerthanthatputforwardfortheWPANstandardIEEE802.11nn,sinceinthelattercase,thecomplexcorrelationcoefÞcientsarecalculatedforeachresolvabletapbasedonanassumedpowerangularspectrum. Fig.1MIMOsystemblockdiagramIETMicrow.AntennasPropag.,Vol.1,No.6,December2007 4UWBSMincorrelatedchannels4.1ChanneldescriptionandmeasurementsetupInthispaper,wecharacterisethesystemperformanceusingtheBERasthemetric.WeemploytwoMIMOdetectors,namelythezeroforcing(ZF)linearreceiverandthemaximumlikelihood(ML)nonlinearreceiverr.Thechannelrealisationsaregeneratedforcomparisonusingboththeproposedcorrelatedchannelmodelandthoseobtainedfromindoormeasurements.Performanceresultsfollowadescriptionofthechannelmodels.WemodifythechannelmodelintheIEEE802.15.3astan-dard[6],whichisformulatedforSISOUWB.Thestandarddescribesfourtypicalindooroperatingenvironments,referredtoaschannelmodels1Ð4(CM1ÐCM4).Weconcentrateontheshort-rangeindoorenvironment,bothshort-rangeline-of-sight(LOS)andnon-line-of-sight(NLOS),asthatislikelytobeacommonscenarioinasmallofÞceorhomeenvironmentforapplicationssuchaswirelessUSB.ThesescenariosarereferredtoasCM1(forLOS)andCM2(forNLOS)intheIEEE802.15.3aUWBchannelmodel[6].Wethusgeneratethetime-domainchannelimpulseresponseusingtheCM1andCM2modelsandusethediscreteFouriertransformtoobtainthefrequency-domainUWBchanneltransferfunction,.ForeachOFDMsub-carrier,,thenarrowbandchannelisconsideredtobeßat.Theindoorchannelsaremeasuredwiththeuseofavectornetworkanalyser(VNA)operatingintheUWBfrequencyband,3.1Ð10.6GHz,inanindoorofÞcesetting.ThedetailsofthemeasurementconÞgurationcanbefoundinFig.2.Wemeasurethecomplexresponseat1601frequencypointsacrossthe7.5GHzbandwidthoftheUWBchannel.Thetransmitterandreceiverarraysaresynthesised,eachwithuptothreeomni-directionalantennaelements,usinganautomatedpositioninggrid.Theadjacentantennasareseparatedby6cmandthemeanseparationbetweentrans-mitterandreceiverantennasiskeptat4.5m.ThearraysareorientatedtoeachotherÕsbroadsidedirection.Intotal,960spatialchannelrealisationsaremeasuredinanareaof.FortheLOSmeasurement,wemaintaintheLOSpaththroughoutthemeasurement,tocorrespondtotheCM1model.FortheNLOSmeasurement,weblocktheLOSpathbyascreenofRFabsorbentmaterial,tocorre-spondtotheCM2model.FurtherdetailsoftheLOSandNLOSMIMOchannelmeasurementscanbefoundinin.4.2SimulationresultsTheUWBsystemsimulationresultspresentedinthissectionarebasedon22,23,and33MIMOarrays.WeuseQPSKmodulationanduncodedtransmissionoverboththeproposedcorrelatedMIMOchannelandthemeasuredMIMOchannel.TheOFDMcyclicpreÞxislongerthanthelengthofthemultipathchannelinordertoavoidinter-symbolinterference.WedonotimplementtimeÐfrequencyinterleaving.Fig.3showstheBERresultsfor2,thatis2)forthesystemsoperatinginthemodiÞedCM1channelwithcorrelationcoefÞcients0.4andalsointhemeasuredUWBLOSchannel.Thevalueofcor-relationcoefÞcientthatmatchesthemeasurementresultisfoundbyexhaustivesearchandisthenroundedtoonedecimalplace.Itcanbeseenthattheselectedvalueof0.4givesBERresults,whichcloselymatchthosegivenbythemeasuredchannels.Notethatthecorre-lationvalueof0.4isspeciÞctoaparticularmeasurementsetting.However,themethodisgeneralandforanyscen-ario,wecanÞndacorrelationvaluethatmatchesthemeasurementresults.Forthemeasurementdatausedinthispaper,theexactcorrelationcoefÞcientshavebeenreportedinin,wherethemeancorrelationvaluesarecloseto0.4.Fig.4presentstheBERperformanceresultsfora22MIMOsystemoperatinginanNLOSpropa-gationenvironment.AsimilartrendasintheLOScaseisobserved,showingthatthecorrelationmodelproposedisapplicabletobothLOSandNLOSindoorUWBenvironments.Fig.5showstheperformanceoftheproposedÞxedanddistance-basedcorrelationmodelina33system Fig.2IndoorMIMOchannelmeasurementenvironmentIETMicrow.AntennasPropag.,Vol.1,No.6,December2007 