东南大学数字通信试卷(附答案)

东南大学考试卷(A卷)课程名称数字通信考试学期04-05-2得分适用专业无线电工程系考试形式闭卷考试时间长度120分钟共页SectionA：TrueorFalse（15%）1.1.Whentheperiodisexactly2m,thePNsequenceiscalledamaximal-length-sequenceorsimplym-sequence.2.2.Foraperiodofthemaximal-lengthsequence,theautocorrelationfunctionissimilartothatofarandombinarywave.3.3.Forslow-frequencyhopping，symbolrateRsofMFSKsignalisanintegermultipleofthehoprateRh.Thatis,thecarrierfrequencywillchangeorhopseveraltimesduringthetransmissionofonesymbol.4.4.Frequencydiversitycanbedonebychoosingafrequencyspacingequaltoorlessthanthecoherencebandwidthofthechannel.5.5.Themutualinformationofachannelthereforedependsnotonlyonthechannelbutalsoonthewayinwhichthechannelused.6.6.Shannon’ssecondtheoremspecifiesthechannelcapacityCasafundamentallimitontherateatwhichthetransmissionofreliableerror-freemessagescantakeplaceoveradiscretememorylesschannelandhowtoconstructagoodcode.7.7.Thesyndromedependsnotonlyontheerrorpattern,butalsoonthetransmittedcodeword.8.8.Anypairofprimitivepolynomialsofdegreemwhosecorrespondingshiftregistersgeneratem-sequencesofperiod2m-1canbeusedtogenerateaGoldsequence.9.9.AnysourcecodesatisfiestheKraft-McMillaninequalitycanbeaprefixcode.10.10.Letadiscretememorylesssourcewithanalphabetϕhaveentropy()HϕandproducesymbolsonceeverysTseconds.LetadiscretememorylesschannelhavecapacityandbeusedonceeveryCcTseconds.Then,if()ϕ≥scHCTT,thereexistsacodingschemeforwhichthesourceoutputcanbetransmittedoverthechannelandbereconstructedwithanarbitrarilysmallprobabilityoferror.SectionB：Fillintheblanks（35%）1.1.Thetwocommonlyusedtypesofspread-spectrummodulation:and.2.2.Apseudo-noise(PN)sequenceisaperiodicbinarysequencewithawaveformthatisusuallygeneratedbymeansofa.3.3.Dueto,wirelesscommunicationisnolongeridealizedAWGNchannelmodel.4.4.Therearethefollowingdiversitytechniquesinourdiscussion，diversity，diversity，diversity.5.5.Threemajorsourcesofdegradationinwirelesscommunicationsare,,and;thelattertwoarebyproductsofmultipath.6.6.TheinformationcapacityofacontinuouschannelofbandwidthBhertz,perturbedbyadditivewhiteGaussiannoiseofpowerspectraldensityN0/2andlimitedinbandwidthtoB,isgivenby.7.7.Theerror-syndromevector(orsyndrome)isdefinedas:.8.8.ForLinearBlockCodes，CorrectallerrorpatternsofHammingweightw(e)≤t2，ifandonlyif.9.9.TCMCombineandasasingleentitytoattainamoreeffectiveutilizationoftheavailableand.10.10.InaDS/BPSKsystem,thefeedbackshiftregisterusedtogeneratethePNsequencehaslengthm=19,thantheprocessinggainis.11.11.LetXrepresenttheoutcomeofasinglerollofafairdie(骰子).TheentropyofXis.12.12.Avoice-gradechannelofthetelephonenetworkhasabandwidthof3.4kHz,theinformationcapacityofthetelephonechannelforasignal-to-noiseratioof30dBis,theminimumsignal-to-noiseratiorequiredtosupportinformationtransmissionthroughthetelephonechannelattherateof9,600b/sis.13.13.Foram-sequencegeneratedbyalinearfeedbackshiftregisteroflength5,thetotalnumberofrunsis,numberoflength-tworunsis,theautocorrelationR(j)=(j≠0).14.14.Ifthecoherentbandwidthofthechannelissmallcomparedtothemessagebandwidth,thefadingissaidtobe.Ifthecoherencetimeofthechannelislargecomparedtothedurationofthesignalduration,thefadingissaidtobe.15.15.Asourceemitsoneoffivesymbolswithprobabilities1/2,1/4,1/8,1/16,1/16,respectively.Thesuccessivesymbolsemittedbythesourcearestatisticallyindependent.Theentropyofthesourceis01234,,sandssss.Theaveragecode-wordlengthforanydistortionlesssourceencodingschemeforthissourceisboundedas.16.16.Forafinitevarianceσ2,therandomvariablehasthelargestdifferentialentropyattainablebyanyrandomvariable,andtheentropyisuniquelydeterminedbythe.17.17.SetpartitioningdesignpartitionstheM-aryconstellationofinterestsuccessivelyandhasprogressivelylargerincreasingbetweentheirrespectivesignalpoints.18.18.codeandcodehaveanerrorperformancewithinahair’sbreadthofShannon’stheoreticallimitonchannelcapacityinaphysicallyrealizablefashion.19.19.Whenaninfinitenumberofdecodingerrorsarecausedbyafinitenumberoftransmissionerrors,theconvolutionalcodeiscalleda.SectionC：Problems（50%）1．Aradiolinkusesapairof2mdishantennaswithanefficiencyof70percenteach,astransmittingandreceivingantennas.Otherspecificationsofthelinkare:Transmittedpower=2dBW（notincludethepowergainofantenna）Carrierfrequency=12GHzDistanceofthereceiverformthetransmitter=200mCalculate(a)thefree-spaceloss,(b)thepowergainofeachantenna,(c)thereceivedpowerindBW.2.Acomputerexecutesfourinstructionsthataredesignatedbythecodewords(00,01,10,11).Assumingthattheinstructionsareusedindependentlywithprobabilities(1/2,1/8,1/8,1/4).(a)(a)ConstructaHuffmancodefortheinstructions.(b)(b)CalculatethepercentagebywhichthenumberofbitsusedfortheinstructionsmaybereducedbytheuseofaHuffmancode.3.Considerthe(15,8)cycliccodedefinedbythegeneratorpolynomial37()1gXXXX=+++(a)(a)Developtheencoderforthiscode.(b)(b)Getthegeneratormatrixandtheparity-checkmatrix.(c)(c)Constructasystematiccodewordforthemessagesequence10110011.(d)(d)Thereceivedwordis110001000000001,determinethesyndromepolynomials(X)forthisreceivedword.4.Considertherater=1/3,constraintlengthK=3convolutionalencoder.Thegeneratorsequen