NILabVIEWModulationToolkitHelpVersion4.1August2008,370940F-01TheNILabVIEWModulationToolkitcontainsVIsthatcanbeusedwithNationalInstrumentshardwareorinasimulationenvironmenttogenerateandanalyzeanaloganddigitallymodulatedsignals.TheModulationToolkitsupportsASK,FSK,MSK,PSK,QAM,CPM,PAM,AM,FM,andPMmodulationformats,andiscapableofIFtoI/Qconversion,I/Qvisualization,andaddingcommonsignalimpairments.Formoreinformationaboutthishelpfile,refertothefollowingtopics:ConventionsRelatedDocumentationImportantInformationTechnicalSupportandProfessionalServicesTocommentonNationalInstrumentsdocumentation,refertotheNationalInstrumentsWebsite.©2002—2008NationalInstrumentsCorporation.Allrightsreserved.

RelatedDocumentationThefollowingdocumentscontaininformationthatyoumightfindhelpfulasyouusethishelpfile:

NIDocumentsNoteForinstructionsonprintingthishelpfile,clicktheSearchtabandtypeprint.NILabVIEWModulationToolkitReadme,installedatStart»AllPrograms»NationalInstruments»Modulation»LabVIEWSupport»ModulationReadme.ThisfilecontainsimportantinformationaboutmodulationVIs.ModulationToolkitexampleVIs,installedatStart»AllPrograms»NationalInstruments»Modulation»LabVIEWSupport»ModulationExamplesFolder.ThisfoldercontainsLabVIEWexampleswhichemployModulationToolkitVIs.YoucanalsobrowseallinstalledexamplesandtheirdescriptionsbyopeningLabVIEW,pullingdowntheHelpmenu,andnavigatingtoToolkitsandModules»Modulation.NISpectralMeasurementsToolkitReadme,installedatStart»AllPrograms»NationalInstruments»SpectralMeasurements»SpectralMeasurementsReadmethishelpfilecontainsimportantinformationaboutmodulationandSpectralMeasurementsToolkitVIs.SpectralMeasurementsToolkitUserGuide,installedinPDFformatatStart»AllPrograms»NationalInstruments»SpectralMeasurements.NILabVIEWSpectralMeasurementsToolkitHelp,installedatStart»AllPrograms»NationalInstruments»SpectralMeasurements»LabVIEWSupportNI-SCOPEVIReferenceHelp,containedintheNIHigh-SpeedDigitizersHelp,installedatStart»AllPrograms»NationalInstruments»NI-SCOPE»Documentation.NIRFVectorSignalAnalyzersHelp,availableatStart»AllPrograms»NationalInstruments»NI-RFSA»Documentation.NIRFVectorSignalAnalyzersGettingStartedGuide,printedandinstalledinPDFformatatStart»AllPrograms»NationalInstruments»NI-RFSA»Documentation.MAXRemoteSystemsHelp,availableinMeasurement&AutomationExplorer(MAX)byselectingHelp»HelpTopics»RemoteSystems.LabVIEWReal-TimeModuleUserManual,availableat

ni.com/manuals.YoucandownloadPDFversionsoftheSpectralMeasurementsToolkitUserGuideandtheNIRFVectorSignalAnalyzersGettingStartedGuideatni.com/manuals(linkopensinanewwindow).ThefollowingresourcescontaininformationaboutconceptsrelatedtotheModulationToolkit.

NoteThefollowingresourcesofferusefulbackgroundinformationaboutthegeneralconceptsdiscussedinthisdocumentation.Theseresourcesareprovidedforgeneralinformationalpurposesonlyandarenotaffiliated,sponsored,orendorsedbyNationalInstruments.Thecontentoftheseresourcesisnotarepresentationof,maynotcorrespondto,anddoesnotimplycurrentorfuturefunctionalityinanyotherNationalInstrumentsproduct.Leiner,BernhardM.J.LDPCCodes–abriefTutorialhttp://users.tkk.fi/pat/coding/essays/ldpc.pdf.2005.Lin,S.,andDJCostello,Jr.ErrorControlCoding:FundamentalsandApplications.EnglewoodCliffs:Prentice-Hall,1983.McEliece,RobertJ.FiniteFieldsforComputerScientistsandEngineers(TheKluwerInternationalSeriesinEngineeringandComputerScience).NewYork:SpringerPublishers,1986.Oerder,Martin,andHeinrichMayer."DigitalFilterandSquareTimingRecovery."IEEETransactionsonCommunications36(5):1988.Premji,Al-Nasir,andDesmondPTaylor."ReceiverStructuresforMulti-hSignalingFormats."IEEETransactionsonCommunications35(4):1987.Richardson,ThomasJ.,andRüdigerL.Urbanke."EfficientEncodingofLow-DensityParity-CheckCodes."IEEETransactionsonInformationTheory47(2):2001.Shokrollahi,Amin.LDPCCodes:AnIntroductionhttp://www.ipm.ac.ir/IPM/homepage/Amin2.pdf.2003.Smith,StevenW.TheScientistsandEngineersGuidetoDigitalSignalProcessing.CaliforniaTechnicalPublishing,1997.Press,WilliamH.,ed.,andTeukolsky,SaulA.,ed.NumericalRecipesinC:TheArtofScientificComputing.2nded.

Cambridge:CambridgeUniversityPress,1992.Proakis,JohnG.,andMasoud,Salehi.CommunicationsSystemsEngineering.UpperSaddleRiver:PrenticeHall,1994.Sharon,E.,S.Litsyn,andJ.Goldberger."AnEfficientMessagePassingScheduleforLDPCDecoding."Proceedingsofthe23rdIEEEConventionofElectricalandElectronicsEngineersinIsrael2004.Sklar,Bernard.DigitalCommunications:FundamentalsandApplications.2nded.EnglewoodCliffs:Prentice-Hall,2001.Sun,Jian.AnIntroductiontoLowDensityParityCheck(LDPC)Codes.WirelessCommunicationResearchLaboratory,LaneDept.ofComp.Sci.andElec.Engr.,WestVirginiaUniversity.Wicker,StephenB.ErrorControlSystemsforDigitalCommunicationsandStorage.EnglewoodCliffs:PrenticeHall,1995.

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DigitalCommunicationSystemFundamentalsAtypicaldigitalcommunicationsystemincludesatransmitter,areceiver,andacommunicationchannel.Thefollowingfigureillustratesthegeneralcomponentsofadigitalcommunicationsystem.Thetransmittercontainsblocksforsourceandchannelcoding,modulation,simulatingreal-worldsignalimpairments,andupconversion.Thereceiverincludesblocksfordownconversion,matchedfiltering,equalization,demodulation,andchannelandsourcedecoding.Youcanquantifytheresultsusingtoolsformeasurementandvisualization.

DecodingDatadecodinginvolvesremovingredundantbitsfromthesequenceandcorrectingforanyerrorsthatmighthavehappenedduringtransmission.Thesignaldecodingprocessisusuallymorecomplicatedthantheencodingprocessandcanbeverycomputationallyintensive.Howeverefficientdecodingschemeshavebeendevelopedovertheyears—oneexampleistheViterbidecodingalgorithm,whichisusedtodecodeconvolutionallyencodeddata.ThefollowingVIsareusedinchanneldecoding:

MTHammingDecoderMTGolayDecoderMTReed-SolomonDecoderMTBCHDecoderMTConvolutionalDecoderMTDespreadSymbolsMTLDPCDecoder

DemodulationThedownconvertedsignalundergoesademodulationprocess.Thisstepistheoppositeofmodulationandreferstotheprocessrequiredtoextracttheoriginalinformationsignalfromthemodulatedsignal.Theprocessofdigitaldemodulationinvolvesmatchedfiltering,symboltimingextraction,andsymbolsynchronizationfollowedbyfrequencyoffsetcorrection.Thefrequency-offset-correctedsignalisdecimateddowntosymbol-spaceddata,whichisthenmappedbacktoarecoveredbitstream.ThefollowingVIsareusedinanalogdemodulation:

MTDemodulateAMMTDemodulateFMMTDemodulatePM

Digitaldemodulationreturnsthetime-aligneddemodulatedwaveform,thedemodulatedinformationbitstream,andmeasurementresultsobtainedduringdemodulation.ThefollowingVIsareusedindigitaldemodulation:

MTDemodulateASKMTDemodulateFSKMTDemodulateMSKMTDemodulatePAMMTDemodulatePSKMTDemodulateQAMMTDemodulateCPM

NoteUsethefollowingVIsifyourapplicationrequiresonlythedemodulatedbitstream.MTDetectASKMTDetectFSKMTDetectMSKMTDetectPAMMTDetectPSKMTDetectQAMMTDetectCPM

DownconversionThefirststepinthedemodulationprocessisdownconversionfromarealpassbandwaveformtoacomplexI/Qbasebandwaveform.Thisprocessinvolvesmixingthereal-valuedpassbandwaveformwithalocallygeneratedcarriertone,followedbylowpassfilteringtogeneratetheI/Qbasebandwaveform.UsetheMTDownconvertPassbandVItodownconvertwaveforms.

