Digital communication practical session assignment 1Word下载.docx

Digital communication practical session assignment 1Word下载.docx

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Thisisamathematicalmodelrepresentedbylinkedblocks.Eachblockdescribesmathematicalrelationshipsbetweensignalsadstates.

1.Randomintegerblockgeneratesrandomintegersfromzeroto255.

2.RectangularQAMmodulatormodulatesthesignalusingbaseband256-aryquadratureamplitudemodulation.

3.AWGNblockaddswhiteGaussiannoisetothemodulatedsignal,actingasanoisechannel.

4.Phasenoiseblockintroducesnoisetothesystem.

5.RectangularQAMblock,totherightofphasenoiseblock,demodulatesthesignal.

6.Errorratecalculationblockcountssymbolsthatdifferbetweenthereceivedsignalandthetransmittedsignal.

7.Displayblockdisplayssymbolerrorrate,thenumberoferrorsandthenumberofsymbolsprocessedduringthemodulation.

8.AWGNplusphasenoiseblockcandrawthescatterplotofthesignalwithaddednoise.

Fig.1.2Thescstterplotofasignalplusnoise

Figure1.2showsthescatterplotofthemodulatedsignalwithnoise.Thepointslieinaradialpattern.

Fig.1.3Resultofsimulation

Figure1.3showsthesignalerrorrateis0.007524,thenumberoftotalerrorsis79andthenumberoftotalsymbolsis10500.

Fig.1.4ThemaskofPhaseNoiseBlock

Fig.1.5Anewscatterplot（constellationdiagram）

Bysettingphasenoiselevelto-150dBc/HzinphasenoiseblockandEs/No（signaltonoiseratio）to100inAWGNblockIobtainsthefigure1.5.Phasenoiserepresentsthenoisepowerrelativetothecarriercontainedina1Hzbandwidthcentredatacertainoffsetsfromthecarrier.Itisquantifiedintheunitofmeasure

called“scriptLofF”,whichisequalto

Whilesignaltonoiseratioisthevalueofsignalpowerdividedbynoisepower.Bysettingthesetwovaluesto-150and100respectively,thenoiseinthesystemisalmostclearedthusthescatterplotlooksliketheconstellationfor256-aryQAM.（Notgoingabove0ofphasenoiselevel）

Fig.1.6Scatterplot（phasenoiselevel-10dBc/Hz）

Whenchangingthephasenoiselevelfrom-150dBc/Hzto-10dBc/Hz,phasenoisehasbeenincreased,thusthepointsdonotlieexactlyontheconstellationanymore.

Fig.1.7PlotofBERatdifferentnoiselevels

Thehorizontalaxisisthesignaltonoiseratio,andtheverticalaxisisbiterrorratio.Differentcurvecorrespondstodifferentphasenoiselevel.

Parttwo:

Bulidingasimplemodel

Fig.2.1Asimplesimulinkmodel

Usingcommandcommstartupbeforesettingupnewmodel,thenselectblocksfromthesimulinklibraryanddragtheseblockstonewmodelwindowtobuildupnewmodel.Finallyconnecttheblocksusingarrowheadlines.

Thensettheparametersofthesinewaveblock.Theamplitudeis5,thefrequencyis30Hzandthesampleperfameis100.Thedefaultvalueofstoptimeinthemodelconfigurationparametersdialogboxisinfinite,inordertocapturetheimageofthesinewave,thevalueshouldbeassignedasafinitenumber.Figure2.2issinewaveobservedfromthevectorscope.Sinethereisnonoiseinthemodel,thewaveformispurelysinusoidal.

Fig.2.2Thesinewaveobservedfromthescope

Fig2.3Asinewavemodelplusnoise

TheAWGNblock,whichstandsforaddictivewhiteGaussiannoise,modifiesthechannelnoiseinthemodel.Whitenoisecontainsequalpowerwithinafixedbandwidthatanycentrefrequency.GaussiannoiseindicatesthatthevaluesofthenoisecantakeonareGaussian-distributed.WhiteGaussiannoisemeansthevaluesatanypairoftimesareidenticallydistributedandstatisticallyindependent.Figure2.3showsthemodelwithchannelnoiseandfigure2.4showsthesimulationresultwithnoise.Becaeseoftheaddednoise,thesinussoidalsignalgeneratedbythesinewavegeneratorisdisturbedandthereforeoutputsignalhassomefluctuationonthebasisofthepuresinusoidalwaveform.

