通信原理Lecture9DeltaSigmaModulationandBaseba

DigitalCommunication－FundamentalsandApplicationsDr.XinZhangSchoolofElectronicsandInformationEngineeringSouthChinaUniversityofTechnologyLecture9SigmaDeltaModulationBasebandDemodulationDigitalCommunication－FundamentalsandApplicationsReviewsofLecture8SourcecodingDiscreteandanalogsourceEntropyUniformandnonuniformquantiationSaturationDitheringDifferentialPlusCodedModulation2DigitalCommunication－FundamentalsandApplicationsThedeltamodulator,oftendenotedmodulator,isaprocessthatembedsalowresolutionA-to-Dconverterinasampleddatafeedbackloopthatoperatesatratesfarinexcessofthesignal’srequiredNyquistrate.Intheconversionprocess,speedislessexpensivethanprecision.Onecanusefastersignalprocessingtoobtainhigherprecision.•13.3.3DeltaModulation（增量调制）∆3DigitalCommunication－FundamentalsandApplications•13.3.3DeltaModulation（增量调制）4DigitalCommunication－FundamentalsandApplicationsThecoderiscompletelycharacterizedbythesamplingfrequency,thequantizingstepsizetoresolvethepredictionerrorordeltaoftheloop,andthereconstructionfilter.•13.3.3DeltaModulation（增量调制）()xt()lxt()lxn抽样脉冲原信号()xt重建信号()lxt()lxn输出脉冲+∆−∆ST编码输出()Cn1111111111110000000005DigitalCommunication－FundamentalsandApplications()xt()lxt()lxn抽样脉冲原信号()xt重建信号()lxt()lxn输出脉冲+∆−∆ST编码输出()Cn11111111000111000ABCDE6DigitalCommunication－FundamentalsandApplications重建信号的最大变化率：若输入信号变化率：则重建信号可跟踪输入的变化。相应地接收端的重建信号可以恢复原信号的基本波形。若输入信号的变化率：则重建信号无法跟踪输入的变化，相应地在接收端也将产生严重的失真。这就是所谓的△M的过载问题。简单△M不发生过载的条件：()lSdxtdtT∆=()()lSdxtdxtdtdtT∆≤=()()lSdxtdxtdtdtT∆≥=()maxSSdxtfdtT∆≤=∆⋅7DigitalCommunication－FundamentalsandApplicationsAsindicatedearlier,theloopreliesonhighcorrelationofsuccessivesamples,aconditionweassurebysignificantoversampling.Wecanenhancethecorrelationofthesampleddatapresentedtothemodulatorbyprefilteringthedatawithanintegratorandthencompensatingfortheprefilterwithapostfilteringdifferentiator.13.3.4Sigma-DeltaModulation（增量总和调制）8DigitalCommunication－FundamentalsandApplications13.3.4Sigma-DeltaModulationThissimplifiedformofthemodifiedDPCMsystemiscalledasigma-deltamodulator,containsanintegrator(thesigma)andaDPCMmodulator(thedelta).9DigitalCommunication－FundamentalsandApplicationsThesecondperspectiveusefulforunderstandingthemodulatoristhatofnoisefeedbackloop.Iffollowsthattheoutputofthemodulatoranditsz-transformcanbewrittenas13.3.4Sigma-DeltaModulationΣ−∆Σ−∆10DigitalCommunication－FundamentalsandApplicationsAboveequationshowsthattheloopdoesnotaffecttheinputsignalsinceonlythenoiseisbeingcirculatedbytheloop,andonlythenoiseexperiencestheeffectoftheloop.Theintegratorinthefeedbackpathofthenoisesignalisinvertedbytheunity-gainfeedbacklooptobecomeadifferentiatortothenoisesource.13.3.4Sigma-DeltaModulation11DigitalCommunication－FundamentalsandApplications13.3.4.1NoisePerformanceof-ModulatorWeimprovetheSNRofanoversampledwhitenoisequantizer,attherateof3-dB(orhalfabit)perdoublingofthesampleraterelativetoNyquistrate.Theshapednoisepowerthatsurvivesthefilteringactionofthelow-passfilterfollowingthe-modulatorisoftheform12DigitalCommunication－FundamentalsandApplicationsChap3BasebandDemodulation/DetectionDigitalCommunication－FundamentalsandApplicationsIndex•SignalsAndNoise•DetectionofBinarySignalsinGaussionNoise•IntersymbolInterference•Equalization14DigitalCommunication－FundamentalsandApplicationsVocabularyIntersymbolInterference(ISI)码间串扰Signal-to-NoiseRation(SNR)信噪比Heterodyning外差FrequencyConversion频率变换FrequencyMixing混频Equalization均衡15DigitalCommunication－FundamentalsandApplicationsIntroduction16DigitalCommunication－FundamentalsandApplicationsThegoalofthedemodulator(receivingfilter)istorecoverabasebandpulsewiththebestpossibleSNR,freeofanyISI.ThefilteringatthetransmitterandthechanneltypicallycausethereceivedpulsesequencetosufferfromISIReceivedsignalappearsasanamorphous“smeared”signal,notquitereadyforsamplinganddetection.Introduction17DigitalCommunication－FundamentalsandApplicationsEffectofnoise1802468101214161820-2-101202468101214161820-2-101202468101214161820-2-1012DigitalCommunication－FundamentalsandApplicationsPerformingbandpasslinearsignalprocessingfollowedbyheterodyningthesignaltobaseband,yieldsthesameresultsasheterodyningthebandpasssignaltobaseband,followedbybasebandlinearsignalprocessing.Theterm“heterodyning”referstoafrequencyconversionormixingprocessthatyieldsaspectralshiftinthesignal.Whatdoesthistheoremtellus?EquivalenceTheorem19DigitalCommunication－FundamentalsandApplicationsAsaresultofthisequivalencetheorem,alllinearsignal-processingsimulationscantakeplaceatbaseband(whichispreferredforsimplicity)withthesameresultsasatbandpass.Thismeansthattheperformanceofmostdigitalcommunicationsystemswilloftenbedescribedandanalyzedasifthetransmissionchannelisabasebandchannel.EquivalenceTheorem20DigitalCommunication－FundamentalsandApplications3.1SIGNALSANDNOISEError-PerformanceDegradationinCommunicationSystemsDemodulationandDetectionAVectorViewofSignalsandNoiseTheBasicSNRParameterforDigitalCommunicationSystemsWhyEb/N0IsaNaturalFigureofMerit21DigitalCommunication－FundamentalsandApplications•3.1.1Erro