EncodingAdatasourcegeneratestheinformationsignalsenttoaparticularreceiver.Thissignalmaybeeitherananalogsignal,suchasspeech,oradigitalsignal,suchasabinarydatasequence.Theinformationsignalistypicallyabasebandsignalrepresentedbyavoltagelevel.TheSourceCodingblocktypicallyinvolvesdatacompression.Forexample,theATSCstandardfordigitalvideobroadcast(DVB)specifiesMPEGIIencodingforthetransmittedimage.A-law,Mu-law,JPEG,A-87.6areexamplesofothercompressionalgorithmscommonlyusedinsourcecoding.TheChannelCodingblocktypicallyinvolvesaddingredundantbitstothedatastreamtoincreasethereceiver'simmunitytonoiseandinterferenceinthechannel.TheoutputoftheChannelCodingblockisaseriesof0sand1s.Amongthemostpopularerror-correctingschemesareblockandconvolutionalcoding.

NoteTheModulationToolkitdoesnotcurrentlysupportsourcecoding.YoucanuseLabVIEWVIsandprimitivestoapplysourcecodinginyourapplication.

TheModulationToolkitprovidesthefollowingVIsforchannelcoding:MTHammingEncoderMTGolayEncoderMTReedSolomonEncoderMTBCHEncoderMTConvolutionalEncoderMTSpreadSymbolsMTLDPCEncoder

DirectSequenceSpreadSpectrum(DSSS)Directsequencespreadspectrum(DSSS)isaprocessbywhichdataistransmittedusingahigherbandwidthsignalthatisdemandedbythedatarate.UsingDSSSallowsmultiplechannelstooccupythesamebandwidth,thusmitigatinginterferencefromotherusersattheexpenseofbandwidthexpansion.DSSSspreadseachbitofsignaldataatthetransmitterintoLchipsusingapseudorandomL-chipspreadingcodecalledacodeword.ThelengthLofthepseudorandomspreadingcodeisalsoknownasthebandwidthexpansionfactorbecausethechipsaretransmittedatarateequaltoL×bitrateofthedata.Thespreadingcodeappearsrandomtoallreceiversexcepttheintendedone,whichusestheknowledgeofthespreadingcodetodemodulateandrecoverthetransmittedinformation.Thusmultiplechannelscanoccupythesameportionofthefrequencyspectrumbyusingcodewordsthathavelittleornocorrelationwithoneanother,andlittleornoautocorrelationforanyshiftotherthanzero.Mathematically,aDSSSsignalisdescribedby

wherey(T)isthetransmittedDSSSsignalg(T)isthepulse-shapingsignalofdurationTcanisthenthinformationbearingsymbolcmisthemthelementoftheL-longpseudorandomspreadingcode(alsoknownasthechipsequence)TcisthechipperiodT=L×Tcisthesymbolperiod

Low-DensityParityCheck(LDPC)EncodingLow-densityparitycheck(LDPC)isalinearerror-correctingcodethatusesaparitycheckmatrixthatprovidesonlyafew1swithrespecttoamuchlargernumberof0s.Themainadvantageoftheparitycheckmatrixisthatitprovidesaperformancethatisclosetothecapacityofmanydifferentchannelsandlineartimecomplexalgorithmsfordecoding.Furthermore,paritycheckmatricesaresuitedforimplementationsthatmakeheavyuseofparallelism.AnLDPCcodeisablockcodethathasaparitycheckmatrixH,everyrowandcolumnofwhichissparse.ARegularGallagerCodeisaLDPCcodeinwhicheverycolumnofHhassomeweight,j,andeveryrowhassomeweight,k.RegularGallagercodesareconstructedatrandomsubjecttotheseconstraints.Forexample,if

thenumberofonesineachcolumn(j)=3thenumberofonesineachrow(k)=6thenumberofcolumns(n)=12thenumberofrows(m)=6(becausem=n*j/k)therateof(n,j,k)LDPCCodeisR≥1-(j/k)

Then

Ifthenumberof1spercolumnorrowisnotconstant,thecodeisanirregularLDPCcode.Usually,irregularLDPCcodesoutperformregularLDPCcodes.RefertothefollowingresourcesformoreinformationaboutthealgorithmsandmethodsusedinLDPCcoding:

BernhardM.J.Leiner,"LDPCcodes-aBriefTutorial,"April2005.http://users.tkk.fi/pat/coding/essays/ldpc.pdfShokrollahi,Amin.LDPCCodes:AnIntroduction.DigitalFountain,Inc.Fremont:2004.

http://www.ipm.ac.ir/IPM/homepage/Amin2.pdfRichardson,ThomasJ.andRüdigerL.Urbanke."EfficientEncodingofLow-DensityParity-CheckCodes."IEEETransactionsonInformationTheory47(2):2001.Thefloodingdecodingalgorithmisaccordingtofollowingreference:Sun,Jian."AnIntroductiontoLowDensityParityCheck(LDPC)Codes."WCRLSeminarSeriesWirelessCommunicationResearchLaboratory,WestVirginiaUniversity:2003.Theserialdecodingalgorithmisaccordingtofollowingreference:Sharon,E.etal."AnEfficientMessagePassingScheduleforLDPCDecoding."200423rdIEEEConventionofElectricalandElectronicsEngineersinIsrael23:2004.

EqualizationTheModulationToolkitemploysanadaptivefeed-forwardequalizer,whichimpliesthattheequalizertapscontinuouslyadaptsitscoefficientstocompensatefortheactionofthechannelfilter.Theadaptivefeed-forwardequalizerusesafeed-forwardadaptiveleast-mean-squared(LMS)algorithmtoadjusttheequalizertaps.Atthestartoftheequalizationprocess,youmustsupplytrainingbitstotraintheequalizer.Aftertraining,theequalizerswitchestodecision-directedfeedbackmode,wheretheequalizertrainsitselfbasedonitsowndecisions.ThefollowingaretypesofdigitalfeedforwardequalizationVIs:

ASKPAMPSKQAM

FilteringInadigitalcommunicationsystem,digitalinformationcanbesentonacarrierthroughchangesinitsfundamentalcharacteristicssuchasphase,frequency,andamplitude.Inaphysicalchannel,thesetransitionscanbesmoothed,dependingonthefiltersimplementedduringtransmission.Infact,filtersplayanimportantpartinacommunicationschannelbecausetheycaneliminatespectralleakage,reducechannelwidth,andeliminateadjacentsymbolinterferenceknownasinter-symbolinterference(ISI).Thematchedfilterisasimportantasthepulse-shapingfilter.Thoughthepulse-shapingfiltergeneratessignalssuchthateachsymbolperioddoesnotoverlap,thematchedfilterisimportantbecauseitfiltersoutthesignalreflectionsthatoccurinthetransmissionprocess.Becauseadirect-pathsignalarrivesatthereceiverbeforeareflectedsignaldoes,itispossibleforthereflectedsignaltooverlapwithasubsequentsymbolperiod.Thematchedfilterreducesthisaffectbyattenuatingthebeginningandendingofeachsymbolperiod.Thus,itcanreduceISI.TheModulationToolkitprovidesthefollowingtypesoffilters:

RaisedcosineRoot-raisedcosineGaussianpulse-shapingandmatchedfilters

FilterDelayModulationToolkitusesfiniteimpulseresponse(FIR)filtersfordifferentoperationslikepulse-shaping,matched,anddownconversionfiltering.Forsuchfilters,theoutputsignalisrelatedtotheinputsignalasshownbythefollowingequation:y[n]=b0x[n]+b1x[n-1]+...+bPx[n-P]

wherePisthefilterorderx[n]istheinputsignaly[n]istheoutputsignalbiarethefiltercoefficients

TheinitialstateforallsamplesinanFIRfilteris0.Thefilteroutputuntilthefirstinputsamplereachesthemiddletap(thefirstcausalsample)iscalledthetransientresponse,orfilterdelay.GivenanFIRfilterwhichhasNtaps,thedelayis(N-1)/2samples.Thisrelationshipisillustratedinthefollowingfigure,whereasinewaveisfilteredbyanFIRfilterwith50taps.

