东南大学数字通信试卷(附答案)-2023修改整理

千里之行，始于足下让知识带有温度。第第2页/共2页精品文档推荐东南大学数字通信试卷(附答案)东南高校考试卷(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光长度120分钟共页

SectionA：TrueorFalse（15%）

1.1.Whentheperiodisexactly2m,thePNsequenceiscalleda

maximal-length-sequenceorsimplym-sequence.

2.2.Foraperiodofthemaximal-lengthsequence,theautocorrelation

functionissimilartothatofarandombinarywave.

3.3.Forslow-frequencyhopping，symbolrateRsofMFSKsignalisan

integermultipleofthehoprateRh.Thatis,thecarrierfrequencywillchangeorhopseveraltimesduringthetransmissionofonesymbol.4.4.Frequencydiversitycanbedonebychoosingafrequencyspacing

equaltoorlessthanthecoherencebandwidthofthechannel.

5.5.Themutualinformationofachannelthereforedependsnotonlyon

thechannelbutalsoonthewayinwhichthechannelused.

6.6.Shannon’ssecondtheoremspecifiesthechannelcapacityCasa

fundamentallimitontherateatwhichthetransmissionofreliableerror-freemessagescantakeplaceoveradiscretememorylesschannelandhowtoconstructagoodcode.

7.7.Thesyndromedependsnotonlyontheerrorpattern,butalsoon

thetransmittedcodeword.

8.8.Anypairofprimitivepolynomialsofdegreemwhosecorresponding

shiftregistersgeneratem-sequencesofperiod2m-1canbeusedtogenerateaGoldsequence.

9.9.AnysourcecodesatisfiestheKraft-McMillaninequalitycanbea

prefixcode.

10.10.Letadiscretememorylesssourcewithanalphabet?haveentropy

H?andproducesymbolsonceeverysTseconds.Letadiscrete()

memorylesschannelhavecapacityandbeusedonceevery

CcT

seconds.Then,if

()?

≥

sc

HC

TT,thereexistsacodingschemeforwhich

thesourceoutputcanbetransmittedoverthechannelandbereconstructedwithanarbitrarilysmallprobabilityoferror.SectionB：Fillintheblanks（35%）

1.1.Thetwocommonlyusedtypesofspread-spectrummodulation:

and.

2.2.Apseudo-noise(PN)sequenceisaperiodicbinarysequencewitha

waveformthatisusuallygeneratedbymeansofa

.

3.3.Dueto,wirelesscommunicationisnolonger

idealizedAWGNchannelmodel.

4.4.Therearethefollowingdiversitytechniquesinourdiscussion，

diversity，diversity，diversity.

5.5.Threemajorsourcesofdegradationinwirelesscommunications

are

,,and;thelattertwoarebyproductsofmultipath.

6.6.TheinformationcapacityofacontinuouschannelofbandwidthB

hertz,perturbedbyadditivewhiteGaussiannoiseofpowerspectraldensityN0/2andlimitedinbandwidthtoB,isgivenby

.

7.7.Theorsyndrome)isdefined

as:.

8.8.ForLinearBlockCodes，CorrectallerrorpatternsofHamming

weightw(e)≤t2，ifandonlyif.

9.9.TCMCombineandasasingleentityto

attainamoreeffectiveutilizationoftheavailable

and.

10.10.InaDS/BPSKsystem,thefeedbackshiftregisterusedto

generatethePNsequencehaslengthm=19,thantheprocessinggainis.

11.11.LetXrepresenttheoutcomeofasinglerollofafairdie(骰子).

TheentropyofXis.

12.12.Avoice-gradechannelofthetelephonenetworkhasabandwidth

of3.4kHz,theinformationcapacityofthetelephonechannelforasignal-to-noiseratioof30dBis,theminimumsignal-to-noiseratiorequiredtosupportinformation

transmissionthroughthetelephonechannelattherateof9,600b/sis.

13.13.Foram-sequencegeneratedbyalinearfeedbackshiftregisterof

length5,thetotalnumberofrunsis,numberoflength-tworunsis,theautocorrelationR(j)=(j≠0).

14.14.Ifthecoherentbandwidthofthechannelissmallcomparedtothe

messagebandwidth,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-aryconstellationof

interestsuccessivelyandhasprogressivelylargerincreasing

betweentheirrespectivesignalpoints.18.18.codeandcodehaveanerror

performancewithinahair’sbreadthofShannon’stheoreticallimitonchannelcapacityinaphysicallyrealizablefashion.

19.19.Whenaninfinitenumberofdecodingerrorsarecausedbyafinite

numberoftransmissionerrors,theconvolutionalcodeiscalleda.

SectionC：Problems（50%）

1．Aradiolinkusesapairof2mdishantennaswithanefficiencyof70percenteach,astransmittingandreceivingantennas.Otherspecificationsofthelinkare:

Transmittedpower=2dBW（notincludethepowergainofantenna）Carrierfrequency=12GHz

Distanceofthereceiverformthetransmitter=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)cycliccodedefinedbythegeneratorpolynomial

37()1gXXXX=+++

(a)(a)Developtheencoderforthiscode.

