无线通信系统第4章课件

MobileRadioPropagation:Small-ScaleFadingandMultipath

11/23/20221MobileRadioPropagation:Smal11/23/2022211/22/20222Fading(small-scale)isamorerapidfluctuationofsignals–causedby•constructiveanddestructiveinterferencebetweentwoormoreversionsofthesamesignal(multipath)•Dopplereffect,duetomovingterminalsorsurroundings•signalswiderthancoherencebandwidthofradiochannelSmall-Scalefading11/23/20223Fading(small-scale)isamoreTime-variantmultipathchannel11/23/20224Time-variantmultipathchannel

DopplerShiftExampleCarrierfrequencyfc

=1850MHz(i.e.=16.2cm)Vehiclespeedv=60mph=26.82m/sIfthevehicleismovingdirectlytowardsthetransmitterIfthevehicleismovingperpendiculartotheangleofarrivalofthetransmittedsignal11/23/20225DopplerShiftExample11/22/2

CoherenceBandwidth&CoherenceTime11/23/20226

CoherenceBandwidth&CoherenceCharacteristicsofRadioChannel(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)11/23/20227CharacteristicsofRadioChannImpulseresponseofwirelesschannelsThemobilechannelcanbemodeledasalinear,timevaryingfilterwithimpulseresponseh(t,t),wheretisthechannelmultipathdelayforafixedt.Theimpulseresponseh(t,t)completelycharacterizesthechannelandisafunctionofbothtand

tThereceivedsignalcanbeexpressedasaconvolutionofthechannelimpulseresponseh(t,t)withthetransmittedsignalx(t)11/23/20228Impulseresponseofwirelessc11/23/2022911/22/20229RandomCharacteristicsofwirelesschannelsTheimpulseresponseofthetime-variantmultipathchannelisarandomprocessThesignalpassedthroughatime-variantmultipathchannelisarandomprocessdescribemultipathdelayastheexcessdelay,relativetothefirstarrivingmultipathcomponentwithexcessdelayt0=0DiscretizeexcessdelayinNequallyspaced“bins”,suchthatallmultipathwavecomponentsinsidebinno.iarerepresentedbyonecomponentwithdelay.?11/23/202210RandomCharacteristicsofwirethetimevaryingdiscrete-timeimpulseresponsemodelforamultipath

radiochannel11/23/202211thetimevaryingdiscrete-timeSofar,wehavechannelmodelGood:itgiveseverydetailaboutthechannelBad:itishardtoseeanyessentialcharacteristicsofchannels,suchaswhatsignalcanpass,whatsignalcannotpassWeneedafewmajorparametersforeasyComparedifferentchannels(delay,bandwidth,spectrum,etc)Developdesignguidelinesforwirelesssignals11/23/202212Sofar,wehavechannelmodel1SuchparameterscanbederivedfromchannelmodelSpecifically,from“powerdelayprofile”ofthechannelPowerdelayprofileisthespatial/timeaverageoveralocalareaItisafunction:power~delay,i.e.,theaveragereceivedpowerwithsomedelay.11/23/202213SuchparameterscanbederivedAremeasuredbychannelsoundingtechniquesPlotsofrelativereceivedpowerasafunctionofexcessdelayTheyarefoundbyaveragingintantenouspowerdelaymeasurementsoveralocalareaLocalarea:nogreaterthan6moutdoorLocalarea:nogreaterthan2mindoorPowerDelayProfiles11/23/202214AremeasuredbychannelsoundiContinuous

Wave(CW)SignalHighbandwidth(Wideband)SignalReceivedpowerforCWsignalsundergoesrapidfadesoversmalldistancesReceivedpowerforwidebandsignalschangesverylittleofsmalldistances.However,thelocalareaaverageofbothsignalsarenearlyidentical.