UsingtheReset?ParameterinIterativeModulator/DemodulatorOperationIntheModulationToolkit,digitalmodulationVIsinitiallyperformmappingoftheinputbitsontosymbolsandsubsequentlyapplyapulse-shapingfiltertothesesymbols.ThedigitaldemodulationVIsperformmatchedfilteringandbufferingontherecoveredcomplexwaveform.Someusefulsamplesareheldinthesefilters.Inaniterativeoperationwherethemodulator/demodulatoriscalledrepeatedlyinsidealooptooperateonblocksofbits/symbols(allofwhicharepartofthesamemessage),twooptionsarepossible:

reset?issettoTRUEoneveryiteration—Thefiltersinthemodulator/demodulatorareinitializedwithzerosoneveryiterationoftheloop,andthereturnedoutputdataisshortenedby(N-1)/2symbolsonalliterations.reset?issettoTRUEonthefirstcallandtoFALSEonsubsequentiterations—Thefiltersinthemodulator/demodulatorareinitializedwithzerosonthefirstiterationoftheloop.Onsubsequentiterationsoftheloop,theVIusesstateinformationfrompreviousiterationstoinitializethefilter.

RecoveringSamplesinSingleShotOperationsInsingle-shotoperationsformodulatorsanddemodulators,thefilterdelayistruncatedbeforethesignalisgeneratedbecausethesesamplesarenotvalid.Somesamplesattheendoftheblockdonotappearatthemodulator/demodulatoroutput,andhenceappeartohavebeenlost.Youcanrecoverthesesamplesbysendingextrasamplestothemodulator/demodulator.Todeterminehowmanyextrasamplesyoumustadded,usethefollowingguidelines:

ForModulationVIs—LetL=pulse-shapingfilterlength,m=numberofsamplespersymbol,andM=modulationorder.Thenumberofbitstobeaddedtotheinputbitstreamisgivenbythefollowingformula:

ForDemodulationVIs—ThedemodulationVIsusefiltersduring

matchedfiltering.LetLbethelengthofthematchedfilter.Thenumberofsamplestobeaddedtotheinputsignalpriortofilteringisgivenbythefollowingformula:

TheNextrasamplesareobtainedbyrepeatingthelastsamplevalueoftheinputsignalNtimestoensuresignalcontinuity.

WorkingwithFilterDelayinModulationToolkit4.1ModulationThemodulationVIsinModulationToolkit4.1containanewparameter,flushbuffers?,thatallowsyoutoflushoutsamplesthathavebeendelayedinthepulse-shapingfilter.WhenthisparameterissettoTRUE,theVIinternallypadstheinputdatatorecoveranylostdata.SetthisparametertoTRUEforsingle-shotapplicationsandduringthelastiterationofacontinuousoperationapplication.DemodulationModulationToolkit4.1providestwomethodsfordemodulation:demodulationVIsanddetectorVIs.ThedemodulationVIscontainthesamebehaviorasinModulationToolkit4.0,thatis,theyallowyoutorecoverthetime-aligneddemodulatedwaveform,thedemodulatedinformationbitstream,andmeasurementresultsobtainedduringdemodulation.ThedetectorVIsreturnonlythedemodulatedbitstream.ThesenewVIscontaintheflushbuffers?parameterthatpadstheincomingsamplesandforcesoutthesamplesdelayedbecauseoftheFIRfiltersusedinthedemodulationalgorithms.

NoteSettingflushbuffers?toTRUEdestroystheinternalstatesofthealgorithmssuchthatyouwillbeunabletoperformcontinuousprocessingonthesignalduringsubsequentiterations.Ifflushbuffers?issettoTRUE,youmustsetreset?toTRUEonthesubsequentiteration.

ImpairmentsAlltransmissionmedia(includingwireless,fiberoptic,andcopper)introducesomeformofdistortiontotheoriginalsignal.Differenttypesofchannelmodelshavebeendevelopedtomathematicallyrepresentsuchreal-worlddistortions.TheModulationToolkitcangenerateamodulatedmessagesignalandoptionallyaddnoise,impairments,andchannelmodels.TheModulationToolkitcanaddthefollowingtypesofimpairments:

AWGNMultiToneI/QImpairmentsPhaseNoiseGenerateFadingProfileFadingProfile

DCOffsetDCoffsetisacomplexsignalimpairmentthatshiftsthelocusofidealsymbolcoordinatesoff-centerintheI/Qplane.ADCoffsetcanbeaddedtothebasebandIcomponent,theQcomponent,orboth.TheDCoffsetcanbeeitherpositiveornegative,withthesignindicatingthedirectionoftheshift.DCoffsetisexpressedasapercentageoffullscale,where"fullscale"(fs)istheamplitudeofthebasebandquadraturemodulation(QM)waveform.IndividualIandQOffsets

CombinedIandQOffset

FrequencySelectiveFadingYoucanusefrequency-selectivefadingtomodeldiscretemultipathwirelesschannelsthataredynamicinbothspaceandtime.Theinput-outputrelationshipforadiscretemultipathmodelisgivenbythefollowingequation:

wherey(t)isthereceivedsignalak(t)isthecomplexpathattenuation,whichismodeledasarandomprocesswithaprobabilitydistributionthatisRayleighorRicianfork=1,,N(t)N(t)isthenumberofpathsinthemultipathchannel(t)istheircorrespondingdelays

tistimeTheRayleighfadingprofilecanbeimplementedusingJakesorGansmodels.Ifthechannelmodelhasaline-of-sightpath,theenvelopeofthedominantpath(thatis,thefirstpath)isRiciandistributed.RicianprofilesalsocanbeimplementedusingJakesorGansmodels.Ifweassumethatthenumberofmultipathcomponentsandthedelaystructurevaryslowlycomparedtothevariationsinak(t),thepreviousrelationshipcanberewrittenasthefollowingequation:

Thistypeofsystemisalineartimevariant(LTV)systemandcanbeimplementedusingatappeddelaylinestructureasillustratedinthefollowingfigure:

TheselectivefadingprofileinstancesoftheMTGenerateFadingProfileVIgenerateRayleighorRiciandistributedfadingprofilesforthespecifiednumberofpathsbasedontheJakesorGansmodel.Thegeneratedfadingprofileisatwo-dimensionalarrayinwhichthenumberofrowsisequaltothenumberofpaths,andthenumberofcolumnsisequaltotheprofilelength.ThegeneratedprofileispassedtotheMTApplySelectiveFadingProfileVI.

PhaseNoisePhasenoisereferstonoiseinacarriersignalduetophaseandfrequencymodulationinthesignal.Phasenoiseisnormallyveryclosetothecarrierandismeasuredindecibelsrelativetothecarrierfrequency(dBc).Phasenoiseisexpressedasafunctionofpowerspectraldensityandfrequency.Ina1Hzbandwidth,phasenoiseisgivenby

=10log[0.5(SΦ(ƒ))]ΦwhereSΦ(ƒ)isthespectraldensityofphasefluctuations.

MeasurementCommunicationsengineersusedifferenttoolstoevaluatehowwellthetransmitteddatawasreceived.Biterrorrate(BER)andmodulationerrorratio(MER)arecommonmetricsforthisjob.ThefollowinglistillustratesthetypesofmeasurementsthatcanbeperformedwithModulationToolkitVIs.

CalculateBitErrorRate(BER)AfterTrigger:BERAccumulatedBERTriggerFoundIndex

DigitalDemodulation:QAM,ASK,PAM,PSK:FrequencyOffset,FrequencyDrift,PhaseOffsetFSK:FrequencyOffset,FrequencyDrift,DeviationError,FSKErrorMSK:FrequencyOffset,FrequencyDrift

MeasureQuadratureImpairments:I/QGainImbalance,QuadratureSkew,MagnitudeError,EVM,PhaseError,MERDCOffsets:I,Q,Origin

MeasureRho(ρ)MeasureBurstTiming

AmplitudeDroop,CrestFactor

AmplitudeDroopAmplitudedroop,measuredindB,isameasureoftheamountthatthesignalpowerfallsfromthestartofaspecifiedmeasurementwindow(di)totheendofthatwindow(df).

BitErrorRate(BER)Biterrorrate(BER)istheratiooferroneousbitstototalbitstransmitted,received,orprocessedoversomestipulatedperiod.TransmissionBERexpressesthenumberoferroneousbitsreceiveddividedbythetotalnumberofbitstransmitted.InformationBERexpressesthenumberoferroneousdecoded(corrected)bitsdividedbythetotalnumberofdecoded(corrected)bits.

DeviationErrorForanM-FSKsystem,theaveragedeviationerrorisdefinedastheaveragespreadmagnitudeoftheFSKdemodulatedsymbolspacedwaveformaroundtheidealsymbol(frequency)locations.Mathematically,thedeviationerrorisdefinedas

whereMistheFSKmodulationformat,ƒideal,iistheidealsymbollocationattheFSKfrequencycorrespondingtolocationi,and<ƒactual,i>isthemeanvalueofthedemodulatedsymbolsatlocationi.

