OFDM的基本原理

OFDM2501001.OFDMOrthogonalFrequencyDivisionMultiplexingOFDMNNNOFDMOFDMFDMOFDM1.5OFDMOFDMQAMOFDMQAMMPSKIFFTFFTOFDMCyclicPrefixCPOFDMOFDM1.6OFDMOFDMOFDMOFDMPeak-to-AveragePowerRatioPAPROFDMOFDMETSIEuropeanTelecommunicationStandardInstituteOFDM1DigitalAudioBroadcasting,DVBDigitalVideoBroadcastingDVBIEEE802.11aIEEE802.16OFDMETSIHiperLANIIOFDMOFDMxDSLOFDM——DMTDiscreteMultitoneOFDMOFDMOFDM2.FFTOFDMNi),,2,1(NkfkL=)2exp(),()(10∑−=π=NkkiitfjtkXts1.2.1kQPSK),(tkXii)(tsii4/π00i)1(22),jtk+=i(Xi(itX)QAMMPSK1.2.1,(tkXi),tk)(kX)2exp()()(10∑−=π=NkktfjkXts1.2.2DiscreteFourierTransform,DFTDFTFFTFastFourierTransformFFTOFDMNDFTDFTNDFTsfk2∑−=π−=∆10)/2exp()/()(NnsNnkjfnsfkS1.2.3Ss∆DFTDFTNDFTt1.2.2)(fk∆k)1,,2,1,0()/(−=NnfnsLsfn/=Nffs/=)/2exp()()/(10∑−=π=NjsjsfnfjjXfns1.2.41.2.41.2.3∑∑−=−=π−π=∆1010)/2exp()/2exp()()(NnNjsjNnkjfnfjjXfkS∑∑−=−=π−π=1010)/2exp()/2exp()(NjNnsjNnkjfnfjjX∑−=−δ=10)()(NjsjNkffjX1.2.5δ=≠=nmnmnm,1,0),(Nkffsk=1.2.6CDFTDFTXQAMMPSKDFT)()(kCXfkS=∆)(kDFTDFT1.2.4Nfs/]/)/(2exp[)()/(10∑−=π=NksssfnNkfjkXfns]/2exp[)(10∑−=π=NkNnjkX1.2.73)1,,2,1,0()(−=NkkXLIDFTInverseDiscreteFourierTransformIDFT)(NXNfs/DFTFFT)(NXIDFTDFTIDFTDFTFFT3.OFDMOFDM1.1IDFTOFDMCPOFDMISIICI1.41.5D/AOFDMA/DCPOFDMDFT)(NX)(NX)(NX1.1OFDMCP[PR1]OFDMISIICIOFDM1.241.2CPOFDMsymbolOFDMOFDMsymbolOFDMOFDMISIOFDM)(NX)N)(NX)(NX(X4.OFDMOFDMOFDM[ESBL1]OFDMOFDMOFDM1.3OFDM1.3OFDMOFDMNWHzTCPTOFDMTkscpcpsTT+=∉∈−π=φ],0[,0],0[)](2exp[1)(TtTtTtkNWjTtcpsk1.4.1tiOFDM],0[cpT∈)()/()(skkkTtWNtt+φ=+φ=φ5∑−=−φ=10)()()(NkkiiiTtkXts1.4.2OFDMOFDM∑∑∑∞−∞=−=∞−∞=−φ==iNkkiiiiTtkXtsts10)()()()(1.4.3CP);(tgτ],0[cpT∈τ∫+ττ−τ=∗=cpTtndtstgtsgtr0)(~)();())(()(1.4.4)(~tnGaussOFDMk[)(tkφ],TTcp∉∈−φ=ψ∗],0[,0],0[),()(sskkTtTttTt1.4.5CPCPISIISIki(1.4.3),(1.4.4),(1.4.5)∫∫∑∫∫∗∗−=′′∞∞−=φ−+φττ−φ′τ=−ψ=ψ∗=TTkTTkNkkTkTtkkcpcpcpdtttTndttdtkXtgdttTtrtry.)