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8.MIMO无线通信基础（2）8.1MIMO信道容量的利用——空时码我们知道，相对于SISO无线系统，MIMO无线系统一般有巨大的信道容量，该信道容量可以用来提高传输的有效性，也可以用来提高传输的可靠性，空时码属于后者。空时码和传统的交错码不同，它们本质上不是纠错，而是在一种分集(diversity)技术，这种技术可用大大改善衰落信道条件下接收机的性能。8.2分集接收介绍窄带无线信道的Rayleigh衰落给SISO系统的接收带来很大的问题，这种系统可以表示为：nnnnyhxv=+(2.1)其中nh为Rayleigh衰落因子，它是实部和虚部都是0均值并且独立同分布(i.i.d.)的复Gaussian随机变量，nv是加性噪声。检测上述信号的方法一般是：先估计出信道增益ˆnnhh≈，再用估计出的信道增益去均衡信道衰落因子的影响，可以用ZF均衡，也可以用MMSE均衡，最后完成检测。当nh的模值低于某一个门限时，接收信号的信噪比就很低，这时我们就说信道发生了选择性衰落。一般来说信道信道发生选择性衰落的概率并不高（与传输环境和移动速度有关），但是，一旦发生选择性衰落，信道的传输可靠性就会大大降低，甚至信道出现不可用的情况，这时信道的传输可靠性受到极大影响。一种常用的改善这种常数环境的传输可靠性的方法是：分集接收。由于接收到的信号受到了随机的乘性因子的干扰使其表现出随机性，使得接收信噪比也是一个随机变量。分集接收的基本思想是：在接收端想办法得到接收信号的多个独立衰落的副本，根据概率知识，多个接收信号的副本都同时发生选择性衰落的可能性大大降低，从而如果采用适当的方法将接收到的信号的多个独立的衰落副本合并在一起，将大大改善接收机的性能。分集根据接收到的信号的多个独立衰落副本的方式不同，可以分为时间分集、频率分集、空间分集等几种形式。空间分集是无线衰落信道分集接收的一种常见形式，这种系统采用若干个接收天线，只要天线的间隔足够大（一般大于若干个波长），多个天线上接收到的信号就有很好的独立性。8.3ASimpleSpace-TimeCode——Alamouti[4]Space-timeblockcodingisasimpleyetingenioustransmitdiversitytechniqueinMIMOtechnology.WeshallfirstexaminetheAlamouticode[1],whichstarteditall.BasicallyAlamoutiproposedasimpleschemefora2×2systemthatachievesafulldiversitygainwithasimplemaximumlikelihooddecodingalgorithm.Ingenerally,thepremiseinallofspace-timecodingapproacheshasbeenthatwehaveperfectknowledgeofthechannelatthereceiverandthatthedatastreamsareindependent.TheAlamoutischemebroughtinarevolutionofsortsinmulti-antennasystemsbyprovidingfulldiversityoftwowithoutCSIatthetransmitterandaverysimplemaximumlikelihooddecodingsystematthereceiver.8.3.1AlamoutiSpace-TimeCodeTheapproachproposedbyAlamoutiisshowninthefollowingFigure.TheinformationbitsarefirstmodulatedusingM-arymodulationscheme.Thetransmitterisequippedwithtwotransmittingantennas.Theencodertakesablockoftwomodulatedsymbols1sand2sineachcodingoperatingandgivesistothetransmittingantennasaccordingtothecodingmatrix,*12*21ssSss⎛⎞−=⎜⎟⎝⎠(3.1)Where“*”indicatesthecomplexconjugate.In(3.1),thefirstcolumnrepresentsthefirsttransmissionperiodandthesecondperiodrepresentsecondtransmissionperiod.Thefirstrowcorrespondsthesymbolstransmittedformthefirstantennaandthesecondrowcorrespondsthesymbolstransmittedformthesecondantenna.Elaboratingfurther,duringthefirstsymbolperiod,thefirstantennatransmits1sandthesecondantennatransmits2s.Duringthesecondsymbolperiod,thefirstantennatransmits*2s−andthesecondantennatransmits*1s.Thisimpliesthatwearetransmittingbothinspace(acrosstwoantennas)andtime(twotransmissiontimeintervals).Thisgivesthename“space-timecoding”.Lookingattheequations,*112*221