Intheprecedingfigure,thehorizontallinesrepresenttheactualFSKdemodulatedsymbollocations,andtheverticallinesrepresenttheidealsymbollocationsfora4-FSKformat.

ErrorVectorMagnitude(EVM)Errorvectormagnitude(EVM)isameasurementofdemodulatorperformanceinthepresenceofimpairments.Thesoftsymboldecisionsobtainedafterdecimatingtherecoveredwaveformatthedemodulatoroutputarecomparedagainsttheidealsymbollocations.Therootmeansquare(RMS)EVMandphaseerrorarethenusedindeterminingtheEVMmeasurementoverawindowofNdemodulatedsymbols.Asshowninthefollowingfigure,thesymboldecisiongeneratedbythedemodulatorisgivenby .However,theidealsymbollocation(usingthesymbolmap)isgivenby .Therefore,theresultingerrorvectoristhedifferencebetweentheactualmeasuredandidealsymbolvectorsgivenby = – .Theerrorvector forareceivedsymbolisgraphicallyrepresentedbythefollowingfigure:

whereistheidealsymbolvectoristhemeasuredsymbolvector isthemagnitudeerrorθisthephaseerror= – istheerrorvector/ istheEVM

EVMquantifies,butdoesnotnecessarilyrevealthenatureoftheimpairment.Toremovethedependenceonsystemgaindistribution,EVMisnormalizedby|v|,whichisexpressedasapercentage.Analytically,RMSEVMoverameasurementwindowofNsymbolsisdefinedas

whereIjistheIcomponentofthej-thsymbolreceivedQjistheQcomponentofthej-thsymbolreceivedistheidealIcomponentofthej-thsymbolreceivedistheidealQcomponentofthej-thsymbolreceived

EVMisrelatedtothemodulationerrorratio(MER)andρ.EVMandMERhaveaone-to-onerelationship.EVMmeasuresthevectordifferencebetweenthemeasuredandidealsignals,whileρmeasuresthecorrelationbetweenthetwosignals.

FrequencyDeviationFrequencydeviationquantifiestheamountthatafrequencydiffersfromitsspecifiedvalue,aswhenmeasuringhowmuchanoscillatorfrequencydeviatesfromitsnominalfrequency.Infrequencymodulation,frequencydeviationreferstothemaximumabsolutedifference,duringaspecifiedperiod,betweentheinstantaneousfrequencyofthemodulatedwaveandthecarrierfrequency.

FrequencyError,QuadratureModulation(QM)Inquadrature-modulated(QM)systems,frequencyerrorreferstothedifferencebetweenthespecifiedcarrierfrequencyandtheactualmeasuredcarrierfrequency.Atbasebandfrequencies,frequencyerrorinQMsystemsisacomplexsignalimpairmentthatmanifestsitselfasarotationofthelocusofsymbolcoordinatesabouttheI/Qplane.Afixedfrequencyoffsetappearstobearotationataconstantangularvelocity.Frequencyerrorcanbeeitherpositiveornegativeinsign,indicatingthedirectionoftherotation.

FrequencyShift-Keying(FSK)ErrorForanM-aryFSKsystem,theaverageFSKerrorisdefinedastheaveragerootmeansquared(RMS)spreadoftheFSKdemodulatedsymbolspacedwaveformaroundtheidealsymbol(frequency)locations.Mathematically,theFSKerrorisdefinedas

whereMistheFSKmodulationformatƒideal,iistheidealsymbollocationattheFSKfrequencycorrespondingtolocationiƒactual,irepresentsthevalueofthedemodulatedsymbolsatlocationi

Intheprecedingfigure,thepointsrepresenttheactualFSKdemodulatedsymbollocations,andtheverticallinesrepresenttheidealsymbollocationsfora4-FSKformat.

I/QGainImbalanceI/QgainimbalancereferstoadifferenceinscalingbetweentheIandQcomponentsofI/Qdata.WhenexpressedindB,I/Qgainimbalancecanbeeitherpositiveornegative,withthesignindicatingwhichcomponenthasbeenimpaired.

MagnitudeError,FrequencyShift-Keying(FSK)InFSK-modulatedsystems,magnitudeerrorreferstothedifferencebetweentheidealmagnitudeoftheI/Qsignalandtheactualmeasuredmagnitudeonasymbol-by-symbolbasis.For2-FSKsystems,forexample,themagnitudeerrorεmisdefinedastheaverageofthespaceandmarkmagnitudeerrorsasshowninthefollowingequation:

where

foralli.

MagnitudeError,QuadratureModulation(QM)Inquadraturemodulated(QM)systems,magnitudeerrorreferstothedifferencebetweentheidealmagnitudeoftheI/Qsignalandtheactualmeasuredmagnitudeonasymbol-by-symbolbasis.MagnitudeerrorinQMsystemscausesthelocusofsymbolcoordinatestoeithermoveawayfromtheoriginandexpandortowardtheoriginandshrink.MagnitudeerroraffectsboththeIandQcomponentssimultaneouslyandcanbeeitherpositiveornegative,indicatingmagnitudegainorattenuation,respectively.

ModulationErrorRatio(MER)Themodulationerrorratio(MER)isameasureofthesignal-to-noiseratio(SNR)inadigitallymodulatedsignal.LikeSNR,MERisusuallyexpressedindB.MERoverNnumberofsymbolsisdefinedas

whereIjistheIcomponentofthej-thsymbolreceivedQjistheQcomponentofthej-thsymbolreceivedistheidealIcomponentofthej-thsymbolreceivedistheidealQcomponentofthej-thsymbolreceived

PhaseDeviationInphasemodulation,phasedeviationquantifiesthemaximumdifferencebetweentheinstantaneousphaseangleofthemodulatedwaveandthephaseangleoftheunmodulatedcarrierwave.

PhaseErrorInaquadraturemodulated(QM)system,phaseerror(shownasθintheequationbelow)occurswhenthemeasuredphaseofthereceivedsymbolsdeviatesfromtheidealphasevalues.Ifthesymbolsequenceisd0,d1,d2,...,dN-1,thenthesequenceofphaseerrorsisθ0,θ1,θ2,...,θN-1.ThepeakphaseerrorovertheNsymbolsisexpressas

θpeak=max(θi)i=0,1,2,...,N-1

andtheRMSphaseerroroverNsymbolsis

QuadratureErrorInaquadraturemodulated(QM)system,quadratureerror,alsoreferredtoasquadratureskew,describesacomplexsignalimpairmentsuchthattheIandQcomponentsarenotperfectlyorthogonal.Quadratureerrorcanbeeitherpositiveornegative,withthesignindicatingtheorientationoftheerror.

Rho(ρ)ρisameasurementthatevaluatesmodulationquality.Itiscalculatedbyfindingthecorrelationbetweentherecoveredwaveformandanidealwaveformthathasbeenreconstructedfromthedemodulatedbits.Thatis,thereceiveddemodulatedwaveformiscomparedtoanidealwaveformobtainedbyremodulatingtheoutputbitstreamofthedigitaldemodulationVI.TheρmeasurementisrelatedtoEVMbecauseEVMmeasuresthevectordifferencebetweenthemeasuredandidealsignals,whileρmeasuresthecorrelationbetweenthetwosignals.Thevalueofρcanrangefrom0.0to1.0.Thefollowingtableillustratestherangesforρanddegreeofcorrelationbetweenmeasuredandidealsignals.

ρ=0.0 uncorrelated0.0<ρ<1.0 partiallycorrelatedρ=1.0 perfectlycorrelated

ModulationThemodulationblockconvertstheinformationsignalbitstreamintoin-phase(I)andquadrature-phase(Q)datacomponents.Thisblocktypicallyalsoinvolvespulseshapingtominimizeintersymbolinterferenceandreducebandwidth.Dependingonthetypeofinformationsignalandtheparticulartransmissionmedium,differentmodulationtechniquesareemployed.Forexample,inamplitudemodulation(AM),theinformationisrepresentedbyamplitudevariationsofthecarriersignal.TheModulationToolkitsupportsthefollowingtypesofanalogmodulation:

AMFMPM

TheModulationToolkitalsosupportsthefollowingtypesofdigitalmodulation:

ASKFSKMSKPAMPSKQAMCPM

ModulationFundamentalsExpandthisbookformoreinformationaboutmodulationterminologyandsignalanalysisfundamentals.

