IEEE TRANSACTIONS ON SIGNAL PROCESSING 2003 (TO AP

IEEETRANSACTIONSONSIGNALPROCESSING2003(TOAPPEAR)Full-DiversityFull-RateComplex-FieldSpace-TimeCodingXiaoliMaandGeorgiosB.Giannakis,Fellow,IEEEAbstract—Excitingrecentdevelopmentsinwirelessmulti-antennacommunicationshaveledtodesignsaimingmainlyatoneoftwoobjectives:eitherhigh-performancebyen-ablingthediversityprovidedbymulti-inputmulti-output(MIMO)channels,or,high-ratesbycapitalizingonspace-timemultiplexinggainstorealizethehighcapacityofMIMOfadingchannels.Byconcatenatingalinearcomplex-fieldcoder(a.k.a.linearprecoder)withalayeredspace-timemapper,wedesignsystemscapableofachievingbothgoals:full-diversityandfull-rate(FDFR),withanynumberoftransmit-andreceive-antennas.WedevelopFDFRdesignsnotonlyforflat-fading,butalsoforfrequency-selective,or,time-selectivefadingMIMOchannels.Furthermore,wees-tablishtheflexibilityofourFDFRdesignsinstrikingdesir-ableperformance-rate-complexitytradeoffs.Ourtheoreticalclaimsareconfirmedbysimulations.IndexTerms—Linearcomplex-fieldcoding,diversity,per-formance,capacity,outageprobability,space-timecoding,frequency-selectivechannels,OFDM,time-selectivewirelessfadingchannelsI.IntroductionRapidincreaseofcellularservicesubscribersandwirelessapplicationshasstimulatedtremendousresearcheffortsindevelopingsystemsthatsupportreliablehighratetrans-missionsoverwirelesschannels.However,thesedevelop-mentsmustcopewithchallenges,whichatthephysicallayerarecausedbyfadingpropagationeffects,aswellasbandwidth,andpowerlimitations.Tothisend,multi-inputmulti-output(MIMO)wirelesslinksareparticularlyattrac-tive,whencomparedtosingle-inputsingle-output(SISO)ones.Relyingonmultiple(Nt)transmitandmultiple(Nr)receiveantennas,existingMIMOdesignsaimmainlyatoneoftwoobjectives:eitherhigh-performancebyenablingtheavailablespace-diversity,or,high-ratesbycapitaliz-ingonthecapacityofMIMOfadingchannels[14,48,54].STOrthogonalDesigns(OD)[1,46],LinearConstellationPrecoding(LCP)STCodes[61],andSTTrellisCodes(TC)[47],fallundertheperformance-orientedclass,whileBLAST-typearchitectures,[57,13],andLinearDispersion(LD)codes[22,24],belongtotherate-orientedalternatives.ST-ODcodesenjoyfulldiversity(FD)atlineardecodingcomplexity,andforsystemswith(Nt,Nr)=(2,1)anten-nastheircapacity-achievingrepresentative[1]isperhapsthemostattractivefromtheperformance-orientedclass,achievingtransmissionrateupto1symbolperchanneluse(pcu).However,relativetofull-rate(FR)MIMOdesignsTheworkinthispaperwassupportedbytheARL/CTAGrantNo.DAAD19-01-2-011.Dept.ofElectricalandComputerEngr.,Univ.ofMinnesota,200UnionStreet,Minneapolis,MN55455,USA.Tel/fax:[phone]-4583,Emails:{xiaoli,georgios}@ece.umn.educapableofNtsymbolspcu,otherST-ODcodesincursig-nificantrateloss:withNt2,theirtransmissionratedoesnotexceed0.75symbolpcu[51].ST-TCschemescanofferbetterrates,butunfortunatelytheyarecomplextodecode,andlackclosed-formconstruction,whiletheirdesigndiffi-cultyincreasesexponentiallywithNt,andthetransmissionrate.Inaddition,high-ratehigh-performanceST-TCoftenrequireslongsizeblocks,whichinturnleadstolongde-codingdelays.LDcodesaredesignedtomaximizeergodiccapacity,acriterionthatisnotonlyknowntobe“diversity-blind”[2],butalsooffersnocapacityorperformanceassur-anceswithfiniteblocksizesusedinpractice.OriginalLDdesignsoffernodiversityguarantees[22],butevenwhendiversityconstraintsareimposed[24],therequiredsearchoverahighdimensionalspacebecomesprohibitivelycom-plexasNt,andtheconstellationsizeincrease.Ontheotherhand,layeredSTmultiplexershavecomplementarystrengthsandlimitations:V-BLASToffersFR(Ntsym-bolspcu),iscapacityachieving,butreliestotallyonSISOerrorcontrolcodingperlayertoofferperformanceguaran-tees;whileD-BLASTenablesspacediversity,butitsrateimprovementscomeatthepriceofincreasingdecodingde-lays.Nevertheless,bothV-BLASTandD-BLASTcanaf-fordreasonablecomplexity(albeitsuboptimal)decoding,andfacilitateusageofSISOcodesinMIMOsettings.Un-fortunately,theirrateefficiencyisoffsetbythebandwidthconsumingSISOcodesrequiredtogainindiversity.Inanutshell,theaforementionedSTcodesdonottakefullad-vantageofthediversityandcapacityprovidedbyMIMOchannels.Existingdesignsdonotalwaysscalewiththenumberofantennas.Andequallyimportantinpractice,theyarenotflexibletostrikedesirabletradeoffsamongperformance,rate,andcomplexity.Aspiringtobridgethesegaps,thispaperreliesontheconcatenationoftwobandwidthefficientmodules:theouteroneimplementsLinearComplex-Field(LCF)codingperlayer,andfeedstheinneronethatperformsacircularformoflayeredSTmultiplexing.Itisusefultoputourcon-tributionsinhistoricalperspective,startingwiththelay-eredSTmultiplexer.ThisinnermodulecanbeviewedasanextensionofFoschini’spioneeringlayeredstructure[13],toavoidrateloss(causedbytheall-zerotrianglesintheSTmatrixofD-BLAST)bycircularlywrappinglayersaround.Itwasintroducedby[12]undertheterm“threadedSTcod-ing”(seealso[29]).Researchontheoutermodulepursuedseparate(andupto2001independent)routesbycodingtheorists(asearlyas1992[3]),andbyresearchersinthesignalprocessingforcommunicationscommunity(startingwiththefilterbankprecodersof[17]in1997).Specifically,Belfiore,Boutros,andco-workersinvestigatedlatticec