(b)(b)Getthegeneratormatrixandtheparity-checkmatrix.

(c)(c)Constructasystematiccodewordforthemessagesequence10110011.

(d)(d)Thereceivedwordis110001000000001,determinethesyndromepolynomials(X)forthisreceivedword.

4.Considertherater=1/3,constraintlengthK=3convolutionalencoder.Thegeneratorsequencestheencoderareasfollows:

(1)(1,0,0)g=,

,(2)(1,0,1)g=(3)

(1,1,1)g=(a)(a)Drawtheblockdiagramoftheencoder.(b)(b)Constructthecodetree

(c)(c)Constructthesignal-flowgraphandobtaintheinput-outputstateequations.

(d)(d)Determinetheencoderoutputproducedbythemessagesequence10111….

(e)(e)Thereceivedsequenceis110,001,101,110,000,011.UsetheViterbi

algorithmtocomputethedecodedsequence.答案

SectionA：TrueorFalse（每题1.5分，共15分）

11.1.Whentheperiodisexactly2m

,thePNsequenceiscalleda

maximal-length-sequenceorsimplym-sequence.（F）

12.2.Foraperiodofthemaximal-lengthsequence,theautocorrelation

functionissimilartothatofarandombinarywave.（T）

13.3.Forslow-frequencyhopping，symbolrateRsofMFSKsignalisan

integermultipleofthehoprateRh.Thatis,thecarrierfrequencywillchangeorhopseveraltimesduringthetransmissionofonesymbol.（F）14.4.Frequencydiversitycanbedonebychoosingafrequencyspacing

equaltoorlessthanthecoherencebandwidthofthechannel.（F）15.5.Themutualinformationofachannelthereforedependsnotonlyon

thechannelbutalsoonthewayinwhichthechannelused.（T）16.6.Shannon’ssecondtheoremspecifiesthechannelcapacityCasa

fundamentallimitontherateatwhichthetransmissionofreliableerror-freemessagescantakeplaceoveradiscretememorylesschannelandhowtoconstructagoodcode.（F）

17.7.Thesyndromedependsnotonlyontheerrorpattern,butalsoon

thetransmittedcodeword.（F）

18.8.Anypairofprimitivepolynomialsofdegreemwhosecorresponding

shiftregistersgeneratem-sequencesofperiod2m-1canbeusedtogenerateaGoldsequence.（F）

19.9.AnysourcecodesatisfiestheKraft-McMillaninequalitycanbea

prefixcode.（F）

20.10.Letadiscretememorylesssourcewithanalphabet?have

entropy()H?andproducesymbolsonceeverysTseconds.Letadiscretememorylesschannelhavecapacityandbeusedonceeveryseconds.Then,if

CcT()sc

HTTC

?≥,thereexistsacodingschemeforwhichthesourceoutputcanbetransmittedoverthechannelandbereconstructedwithanarbitrarilysmallprobabilityoferror.（F）

SectionB：Fillintheblanks（每空1分，共35分）

20.1.Thetwocommonlyusedtypesofspread-spectrummodulation:

directsequenceandfrequencyhopping.

21.2.Apseudo-noise(PN)sequenceisaperiodicbinarysequencewitha

noiselikewaveformthatisusuallygeneratedbymeansofafeedbackshiftregister.

22.3.Duetomultipath,wirelesscommunicationisnolongeridealized

AWGNchannelmodel.

23.4.Therearethefollowingdiversitytechniquesinourdiscussion，

Frequencydiversity，Timediversity，Spacediversity.

24.5.Threemajorsourcesofdegradationinwirelesscommunications

areco-channelinterference,fading,anddelayspread;thelattertwoarebyproductsofmultipath.

25.6.TheinformationcapacityofacontinuouschannelofbandwidthB

hertz,perturbedbyadditivewhiteGaussiannoiseofpowerspectraldensityN0/2andlimitedinbandwidthtoB,isgivenby

20log(1)bitspersecond=+P

CBNB.

26.7.Theerror-syndromevector(orsyndrome)isdefinedas:s=rHT

27.8.ForLinearBlockCodes，CorrectallerrorpatternsofHamming

weightw(e)≤t2，ifandonlyifdmin≥2t2+1.

28.9.TCMCombinecodingandmodulationasasingleentitytoattaina

moreeffectiveutilizationoftheavailablebandwidthandpower.

29.10.InaDS/BPSKsystem,thefeedbackshiftregisterusedto

generatethePNsequencehaslengthm=19,thantheprocessinggainis57dB.

30.11.LetXrepresenttheoutcomeofasinglerollofafairdie(骰子).

TheentropyofXislog2(6)=2.586bits/symbol.

31.12.Avoice-gradechannelofthetelephonenetworkhasabandwidth

of3.4kHz,theinformationcapacityofthetelephonechannelforasignal-to-noiseratioof30dBis33.9kbits/second,theminimumsignal-to-noiseratiorequiredtosupportinformationtransmissionthroughthetelephonechannelattherateof9,600b/sis7.8dB.32.13.Foram-sequencegeneratedbyalinearfeedbackshiftregisterof

length5,thetotalnumberofrunsis16,numberoflength-tworunsis4,theautocorrelationR(j)=-1/31(j≠0).