DifferentBasebandSignals11/23/202215Continuous

Wave(CW)HighbandwParametersofMobileMultipathChannelsTimeDispersionParametersCoherentbandwidthDopplerSpreadCoherenceTime11/23/202216ParametersofMobileMultipathTimeDispersionParametersMeanexcessdelayRMSdelayspreadwhere11/23/202217TimeDispersionParametersMeanPowerdelayProfileReceivedSignalLevel(dBm)-105-100-95-90050100150200250300350400450RMSDelaySpread()=46.4nsMeanExcessdelay()=45nsMaximumExcessdelay<10dB=110nsNoisethreshold11/23/202218PowerdelayProfileReceivedSi-30dB-20dB-10dB0dB0125(µs)1.37µsExample11/23/202219-30dB-20dB-10dB0dB0125CoherenceBandwidthCoherencebandwidthisastatisticalmeasureoftherangeoffrequenciesoverwhichthechannelcanbeconsider“flat”(i.e.,achannelwhichpassesallspectralcomponentswithapproximatelyequalgainandlinearphase)TwofrequenciesseparatedgreaterthanBchavedifferentchannelresponseIfthecoherencebandwidthisdefinedasthebandwidthoverwhichthefrequencycorrelationfunctionisabove0.5,thenthecoherencebandwidthisapproximatelyWhereRMSdelayspreadRMSdelayspread(timedispersionparameters)andcoherencebandwidthareparameterswhichdescribemultipathnatureoftheradiochannel11/23/202220CoherenceBandwidthCoherencebSinceBc

isgreaterthan30kHz,AMPSwillworkwithoutanequalizer.However,GSMrequires200kHzbandwidthwhichexceedsBc,thusanequalizerwouldbeneededforthischannel.

11/23/202221SinceBcisgreaterthan30kHDopplerSpreadandCoherence

TimeCoherencetimeisactuallyastatisticalmeasureofthetimedurationoverwhichthechannelimpulseresponseisessentiallyinvariant,andquantifiesthesimilarityofthechannelresponseatdifferenttimes.ApopulardefinitionofcoherencetimefordigitalcommunicationsisDopplerSpreadandCoherenceTimeareparameterswhichdescribethetimevaryingnatureofthechannelinasmall-scaleregion.11/23/202222DopplerSpreadandCoherenceTExampleThespatialsamplingintervalrequiredtomakesmall-scalepropagationmeasurementsisTc/2.Howmanysampleswillberequiredover10mtraveldistanceiffc

=1900MHzandv=50m/s.Howlongwouldittaketomakethesemeasurements,assumingtheycouldbemadeinrealtimefromamovingvehicle?Solution11/23/202223ExampleThespatialsamplinginFadingEffectsDuetoMultipathTimeDelaySpread11/23/202224FadingEffectsDuetoMultipa11/23/20222511/22/202225DuetoDopplerSpreadRateofchangeofthe

channelcharacteristics

islargerthanthe

Rateofchangeofthe

transmittedsignalThechannelchangesduringasymbolperiod.Thechannelchangesbecauseofreceivermotion.CoherencetimeofthechannelissmallerthanthesymbolperiodofthetransmittersignalBS:Bandwidthofthesignal

BD:DopplerSpreadTS:SymbolPeriod

TC:CoherenceBandwidthOccurswhen:BS<BDandTS

>

TCFastFading11/23/202226DuetoDopplerSpreadBS:BandwDuetoDopplerSpreadRateofchangeofthe

channelcharacteristics

ismuchsmallerthanthe

Rateofchangeofthe

transmittedsignalOccurswhen:BS>>BDandTS

<<TCBS:Bandwidthofthesignal

BD:DopplerSpreadTS:SymbolPeriod

TC:CoherenceBandwidthSlowFading11/23/202227DuetoDopplerSpreadOccurswh

Fastfading&Slowfading11/23/202228

Fastfading&Slowfading11/22TypesofSmall-ScaleFading11/23/202229TypesofSmall-ScaleFading1111/23/20223011/22/202230SmallscalefadingandmultipathImpulseresponsemodelofchannelDiscretechannelmodelParametersofchannelsrmsdelayspreadCoherencebandwidthDopplerSpreadCoherenceTimeRelationshiptosignalbandwidthandsymbolrate11/23/202231SmallscalefadingandmultipaEqualization

