ofdm实现文档.docx

ofdm实现文档.docx

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ofdm实现文档

Designoverview

TheOFDMtechnique（OrthogonalFrequencyDivisionMultiplexing）hasbeenusedinthelastyearsinapplicationsthatrequireahugetransmissionratelikeADSLmodem,wirelessnetwork（Wi-Fi802.11）,DVB（DigitalVideoBroadcasting）andDAB（DigitalAudioBroadcasting）.Inallthesecases,oneneedstoimplementanintegratedcircuit（IC）thatperformsthenecessarychipfunctions.ForprototypingcircuitsFPGAisbetterchoicethanusingASIC（applicationSpecificIntegratedCircuit）,CUSTOMorSEMICUSTOM.FPGAimplementationsbecauseavoidthe:

∙Initialcosts;

∙GreatdevelopmenttimeandtheinherentrisksofconventionalASIC.

So,inthisway,thedevelopmentofhighadvancedtechniquesofdigitaldatatransmissionandtheactualFPGAstageofintegrationmakepossiblethebuildingallthecircuitsthatcompoundsadigitalcommunicationsystemsinanuniquechip.

Tomakeuseofthismoderntechnologiesofdatatransmission,itisnecessarythedevelopmentefficienttechniquesofdigitalmodulation.TheOFDMisthebiggestutilizedrecently,principally,becauseofitusetheefficientFFTtodothemodulation.

ThisworkdescribeshowimplementanOFDMmodemonFPGAusingVHDLfora31subcarrier（channels）OFDMsystemusing64pointsradix-4FFTtimedecimation,aCORDICimplementationtoperformthebutterflycalculus,andeachchannelmodulationwillusea4-QAMconstellation.Thesystemisdividedinatransmissionsectionandareceptionsection.

Blockdiagram

Detaileddescription

Introduction

Basically,OFDMtechniqueconsistsofdividingtheflowofentrancedataoverorthogonalchannels.Inthisway,andbasedontheorthogonalityprinciple,theinterferencebetweeneachtransmissionchannelisminimal.Anotheradvantagethatcomesfromthisapproachisrelatedtotheassumptionsaboutthenoiseineachchannel.Overalargeanduniquepassbandchannelitisdifficult（impossibleinfact,inmanysituations）toassumethatthemodelnoiseisAWGN（AdditiveNoiseGaussianNoise）.Thatisimportantbecauseifthemodelisknow,anditiscorrect,onecanselectthebestwayoffrequencyequalization.But,inlargepassbandchannels（tenthsofMhz）thenoisemodelisunknownandunpredictable.Thesolutionofdividingauniquechannelinsubchannelssimplifiestheassumptionsofthenoiseovereachsubchanneland,ofcourse,onecansupposeitapproximatelyAWGN.

Ineachoneofthesesubchannels,adigitalmodulationismade,eachonewithasubcarrierthatpresentsdifferentfrequency,inasuchformthatachanneldoesnotintervenewithanotherone,thuskeepingtheorthogonallity.

Thewayofimplementationandtheorthogonallitypropertyofasystemofthistypecanvarysufficiently:

sincebandpassfilterseachfrequencyuntilsophisticatedtechniquesastheuseoftheFFTwithguardinterval,whichistheusedonefortheOFDM.

Inliterature,thistechniquehasbeencalledforsomedesignationsasorthogonallymultiplexedQAM（O-QAM）,parallelquadratureAM,andsoone.However,OFDMforwirelessandDMTforsystemswired（likeDSL）arethemostcommondesignationsthatonecanfindinliterature.Asalltheabovetechniquesbasicallyusethesameprinciple,itiscommontorefertothembymeansofagenericname:

MCM（toMulti-CarrierModulation）.Inthatway,MCMisthetechniqueinthegeneraldirection,andOFDMisrelatedtotheimplementationoftechniqueMCMusingtheFFT.

Implementation

Mappingtheconstellation

Theencoderoftheconstellationmapsthembitsofthechannelinapointa+jbintheconstellationofthemodulator.Decodingreceivesthatpointandtheremapasthemtransmittedbits.

Encoderoftheconstellation

Itisimportanttonoticethatinthatmappingitisjustmadeaconversionofbitsforthefasorthatacts,howeveritisnotmadeanymodulation,asinthecaseofQAM,becausethatasshown,itisdonebyIFFT.

Itisnecessarytospecifyhowtheconstellationwillbetobemapped,toimplementthatblock.However,independentlyoftheformatoftheconstellation,theblockencodercanbemadethroughaconsultationataconversiontable,implementedbyLUTthatexistsinLCsofFPGAs.

Forinstance,fora4-QAMconstellationinsuchawaythataandbarebinarynumbersof3bits,andareconvertedtocomplementtwo.

Attemptthattheentranceoftheencoderabinarynumberofmbits,andthattheexitgeneratestwobinarynumbers,oneinphase,the,andotherinquadrature,b,whosesizeisdefinedbyIFFT.

Decoderoftheconstellation

Inthereceiver,thepointoftheconstellationtransmitteditcanhavechangedduetothenoisesofthetransmissionchannel,mistakeinthetimeofsamplingofthereceiverandseveralothercauses.

Thereforeitisnecessarytodefineathresholdsothatitcanbemadethedecisiononwhichpointintheconstellationthereceivedsignisacting.Thatisthefunctionofthedecoder.