33.14.Ifthecoherentbandwidthofthechannelissmallcomparedtothe

messagebandwidth,thefadingissaidtobefrequencyselective.Ifthecoherencetimeofthechannelislargecomparedtothedurationofthesignalduration,thefadingissaidtobetimenonselectiveortimeflat.34.15.Asourceemitsoneoffivesymbolswithprobabilities1/2,1/4,1/8,1/16,1/16,respectively.Thesuccessive

symbolsemittedbythesourcearestatisticallyindependent.Theentropyofthesourceis15/8=1.875bits/symbol01234,,sand

ssss.Theaveragecode-wordlengthforanydistortionlesssourceencodingschemeforthissourceisboundedas?≥()LH.

35.16.Forafinitevarianceσ2,theGuassianrandomvariablehasthe

largestdifferentialentropyattainablebyanyrandomvariable,andtheentropyisuniquelydeterminedbythevarianceofX.

36.17.SetpartitioningdesignpartitionstheM-aryconstellationof

interestsuccessivelyandhasprogressivelylargerincreasingminimumEuclideandistancebetweentheirrespectivesignalpoints.

37.18.TurbocodesandLow-densityparity-checkcodeshaveanerror

performancewithinahair’sbreadthofShannon’stheoreticallimitonchannelcapacityinaphysicallyrealizablefashion.

38.19.Whenaninfinitenumberofdecodingerrorsarecausedbyafinite

numberoftransmissionerrors,theconvolutionalcodeiscalledacatastrophiccode.

SectionC：Problems

1．Aradiolinkusesapairof2mdishantennaswithanefficiencyof70percenteach,astransmittingandreceivingantennas.Otherspecificationsofthelinkare:

Transmittedpower=2dBW（notincludethepowergainofantenna）Carrierfrequency=12GHz

Distanceofthereceiverformthetransmitter=200mCalculate(a)thefree-spaceloss,

(b)thepowergainofeachantenna,

(c)thereceivedpowerindBW.（本题10分）

Solution:

(a)Free-spaceloss2

1010log4λπ??

=????

freespaceLd

8910310/12/1020log1004200π??

×==??××??

dB?

(b)Thepowergainofeachantennais1010102

410log10log10logπλ××??

==????

trAGG()102

8940.710log310/12/1046.46ππ??

×××??=??×??

=dB

(c)Thereceivedpower=transmittedpower+Gt+Gr+free-spaceloss=2+46.46+46.46+(-100)=-5.08dBW

2.Acomputerexecutesfourinstructionsthataredesignatedbythecode

words(00,01,10,11).Assumingthattheinstructionsareusedindependentlywithprobabilities(1/2,1/8,1/8,1/4).

(c)(a)ConstructaHuffmancodefortheinstructions.

(d)(b)Calculatethepercentagebywhichthenumberofbitsusedforthe

instructionsmaybereducedbytheuseofaHuffmancode.

（本题10分）

Solution:

(a)Aslowaspossible

Ashighaspossible

ComputercodeProbabilityHuffmanCode

001/21

111/401

000

011/8

101/8001

(e)(c)Thenumberofbitsusedfortheconstructionsbasedonthe

computercode,inaprobabilisticsense,isequalto

3.Considerthe(15,8)cycliccodedefinedbythegeneratorpolynomial

37()1gXXXX=+++842()1hXXXXX(++++)

=(e)(a)Developtheencoderforthiscode.

(f)(b)Getthegeneratormatrixandtheparity-checkmatrix.

(g)(c)Constructasystematiccodewordforthemessagesequence10110011.

(h)(d)Thereceivedwordis110001000000001,determinethesyndromepolynomials(X)forthisreceivedword.（本题15分）Solution:(a)

(b)generatormatrix

37248223533464

4

5

7

55686679177810()1()()()()()()()=+++=+++=+++=+++=+++=+++=+++=+++gXXXXXgXXXXX91011

12314

XgXXXXXXgXXXXXXgXXXXX

XgXXXXXXgXXXXXXgXXXXX

110100010000000011010001000000001101000100000000110100010000000011010001000000001101000100000000110100010000000011010001?????

????

??

?′=???

???????????G1101000100000000110100010000000011010001000000001101000100001101110000010000110111000001001110011000000101010001000

1?????

????

??

?=???

???????????

GParity-checkmatrix

81467891578910

1

2

6

8

9

10

1113791011()1()()()XhXXXXXXhXXXXXXXhXXXXXX

XhXXXXXX????=++++=++++=++++=++++

121481011121315911121141610121314

()()()3XhXXXXXXXhXXXXXXXhXXXXXX???=++++=++++=++++

100010111000000010001011100000001000101110000'0

00100010111000000010001011100000001000101110000000100010111??????????=????????????H1000000100010110100000110011100010000011001110

0010001011100000001000101110000000100010111000000010001011

1??????????=???????????

?

H(c)F