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Pulsepositionmodulationforspectrum-slicedtransmissionProponentsofultra-wideband(UWB)technologypromisetodeliverlargeamountsofdatawithverylowpowerspectraldensity.Theultra-widebandradioconceptisveryattractiveasitpromisestoopenlargeamountsofspectrumtoavarietyofusersandatthesametimeitclaimslittleinterferenicebetweenusers.Unlikeconventionalwirelesscommunicationssystemsthatarecarrierbased,UWB-basedcommunicationsisbaseband.ItusesaseriesofshortpulsesthatspreadtheenergyofthesignalfromnearDCtoafewGHz.Onetypicaltechniqueistoassignawindowintimeandshifthepositionofthepulsewithinthatwindow.Thisisclassicalpulsepositionmodulation.Withbandwidthrestrictionseffectivelyremoved,UWBpromisestospeedupwirelessdatatransferrates.SomepublishedworkhasaddressedtheissueofhowmanyuserscantheUWBchannelsupport[2][3].Thisworkconsideredonetypeofcapacity-thecapacityintermsonthenumberofusers.Thecapacitywasderivedfromsignal-to-noiseratio(SNR)considerations.AcertainSNRisrequiredtoachieveaspecifiedbiterrorprobability(BEP).Thenoisefloorraiseswiththenumberofusers.AmorefundamentaltypeofcapacityisthewellknownShannoncapacityinbits/s.OurgoalistodevelopanunderstandingoftheroleofvariousparametersontheShannoncapacityofUWBcommunications.ThewellknownShannon!sformulC=Wlog(l+SNR),whereSNRisthe2signal-to-noiseratioandWisthechannelbandwidth,predictsthechannelcapacityCforanadditivewhiteGaussiannoise(AWGN)channelwithcontinuousaluedinputsandoutputs.ThisexpressiondoesnotapplytocommunicationswithPPMsignals.PPmisamodulationwithdiscrete-valuedinputsandcontinuous-valuedoutputs.Furthermore,PPmsignalsareorthogonal,whichimposesanadditionalconstraintonthecapacitycalculations.Newcapacitycalculationsarerequired,whichhtakeintoaccounttheseconstraints.PPMcapacitywasstudiedinthecontextofwirelessinfraredandopticalchannels[4].ThecapacityofPPMmodulationservesasthestartingpointtowhichUWB-specificconstraintsareadded.TheconstraintsarethepowerspectrumdensitylimitationunderFCCPart15rulesandthespreadingratioconstraint.Sincegigahertzunoccupie
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