Forthesystemexemplifiedabovethebit0isconvertedfor010bandthebit1for110b.Inthatcase,thedecoderisimplementedinasimpleway,stickstothemostsignificant（thatindicatesthesign）bittodothedecoding,andgeneratingabinarynumberofmbitsagain.

Forsystemsinthattheconstellationdiagramislargerthan4-PSKitwillbenecessarytheimplementationofmoreadvancedmethods,likeaneuralnetwork.

TheHemetiansymmetry

AfterhavingmappedtheNchannelsitisappliedtheHermetiansymmetrysothatthemodulationcanbemadebyanIFFT.Itisgenerated2N+2channelsinsymmetry.

Inthereceiver,totheendoftheprocessingofFFT,theyaresenttothedecoderonlyNchannels,beingeliminatedthechannelsgeneratedduetoHermetiansymmetry.

TheHermetiansymmetryisimplementedinagreementwith

fork=1,2...,N-1,whereN=N+1.

Forinstance,totransmitN=3channels（d1,d2,d3）N=4,2N=8andk=1,2,3.Applyingintheaboveequationitisobtainedtheresultshowninthefollowingtable.

KnowingthatX0=XN=4=0+j0,isobtainedinagreementwiththeTable2theresultshowninthefollowingequation:

Inthatway,itcanstayX0andXNalwaysinzero.WhileitismadeXN+1evenX2n-isametotheconjugatedofXn-1.

BeingitconjugatedofZ=a+jbthesameofZ*=a-jb,thentodotheoperationofhavingconjugatedheshouldmovethesignoftheimaginarypart,inotherwords,todoasigninversion.Inhardware,theinversionofsignofabinarynumberincomplementtwo.

The（I）FFT

ThemodulationOFDMcanbemadethroughanIDFT.ThefastimplementationofIDFT,IFFT,canbeusedreducingthetimeofprocessingandtheusedhardware.Thedemodulation,inthesameway,canbemadebyDFT,orbetter,byFFT,thatisitefficientimplementation.

FFTcalculatesDFTwithagreatreductionintheamountofoperations,leavingseveralexistentredundanciesinthedirectcalculationofDFT.Thatefficiencyisgottenatthecostofanadditionalsteptoreverse-orderthedatainordertobedeterminedthefinalresult.Thatadditionalstep,sinceimplementedefficiently,theywon'tincreaseinasignificantwaythecomplexitycomputationalofthecalculation.Asresult,FFTisanextremelyefficientalgorithmthatprovidesagoodimplementationinhardware.

ForgreatvaluesofN,thecomputationalefficiencyisgottenbeingbrokenDFTsuccessivelyinsmallercalculations.Thatcanbemadesomuchinthedomainofthetime,asinthedomainofthefrequency,asdiscussedahead.

Decimationintimeandinfrequency

Asmentioned,itispossibletodividetheentranceofFFTsuccessivelygeneratingsmallsequenceinthedomainofthetime,forthatthenamedecimationinthetime,TD.ItisalsopossibletobecomeseparatedthesequenceofexitofFFTsuccessively,insteadofdividingtheentrance.Thatimplementationiscalledofdecimationinthefrequency,FD.ThedecimationcanbeusedsomuchforFFTasforIFFT.

Itispossibletorepeattheprocessuntilreachingthepossiblemaximumlevelofdivision.InthatpointthebasicblockdecimationisgeneratedsoitwillbeusedinthewholeFFT（calledbutterfly）.AnexampleofthebutterflyoftheFFTradix-2TDisinthefollowingillustration.

AnexampleofaFFTradix-2DT,forN=8areshownbelow.Itisnoticedthatisnecessaryanalterationintheentranceofdata,becausehe/shehastoseparatetheequalpartoftheoddpart.

Inthesamewaythatthedecimationinthetimegeneratesabutterfly,thedecimationinthefrequencygeneratesacorrespondingbutterfly.

Howeverthealterationintheflowofdatawillhavetobedoneintheexit,andnomoreintheentrance.

ImplementationofButterfly

Thesumusedinthebutterflypossessesthesamealgorithm,somuchforFFTasforIFFT.Toavoidoverflowdangerduetosumincomplementtwo,itismadetheextensionofthesigninthebinarynumber,repeatingthemostsignificantbit,likethistotheifitadds2binarynumbersof10bits,wewillhaveoffirsttodotheextensionofthesign,obtaininglikethis,twonumbersof11bits,todothesum,wheretheresultwillalsobeof11bits.Thatprocedurehastobedoneeverytimethatwilladdortosubtractanumber.

Alreadyforthemultiplication,theexithastobeofthesizeofthesumofthenumberofbitsofthetwomultiplicands.Inthatway,todothemultiplicationoftwonumbersof10bits,wewillhavetoanexitof20bits.Thatprocedurehastobedonetoeachmultiplication.

Ifthereisnotimpediment,itcanbemadearotationforright（divisionsfortwo）inthenumbersandtoreduceitssize,sinceintheendoftheprocedureacorrespondingmultiplierisapplied.

Theorderasitwillbemadethebutterflyisdefinedbythedecimationoftheradix.IfitgoesTD,firstitismademultiplicationandlaterthesum.IfitgoesFD,firstit