()(~)()()();()()())((100OFDM)(τg∫∫∫∑∗∗′−=′φ−+φττ−φτ′=TTkTTkTkNkkcpcpcpdtttTndttdtgkXy.)()(~)()()()(010TTtcpcpTτ0Ttτ−0TtTdNWkjgTNWTtkjdTNWTtkjgdtgcpTscpTscpTkcpcpcpττ′π−τ−′π=τ−τ−′πτ=ττ−φτ∫∫∫′,]/2exp[)(]/)(2exp[]/)(2exp[)()()(0006NWkf/′=k′∫ττ′π−τ=′=′cpTkdNWkjgNWkGh0,)/2exp()()(GFourier)(f)(τg∫∫∑∗∗′−=′φ−+φ−′π′=TTkTTkkscpNkkcpcpdtttTndtthTNWTtkjkXy)()(~)(/)(2exp()(10∑∫−=′∗′′′+φφ=10,)()(NkTTkkkkkcpndttthx1.4.6n∫∗φ−=TTkkcpdtttTn)()(~dtTNWTtkjTNWTtkjdtttscpTTscpTTkkcpcp/)(2exp(/)(2exp()()(−π−′π=φφ∫∫∗′),(kk′−δ=δKronecker1.4.6)(kδkkknkXhy+=)(1.4.7nAWGNk5.OFDMOFDM1.471.4OFDMOFDMOFDMOFDM)(ns)(ng)(nr)(~)()()(nNngnsnr+∗=∗CPCPrr)(ns)(1ns)(ng)(n)(1n)(~)()()(111nNngnsnr+⊗=[WSY1]⊗DFTFFT)(1nr)(ny)()()()()]([)()}(~)()](({[)(111nNnGnXnNngDFTnXnNngnXIDFTDFTny+⋅=+⋅=+⊗=)(nG)(nXCPISIICICPDFTOFDMDFT)(NX8NNDFTNDFTDFTDFTDFTCPCPDFTCPCPOFDMDFTCPIntercarrierInterferenceICI6.OFDMQAMMPSKHzTOFDMCPTOFDMNOFDMTOFDM)(xSassTsT/2f=∆sNs/Nfs/sfsf=N/ssTNff/1/==∆1.7.121OFDM)(xSasT/sT/)(xSaOFDM1.5OFDMQAMMPSKOFDMOFDMOFDMOFDM9OFDM1.6OFDM1.5OFDMNN1.6OFDMOFDMOFDMFFTOFDMOFDM7.OFDMOFDMQAMMPSKOFDMIDFTQAMMPSKbiaiiijbaiX+=)(i10OFDMOFDMIDFTIDFTD/A2N+21.7IDFT)(NXj33−16QAM16QAM16QAM1.816QAM[Chen1]1.711100001110100101.816QAMk11011.8X1010k)(=jkX+−=3)(OFDMIDFTOFDMDSPFPGAOFDMOFDMOFDMOFDM11[Chen1]..1998,9[ESBL1]Edforsetal.Anintroductiontoorthogonal-frequencydivisionmultiplexing.ResearchReport1996:16,DivisionofSignalProcessing,LuleåUniversityofTechnology,Sept.1996[PR1]PeledAandRuizA.Frequencydomaindatatransmissionusingreducedcomputationalcomplexityalgorithms.InProc.IEEEInt.Conf.Acoust.,Speech,SignalProcessing,pp.964-967,Denver,CO,1980[PB1]PolletT,BladelMandMoeneclaeyM.BERsensitivityofOFDMsystemstocarrierfrequencyoffsetandWienerphasenoise.IEEETrans.Commun.,43(2/3/4):191-193,Feb/Mar/Apr1995[Proakis1]ProakisJG.DigitalCommunications.Prentice-Hall,3rdedition,1995[WSY1]..198712