无线电通信原理-第四章(英文)

2024/12/221MobileRadioPropagation:Small-ScaleFadingandMultipath

2024/12/2222024/12/223Fading(small-scale)isamorerapidfluctuationofsignals–causedby•constructiveanddestructiveinterferencebetweentwoormoreversionsofthesamesignal(multipath)•Dopplereffect,duetomovingterminalsorsurroundings•signalswiderthancoherencebandwidthofradiochannelSmall-Scalefading2024/12/224Time-variantmultipathchannel2024/12/225

DopplerShiftExampleCarrierfrequencyfc

=1850MHz(i.e.=16.2cm)Vehiclespeedv=60mph=26.82m/sIfthevehicleismovingdirectlytowardsthetransmitterIfthevehicleismovingperpendiculartotheangleofarrivalofthetransmittedsignal2024/12/226

CoherenceBandwidth&CoherenceTime2024/12/227CharacteristicsofRadioChannel(Largepathloss)Multipath(reflection,scattering)Time-variant(time-varying,aconsequenceoftheconstantlychangingphysicalcharacteristicsofthemedia,e.g.movingofobjects)Itisreasonabletocharacterizethetime-variantmultipathchannelsstatistically.Fading[pathloss,slowfading,fastfading](multipathandtime-variant)Timespread(multipath)Frequencyspread(time-variant)2024/12/228ImpulseresponseofwirelesschannelsThemobilechannelcanbemodeledasalinear,timevaryingfilterwithimpulseresponseh(t,t),wheretisthechannelmultipathdelayforafixedt.Theimpulseresponseh(t,t)completelycharacterizesthechannelandisafunctionofbothtand

tThereceivedsignalcanbeexpressedasaconvolutionofthechannelimpulseresponseh(t,t)withthetransmittedsignalx(t)2024/12/2292024/12/2210Impulseresponseofwirelesschannels(con’t)Theimpulseresponseofthetime-variantmultipathchannelisarandomprocessThesignalpassedthroughatime-variantmultipathchannelisarandomprocessdescribemultipathdelayastheexcessdelay,relativetothefirstarrivingmultipathcomponentwithexcessdelayt0=0Discretize

excessdelayinNequallyspaced“bins”,suchthatallmultipathwavecomponentsinsidebinno.iarerepresentedbyonecomponentwithdelay.2024/12/2211thetimevaryingdiscrete-timeimpulseresponsemodelforamultipath

radiochannel2024/12/2212Sofar,wehavechannelmodelGood:itgiveseverydetailaboutthechannelBad:itishardtoseeanyessentialcharacteristicsofchannels,suchaswhatsignalcanpass,whatsignalcannotpassWeneedafewmajorparametersforeasyComparedifferentchannels(delay,bandwidth,spectrum,etc)Developdesignguidelinesforwirelesssignals2024/12/2213SuchparameterscanbederivedfromchannelmodelSpecifically,from“powerdelayprofile”ofthechannelPowerdelayprofileisthespatial/timeaverageoveralocalareaItisafunction:power~delay,i.e.,theaveragereceivedpowerwithsomedelay.2024/12/2214AremeasuredbychannelsoundingtechniquesPlotsofrelativereceivedpowerasafunctionofexcessdelayTheyarefoundbyaveraginginstantenouspowerdelaymeasurementsoveralocalareaLocalarea:nogreaterthan6moutdoorLocalarea:nogreaterthan2mindoorPowerDelayProfiles2024/12/2215ParametersofMobileMultipathChannelsTimeDispersionParametersCoherentbandwidthDopplerSpreadCoherenceTime2024/12/2216TimeDispersionParametersMeanexcessdelayRMSdelayspreadwhere2024/12/2217-30dB-20dB-10dB

0dB0125(µs)

1.37µsExample2024/12/2218CoherenceBandwidthCoherencebandwidthisastatisticalmeasureoftherangeoffrequenciesoverwhichthechannelcanbeconsider“flat”(i.e.,achannelwhichpassesallspectralcomponentswithapproximatelyequalgainandlinearphase)TwofrequenciesseparatedgreaterthanBchavedifferentchannelresponseIfthecoherencebandwidthisdefinedasthebandwidthoverwhichthefrequencycorrelationfunctionisabove0.5,thenthecoherencebandwidthisapproximatelyWhere

RMSdelayspreadRMSdelayspread(timedispersionparameters)andcoherencebandwidthareparameterswhichdescribemultipathnatureoftheradiochannel2024/12/2219SinceBc

isgreaterthan30kHz,AMPSwillworkwithoutanequalizer.However,GSMrequires200kHzbandwidthwhichexceedsBc,thusanequalizerwouldbeneededforthischannel.