AngleModulationAnglemodulationvariestheangleofacarrierwaveaccordingtotheamplitudeofthemodulatingbasebandsignal(themessagesignal).Theamplitudeofthecarrieriskeptconstant.Phasemodulationandfrequencymodulationareparticulartypesofanglemodulation.Anglemodulationcanbeexpressedusingthefollowingequation:

whereAcisthecarrieramplitudefcisthecarrierfrequencykfisthefrequencydeviationconstantinHz/Vfmisthefrequencyofthemessagesignal

BasebandThebasebandistherangeinthefrequencyspectrumoccupiedbytheunmodulatedmessagesignal.BoththemessagesignalandthedownconvertedcomplexI/Qsignalarereferredtoasbasebandsignals.RefertotheNIDeveloperZoneatni.com/zoneformoreinformationaboutbasebandsignals.

CarrierWaveThecarrierwaveisasinewavethatismodulatedbyamessagesignalpriortotransmission.Themessagesignalmodifiesthecarrierwaveamplitude,frequency,orphasepriortotransmission.Duringmodulation,thesecharacteristicsmaybevariedindividuallyorincombination.Themodifiedcarriersignal,alsoreferredtoasthemodulatedwave,istransmittedtoareceiver.

Themessagesignaldatainthereceivedmodulatedwaveisrecoveredbyremovingthecarriersignalthroughdemodulation.Inadvancedcommunicationsystems,thecarriermaybeamovingsignal,alsoknownasaspreadspectrum.Whenthecharacteristicsofthecarriersignalaredeterministicandknownbythereceiver,virtuallyanytypeofcarriersignalcanbeused.

Thenominalfrequencyofthecarrierwaveisthecarrierfrequency.Infrequencymodulation,thecarrierfrequencyisthecenterfrequency.

Carson'sRuleCarson'sruledefinestheapproximatemodulationbandwidthrequiredforacarriersignalthatisfrequency-modulatedbyaspectrumoffrequenciesratherthanasinglefrequency.TheCarsonbandwidthruleisexpressedbytherelationCBR=2(Δf+fm),whereCBRisthebandwidthrequirement,Δfisthecarrierpeakdeviationfrequency,andfmisthehighestmodulatingfrequency.

CCDFMeasurementThecomplementarycumulativedistributionfunction(CCDF)isastatisticalcharacterizationofthetime-domainwaveformthatcompletelydescribesthepowercharacteristicsofasignal.ACCDFgraphrelatesaveragesignalpower(Xaxis)tosignalpowerstatistics(Yaxis)suchthateachpointontheCCDFcurveshowshowmuchtimeasignalspendsatoraboveagivenpowerlevel.ThepowerlevelisexpressedindBrelativetotheaveragesignalpowerlevel.

CenterFrequencyThecenterfrequencyisthemiddlefrequencyofthechannelbandwidth.Infrequencymodulation,thecenterfrequencyisequaltotherestfrequency—specifically,thefrequencyoftheunmodulatedcarrierwave.

DemodulationDemodulationdescribestherecovery,fromamodulatedwave,ofasignalhavingthesamecharacteristicsastheoriginalmessagesignal.

FrequencyFrequencyreferstoabasicunitofratemeasuredineventsoroscillationspersecond.Frequencyalsoreferstoanumberrepresentingaspecificpointintheelectromagneticspectrum.Thefollowinggraphillustratesoneperiodofasinewave.

Frequencycanberepresentedaccordingtothefollowingequation:

whereTistheperiodofoneoscillation.

RefertotheNIDeveloperZoneni.com/zoneformoreinformationaboutfrequency.

IntermediateFrequency(IF)Theintermediatefrequency(IF)isanintermediatesignalthatistheproductoftheRFdownconversionprocess.AnRFsignalisconvertedtoanIFsignaltobedigitized,demodulated,displayed,orprocessed.Forexample,theNIPXI-5600downconvertermoduleconvertsRFsignalstoIFsignalsinabandbetween5–25MHz.

I/QDataI/Qdataisanalternativemethodofdescribingthemagnitudeandphasedataofasignal.Asinusoidalwavecanbewritteninpolarcoordinateformasshowninthefollowingequation:f(t)=Acos(2 ft+φ)

whereAistheamplitude2 fisthefrequencyφisthephase

AsinusoidalwavecanalsoberepresentedinacomplexCartesiancoordinatesystembyitsrealandcomplexcomponentssuchthatthein-phase(I)componentcanbewrittenasI(t)=Acos(φ)cos(2 ft)

andthequadrature(Q)componentcanbewrittenasQ(t)=Asin(φ)sin(2 ft)

Graphically,IandQprojectionsofthepolarcoordinatesinusoidalwaveareonthexandyaxis,respectively,asillustratedinthefollowinggraph.

Intheprecedingfigure,thesinusoidalwavefrequencyisshownastherotationalrateofthevector aroundthecircle.Thevectormagnitude(M)isgivenby

M=(I(t)2+Q(t)2)1/2

andthevectorphaseisgivenby

φ=tan–1(Q/I).

Whilemagnitudeandphasedataseemmoreintuitive,hardwaredesignconcernsmakeIandQdatathebetterchoiceforRFwaveforms.I/Qrepresentationprovidesaneffectivewaytovisualizeandmeasurethequalityofmodulation.ThefollowingfigureisagenericblockdiagramofanI/Qdemodulator,whichtakesanRFsignalandseparatesouttheIandQcomponentfromthatincomingRFsignal.ThefollowingfigureisagenericblockdiagramofanI/Qdemodulator.

Thecircleswithan'X'representmixers.TheI/Qmodulatorisrepresentedhereaspartofadownconvertermodule.Theincomingmessagesignalsplitsandonesignalismultipliedbyanin-phasecarriersignal(I)whiletheothersignalismultipliedbyaquadraturesignal(Q).Thismultiplicationseparatesthein-phaseandquadraturecomponentsfromtheincomingsignal.

MessageSignal/InformationSignalThemessagesignal,orinformationsignal,containsthedatafortransmission.Themessagesignalisusedtomodulatethecarrierwavetocreatethemodulatedwavefortransmission.Themessagesignaldataisrecoveredfromthemodulatedwavebyaprocessofdemodulation.Themessagesignalisoftenreferredtoasthebasebandsignal.

ModulatedWaveThemodulatedwave,ormodulatedsignal,referstothesignalfortransmissionthatconsistsofthecarrierwavemodulatedbythemessagesignal.Themessagesignalisrecoveredbythereceiverthroughaprocessofdemodulation.Typically,theincomingwaveisanRFsignalfromaunitundertest(UUT).

ModulationModulationisaprocessthataltersthecharacteristicsofacarrierwaveaccordingtoinformationinthemessagesignaltogenerateamodulatedwavethatistransmitted.ModulationToolkitVIsarecapableofanalyzingcarrierwaveformswithamplitude,phase,orfrequencymodulation.Theunmodulatedcarrierisrepresentedbythefollowingequation:

v(t)=Accos(ωct+θ)

Theamplitude-modulatedcarriersignalisrepresentedbythefollowingequation:

v(t)=(m(t)+Ac)cos(ωct+θ)

Thefrequency-modulatedcarriersignalisrepresentedbythefollowingequation:

v(t)=Accos((m(t)+ωct)+θ)

Thephase-modulatedcarriersignalisrepresentedbythefollowingequation:

v(t)=Accos(ωct+θ+m(t))

wherem(t)isthetime-varyingmodulation,Acistheamplitudeofthecarrierwave,andωcisthefrequencyofthecarrierwave.

ModulationDepthInamplitudemodulation,modulationdepthreferstotheratiooftheunmodulatedcarrieramplitudetotheamplitudedeviationforwhichthemodulatedcarrierwavereachesitsminimumvalue.Ifthisminimumvalueiszero,themodulationdepthis100%.Themodulationdepthratioisalsoreferredtoasthemodulationindex.

ModulationIndexThemodulationindexistheratioofthefrequencydeviationofthemodulatedsignaltothemessagesignalbandwidth.ForFSKmodulation,themodulationindexhisdefinedastheratioofthespacingbetweenconsecutivefrequenciesintheFSKsymbolmap,tothesymbolrate.Moreprecisely,h=2×fdT/(M-1)

whereMisthemodulationformatTisthesymbolperiodfdisthepeakfrequencydeviation

Forexample,in4-FSK,thespacingbetweenconsecutivefrequenciesequals2fd/3,hencethemodulationindexequals(2fd×T)/3.

Formoreinformationaboutamplitudemodulation,refertomodulationdepth.

On-OffKeying(OOK)On-offkeying(OOK)isamodulationschemethatconsistsofkeyingasinusoidalcarriersignalonandoffwithaunipolarbinarysignal.OOKisequivalenttotwo-levelamplitude-shiftkeying(ASK).

