东南大学通信原理试卷及参考答案

共10共10页1页线名姓封密号学东南大学考试卷〔线名姓封密号学课程名称 通信原理 考试学期 04-05-3 得分适用专业 考试形式 闭卷 考试时间长度 150分钟SectionA(30%):TrueorFalse(GiveyourreasonifFalse，2%foreachquestion)Atypicalmobileradiochannelisafreepropagation,linear,andtimeinvariantchannel.( )Thepowerspectraldensityofastationaryprocessisalwaysnonnegative. ( )Inacommunicationsystem,noiseisunwantedandoverwhichwehaveincompletecontrol. ( )Ifarandomprocessisstationary,itisergodic;ifaGaussianrandomprocessisstationary,thenitisalsostrictlystationary. ( )DoubleSideband-SuppressedCarrier(DSB-SC),SingleSideband(SSB),andFrequencyModulation(FM)arealllinearmodulationschemes. ( Figureofmerit(definedas(SNR)O/(SNR)C)ofAMofDSB-SCis1/3,andfigureofmeritofAmplitudeModulation(AM)islessthanorequalto1/3. ( )-lawisanonlinearcompressionlawandA-lawisalinearcompressionlaw. ( )Thematchedfilteratthereceivermaximizesthepeakpulsesignal-to-noiseratio,thusisoptimalinabasebanddatatransmissionsystemwithInter-SymbolInterference(ISI).( )Correlative-levelcoding(alsoknownaspartial-responsesignaling)schemesareusedtoavoidISI. ( )Time-DivisionMultiplexing(TDM)isusedinAsymmetricDigitalSubscriberLines(ADSL)toseparatevoicesignalsanddatatransmission. ( )IfcoefficientsofanequalizerisadjustedusingtheLeast-Mean-Square(LMS)algorithmadaptively,thenthematchedfilterinfrontoftheequalizerisnotnecessary. ( InanM-aryPhase-ShiftKeying(M-PSK)system,iftheaverageprobabilityofsymbolerrorisPe,thentheaverageBitErrorRate(BER)ofthesystemisPe/log2M. ()WiththesameSignal-to-NoiseRatio(SNR),16-aryQuadratureAmplitudeModulation(16-QAM)hasbetterperformancethan16-aryPhase-ShiftKeying(16-PSK).Thereasonisthat16-QAMhasconstantenvelop. ()WiththesameSNR,MinimumShiftKeying(MSK)hasbetterperformancethanSundesFrequency-ShiftKeying(FSK).TheyarebothContinuous-PhaseFrequency-ShiftKeying(CPFSK). ()Ifthelargestfrequencycomponentofanband-limitedsignalX(t)isat100Hz,thenthecorrespondingNyquistrateis200Hz. ()SectionB(30%):FillintheBlanks(3%foreachquestion)ThepowerspectraldensityofastationaryprocessX(t)isSX(f),thentheautocorrelationfunctionofX(t)isRX(t)= .ArandomprocessY(t)isdefinedasY(t)=X(t)cos(2fct+),whereX(t)isastationaryprocess,fcisaconstantfrequency,andthephaseisrandomlydistributedovertheinterval[0,2].SupposethepowerspectraldensityofX(t)isSX(f),thepowerspectraldensityofY(t)isSY(f)= .InaFrequencyModulation(FM)system,themodulatingsignalism(t)=2cos(6t)V,thefrequencysensitivityiskf=0.3Hz/V. UsingCarson’srule,bandwidthoftheFMsignalisapproximately Hz.AnanalogsignalisfirstencodedintoabinaryPulse-CodeModulation(PCM)wave.SamplingrateofthePCMsystemis8kHz,numberofrepresentationlevelsis64. ThebinaryPCMwaveistransmittedoverabasebandchannelusinga4-aryPulse-AmplitudeModulation(PAM)(thatis,aPAMwith4amplitudelevels). TheminimumbandwidthrequirementfortransmittingthePAMwaveis kHz.Basic operations performed in the transmitter of a PCM systeminclude , ,and .Bandwidthefficiencyof4-aryQuadratureAmplitudeModulation(QAM)is bandwidthefficiencyof8-aryPhase-ShiftKeying(8PSK)is .InaDeltaModulation(DM)system,samplingrateisfs=8kHzandstepsizeis=0.1V.IftheinputtotheDMsystemisa1kHzsinusoidalsignal,thentoavoidslopeoverload,themaximumamplitudeofthisinputsignalis V.12differentmessagesignals,eachwithabandwidthof20kHz,aretobemultiplexedandtransmitted. If the multiplexing and modulationmethods are Frequency-DivisionMultiplexing(FDM)andSingle-SidebandModulation(SSB),respectively,thentheminimumbandwidthrequiredis kHz;ifthemultiplexingandmodulationmethodsareTime-DivisionMultiplexing(TDM)andPAM,thentheminimumbandwidthrequiredis kHz;kThebinarydatasequence{bk}=1010110isappliedtoaduobinary(classIpartialresponse)systemwithprecoding,asshowninFig.P1-9(seenext),wheredk=bkdk-1,denotesmodulo-twoaddition,andak=2×dk–1.Theinitialvalueofdkis1.Theoutputoftheduobinaryencoderis{ck}= .Ifatthereceivingend,thefirstreceiveddigitis1.25duetonoise,thenthereceiveroutputis{bˆ}k= .Fig.P1-9Acommunicationsystemhasthesignal-spacediagramshowninFig.P1-10,wheremessagepointshaveequalprobabilityoftransmitting.AssumecommunicationchannelinthissystemisAdditiveWhiteGaussianNoise(AWGN)channel,andE/N0is12,whereN0issingle-sidebandpowerspectraldensityoftheAWGN.Usingunionband,theaverageprobabilityofsymbolerrorisoverboundedasPe .(Expressusingcomplementaryerrorfunctionerfc().)Messagepoint2