Compensatesforintersymbolinterference(ISI)createdbymultipathwithintimedispersivechannels.Anequalizerwithinareceivercompensatesforaveragerangeofexpectedchannelamplitudeanddelaycharacteristics.Equalizersaregenerallyadaptivesincechannelisunknownandtimevarying,forexampleGSM.Channelmustbelearnedthroughtrainingandtrackedduringdatatransmission.Sometechniquestomitigatefading11/23/202232EqualizationSometechniquestTheintersymbolinterferenceofreceivedsymbols(bits)mustberemovedbeforedecisionmaking(thecaseisillustratedbelowforabinarysignal,wheresymbol=bit):DecisioncircuitAdaptiveequalizerSymbolswithISISymbolswithISIremoved“Clean”symbolsDecisiontimeinstantDecisionthreshold11/23/202233TheintersymbolinterferenceoZ-1Z-1Z-1∑w0kw1kw2kwNkAdaptiveAlgorithm∑+-TimeDomainEqualization11/23/202234Z-1Z-1Z-1∑w0kw1kw2kwNkAdaptivePowerfulcommunicationstechniquethatprovideswirelesslinkimprovementatrelativelylowcost.Unlikeequalization,diversityrequiresnotrainingoverhead.SendbitsoverindependentfadingpathsCombinepathstomitigatefadingeffects.IndependentfadingpathsSpace,time,frequency,polarizationdiversity.Diversity

11/23/202235Diversity11/22/202235Spacediversity11/23/202236Spacediversity11/22/202236xxsc(t)sc(t-iTc)xsc(t-NTc)DemodDemodDemody(t)DiversityCombinerdk^CDMARAKEReceiver11/23/202237xxsc(t)sc(t-iTc)xsc(t-NTc)Demoimprovesthesmall-scalelinkperformancebyaddingredundantdatabitsinthetransmittedmessagesothatifaninstantaneousfadeoccursinthechannel,thedatamaystillberecoveredatthereceiver.Channelcodingareusedtodetecterrorsandcorrecterrors.Blockcodes,convolutionalcodesChannelcoding11/23/202238Channelcoding11/22/202238DividesbitstreamintoNsubstreamsModulatessubstreamwithbandwidthB/NSeparatesubcarriersB/N<Bcflatfading(noISI)OFDMisatransmissiontechniquethatisinherentlyresistanttoISI.

OFDMwillnodoubtplayalargeroleintheemergingwirelessLAN/MANstandardsand4Gnetworkdeployments.OFDM11/23/202239OFDM11/22/202239FadingDistributionsDescribeshowthereceivedsignalamplitudechangeswithtime.Rememberthatthereceivedsignaliscombinationofmultiplesignalsarrivingfromdifferentdirections,phasesandamplitudes.Withthereceivedsignalwemeanthebasebandsignal,namelytheenvelopeofthereceivedsignal(i.e.r(t)).Itsisastatisticalcharacterizationofthemultipathfading.TwodistributionsRayleighFadingRiceanFading11/23/202240FadingDistributionsDescribesRayleighfading11/23/202241Rayleighfading11/22/20224111/23/20224211/22/2022420.000010.00010.0010.010.110102030GAUSSIAN

CHANNELRAYLEIGH

FADINGsignal-to-noise

ratio

(dB)bit

error

probability,

binary

antipodal

signalsEFFECTOFFADINGONERRORPROBABILITIES11/23/2022430.000010.00010.0010.010.110102RiceanfadingWhenthereisadominantstationary(nonfading)signalcomponentpresent,suchasaline-of–sightpropagationpath,thesmall-scalefadingenvelopedistributionisRicean.11/23/202244RiceanfadingWhenthereisadStatisticalModelsforFlatFadingChannelTheRiceandistributiondegeneratestoaRayleighdistributionwhenthedominantcomponentfadesaway.11/23/202245StatisticalModelsforFlatFa1.ForthepowerdelayprofilesinFigure,estimatethe90%correlationand50%correlationcoherencebandwidths.