[,][,]ssss=−=ss(3.2)Where1sistheinformationsequencefromthefirstantennaand2sistheinformationsequencefromthesecondantenna.Acloseexaminationof(3.1)revealsthatthesequencesareorthogonal(i.e.,theinnerproductof1sand2siszero).Theinnerproductisgivenby,****121221,()()0ssss=+−=ss(3.3)Ifweassumejustoneantennaatthereceiver,thereceiversignalsaredefinedasfollows,basedontheschemeatthefollowingfigure.Thefadingcoefficientsfromantennas1and2aredefinedby1()htand2()ht,respectively,attimet.Ifweassumethatthesecoefficientsareconstantacrosstwoconsecutivesymboltransmissionperiods,weobtain,1211112222()()||()()||jjhthtThhehthtThheθθ=+===+==(3.4)Where||ihand,1,2iiθ=aretheamplitudegainandphaseshitforthepathfromantennaitothereceiveantenna,andTisthesymbolduration.Atthereceiver,thesignalsafterpassingthroughthechannelcanbeexpressedas,111121**222212rhshsnrhshsn=++=−++(3.5)Where1nand2naretheindependentcomplexrandomvariableswithzeromeanandunitvariance,representingtheadditivewhiteGaussiannoisesamplesattimetandt+T,respectively.8.3.2DecodingMethodWenowassumethatthechannelcoefficientscanberecoveredperfectlyatthereceiver.WeusethiscoefficientsastheCSI(ChannelStateInformation).Thecombinercombinesthereceivedsignalasfollows,**22**111221211122***22*121121221221(||||)(||||)shrhrhhshnhnshrhrhhshnhn=+=+++=−=+−+(3.6)Andsendthemtothemaximumlikelihooddetectorwhichminimizesthefollowingdecisionmetric,12**1111222221,min||||ssrhshsrhshs⎡⎤−−++−⎣⎦(3.7)overallpossiblesymbol1sand2s.Expandingthisanddeletethetermsthatindependenttothecodewords,theaboveminimizationreducestoseparatelyminimizing**222211221121||(||||)1||rhrhshhs⎡⎤+−++−⎣⎦(3.8)fordetecting1s,and**222212222122||(||||)1||rhrhshhs⎡⎤−−++−⎣⎦(3.9)fordetecting2s.Equivalently,ifweusenotation2**2(,)()()||dxyxyxyxy=−−=−(3.10)Thedecisionruleforeachcombinedsignal,1,2jsj=becomes:Pickisiff222222221212(,)(||||)1||(,)(||||)1||jiijkkdsshhsdsshhsik⎡⎤⎡⎤++−≤++−∀≠⎣⎦⎣⎦(3.11)ForPSKsignals(equalenergyconstellations),thissimplifiesto22(,)(,)jijkdssdssik≤∀≠(3.12)i.e.,thedecisionruleisjustthefamousEuclidcriterion.8.3.3MaximumRatioCombiningInthecaseofmaximumratiocombining(seethefollowingfigure),theresultingreceivedsignalsare11012202rhsnrhsn=+=+(3.13)andthecombinedsignalis**22**011221201122||||shrhrhhshnhn⎡⎤=+=+++⎣⎦(3.14)Themaximumlikelihooddetectordecidessignalisusingexactlythesamerulein(3.11)or(3.12)forPSKsignals.NotethattheMRCsignal0sin(3.14)isequivalenttotheresultingcombinedsignalsofthetransmitdiversityschemein(3.6),exceptforaphasedifferenceinthenoisecomponentsthatdon’taffecttheeffectiveSNR.Thisshowsth