UnipolarBinaryBasebandSignal

ResultingOOKModulatedSignal

PhasePhasereferstoperiodicchangesinwaveformmagnituderelativetoastandardpositionorinstantofstarting.Forexample,thephaseofawaveofperiodTwithitsstartingpointatt0canbedefinedinradians:

orindegrees:

AnyvectorcanberepresentedeitherinpolarcoordinatesbyM ,whereMisthemagnitudeand isthephaseangle,orinCartesiancoordinates,specifically,anArganddiagram,as(a+jb),whereaisarealcomponentandbisanimaginarycomponentsuchthattan =(b/a),where isthephaseangle,andthemagnitude,M,is(a2+b2)½.RefertotheNIDeveloperZoneatni.com/zoneformoreinformationaboutphase.

PhaseAnglePhaseanglereferstotheanglebetweenapointonaperiodicwaveandareferencepoint.Thereferencepointmaybeapointonanotherperiodicwave.TheangularmeasurementthatdefinestherelationshipbetweentheperiodicwaveandthereferencepointisderivedfromaprojectionofarotatingvectorontotherealaxisofanArganddiagram.Thephaseangleofapointonawaveisthevalueofthepointontheabscissathatcorrespondstothepointonthewave.ThephaseangleofavectormaybewrittenasM ,whereMisthemagnitudeofthevectorand isthephaseanglerelativetothespecifiedreference.

Phase-LockedLoop(PLL)APhase-lockedloop(PLL)isanelectroniccircuitthatcontrolsanoscillatorsothatthecircuitmaintainsaconstantphaseanglerelativetoareferencesignal.

TheoperationoftheabovecircuitistypicalofallPLLs.Thiscircuitisafeedbackcontrolsystemthatcontrolsthefrequencyandphaseofavoltage-controlledoscillator(VCO).AninputsignalisappliedtoaphasedetectorandtheoutputoftheVCOconnectstotheotherphasedetectorinput.Asshowninthepreviousdiagram,thefrequenciesofbothsignalsarethesame.Theoutputofthephasedetectordevelopsavoltageproportionaltothephasedifferencebetweenthetwoinputsignals.ThelowpassfilterreceivesthissignalfromthephasedetectoranddeterminesthedynamiccharacteristicsofthePLL.ThisoutputsignalisthefilteredsignalthatcontrolstheVCO.

ModulationSchemesExpandthisbookformoreinformationaboutsupportedmodulationschemes.

AmplitudeModulation(AM)Amplitudemodulation(AM)isaprocessthatvariestheamplitudeofanRFcarriersignalaccordingtotheamplitudeofthemessagesignal.Therecoveryofthemessagesignaliscalleddemodulation.Oneofthebenefitsofamplitudemodulationsystemsistheeasewithwhichthebasebandmessagesignalcanberecovered.Amplitudemodulationgeneratesdiscreteupperandlowersidebands,whicharethesumanddifferencebetweenfrequenciesofthemessagesignalandthecarriersignal.Thefollowingfigureillustratesthemodulationofacarriersignal,figurea,byamessagesignal,figureb.Themessagesignalshapeisalsoreferredtoastheamplitudeenvelope.Theresultisthemodulatedwave,figurec.

FigureashowsacarriersignalwithamplitudeAc.Figurebshowsthebasebandmessagesignal.ThetransmittedsignalinFigurecisgivenbythefollowingequation:

wherem(t)isthetime-varyingmodulation.

RefertotheNIDeveloperZoneatni.com/zoneformoreinformationaboutamplitudemodulation.

Amplitude-ShiftKeying(ASK)Amplitude-shiftkeying(ASK)referstoatypeofamplitudemodulationthatassignsbitvaluestodiscreteamplitudelevels.Thecarriersignalisthenmodulatedamongthemembersofasetofdiscretevaluestotransmitinformation.

ContinuousPhaseModulation(CPM)Continuousphasemodulation(CPM)isaconstant-amplitudemodulationschemethatcanbeconsideredtobeageneralizationofcontinuousphasefrequencyshift-keying(CPFSK)orminimumshift-keying(MSK).Thelackofphasediscontinuitiesreduceshigh-frequencyspectralcontent,makingCPMahighlyspectrallyefficientscheme.AformofCPMthatcanresultinsignificantcodinggainsismulti-hphasecoding,wherehstandsforthemodulationindex.ThisschememaybeviewedasageneralizationofCPFSKschemesbecausedifferentphasechangesresultfromthetransmissionofthesamesymbolintwocontiguoussymbolintervals.Amathematicalrepresentationofthesignalduringtheithinterval,iT≤t(i+1)T,isexpressedbythefollowingformula:

whereEsisthesymbolenergy

Tisthesymboldurationωcisthecarrierfrequencyinradians/second

dandωarethesequencesthatrepresenttheM-aryinformationsequence.diωi(t-iT)andφaredataphasetermsthatcorrespondtothephaseassociatedwiththecurrentdatasymbolandthephaseaccumulationduetothepreviousdatasymbolsuchthat

and

where istheangularfrequencycorrespondingtothemodulationindexusedduringtheithbaud.Thedifferentvaluesofh

canbeusedbetweensymbolintervalsinaroundrobinfashion.RefertothefollowingresourcesformoreinformationaboutthealgorithmsandmethodsusedinCPM:

Premji,Al-NasirandDesmondP.Taylor."ReceiverStructuresforMulti-hSignalingFormats."IEEETransactionsonCommunications35,4(1987).Oerder,MartinandHeinrichMayer."DigitalFilterandSquareTimingRecovery."IEEETransactionsonCommunications36,5(1988).

FrequencyModulation(FM)Frequencymodulation(FM)isatypeofanglemodulationinwhichthefrequencyofasinusoidalcarrierwavedeviatesfromacenterfrequencybyanamountproportionaltotheinstantaneousvalueofthemessagesignal.InFM,thecenterfrequencyisthecarrierfrequency.Frequencymodulationcanbeexpressedusingthegeneralequationforanglemodulation.

whereAcisthecarrieramplitudefcisthecarrierfrequencykfisthefrequencydeviationconstantinHz/Vfmisthefrequencyofthemessagesignal

RefertotheNIDeveloperZoneatni.com/zoneformoreinformationaboutfrequencymodulation.

Frequency-ShiftKeying(FSK)Frequency-shiftkeying(FSK)referstoatypeoffrequencymodulationthatassignsbitvaluestodiscretefrequencylevels.InnoncoherentformsofFSK,theinstantaneousfrequencyisshiftedbetweentwodiscretevaluestermedthemarkandspacefrequencies.CoherentformsofFSKexistthathavenophasediscontinuityintheoutputsignal.FSKmodulationformatsgeneratemodulatedwaveformsthatarestrictlyreal-values,andthustendnottosharecommonfeatureswithquadraturemodulation(QM)schemes.

MinimumShift-Keying(MSK)Minimumshiftkeying(MSK)modulationisasubtypeofFSKmodulation.MSKusesahalf-cyclesinusoidalpulse,makingthephasechangelinearandkeepingsidelobeslowtocontroladjacent-channelinterference.

PhaseModulation(PM)Phasemodulation(PM)isatypeofanglemodulationinwhichthephaseangleofacarrierwaveismadetodeviatefromitsreferencevaluebyanamountproportionaltotheinstantaneousvalueofthemodulatingmessagesignal.Theresultingphase-modulatedwaveistransmitted.Phasemodulationcanbeexpressedusingthefollowinggeneralequationforanglemodulation:

whereAcisthecarrieramplitudefcisthecarrierfrequencykfisthefrequencydeviationconstantinHz/Vfmisthefrequencyofthemessagesignal

RefertotheNIDeveloperZoneatni.com/zoneformoreinformationaboutphasemodulation.

Phase-ShiftKeying(PSK)Phase-shiftkeying(PSK)inadigitaltransmissionreferstoatypeofanglemodulationinwhichthephaseofthecarrierisdiscretelyvariedtorepresentdatabeingtransmitted—eitherinrelationtoareferencephaseortothephaseoftheimmediatelyprecedingsignalelement.

Forexample,whenencodingbits,thephaseshiftcouldbe0°forencodinga0and180°forencodinga1,orthephaseshiftcouldbe-90°for0and+90°fora1,thusmakingtherepresentationsfor0and1atotalof180°apart.InPSKsystemsdesignedsothatthecarriercanassumeonlytwodifferentphaseangles,eachchangeofphasecarriesonebitofinformation,thatis,thebitrateequalsthemodulationrate.Ifthenumberofrecognizablephaseanglesisincreasedtofour,then2bitsofinformationcanbeencodedintoeachsignalelement;likewise,eightphaseanglescanencode3bitsineachsignalelement.

QuadratureModulation(QM)Quadraturemodulation(QM)referstoanymodulationschemethatusestwocarrierwavesoutofphaseby90°thataremodulatedbyseparateinformationsignals.TheQMformatsavailableinthistoolkitarephase-shift-keying(PSK),quadrature-amplitudemodulation(QAM),andminimum-shiftkeying(MSK).

QuadratureModulated(QM)Waveform,IdealInaquadraturemodulates(QM)system,theQMidealwaveformisthesumoftheIandQcomponentofasignalasfollows:

ToobtaintheQMwaveform,thebasebandcomponentsaremodulatedorthogonallyas

thus

wherei(t)andq(t)arethebasebandIandQwaveforms,respectively.

QuadratureModulated(QM)Waveform,PracticalInaquadraturemodulated(QM)system,theQMpracticalwaveformdiffersfromtheQMidealwaveform.AgeneralizedadjustedQMwaveformcanbeexpressedas

where

I/ QistheI/Qgainimbalance

ΔIisthein-phaseDCoffset

ΔQisthequadratureDCoffset

φisthequadratureerror

Quadrature-AmplitudeModulation(QAM)Quadrature-amplitudemodulation(QAM)isaformofquadraturemodulationinwhichthetwocarriersarebothamplitude-modulated.

Quadrature-PhaseShift-Keying(QPSK)Quadrature-phaseshiftkeying(QPSK)isaformofphase-shiftkeyinginwhichfourdifferentphaseanglesareused.InQPSK,thefouranglesareusuallyseparatedby90°spacing.

UpconversionThebasebandmodulatedsignalundergoesanalogupconversiontofrequency-translatethesignaltotheRFfrequencyatwhichthesignalistransmitted.UsetheMTUpconvertBasebandVItoupconvertwaveforms.

VisualizationVisualizationtools,suchasconstellationplotsandeyediagrams,areusedtovisualizecommunicationsmeasurements.

ModulationToolkitsupportsthefollowingtypesofdigitalvisualization:

3DEyeDiagram2DEyeDiagramConstellationPlotTrellisDiagramXYgraph

OperatingSystemSupportForinformationaboutthesupportedoperatingsystem(OS)fortheNIModulationToolkit,refertotheModulationReadme.

ProgrammingExamplesTheModulationToolkitincludesseveralexamplesforLabVIEW.Theseexamplesserveasinteractivetools,programmingmodels,andbuildingblocksinyourownapplications.WithLabVIEWrunning,selectHelp»FindExamplestolaunchtheLabVIEWExampleFinder.TheExampleFinderofferstwowaystoaccessallinstalledLabVIEWexampleVIsandtheirdescriptions:

ClicktheBrowsetabtolocatemodulationVIexamplesbytaskatToolkitsandModules»ModulationorbydirectorystructureatModulation.ClicktheSearchtabtosearchallinstalledexamplesbykeyword.EnterthekeywordFM,forinstance,tolocateaexamplesdemonstratingFMmodulationanddemodulation.

ForthelocationoftheinstalledmodulationVIexamplefiles,refertotheNIModulationToolkitforLabVIEWReadme.

ExamplesAvailableOnlineModulationToolkitVIexamplesarealsoavailableonlineattheNIDeveloperZoneoratni.com/examples.RefertotheNIDeveloperZoneatni.com/zoneformoreinformationaboutintegratingtheModulationToolkitwiththeRFsignalanalyzerandRFsignalgenerator.

ConsiderationsforUsingtheLabVIEWReal-TimeModuleTodevelopaModulationToolkitforLabVIEWapplicationintheLabVIEWReal-TimeModule,followthesamestepsusedfordevelopinganyapplicationintheLabVIEWReal-TimeModule,withtheadditionofusingtheModulationToolkitforLabVIEWVIs.

NoteApplicationsrunningModulationToolkitintheLabVIEWReal-TimeModuleonanRTtargetmaybecompromisedand/orslowat64MB.UsingModulationToolkitVIsmayintroducehighjitterintotheentiresystem.NIdoesnotrecommendusingtheseVIsinapplicationswithdeterministicrequirements.TheModulationToolkitsupportstheLabVIEWReal-TimeModule8.5andlater.TheModulationToolkitissupportedonlyonPXIReal-Timesystems.

RelatedDocumentationForconfigurationinstructionsforremotesystems,refertotheMAXRemoteSystemsHelpinMeasurement&AutomationExplorer(MAX)byselectingHelp»HelpTopics»RemoteSystemsinMAX.FormoreinformationabouttheLabVIEWReal-TimeModule,refertotheLabVIEWReal-TimeModuleUserManualatni.com/manuals.Foradditionaltroubleshootingandsupportinformation,refertotheLabVIEWReal-TimeSupportmainpageatni.com/support/labview/real-time.

GlossaryPrefixes Numbers/Symbols A B C D E F G H I J

K L M N O P Q R S T U V W X Y Z

PrefixesSymbol Prefix Valuen nano 10-9

µ micro 10-6

m milli 10-3

k kilo 103

M mega 106

G giga 109

Numbers/SymbolsnV nanovolts 10-9volts

µV microvolts 10-6volts

µΩ microohms 10-6ohms

mΩ milliohms 10-3ohms

MΩ megaohms 106ohms

nA nanoamps 10-9amperes

µA microamps 10-6amperes

mA milliamps 10-3amperes

Aamplitudedroop

MeasuredindB,isameasureoftheamountthatthesignalpowerfallsfromthestartofaspecifiedmeasurementwindow(di)totheendofthatwindow(df).

amplitudemodulation(AM)

Aprocessthatvariestheamplitudeofanradiofrequency(RF)carriersignalaccordingtotheamplitudeofthemessagesignal.

amplitude-shiftkeying(ASK)

Referstoatypeofamplitudemodulationwhichassignsbitvaluestodiscreteamplitudelevels.Thecarriersignalisthenmodulatedamongthemembersofasetofdiscretevaluestotransmitinformation.

analog-to-digitalconverter(ADC)

Ahardwarecomponentthatconvertsanalogvoltagestodigitizedvalues.AnADCcanconvertananalogsignaltoadigitalsignalrepresentingequivalentinformation.

Bbiterrorrate(BER)

Theratiooferroneousbitstototalbitstransmitted,received,orprocessedoversomestipulatedperiod.TransmissionBERexpressesthenumberoferroneousbitsreceiveddividedbythetotalnumberofbitstransmitted.InformationBERexpressesthenumberoferroneousdecoded(corrected)bitsdividedbythetotalnumberofdecoded(corrected)bits.

bursttiming

Forburstsignals,bursttimingreferstothelocationoftheburst,obtainedbyitscorrelationagainstanidealpowercurve.Inaddition,anupperandlowermaskareusedfortestingwhethertheburstsignalsatisfiesmaskspecifications.Thefollowingfigureshowsuppermask,lowermask,andidealpowercurve.

CCarson'sRule

Definestheapproximatemodulationbandwidthrequiredforacarriersignalthatisfrequency-modulatedbyaspectrumoffrequenciesratherthanasinglefrequency.TheCarsonbandwidthruleisexpressedbytherelationCBR=2(Δf+fm)whereCBRisthebandwidthrequirement,Δfisthecarrierpeakdeviationfrequency,andfmisthehighestmodulatingfrequency.

CCDFmeasurement

Thecomplementarycumulativedistributionfunction(CCDF)isastatisticalcharacterizationofthetime-domainwaveformthatcompletelydescribesthepowercharacteristicsofasignal.

centerfrequency

Themiddlefrequencyofthechannelbandwidth.Infrequencymodulation,thecenterfrequencyisequaltotherestfrequency—specifically,thefrequencyoftheunmodulatedcarrierwave.

codeword Thegeneratedcodedbits/numbersfromachannelcodingsystem.

complexenvelope

Acomplexrepresentationofthebasebandmodulatedsignal.

component Therealandimaginarypartsofacomplexnumberarereferredtoascomponents.ModulationToolkitVIscanusecomplexcomponentstodescribesignalproperties.Forexample,youcanrepresentatwo-dimensionalvectoroflengthSbyitscomponentsS=A+iB,whereAandBarethevectorx-andy-components.Therealpartofthevectorcorrespondstothex-component(A),whiletheimaginarypartcorrespondstothey-component(B).