11/23/2022461.Forthepowerdelayprofile2.IfabasebandbinarymessagewithabitrateRb=100kbpsismodulatedbyanRFcarrierusingBPSK,answerthefollowing:(a)Findtherangeofvaluesrequiredforthermsdelayspreadofthechannelsuchthatthereceivedsignalisaflat-fadingsignal.(b)Ifthemodulationcarrierfrequencyis5.8GHz,whatisthecoherencetimeofthechannel,assumingavehiclespeedof50kilometersperhour?(use4.40b)(c)Foryouranswerin(b),isthechannel"fast"or"slow"fading?(d)Givenyouranswerin(b),howmanybitsaresentwhilethechannelappears"static"?(e)ACDMARakereceiverisabletoexploitmultipathwhenthechannelis(a)flat;(b)slow;(c)fast;(d)frequencyselective11/23/2022472.Ifabasebandbinarymessage3.Trytoexplainthemeaningofthefollowing:(i)thechannelisfrequency-nonselective;(ii)thechannelisslowlyfading;(iii)thechannelisfrequency-selective.

11/23/2022483.TrytoexplainthemeaningoMobileRadioPropagation:Small-ScaleFadingandMultipath

11/23/202249MobileRadioPropagation:Smal11/23/20225011/22/20222Fading(small-scale)isamorerapidfluctuationofsignals–causedby•constructiveanddestructiveinterferencebetweentwoormoreversionsofthesamesignal(multipath)•Dopplereffect,duetomovingterminalsorsurroundings•signalswiderthancoherencebandwidthofradiochannelSmall-Scalefading11/23/202251Fading(small-scale)isamoreTime-variantmultipathchannel11/23/202252Time-variantmultipathchannel

DopplerShiftExampleCarrierfrequencyfc

=1850MHz(i.e.=16.2cm)Vehiclespeedv=60mph=26.82m/sIfthevehicleismovingdirectlytowardsthetransmitterIfthevehicleismovingperpendiculartotheangleofarrivalofthetransmittedsignal11/23/202253DopplerShiftExample11/22/2

CoherenceBandwidth&CoherenceTime11/23/202254

CoherenceBandwidth&CoherenceCharacteristicsofRadioChannel(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)11/23/202255CharacteristicsofRadioChannImpulseresponseofwirelesschannelsThemobilechannelcanbemodeledasalinear,timevaryingfilterwithimpulseresponseh(t,t),wheretisthechannelmultipathdelayforafixedt.Theimpulseresponseh(t,t)completelycharacterizesthechannelandisafunctionofbothtand

tThereceivedsignalcanbeexpressedasaconvolutionofthechannelimpulseresponseh(t,t)withthetransmittedsignalx(t)11/23/202256Impulseresponseofwirelessc11/23/20225711/22/20229RandomCharacteristicsofwirelesschannelsTheimpulseresponseofthetime-variantmultipathchannelisarandomprocessThesignalpassedthroughatime-variantmultipathchannelisarandomprocessdescribemultipathdelayastheexcessdelay,relativetothefirstarrivingmultipathcomponentwithexcessdelayt0=0DiscretizeexcessdelayinNequallyspaced“bins”,suchthatallmultipathwavecomponentsinsidebinno.iarerepresentedbyonecomponentwithdelay.?11/23/202258RandomCharacteristicsofwirethetimevaryingdiscrete-timeimpulseresponsemodelforamultipath

