Giannakis, “Space-time-Doppler block coding for co

IEEETRANSACTIONSONSIGNALPROCESSING,VOL.53,NO.6,JUNE20052167Space-Time-DopplerBlockCodingforCorrelatedTime-SelectiveFadingChannelsXiaoliMa,Member,IEEE,GeertLeus,Member,IEEE,andGeorgiosB.Giannakis,Fellow,IEEEAbstract—Copingwithtime-selectivefadingchannelsischal-lengingbutalsorewarding,especiallywithmultiantennasystems,wherejointspace-Dopplerdiversityandcodinggainscanbecollectedtoenhanceperformanceofwirelessmobilelinks.Thesegainshavenotbeenquantified,andspace-timecodedsystemsmaximizingjointspace-Dopplerbenefitshavenotbeendesigned.Basedonaparsimoniousbasisexpansionmodelfortheun-derlyingtime-selective(andpossiblycorrelated)channels,wequantifythesegainsinclosedform.Furthermore,wedevelopspace-time-Dopplercodedsystemsthatguaranteethemaximumpossiblespace-Dopplerdiversity,alongwiththelargestcodinggainswithinalllinearlycodedsystems.OurthreenoveldesignsexploitknowledgeofthemaximumDopplerspread,andeachoffersauniquelydesirabletradeoff,includinghighspectralef-ficiency,lowdecodingcomplexity,andhighperformance.Ouranalyticalresultsareconfirmedbysimulationsandrevealtherelativeofmeritsofourthreedesignsincomparisonwithanexistingapproach.IndexTerms—Basisexpansionchannelmodel,diversity,fading,phasesweeping,space-timecoding,time-varyingchannel.I.INTRODUCTIONMODELINGtemporalchannelvariationsandcopingwithtime-selectivefadingareimportantandchal-lengingtasksinmobilecommunications.Time-selectivityarisesduetooscillatordrifts,phasenoise,multipathpropa-gation,andrelativemotionbetweenthetransmitterandthereceiver.Inwirelessmobilecommunications,time-variationsandfadingintroduceselectivityinthetime-domain,whichinturncausesperformancedegradation.Thismotivatesresearchtowardefficientcodingandmodulationschemesthatimprovethereliabilityofinformationtransmissionoverrapidlyfadingwirelesslinks.ManuscriptreceivedOctober23,2003;revisedJuly8,2004.ThisworkwaspreparedthroughcollaborativeparticipationintheCommunicationsandNetworksConsortiumandsupportedbytheU.S.ArmyResearchLaboratoryundertheCollaborativeTechnologyAllianceProgram,CooperativeAgreementDAAD19-01-2-0011.TheU.S.GovernmentisauthorizedtoreproduceanddistributereprintsforGovernmentpurposesnotwithstandinganycopyrightno-tationthereon.PartoftheworkinthispaperwaspresentedattheInternationalConferenceonAcoustics,Speech,andSignalProcessing,Orlando,FL,May13–17,2002.TheassociateeditorcoordinatingthereviewofthismanuscriptandapprovingitforpublicationwasProf.ZhiDing.X.MaiswiththeDepartmentofElectricalandComputerEngineeringAuburnUniversity,Auburn,AL36849USA(e-mail:[e-mail]).G.LeusiswiththeFacultyofElectricalEngineering,Mathematics,andCom-puterScience,DelftUniversityofTechnology,2628CDDelft,TheNetherlands(e-mail:[e-mail]).G.B.GiannakisiswiththeDepartmentofElectricalandComputerEn-gineering,UniversityofMinnesota,Minneapolis,MN55455USA(e-mail:[e-mail]).DigitalObjectIdentifier10.1109/TSP.2005.847850Traditionally,thepopularapproachtocopewithfadinghasbeentorelyondiversity-enrichedtransmissionandreception.Usingmultipleantennas,Space-Time(ST)codingofferssuchanapproachandpotentiallyboostsdatarateswhencommuni-catingoverflat[4]orfrequency-selectivechannels[1].Whentransmissionsareproperlydesigned,quasistatic(constantoverablock)frequency-selectivechannelsofferalsomultipathdiver-sity[13],[25],[26].If,ontheotherhand,thechannelsaretime-varying,judiciousdesignofevensingle-antennatransmissionsenablesanadditionaldiversitydimension,namely,Doppler-di-versity[15].JointexploitationoftheSTandDoppler(STDO)diversitydimensionswithmultipletransmit-antennasisthegoalofthispaper.TheDopplerdimensioncanbeinducednaturallybytime-se-lectivechanneleffects,butitcanalsobeinjectedintentionallytoenhancediversity,orevenintroduceit,byaso-termedphasesweepingtransmissionthataddstime-variationstoanoriginallyslow-fadingchannel[8],[11].Unfortunately,theanalogphase-sweeping-basedapproachesof[8],[11]consumeextraband-width,andtheyarenotdesignedtobringjointSTDObenefits.ThepotentialofSTDOdiversitywasalludedtoin[16],whichdealtwithquasistaticfadingchannels.AnattempttocollectSTDOgainswasalsomadein[19]throughthedesignoftheso-called“smart-greedy”codes.Interestingly,althoughallex-istingworks[8],[11],[16],[19]appreciatedtheimportanceofcapitalizingontime-selectivity,nonetailoreditsdesigntoanex-plicitmodeloftheunderlyingtime-variations.STDOgainshavenotbeenquantified,anddesignsenablingthemaximumSTDOdiversityprovidedbythechannelalongwithlargecodinggainsaremissing.Thepresentpaperfillsthesegapsbymakinguseofanex-istingbasisexpansionmodel(BEM)[5],[15],whichweadopttocaptureparsimoniouslythetime-selectivemultiantennachan-nels.ThebasicideabehindournovelSTDOcodeddesignsistoutilizeknowledgeofthemaximumDopplerspreadatthetrans-mitter.Thiskeyparameterthatisreadilymeasurablefromtheoperationalenvironmentspecifiesallourmultiantennatransmit-tersneedtoknowabouttheBEMandallowsustoquantifyrig-orouslythemaximumSTDOdiversityandcodinggains.ThesegainsbenchmarktheperformanceofSTDOcodedschemesinthepresenceof(evencorrelated)rapidlyfadingchannels.Equallyimportant,theBEMfacilit