Polarized MIMO channels in 3-D Models, measurement

1PolarizedMIMOChannelsin3D:Models,MeasurementsandMutualInformationMansoorShafi,MinZhang,ArisL.Moustakas,PeterJ.Smith,AndreasF.Molisch,FredrikTufvessonandStevenH.SimonAbstract4Gsystemsareexpectedtosupportdataratesoftheorderof100Mbpsintheoutdoorenvironmentand1Gbpsintheindoor/stationaryenvironment.Inordertosupportsuchlargepayloads,theradiophysicallayermustemployreceiveralgorithmsthatprovideasignificantincreaseinspectrumefficiency(andhencecapacity)overcurrentwirelesssystems.RecentlyanexplosionofMIMOstudieshaveappearedwithmanyjournalspresentingspecialissuesonthissubject.ThishasoccuredduetothepotentialofMIMOtoprovidealinearincreaseincapacitywithantennanumbers.Environmentalconsiderationsandtowerloadswilloftenrestricttheplacingoflargeantennaspansonbasestations.Similarly,customerdeviceformfactorsalsoplacealimitontheantennanumbersthatcanbeplacedwithamutualspacingof0.5wavelength.Theuseofcross-polarizedantennasiswidelyusedinmoderncellularinstallationsasitreducesspacingneedsandtowerloadsonbasestations.Hence,thisapproachisalsoreceivingconsiderableattentioninMIMOsystems.InordertostudyandcomparevariousreceiverarchitecturesthatarebasedonMIMOtechniques,oneneedstohaveanaccurateknowledgeoftheMIMOchannel.However,veryfewstudieshaveappearedthatcharacterizethecross-polarizedMIMOchannel.Recently,thethirdgenerationpartnershipstandardsbodies(3GPP/3GPP2)havedefinedacross-polarizedchannelmodelforMIMOsystemsbutthismodelneglectstheelevationspectrum.Inthispaperweprovideadeeperunderstandingofthechannelmodelforcross-polarizedsystemsfordifferentenvironmentsandproposeacompositechannelimpulsemodelforthecross-polarizedchannelthattakesintoaccountbothazimuthandelevationspectrum.Weusetheresultingchannelimpulseresponsetoderiveclosedformexpressionsforthespatialcorrelation.Wealsopresentmodelstodescribethedependenceofcross-polarizationdiscrimination(XPD)ondistance,azimuthandelevationanddelayspread.Inaddition,westudytheimpactofarraywidth,SNRandantennaslantangleonthemutualinformation(MI)ofthesystem.InparticularwepresentananalyticalmodelforlargesystemmeanmutualinformationvaluesandconsidertheimpactofelevationspectrumonMI.Finally,theimpactofmultipathdelaysonXPDandMIisalsoexplored.IndexTermsMIMO,cross-polarizedchannels,capacity.I.INTRODUCTIONTheuseofcross-polarizedantennasformultiple-input-multiple-output(MIMO)systemsisnowre-ceivingconsiderableattention.Itiswellknownthatforafixedratiooftransmittoreceiveantennanumbers,andundercertainchannelconditionsMIMOsystemcapacitycanbelinearlyproportionaltotheminimumofthenumberoftransmitandreceiveantennas.Cross-polarizedsystemsareofinterestsincetheyareabletodoubletheantennanumbersforhalfthespacingneedsofco-polarizedantennas.SlantpolarizedantennasarealreadyusedforcellularmobilesystemsforuplinkreceivediversityandarethereforepotentialcandidatesforuseonsystemsthatuseMIMOreceivers.Veryfewstudiesareavailableonpropagationmodelsforcross-polarizedchannels.Thepapersmostoftencitedarethoseof[1],[2].MansoorShafiiswithTelecomNewZealandLtd,49-55ToryStreet,Wellington,NewZealand,email:Mansoor.Shafi@telecom.co.nzMinZhangandPeterJ.SmitharewiththeDepartmentofElectricalandComputerEngineering,UniversityofCanterbury,PrivateBag4800,Christchurch,NewZealand,email:[e-mail],[e-mail]logies,BellLabs,600MountainAve.,MurrayHill,NJ07974,USA,email:arislm,[e-mail]lectricResearchLabs,Cambridge,MA,USA,andtheDepartmentofElectroscience,LundUniversity,Box118,SE-22100Lund,Sweden,email:[e-mail]htheDepartmentofElectroscience,LundUniversity,Box118,SE-22100Lund,Sweden,email:[e-mail]2Howeverboththesepapersconsideronlytransmissionfromaverticallypolarizedantennaandalsodonotconsidertheimpactofelevationspectrum.Formobileterminalslocatedinindoorbuildingsandinvehicles,theelevationspectrummustalsobeconsidered.ThereisarealscarcityofpublishedmodelsfortheelevationspectrumintheenvironmentsthataresuitableforMIMOsystemstudies.InastudydoneinurbanTokyo[3],aGaussianelevationspectrumisproposedandmeasurementsareusedtoderiveanexpressionforthemeaneffectivegainofamobileantenna.Inarecentstudy[4]theelevationspectrumandcross-polarizationdiscrimination(XPD)weremeasuredindifferentradiopropagationenvironmentsinFinland.Inanotherrecentstudydoneundertheauspicesofthe3GPPand3GPP2,across-polarizedchannelmodelforMIMOsystemswasdeveloped[5],buttheelevationspectrumimpactsareneglected.Inthispaperwemakethefollowingcontributions:²Wepresentacomprehensivemodelforthecross-polarizedchannelandextendthe3rdGenerationPartnershipProject(3GPP)modeltoincludeathree-dimensional(3D)component.Wecallthisthecompositechannel.²WediscussamodelforXPDanddiscussitsdependenceondistance,anglesanddelayspread,partlyderivedfromanewmeasurementcampaign.²Usingthecompositechannel,wedevelopclosedformexpressionsforspatialcorrelationsandverifytheiraccuracybysimulations.Theoverallspatialcorrelationisaweightedsumoftheconstituent2Dand3Dcomponents.Wealsoshowthat