signal processing techniques for software radio-chp3

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1、Chapter3DigitalTransmissionSystemsThischapterisdevotedtoareviewofdigitaltransmissionsystems.Severalaspectsofdigitaltransmissionthroughband-limitedchannelsarediscussed.Webeginwithintroducingtheconceptofdigitalpulseamplitudemodulation(PAM)andtheroleofpulseshapinginlimitingthebandwidthofPAMsignals.Wea

2、lsodiscusstheproblemofjointdesignoftransmitterandreceiverfiltersforoptimumdetection.Inlatersectionsofthechapter,variouscarriermodulationsarereviewed.Thechapterendswithadiscussionofbasebandequivalentofpassbandchannels.3.1PulseAmplitudeModulationInbasebanddigitalPAM,asequenceof(coded)informationbitsis

3、firstpartitionedintoblocksofMbits.Forexample,whenM=2,thesequence1,0,1,1,0,1,0,0,1,1,1,0ispartitionedas{1,0},{1,1},{0,1},{0,0},{1,1},{1,0}.Then,eachgroupismappedtoasymbols[n]whoseamplitudeisdeterminedbythebitsinthegroup.Inthelatterexample,sincetwobitscantakefourdifferentcombinations,thedatasymbolswill

4、havefourdifferentamplitudes.Table3.1presentstwopossiblemappingofapairofbitstofourlevelsofPAMsymbols.Inthedirectmapping,theorderedpairs{0,0},{0,1},{1,0}and{1,1}aremappedtotheamplitudelevels−3,−1,+1and+3,respectively.IntheGraymapping,ontheotherhand,themappingisdonesothatthereisonlyonebitchangeingoingf

5、romeachPAMsymboltooneofitsadjacentneighbors.Sincemostoftheerrorscausedbynoisearelikelyduetodetectionofanadjacentsymbolinplaceoftheactualtransmittedsymbol,Graymappingminimizesthebit-error-rate(BER)ofthesystem.Mathematically,aPAMsignalattheoutputofthetransmitterhastheformX∞x(t)=s[n]p(t−nTb)(3.1)n=−∞w

6、heres[n]arePAMsymbols,Tbisthesymbol/baudduration,andp(t)isthesymbol2122DigitalTransmissionSystemsChap.3Table3.1:TwopossiblemappingofapairofbitstoPAMsymbols.DirectmappingGraymappingPAMsymbols0,00,0−30,10,1−11,01,1+11,11,0+3pulse-shape.Figure3.1presentsablockschematicthatprovidesainstructiveviewof(3.

7、1).Here,thedatasourceismodeledasasequenceofimpulseswhoseamplitudesaredeterminedbythePAMsymbols,s[n].Thesymbolpulse-shapep(t)istheimpulseresponseofanLTIsystemthattakess(t)asitsinputandgeneratesx(t)atitsoutpu