radiochannel11/23/202259thetimevaryingdiscrete-timeSofar,wehavechannelmodelGood:itgiveseverydetailaboutthechannelBad:itishardtoseeanyessentialcharacteristicsofchannels,suchaswhatsignalcanpass,whatsignalcannotpassWeneedafewmajorparametersforeasyComparedifferentchannels(delay,bandwidth,spectrum,etc)Developdesignguidelinesforwirelesssignals11/23/202260Sofar,wehavechannelmodel1SuchparameterscanbederivedfromchannelmodelSpecifically,from“powerdelayprofile”ofthechannelPowerdelayprofileisthespatial/timeaverageoveralocalareaItisafunction:power~delay,i.e.,theaveragereceivedpowerwithsomedelay.11/23/202261SuchparameterscanbederivedAremeasuredbychannelsoundingtechniquesPlotsofrelativereceivedpowerasafunctionofexcessdelayTheyarefoundbyaveragingintantenouspowerdelaymeasurementsoveralocalareaLocalarea:nogreaterthan6moutdoorLocalarea:nogreaterthan2mindoorPowerDelayProfiles11/23/202262AremeasuredbychannelsoundiContinuous

Wave(CW)SignalHighbandwidth(Wideband)SignalReceivedpowerforCWsignalsundergoesrapidfadesoversmalldistancesReceivedpowerforwidebandsignalschangesverylittleofsmalldistances.However,thelocalareaaverageofbothsignalsarenearlyidentical.

DifferentBasebandSignals11/23/202263Continuous

Wave(CW)HighbandwParametersofMobileMultipathChannelsTimeDispersionParametersCoherentbandwidthDopplerSpreadCoherenceTime11/23/202264ParametersofMobileMultipathTimeDispersionParametersMeanexcessdelayRMSdelayspreadwhere11/23/202265TimeDispersionParametersMeanPowerdelayProfileReceivedSignalLevel(dBm)-105-100-95-90050100150200250300350400450RMSDelaySpread()=46.4nsMeanExcessdelay()=45nsMaximumExcessdelay<10dB=110nsNoisethreshold11/23/202266PowerdelayProfileReceivedSi-30dB-20dB-10dB0dB0125(µs)1.37µsExample11/23/202267-30dB-20dB-10dB0dB0125CoherenceBandwidthCoherencebandwidthisastatisticalmeasureoftherangeoffrequenciesoverwhichthechannelcanbeconsider“flat”(i.e.,achannelwhichpassesallspectralcomponentswithapproximatelyequalgainandlinearphase)TwofrequenciesseparatedgreaterthanBchavedifferentchannelresponseIfthecoherencebandwidthisdefinedasthebandwidthoverwhichthefrequencycorrelationfunctionisabove0.5,thenthecoherencebandwidthisapproximatelyWhereRMSdelayspreadRMSdelayspread(timedispersionparameters)andcoherencebandwidthareparameterswhichdescribemultipathnatureoftheradiochannel11/23/202268CoherenceBandwidthCoherencebSinceBc

isgreaterthan30kHz,AMPSwillworkwithoutanequalizer.However,GSMrequires200kHzbandwidthwhichexceedsBc,thusanequalizerwouldbeneededforthischannel.

11/23/202269SinceBcisgreaterthan30kHDopplerSpreadandCoherence

TimeCoherencetimeisactuallyastatisticalmeasureofthetimedurationoverwhichthechannelimpulseresponseisessentiallyinvariant,andquantifiesthesimilarityofthechannelresponseatdifferenttimes.ApopulardefinitionofcoherencetimefordigitalcommunicationsisDopplerSpreadandCoherenceTimeareparameterswhichdescribethetimevaryingnatureofthechannelinasmall-scaleregion.11/23/202270DopplerSpreadandCoherenceTExampleThespatialsamplingintervalrequiredtomakesmall-scalepropagationmeasurementsisTc/2.Howmanysampleswillberequiredover10mtraveldistanceiffc

=1900MHzandv=50m/s.Howlongwouldittaketomakethesemeasurements,assumingtheycouldbemadeinrealtimefromamovingvehicle?Solution11/23/202271ExampleThespatialsamplinginFadingEffectsDuetoMultipathTimeDelaySpread11/23/202272FadingEffectsDuetoMultipa11/23/20227311/22/202225DuetoDopplerSpreadRateofchangeofthe

channelcharacteristics

islargerthanthe

Rateofchangeofthe

transmittedsignalThechannelchangesduringasymbolperiod.Thechannelchangesbecauseofreceivermotion.CoherencetimeofthechannelissmallerthanthesymbolperiodofthetransmittersignalBS:Bandwidthofthesignal

