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tx097 宽带 信号 最佳 接收 问题 分析

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tx097超宽带信号的最佳接收问题分析,tx097,宽带,信号,最佳,接收,问题,分析

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SignalSelectionfortheIndoorWirelessImpulseRadioChannelFernandoRam?rez?Mireles?MoeZ?Win?andRobertA?ScholtzCommunicationSciencesInstituteDepartmentofElectricalEngineering?SystemsUniversityofSouthernCalifornia?LosAngeles?CA?USAABSTRACT?Inthispaperweinvestigatecommunicationsusingquaternarypulsepositiondatamodulationoverthein?doorimpulseradiomultipleaccesschanneldisturbedwithmultipath?Theperformanceoffourquaternarysignalsetswithdi?erentcorrelationpropertiesisassessed?I?INTRODUCTIONReliablesimultaneouscommunicationsamongmultipleusersexchanginginformationatratesoftheorderofMegabits?secondovertheindoorwirelesschannel?overcom?ingmultipath?fading?shadowing?powerlimitationsandin?terference?isatechnicalchallenge?AnovelmodulationschemepotentiallywellsuitedforsuchademandingapplicationisImpulseRadioMultipleAccess?IRMA?techniqueproposedin?Scholtz?Win?a?IRMAisaSpreadSpectrum?SS?schemewhichusestimehopping?TH?fortheSSsequencemodulation?andpulsepo?sitionmodulation?PPM?forthedatamodulation?Thecom?municationswaveformsconveyinformationexclusivelyinthetimeshiftvaluesandconsistoftrainsoftime?shiftedultra?narrowpulses?IRMAisanon?constantenvelope?ultra?wide?band?carrier?less?modulationwithbandwidthinexcessof?GHz?Theanalysisin?Scholtz?focusedoncommunicationsusingbinarydataPPMovertheIRMAchanneldisturbedwithadditivewhiteGaussiannoise?AWGN?InthepresentpaperweinvestigatecommunicationsusingquaternarydataPPMovertheindoorwirelessIRMAchanneldisturbedwithmultipathinadditiontoAWGN?Theunderlyingquestionis?Doesmultipathsigni?cantlyinterfereswithPPMdatamodulation?Morespeci?cally?weusetheresultsin?Scholtz?todesignfoursetsofquaternarydataPPMsignals?WewanttoinvestigatethebehaviorofthesesignalssetsinthepresenceofmultipathundertheassumptionofconstantSNR?TheresearchdescribedinthispaperwassupportedinpartbytheJointServicesElectronicsProgramundercontractF?ThegraduatestudiesofMr?Ram?rezaresupportedbytheConacytGrant?TheauthorscanbereachedbyE?mailatramirezm?milly?usc?edu?win?milly?usc?edu?scholtz?milly?usc?eduII?IRMACOMMUNICATIONSWAVEFORMSTheTH?PPMsignalconveyingtheuser?sinformationcanbewrittenas?Scholtz?x?t?Xj?p?t?jTf?cjTc?Td?j?Ns?wherep?t?isanultra?narrow?sub?nanoseconds?pulse?TfandTcarethetimeshiftvaluescorrespondingtotheframeperiodandtheSSsequencemodulation?respec?tively?Td?j?Ns?f?Mdg?isthetimeshiftvaluecorrespondingtothethedatamodulation?ck?f?Nh?gisthetimehoppingsequenceassociatedwitheachuser?andNs?isthehoppingrateinhopsperdatasymbol?GiventheTHsequence?thevaluesofTfandTc?andwiththeshapeofthepulse?xedbythegeneratordeviceandtheantennatype?thesignaldesigntaskconsistsin?ndingtheoptimumvaluesofthesetofshifts?i?i?Mdsatis?fying?i?Tf?NhTcforeachdatasymboli?III?CHANNELCHARACTERIZATIONTheIRMAchannelintheabsenceofmultipathe?ectsbutwithAWGNwillbecalledIRMA?IDEAL?Whenmultipathispresent?itwillbecalledIRMA?MP?Thee?ectoftheIRMA?IDEALandIRMA?MPchannelsonthetransmittedwave?formcanbecharacterizedbythesignalcorrelationfunctionofthereceivedwaveform?FortheIRMA?IDEALchannel?theactualsignalcorrela?tion?ideal?canbeanalyticallymodeledby?model?n?n?exp?n?andthesignal?to?noise?ratio?SNR?value?canbemodeledasaconstant?Inordertocalculate?ideal?thereceiver?rstformsthecorrelationRideal?RT?Srx?t?Sloc?t?dt?whereSrx?t?isthesignalreceivedovertheIRMA?IDEALchannelwhenp?t?istransmittedandSloc?t?isthesignalgeneratedlocallyat?Thequantity?j?Ns?denotes?integerpart?thereceiver?Thefunction?ideal?isthenormalizedversionofRideal?Figure?a?plots?ideal?themeasuredIRMA?IDEALcorrelation?Figure?b?plots?model?theanalyticalIRMA?IDEALcorrelationmodel?usingavalueof?n?ns?01234567101Signal correlation functionsIRMAIDEAL01234567101Analytic model01234567101IRMAMP samples01234567101time (ns)IRMAMP Ave.Fig?Signalcorrelationfunctions?a?MeasuredIRMA?IDEALcorrelation?b?AnalyticalIRMA?IDEALcorrelationmodel?c?MeasuredIRMA?MPcorrelation?Theplotshowsdi?erentrealiza?tions?measurements?d?MeasuredIRMA?MPcorrelation?Theplotshowsthesampleaveragetakenovertherealizationsin?c?FortheIRMA?MPchannel?theactualsignalcorrelationfunction?MP?u?canbeconsideredarandomprocess?whereudenotesaneventtakingplaceinthesamplespaceofacertainrandomexperiment?e?g?ameasurementex?periment?Duetothepresenceoffading?theSNRvalue?u?E?u?No?withE?u?thetotalenergyofthereceivedsignalandNothepowerspectrumdensityoftheAWGN?ismodeledasarandomvariable?Inordertocalculatethefunction?MP?u?thereceiver?rstformsthecorrelation?RMP?u?RT?Srx?u?t?Sloc?u?t?dt?whereSloc?u?t?isthesignalgen?eratedlocallyatthereceiverandSrx?u?t?isthesignalre?ceivedovertheIRMA?MPchannelwhenthepulsep?t?istransmitted?Thefunction?MP?u?isthenormalizedver?sionofRMP?u?Figure?c?plotsseveralrealizationsof?MP?u?themeasuredIRMA?MPcorrelation?Figure?d?plotsthesam?pleaverageof?MP?u?theaveragebeingtakenoverthemeasurementsof?gure?c?Inboth?gures?c?and?d?themultipathe?ectscanbeobservedclearlyinthedistortion?For?ideal?tobethetruesignalautocorrelationfunction?weneedSrx?t?tohavenonoisecomponent?Here?ideal?isconsideredadeterministicprocess?butactuallyistheaverageofseveralmeasurements?Thisvalueof?nistheonethatminimizesthesquarederrorbetweenthesignalanalyticmodelandatemplateformedfromexperimentalmeasurements?Itisassumedthattheoperationsinvolvingrandomprocessarewellde?ned?For?MP?u?tobethetruesignalautocorrelationfunction?weneedSrx?u?t?tohavenonoisecomponent?andSloc?u?t?tobeper?fectlymatchedtoSrx?u?t?Hence?weneedareceiverabletoperfectlyreconstructSrx?u?t?ofthewaveformsaswellasinthepresenceoflongtails?IV?SIGNALSELECTIONFORTHEIRMA?IDEALCHANNELTheoptimumsingle?userreceiverfortheIRMA?IDEALchannelconsistsofaTHdespreadingoperationfollowedbyacorrelationreceiver?Scholtz?Thesymbolerrorprob?abilityPe?forthisreceiverdependsonlyonthesymbolSNRvalue?andthecorrelationproperties?ofthecommu?nicationssignalset?Weber?ThesameappliestotheunionboundonthesymbolerrorprobabilityUBPe?Foragiven?model?andaparticularsignalsetde?nedbythetimeshifts?j?j?Md?wecanusetherela?tion?j?k?model?j?k?inUBPe?toinvestigatetheperformanceofthisparticularsignalset?Figure?showsfourdi?erentquaternaryPPMsignalsetsthatweredesignedbasedon?model?Thetimeshifts?innanoseconds?correspondingtothissignalsetsaref?optjg?j?f?q?biorthojg?j?f?q?orthojg?j?f?orthojg?j?Thecorrespondingcorrelationmatricesaregivenintheequa?tionsbelow?opt?BB?CCA?q?biortho?BB?CCA?q?ortho?BB?CCA?ortho?BB?CCAFigure?a?showstheperformanceofthefoursetsofsig?nalsintheIRMA?IDEALchannel?Thecurvesrepre?Thesignalsetin?gure?d?iscalledorthogonalforobviousreasons?see?ortho?Thequasi?biorthogonalandquasi?orthogonalsignalsetsin?gures?c?and?d?receivetheirnamefromtheirsimilarity?incorrelationproperties?withthebiorthogonalandorthogonalsignalsets?respectively?Thesignalsetin?gure?a?isoptimuminthesensethatitwasdesignedtominimizeUBPe?athigh?values?Notethetheoptimum?mightbeafunctionof?Weber?Ingeneral?themorenegativecorrelationvalues?has?thesmallerUBPe?is?Hence?in?gure?a?UBPe?opt?UBPe?q?biortho?UBPe?q?ortho?UBPe?ortho?02460.500.51set of optimum signalsamplitude02460.500.51set of quasibiorthogonal signalsamplitude02460.500.51set ofquasiorthogonal signalstime (ns)amplitude02460.500.51set of orthogonal signalstime (ns)amplitudeFig?ThefoursetsofquaternaryPPMdatasignalsunderstudy?a?Optimum?b?Quasi?biorthogonal?c?Quasi?Orthogonal?d?Orthogonal?sentUBPe?versus?forthecases?opt?q?biortho?q?ortho?and?ortho?Figure?b?showtheperformanceofthefoursetsofsignalswhen?opt?q?biortho?q?ortho?and?orthoarecalculatedusing?ideal?insteadof?model?V?SIGNALSELECTIONFORTHEIRMA?MPCHANNELToinvestigatethebehaviorofthefoursignalsetsinthepresenceofmultipathinanindoorenvironment?wemadeuseofsignalpropagationdatarecordedinanultra?wide?bandmeasurementsexperiment?Win?Inthisexperiment?multipathpro?lesaremeasuredat?di?erentroomsandhallways?Ineachroom?nanosecond?longwindowsofmultipathmeasurementsarerecordedat?di?erentloca?tionsovera?feetby?feetgrid?Theyarearrangedspatiallyina?x?squaregridwith?inchspacing?Duringeachofthemultipathpro?lemeasurementthetransmitter?thereceiverandtheenvironmentarekeptstationary?Onehundredandfortysevennormalizedcorrelationfunctionswerecalculatedfromthesamenumberofmeasuredsignalsreceivedinthreedi?erento?ces?Duetothemultipathe?ects?thesignalcor?relationsateachpointaredi?erentfromeachother?Theyarethesamplefunctionsof?MP?u?asdescribedbefore?Atypicalsetofsamplefunctionsmeasuredinasingleo?cewasshownin?gure?c?Wecanextendtheanalysisintheprevioussectionbyusingthesamplefunctionsof?MP?u?insteadof?model?Forthefoursignalsetsunderconsiderationwecande?nethenormalizedrandomcorrelationvalues?j?k?u?MP?u?j?k?andusethisvaluesintheunionboundonprobabilityoferrorUBPe?u?toinvestigatetheperformanceofeachparticularsignalsetintheIRMA?MPchannel?Speci?cally?forthefoursignalsetsunderconsideration?wecande?nethenormalizedrandomcorrelationvalues?j?kopt?u?MP?u?optj?optk?j?kq?biortho?u?MP?u?q?biorthoj?q?biorthok?j?kq?ortho?u?MP?u?q?orthoj?q?orthok?j?kortho?u?MP?u?orthoj?orthok?Wewanttoinvestigatehow?foreachvalueofSNRconsid?ered?thevalueofUBPeintheIRMA?MPcurvedeviatefromthevaluecorrespondingtotheIRMA?IDEALcurve?Fortheoptimumsignal?itisclearthat?UBPe?opt?UBPe?u?opt?u?ThisdegradationintheprobabilityoferrorintheIRMA?MPcaseiscausedbytwofactors?uctuationsintheSNRvalue?u?andseveredistortionsandlongtailsinRMP?u?Inthispaperwewillworkwiththenormalizedsignalcorre?lationfunction?MP?u?NormalizationwillmaketheTO?TALSNRapproximatelyconstantforeveryrandomeventu?i?e?u?Hence?theUBPedegradationcausedbyto?talSNR?uctuationsduetofadingarenotconsideredhere?andUBPedegradationwillbemainlycausedbythesignalcorrelationfunctiondistortionsduetomultipath?Figures?a?and?b?showtheperformanceofthesignalsetsintheIRMA?MPchannel?Thecurvesin?gure?a?rep?resentEufUBPe?u?g?andthecurvesin?gure?b?representtheworstcaseeventmaxfugfUBPe?u?gversus?forthecases?u?opt?u?q?biortho?u?q?ortho?u?and?ortho?u?Euf?gistheexpectedvalueoperator?Fig?ure?a?wasplottedusingthesampleaveragetakenover?Notethat?u?isthefadedversionof?hence?u?Alsonotethatbytheoptimalityof?optwehavethatUBPe?opt?UBPe?opt?u?In?Win?measurementsoveranIMRA?MPchannelshowedthattherangeoffadingislessthan?dB?NotethatEufUBPe?u?u?gistheunionboundontheprobabilityoferrorforanIdealRAKE?IRAKE?receiver?idealinthesensethathasunlimitednumberofcorrelatorsandperfectestimates?thereforeitisabletoperfectlymatch?lterthesignalreceivedthroughtheIMRA?MPchannel?681012105104103102101(a) IRMAIDEAL modelUnion Bound PWEEw/No (dB)o:opt*:qbiorthox:qortho+:ortho681012105104103102101(b) IRMAIDEAL measuredUnion Bound PWEEw/No (dB)o:opt*:qbiorthox:qortho+:orthoFig?Performanceofthefoursetsofsignalsin?a?IRMA?IDEALchannel?when?model?isused?b?IRMA?IDEALchannel?when?ideal?isused?681012105104103102101(a) mean IRMAMP measuredUnion Bound PWEEw/No (dB)o:opt*:qbiorthox:qortho+:ortho681012105104103102101(b) max IRMAMP measuredUnion Bound PWEEw/No (dB)o:opt*:qbiorthox:qortho+:orthoFig?PerformanceofthefoursetsofsignalsintheIRMA?MPchannel?when?a?MP?u?isused?Thecurvescorrespondtothesampleaveragetakenovertherealizationsof?MP?u?b?MP?u?isused?Thecurvescorrespondtothemaximumvaluetakenovertherealizationsof?MP?u?the?di?erentrealizationsof?MP?u?Figure?b?wasplottedtakingthemaximumoverthedi?erentrealizationsof?MP?u?VI?DISCUSSIONOFRESULTSThepurposeofthepresentanalysisistoinvestigatewhichofthefoursetsofsignalshasbetterperformanceundervari?ationsintheshapeof?MP?u?causedbymultipath?ThisanalysiswasdoneundertheassumptionsthattheSNRisconstant?i?e?intheabsenceoffading?andthatfadingisrelativelyindependentofwhichsetofsignalsisactuallyused?Comparingtheperformancecurveswhenboth?model?and?ideal?areused?weseethatforthecurvesin?gure?a?UBPe?opt?UBPe?q?biortho?UBPe?q?ortho?UBPe?ortho?butforthecurvesin?gure?b?UBPe?q?biortho?UBPe?q?ortho?UBPe?ortho?andUBPe?q?biortho?UBPe?opt?Hencetheoptimumsignalsetistheonlyonethatchangeitsperformancesigni?cativelywhen?insteadofthemodel?model?themeasured?ideal?isused?Analyzingtheperformancecurveswhen?MP?u?isused?weseethatforthecurvesin?gure?a?EufUBPe?q?biortho?u?g?EufUBPe?q?ortho?u?g?EufUBPe?ortho?u?gandEufUBPe?q?biortho?u?g?EufUBPe?opt?u?gandforthecurvesin?gure?b?maxfugfUBPe?q?biortho?u?g?maxfugfUBPe?q?ortho?u?g?maxfugfUBPe?opt?u?g?maxfugfUBPe?ortho?u?gFromthisresults?itisevidentthattheoptimumsignalac?tuallyperformsworsethanthequasi?biorthogonalandquasi?orthogonalsignalsetsintheIRMA?MPchannel?Thiscouldbeattributedtothefactthatthequasi?biorthogonalandquasi?orthogonalsetsofsignalsweredesignedusingthemin?imumvaluepointof?model?andthezerocrossingpointsthatare