(t)2

EMessagepoint1

(t)1Messagepoint3Fig.P1-10共10页 第3页共10共10页6页SectionC(40%):Calculations(8%foreachquestion)InacoherentBinaryPhase-ShiftKeying(BPSK)system,symbols1and0arerepresentedbysignalss1(t)ands2(t),respectively. Thesignalsaredefinedby2EbTbs(t) cos(22EbTb1 ()

c2Eb2EbTb

)

0tTbs t ft2 cwhereEbisthetransmittedsignalenergyperbit,andTbisonebitduration.Determinethebasisfunction(s)ofcoherentBPSKsignalconstellation;Plotthesignal-spacediagramofcoherentBPSKsystem;DeterminetheerrorprobabilityofBPSK;Ifthereisaphaseerrorbetweenthephasereferencesofthetransmitterandreceiver,determinetheerrorprobabilityofBPSKinthisconditionagain.Spectrumofamessagesignalm(t)isshowninFig.P3-2. ThismessagesignalisDoubleSideband-SuppressedCarrier(DSB-SC)modulatedwithacarrierwaveAccos(2fct).Iffc=2kHz,plotthespectrumofthemodulatedsignals(t);WhatisthebasebandbandwidthWofthemessagesignalm(t)?WhatisthetransmissionbandwidthBToftheDSB-SCmodulatedsignal?WhatisthelowestvalueoffcthatkeepstheDSB-SCmodulationfromsidebandoverlap?M(f)M(f)-1kHz 0 1kHz fFig.P3-2ConsideraQuadriphase-ShiftKeying(QPSK)system. Thetransmittedsignalsetisdefinedas:cos[2fs(t)

t(2i1)/4], 0tTci 0, otherwisewherei=1,2,3,4. Everytwoinputbitsselectoneofthesignalsintransmittedsignalsettotransmit. Theruleofmappingis10s1(t),00s2(t),01s3(t),11s4(t).Determinethebasisfunction(s)ofQPSKsignalconstellation;Expresssi(t)usingthebasisfunction(s);Iftheinputbinarysequenceis01101000,andsupposefc=2/T,plottheQPSKwaveform;IstheQPSKwaveformcontinuousphase?Considerthesignals(t)showninFig.P3-4,Assumingh(t)isthematchedfilterofs(t),plottheimpulseresponseofh(t);Whens(t)isappliedtoh(t),plotthematchedfilteroutputinthetimedomain.s(t)As(t)A2T/3T0T/3-AFig.P3-4SupposeX(t)=Acos(2ft–),whereAisaconstant,andfandareindependent.isuniformlydistributedovertheinterval[0,2].DeterminethepowerspectrumdensityofX(t)intermsoftheprobabilitydensityfunctionofthefrequencyf.考试学期：04-05-3SectionA:(30分)1. Themobileradiochannelistypicallytimevariant.2. 3. Stationaryisnotnecessaryergodic. FMisnotalinearmodulationscheme FigureofmeritofDSB-SCis1,not1/3. A-lawisalsoanonlinearcompressionlaw. ThematchedfilterisoptimalwithAWGNchannel. Correlative-levelcodingistouseISItoachieve2WsignalingrateinabandwidthofWHz. FDMisusedinADSL.11. TheBERisusuallynotPe/log2M. 16-QAMisnotconstantenvelop.14.15.SectionB:〔30分〕1. S X

(f)exp(j2f)df2. 1[S4 X3. 7.24. 12

(ffc

)SX

(ff)]c5. Sampling,Quantizing,andEncoding6. 1,1.57. 1.278. 240,2409. 0-202002,001011010.erfc(3)SectionC:〔40分〕(a)Thebasisfunctionis:(t)1

cos(2f

t), 0tTc

. (2分)2TbThesignal-spacediagramis: (22TbtEbEbEbEbEbN01 EbN0Theerrorprobabilityis Pe

22

. (2分)EbN01 EbN0Withphaseerror,theerrorprobabilitybecomes Pe

22

cos.(2分)(a)Thespectrumis:(2分)S(f)-2kHz 0 2kHz fW=1kHz;(2分)BT2kHz;(2分)