BD:DopplerSpreadTS:SymbolPeriod

TC:CoherenceBandwidthOccurswhen:BS<BDandTS

>

TCFastFading11/23/202274DuetoDopplerSpreadBS:BandwDuetoDopplerSpreadRateofchangeofthe

channelcharacteristics

ismuchsmallerthanthe

Rateofchangeofthe

transmittedsignalOccurswhen:BS>>BDandTS

<<TCBS:Bandwidthofthesignal

BD:DopplerSpreadTS:SymbolPeriod

TC:CoherenceBandwidthSlowFading11/23/202275DuetoDopplerSpreadOccurswh

Fastfading&Slowfading11/23/202276

Fastfading&Slowfading11/22TypesofSmall-ScaleFading11/23/202277TypesofSmall-ScaleFading1111/23/20227811/22/202230SmallscalefadingandmultipathImpulseresponsemodelofchannelDiscretechannelmodelParametersofchannelsrmsdelayspreadCoherencebandwidthDopplerSpreadCoherenceTimeRelationshiptosignalbandwidthandsymbolrate11/23/202279SmallscalefadingandmultipaEqualization

Compensatesforintersymbolinterference(ISI)createdbymultipathwithintimedispersivechannels.Anequalizerwithinareceivercompensatesforaveragerangeofexpectedchannelamplitudeanddelaycharacteristics.Equalizersaregenerallyadaptivesincechannelisunknownandtimevarying,forexampleGSM.Channelmustbelearnedthroughtrainingandtrackedduringdatatransmission.Sometechniquestomitigatefading11/23/202280EqualizationSometechniquestTheintersymbolinterferenceofreceivedsymbols(bits)mustberemovedbeforedecisionmaking(thecaseisillustratedbelowforabinarysignal,wheresymbol=bit):DecisioncircuitAdaptiveequalizerSymbolswithISISymbolswithISIremoved“Clean”symbolsDecisiontimeinstantDecisionthreshold11/23/202281TheintersymbolinterferenceoZ-1Z-1Z-1∑w0kw1kw2kwNkAdaptiveAlgorithm∑+-TimeDomainEqualization11/23/202282Z-1Z-1Z-1∑w0kw1kw2kwNkAdaptivePowerfulcommunicationstechniquethatprovideswirelesslinkimprovementatrelativelylowcost.Unlikeequalization,diversityrequiresnotrainingoverhead.SendbitsoverindependentfadingpathsCombinepathstomitigatefadingeffects.IndependentfadingpathsSpace,time,frequency,polarizationdiversity.Diversity

11/23/202283Diversity11/22/202235Spacediversity11/23/202284Spacediversity11/22/202236xxsc(t)sc(t-iTc)xsc(t-NTc)DemodDemodDemody(t)DiversityCombinerdk^CDMARAKEReceiver11/23/202285xxsc(t)sc(t-iTc)xsc(t-NTc)Demoimprovesthesmall-scalelinkperformancebyaddingredundantdatabitsinthetransmittedmessagesothatifaninstantaneousfadeoccursinthechannel,thedatamaystillberecoveredatthereceiver.Channelcodingareusedtodetecterrorsandcorrecterrors.Blockcodes,convolutionalcodesChannelcoding11/23/202286Channelcoding11/22/202238DividesbitstreamintoNsubstreamsModulatessubstreamwithbandwidthB/NSeparatesubcarriersB/N<Bcflatfading(noISI)OFDMisatransmissiontechniquethatisinherentlyresistanttoISI.

OFDMwillnodoubtplayalargeroleintheemergingwirelessLAN/MANstandardsand4Gnetworkdeployments.O