Ddataword Theincomingmessagebitstoachannelcodingsystem.DCoffset Acomplexsignalimpairmentthatshiftsthelocusof

idealsymbolcoordinatesoff-centerintheI/Qplane.ADCoffsetcanbeaddedtothebasebandIcomponent,theQcomponent,orboth.TheDCoffsetcanbeeitherpositiveornegative,withthesignindicatingdirectionoftheshift.DCoffsetisexpressedasapercentageoffullscale,where"fullscale"(fs)istheamplitudeofthebasebandQMwaveform.

depuncture Theprocessofinsertingerasurevaluesintotheinputdatastreampriortoitsinputtothedecoder.Iftheinputdataisreal-valuedBPSKmodulateddata(asinthecaseofunquantizedsymboldecisionsfromademodulatororequalizer),theerasurevaluesequal0.IftheinputdatastreamconsistsofquantizedintegerscomingfromanA/Dconverter(ADC)attheoutputofademodulator,theerasurevaluescorrespondtotheintegerrepresentationthatishalfthemaximumoutputsamplevaluegeneratedbytheanalog-to-digitalconversionprocess.

deviationerror ForanM-FSKsystem,theaveragedeviationerrorisdefinedastheaveragemagnitudeofthespreadoftheFSKdemodulatedsymbolspacedwaveformaroundtheidealsymbol(frequency)locations.Mathematically,thedeviationerrorisdefinedas:

whereMistheFSKmodulationformat,ƒideal,iistheidealsymbollocationattheFSKfrequencycorrespondingtolocationi,and<ƒactual,i>isthemeanvalueofthedemodulatedsymbolsatlocationi.

digital-to-analog

Ahardwarecomponentthatconvertsdigitalvaluestoanalogvoltages.ThusaDACcanconvertadigital

converter signaltoananalogsignalrepresentingequivalentinformation.

directsequencespreadspectrum(DSSS)

Aprocessbywhichdataistransmittedusingahigherbandwidthsignalthatisdemandedbythedatarate.UsingDSSSallowsmultiplechannelstooccupythesamebandwidth,mitigatinginterferencefromotherusersattheexpenseofbandwidthexpansion.DSSSisaccomplishedbyspreadingeachbitofsignaldataisspreadatthetransmitterintoLchips,usingapseudorandomL-chipspreadingcodecalledacodeword.ThelengthLofthepseudorandomspreadingcodeisalsoknownasthebandwidthexpansionfactorbecausethechipsaretransmittedatarateequaltoL×bitrateofthedata.Thespreadingcodeappearsrandomtoallreceiversexcepttheintendedone,whichusestheknowledgeofthespreadingcodetodemodulateandrecoverthetransmittedinformation.Thusmultiplechannelscanoccupythesameportionofthefrequencyspectrumbyusingcodewordsthathavelittleornocorrelationwithoneanother,andlittleornoautocorrelationforanyshiftotherthanzero.Mathematically,aDSSSsignalisdescribedby:

wherey(t)isthetransmittedDSSSsignalg(t)isthepulse-shapingsignalofdurationTcaiistheithinformationbearingsymbolckisthekthelementoftheL-longpseudorandomspreadingcode(alsoknownasthechipsequence)Tcisthechipperiod,andT=L×Tcisthesymbolperiod

downconverter Asignalconditioningdevicethatconvertsaspecificbandofhigh-frequency(RF)signalstomoremanageableintermediatefrequencies(IF)thatcanbe

digitized.

Ffrequency Referstoabasicunitofratemeasuredineventsor

oscillationspersecond.Frequencyalsoreferstoanumberrepresentingaspecificpointintheelectromagneticspectrum.

Iinformationsignal

Containsthedatafortransmission.Theinformationsignalisusedtomodulatethecarrierwavetocreatethemodulatedwavefortransmission.Theinformationsignaldataisrecoveredfromthemodulatedwavebyaprocessofdemodulation.Theinformationsignalisoftenreferredtoasthebasebandsignalormessagesignal.

interleaver Adevicethatensuresthesymbolsfromseveraldifferentcodewordsarewellseparatedduringtransmissionoverasinglepath,sothatthesymbolsfromanygivencodewordareclearlyreceivedintime-divisionsequence.Interleaversareusedinconjunctionwitherror-correctingcodestocounteracttheeffectsofbursterrors.

Mmessagesignal

Containsthedatafortransmission.Themessagesignalisusedtomodulatethecarrierwavetocreatethemodulatedwavefortransmission.Themessagesignaldataisrecoveredfromthemodulatedwavebyaprocessofdemodulation.Themessagesignalisoftenreferredtoasthebasebandsignalorinformationsignal.

mixer Anonlinearanalogcircuitthatmultipliestwosignals.Mixersaretypicallyusedtoshiftsignalfrequencies.Amixerreceivestwosinusoidalinputsignalsatdifferentfrequenciesandreturnsasignalwithcomponentsatfrequenciesequaltothesumanddifferenceofthetwooriginalinputfrequencies.NonlinearmixersareusedwhenperformingamplitudemodulationofRFcarriersignals.

Nnoisefigure(NF)

Theratiooftheactualoutputnoisetothenoisethatwouldremainiftheinstrumentdidnotcontributeitsownthermalnoise.Inheterodynesystems,outputnoisepowerincludesspuriouscontributionsfromimage-frequencytransformation.However,theportionattributabletothermalnoiseintheinputterminationincludesonlywhatappearsintheoutputduetotheprincipalfrequencytransformationofthesystem,anditexcludeswhatappearsviatheimagefrequencytransformation.

Ooffsetquadraturephase-shiftkeying(OQPSK)

Avariantofphase-shiftkeyingmodulationusing4differentvaluesofthephasetotransmitthesignal.Thisschemeissometimesreferredtoasstaggeredquadraturephase-shiftkeying(SQPSK).

Pphase-lockedloop(PLL)

Anelectroniccircuitthatcontrolsanoscillatorsothatthecircuitmaintainsaconstantphaseanglerelativetoareferencesignal.

puncture Theprocessofartificiallyincreasingthecoderateofthedatastream,generatedfromablockorconvolutionalencoder,byselectivelydeletingcertainelementsinthedatastream.

Rradiofrequency(RF)

referstotheradiofrequencyrangeoftheelectromagneticspectrum.RFisoftenusedtodescribearangeofsub-infraredfrequenciesfromthetensofMHztoseveralGHz.

RFsignalanalyzer(RFSA)

referstoafamilyofPXIandPXIExpress(PXIe)devicesthatincludetheNIPXI-5660,theNIPXI-5661,andtheNI5663RFvectorsignalanalyzers.DeviceName DeviceComponents

NIPXI-5660

NIPXI-5600RFdownconvertermoduleandanNIPXI-5620IFdigitizermodule

NIPXI-5661

NIPXI-5600RFdownconvertermoduleandanNIPXI-5142IFdigitizermodule

NIPXIe-5663

NIPXIe-5601RFdownconvertermodule,anNIPXIe-5622IFdigitizermodule,andanNI5652localoscillator(LO)source

TheNI5660usestheni5660VisinLabVIEWandtheNI-TUNERandNI-SCOPEinstrumentdriversinC,C++,andLabWindows™/CVI™.TheNI5661andNI5663usetheNI-RFSAdriverforcontrollingtheRFdownconvertermodule,theRFdigitizermodule,andanLOsource(NI5663only).AllNIRFsignalanalyzersincludetheNISpectralMeasurementsToolkitforperformingfrequency-domainanalysis,andmodulationVIsforperforminganalogmodulationanddemodulationmeasurements.

Ssamplerate

Thesamplerateistherateatwhichadeviceacquiresananalogsignal,expressedinsamplespersecond(S/s).Thesamplerateisusuallytheclockspeedoftheanalog-to-digitalconverter(ADC).

signal-to-noiseratio(SNR)

Theratioofthedesiredsignalamplitudetothenoisesignalamplitudeatagivenpointintime.SNRisexpressedas20timesthelogarithmoftheamplituderatio,or10timesthelogarithmofthepowerratio.SNRisusuallyexpressedindBandintermsofpeakvaluesforimpulsenoiseandrootmeansquare(RMS)valuesforrandomnoise.IndefiningorspecifyingtheSNR,specifythesignalandnoisecharacterizations,forexample,peak-signal-to-peak-noiseratiotoavoidambiguity.

signal-to-quantized-noiseratio(SQNR)

Ameasurementoftheeffectofquantizationerrorsintroducedbyanalog-to-digitalconversionattheanalog-to-digitalconverter(ADC).ExceedingtheSQNRofyourinstrumentclipsthesignal.

spectraldensity

Ameasureoftotalsignalpowerinaspecifiedspectralbandwidthdividedbythebandwidth,expressedinwattsperhertz(W/Hz).

symbolrate

Expressesthenumberofsymbolstransmittedpersecond(symbols/s).Toconvertsymbolrateintobitrate,whichexpressesthenumberofbitstransferredpersecond,multiplythesymbolratebythenumberofbitspersymbolusedinthedigitalmodulationschemeofinterest.Symbolrateisalsoknownasbaudrate.

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