2024/12/22202024/12/2221DopplerSpreadandCoherence

TimeCoherencetimeisactuallyastatisticalmeasureofthetimedurationoverwhichthechannelimpulseresponseisessentiallyinvariant,andquantifiesthesimilarityofthechannelresponseatdifferenttimes.ApopulardefinitionofcoherencetimefordigitalcommunicationsisDopplerSpreadandCoherenceTimeareparameterswhichdescribethetimevaryingnatureofthechannelinasmall-scaleregion.2024/12/2222

FadingEffectsDuetoMultipathTimeDelaySpread2024/12/22232024/12/2224DuetoDopplerSpreadRateofchangeofthe

channelcharacteristics

islargerthanthe

Rateofchangeofthe

transmittedsignalThechannelchangesduringasymbolperiod.Thechannelchangesbecauseofreceivermotion.CoherencetimeofthechannelissmallerthanthesymbolperiodofthetransmittersignalBS:Bandwidthofthesignal

BD:DopplerSpreadTS:SymbolPeriod

TC:CoherenceTimeOccurswhen:BS<BDandTS

>

TCFastFading2024/12/2225DuetoDopplerSpreadRateofchangeofthe

channelcharacteristics

ismuchsmallerthanthe

Rateofchangeofthe

transmittedsignalOccurswhen:BS>>BDandTS

<<TCBS:Bandwidthofthesignal

BD:DopplerSpreadTS:SymbolPeriod

TC:CoherenceTimeSlowFading2024/12/2226

Fastfading&Slowfading2024/12/2227TypesofSmall-ScaleFading2024/12/22282024/12/2229SmallscalefadingandmultipathImpulseresponsemodelofchannelDiscretechannelmodelParametersofchannelsrmsdelayspreadCoherencebandwidthDopplerSpreadCoherenceTimeRelationshiptosignalbandwidthandsymbolrate2024/12/2230Equalization

Compensatesforintersymbolinterference(ISI)createdbymultipathwithintimedispersivechannels.Anequalizerwithinareceivercompensatesforaveragerangeofexpectedchannelamplitudeanddelaycharacteristics.Equalizersaregenerallyadaptivesincechannelisunknownandtimevarying,forexampleGSM.Channelmustbelearnedthroughtrainingandtrackedduringdatatransmission.Sometechniquestomitigatefading2024/12/2231Theintersymbolinterferenceofreceivedsymbols(bits)mustberemovedbeforedecisionmaking(thecaseisillustratedbelowforabinarysignal,wheresymbol=bit):DecisioncircuitAdaptiveequalizerSymbolswithISISymbolswithISIremoved“Clean”symbolsDecisiontimeinstantDecisionthreshold2024/12/2232xxsc(t)sc(t-iTc)xsc(t-NTc)DemodDemodDemody(t)DiversityCombinerdk^CDMARAKEReceiver2024/12/2233FadingDistributionsDescribeshowthereceivedsignalamplitudechangeswithtime.Rememberthatthereceivedsignaliscombinationofmultiplesignalsarrivingfromdifferentdirections,phasesandamplitudes.Withthereceivedsignalwemeanthebasebandsignal,namelytheenvelopeofthereceivedsignal(i.e.r(t)).Itsisastatisticalcharacterizationofthemultipathfading.TwodistributionsRayleighFadingRiceanFading2024/12/2234Rayleighfading2024/12/22352024/12/22360.000010.00010.0010.010.110102030GAUSSIAN

CHANNELRAYLEIGH

FADINGsignal-to-noise

ratio

(dB)bit

error

probability,

binary

antipodal

signalsEFFECTOFFADINGONERRORPROBABILITIES2024/12/2237RiceanfadingWhenthereisadominantstationary(nonfading)signalcomponentpresent,suchasaline-of–sightpropagationpath,thesmall-scalefadingenvelopedistributionisRicean.2024/12/2238StatisticalModelsforFlatFadingChannelTheRiceandistributiondegeneratestoaRayleighdistributionwhenthedominantcomponentfadesaway.2024/12/2239

1.ForthepowerdelayprofilesinFigure,estimatethe90%correlationand50%correlationcoherencebandwidths.

2024/12/22402.IfabasebandbinarymessagewithabitrateRb

=100kbpsismodulatedbyanRFcarrierusingBPSK,answerthefollowing:(a)Findtherangeofv