Fromtheresultspresentedinthispaper,itcanbeseenthatMIMOspatialcorrelationisasigniÞcantfactorindeter-miningtheBERperformance,andoursimplecorrelationmodelcorrectlypredictstheperformanceofindoormultiple-antennaUWBsystems.5ConclusionWehaveproposedaÞxedcorrelationmodelfortheMIMOUWBchannelandpresentedacomprehensivecomparativeanalysisofthismodelwithadistance-basedspatialcorre-lationmodel.AcomparisonbetweentheBERresultsfrommeasuredchannelsandthosebasedonourÞxedcorrelationmodelshowthatthemodelcancloselyapproximatetheMIMOUWBindoorenvironment.Itisfoundtobeappli-cabletoavarietyoflineararrayconÞgurations,speciÞed,forarangeofvaluesofInaddition,thecorrelationcoefÞcientintheproposedchannelmodelisvariedfrom0(independentchannels)to0.8(highlycorrelatedchannel)inordertoinvestigatetheBERperformanceoftheMIMOUWBreceivers.WhenthecorrelationcoefÞcientisincreasedfrom0to0.8,itisobservedthatMLdetectorperformanceisdegradedby7.5dBatBER.TheBERperformanceoflineardetectorsisdegradedevenmoreseverelyduetospatialcor-relation,withanSNRpenaltyof12dB,andthereforeitisimportanttotakespatialcorrelationintoaccountinpracticalUWBsystemdesign.Ourproposedcorrelationmodelservesthispurposeverywell:itissimpleenoughwithasinglepar-ametertobeestimated,yetitisaccurateenoughtocorrectlypredicttheMIMOUWBsystemBERperformanceintheindoorenvironment.Owingtoitssimplicity,ourproposedcorrelatedUWBMIMOchannelmodelcanbereadilyinte-gratedwiththeexistingIEEE802.15.3aandothersingle-antennaUWBstandardsandchannelmodels.6AcknowledgmentThisworkwassupportedinpartbytheUKEngineeringandPhysicalSciencesResearchCouncilviaGrantGR7References1Allen,B.,Dohler,M.,Okon,E.E.,Malik,W.Q.,Brown,A.K.,andEdwards,D.J.(Eds.):ÔUltra-widebandantennasandpropagationforcommunications,radarandimagingÕ(Wiley,London,UK,2006)2Paulraj,A.J.,Nabar,R.,andGore,D.:ÔIntroductiontoSpace-TimeWirelessCommunicationsÕ(CambridgeUniversityPress,Cambridge,UK,2003)3Malik,W.Q.,Edwards,D.J.,andStevens,C.J.:ÔMeasuredMIMOcapacityanddiversitygainwithspatialandpolararraysinultrawidebandchannelsÕ,IEEETrans.Commun.,December2007,,(12)4Adeane,J.,Wassell,I.J.,andMalik,W.Q.:ÔErrorperformanceofultrawidebandMIMOspatialmultiplexingsystemsÕ.Proc.IETUWBSymp.JointwithEuropeanUWBRadioTechnologyWorkshop,Grenoble,France,May20075Yang,L.,andGiannakis,G.B.:ÔAnalogspaceÐtimecodingformultiantennaultra-widebandtransmissionsÕ,IEEETrans.Commun.,(3),pp.507Ð5176Molisch,A.F.:ÔUltrawidebandpropagationchannelsÑtheory,measurement,andmodelingÕ,IEEETrans.Veh.Technol.,2005,,(5),pp.1528Ð15457Kyritsi,P.,Cox,D.C.,Valenzuela,R.A.,andWolniansky,P.W.:ÔCorrelationanalysisbasedonMIMOchannelmeasurementsinanindoorenvironmentÕ,IEEEJ.Sel.AreasCommun.,2003,,(5),pp.713Ð7208Chiani,M.,Win,M.Z.,andZanella,A.:ÔOnthecapacityofspatiallycorrelatedMIMORayleigh-fadingchannelsÕ,IEEETrans.Info.,2003,,(10),pp.2363Ð23719Kermoal,J.P.,Schumacher,L.,Pedersen,K.I.,Mogensen,P.E.,andFrederiksen,F.:ÔAstochasticMIMOradiochannelmodelwithexperimentalvalidationÕ,IEEEJ.Sel.AreasCommun.,2002,(6),pp.1211Ð122610McNamara,D.P.,Beach,M.A.,andFletcher,P.N.:ÔSpatialcorrelationinindoorMIMOchannelsÕ.Proc.IEEEInt.Symp.onPersonal,IndoorandMobileRadioCommunications,September200211Ercey,V.,Hari,K.V.S.,etal.:ChannelmodelsforÞxedwirelessapplicationsÕIEEE802.16BroadbandWireless,AccessWorkingGroup,June200312vanZelst,A.,andHemmerschmidt,J.S.:ÔAsinglecoefÞcientspatialcorrelationmodelformultiple-inputmultiple-output(MIMO)radiochannelsÕ.Proc.GeneralAssemblyoftheInt.UnionofRadioScience(URSI),Maastricht,TheNetherlands,August200213Durgin,G.D.,andRappaport,T.S.:ÔEffectsofmultipathangularspreadonthespatialcross-correlationofreceivedvoltageenvelopesÕ.Proc.IEEEVehicularTechnologyConf.,Houston,TX,USA,May199914Erceg,V.,Schumacher,L.,Kyritsi,P.,etal.:ÔTGnchannelmodelsÕ.ÔIEEE802.11-03940r2,January2004 Fig.8ComparisonbetweenBERperformanceof8MIMO-UWBsystemsintheLOSindoorchannelmodel(CM1)gen-eratedbysimulationbasedonÞxedcorrelationanddistance-based Fig.7ComparisonbetweenBERperformanceof2MIMO-UWBsystemsforvariousdetectionalgorithmsintheLOSindoorchannelmodel(CM1)withr0.4andfortheLOSmeasuredchannelIETMicrow.AntennasPropag.,Vol.1,No.6,December2007