Fig.2.4Sinewavewithaddednoise

Partthree:

Buildingachannelnoisemodel

Fig.3.1Channelnoisemodel

Figure3.1isachannelnoisemodel.Thebernoullibinarygeneratorblockgeneratesabinarysignalasasource,thebinarysymmetricchannelblockdisturbsthesignalbychanginga0toa1ortheviceverse,theerrorratecalculationblockcalculatestheerrorratebycomparingthetwosignalsfromTxportandRxportandfinallytheresultisshowninthedisplayblock.

Beforerunningthemodel,changetheerrorprobabilityto0.01andcleartheoutputerrorcheckboxofthebinarysymmetricchannel’smask,setoutputdatatoportoftheerrorratecalculationblock’smask.

Fig.3.2Theresultofchannelnoisemodelsimulation

Figure3.2showstheresultofthissimulation.biterrorrateis0.01147,thenumberoferrorsis100andnumberoftransmittedbitsis8717.Theerrornumbercanbechangedintheerrorratecalculationblock.Thebiterrorrateisthenumberofbiterrorsdividedbytotalnumberoftransferredbits.

Partfour:

Reducingtheerrorrateusingahammingcode

Fig.4.1Hammingcodemodel

Inordertoreducethebiterrorrate,ahammingencoderanddecoderblockareaddedbeforeandafterthebinarysymmetricchannelblock.Thedefaulthammingcodeis[7,4]codewhichmeansthe4-bitinputdatacanbeencodedinto7-bitoutputdatabyaddingthreebitsattheendofeachcode.Thusthecodepatternexpandsfrom

to

.Thereforeeachoutputdatacanbeseentodifferfromotherdatabyatleastthreebits.Whenthedecoderreceivesthemessage,iftherulediscussedaboveisnotsatisfied,itcanrealizethatthedataisnotcorrect.Itcaneithercorrectthefaultmessageorjustignoreit.

Beforerunningthehammingcodemodel,Iselecttheframe-basedoutputsboxandsetsampleperframeto4inthemaskofbinarygeneratorblock.Becausehammingencoderblockrequirestheinputtobeavectorofaspecificsize,inthiscase,thesizeis4.Theerroris0.001044accordingtofigure4.1.

Theframesizecanbedisplayedintheblockbyselectingsignaldimensionsfromtheport/signaldisplaysubmenuoftheformatmenu.[4*1]indicatesthattheblockgeneratescolumnvectorofsize4.

Fig.4.3Anexpandedmodelwithascopetoseethechannelerrors

Fig.4.4Channelerrorsobservation

Byaddingascopeblockinthemodel,thechannelnoiseproducedbythebinarysymmetricchannelcanbeseen.Beforerunningthemodel,thestopsimulationboxshouldbeclearedintheerrorratecalculationblock’smask.Theupperscopeshowsthechannelerrorsgeneratedbythebinarysymmetricchannel.Thelowerscopeshowstheuncorrectederrors.

Fig.4.5Zoominginonthescope

Thenarrowrectangularpulserepresentsonetimeinterval,whichis1secondinthisscope.Thewiderrectangularpulseintheupperscopehasacorrespondingnarrowrectangularpulseinthelowerscope,whichmeansthewideronehasnotbeencorrectedbythehammingencodeblock.Whilethenarrowonetotherightofthewideroneintheupperscoperepresentsacorrectedsingleerror.

Partfive:

Modelingachannelwithmodulation

Fig.5.1Channelmodellingwithdigitalmodulation

Themodelinfigure5.1usestheBPSKmodulatorbaseband,AWGNchannelandtheBPSKdemodulatorbasebandblockstoSimulinkachannelwithnoise.Phaseshiftkeyingisadigitalmodulationschemethattransmitsdatabymodulatingthecarrierwave.Theinformationiscontainedintheinstantaneousphaseofthemodulatedcarrierwaveandthephaseisusuallyimposedandmeasuredwithrespecttoafixedknowncarriercalledcoherentcarrier.BinaryPSKusestwophaseswhichareseparatedby180degree.ThusitisthemoststablemodulationofallthePSKs.