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ACOGNITIVEPHY-MACCOOPERATIVEPROTOCOLFORLOW-POWER SHORT-RANGEWIRELESSAD-HOCNETWORKSUSINGUWBPPMRADIOS By JOSEM.ALMODOVAR-FARIA ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2014
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c 2014JoseM.Almodovar-Faria 2
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Tomyparents,MabelandJoe,fortheirsupport,encouragement,andinspiration. 3
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ACKNOWLEDGMENTS ThroughoutmyyearsasagraduatestudentIhavereceivedhelp,support,and encouragementfrommanyindividuals.Theyallhavecontributedindifferentwaystothis dissertationandforthatIwillbeforeverthankful. First,Iwanttothankmyadvisor,Dr.JaniseMcNair,forallherhelpandguidance throughtheentiredoctorateprogram.Shewasalwaysavailableandveryhelpful.Icould nothavehadabetteradvisorandmentor. Thesupportandencouragementfrommyfamilykeptmealwaysmotivatedand hasbeenoneofthemainreasonsIhavecomethisfar.Aspecialfeelingofgratitude goestoallofthem,inparticulartomyparents,MabelandJoe.Withouttheireffortand inspiration,IwouldnotbewhereIamtoday.Ithankmysister,Amarilys,andbrothers, ArturoandJoseAngel,fortheirunconditionalsupportandforalwaysbeingthereforme. Theyhavebeenandwillalwaysbeagreatmotivationforme. LikewiseIthankallmyfriendsforbeingsupportiveandbelievinginmeunconditionally.AspecialacknowledgementgoestoPabloRivera,myhousemateandanold-time dearfriendwhofollowedmyprogressasagraduatestudentandwasalwaysveryencouraging,andtoEdwardLatorre,myECEpartnerandaverygoodfriendthroughoutall theseyearsatUF. IwanttothankalsoallthestudentsintheWAMSLaboratory.Theywerecooperativeandsupportivethroughouttheentiredoctorateprogram.Thatwillbealways appreciated. ForagreeingtoserveinmyPhDsupervisorycommittee,IwanttoacknowledgeDr. Xiaolin"Andy"Li,Dr.RichardNewman,andDr.HaniphLatchman.Ireallyappreciate theiravailabilityandtime. Finally,IexpressmygratitudetoDr.DavidWentzloffwhowasmyrstadvisoras agraduatestudentandawakenedmyinterestinUWBcommunications.ForthatIam deeplythankful. 4
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Contents page ACKNOWLEDGMENTS..................................4 LISTOFTABLES......................................9 LISTOFFIGURES.....................................10 LISTOFABBREVIATIONSANDVARIABLES......................13 ABSTRACT.........................................18 CHAPTER 1INTRODUCTION...................................20 2BACKGROUNDANDMOTIVATION........................23 2.1ChapterContributions.............................23 2.2HistoryoftheDevelopmentofUWBCommunications...........23 2.3KeyConceptsinWirelessCommunications.................24 2.3.1MultipathandSmall-ScaleFading...................24 2.3.2PathLossandLarge-ScaleFading..................25 2.3.3Noise..................................26 2.3.4Interference...............................28 2.4UWBDenitions................................30 2.5UWBBenets..................................32 2.5.1HDRandLowSNROperation....................32 2.5.2LowInterference............................33 2.5.3MultipathRobustness.........................33 2.5.4HighInterferenceRejection......................34 2.5.5Low-Cost,Low-Complexity,andLow-EnergyArchitectures.....35 2.6CommonDigitalModulationSchemesForUWBRadios..........36 2.6.1CoherentModulationSchemes....................37 2.6.2Non-CoherentModulationSchemes.................38 2.6.3OtherCoherentandNon-CoherentModulationSchemes......39 2.7UWBApplications...............................41 2.8UWBChannelModeling............................43 2.8.1Large-ScalePathLossforIndoorUWBChannels..........43 2.8.2Small-ScaleFadingModelforIndoorUWBMultipathChannels..44 3OPTIMIZATIONOFENERGY-DETECTIONPPMRECEIVERS.........49 3.1ChapterContributions.............................50 3.2Previouswork..................................50 3.3Energy-DetectionDemodulationforPPM..................51 3.3.1ProbabilityofBit-Error.........................53 5
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3.4OptimalReceiverBandwidth.........................53 3.4.1EffectofReceiverBandwidthReduction...............54 3.4.2ModiedProbabilityofBit-ErrorandOptimalReceiverBandwidth.55 3.4.2.1ProbabilityofBit-ErrorandReceiverBandwidth......56 3.4.2.2OptimalReceiverBandwidth................57 3.4.3Adjacent-ChannelInterference....................58 3.4.3.1EffectofACIontheReceiverPerformance.........59 3.4.3.2AnApproximationfortheOptimalReceiverBandwidth inthePresenceofACI...................61 3.4.4SimulationSetupandValidation....................62 3.4.4.1Setup.............................62 3.4.4.2Validation...........................63 3.4.5Analysis.................................64 3.4.5.1TheoryCorroboration....................64 3.4.5.2NumericalResults......................65 3.5OptimalIntegrationTime............................66 3.5.1EffectofIntegrationTimeduetoMultipathFading..........66 3.5.2ModiedProbabilityofBit-ErrorandOptimalIntegrationTime...68 3.5.2.1ProbabilityofBit-ErrorandIntegrationTime........68 3.5.2.2OptimalIntegrationTime..................69 3.5.3Inter-SymbolandInter-FrameInterference..............71 3.5.3.1EffectofISIandIFIontheReceiverPerformance....71 3.5.3.2OptimalIntegrationTime..................73 3.5.4SimulationSetupandValidation....................73 3.5.4.1Setup.............................73 3.5.4.2Validation...........................75 3.5.5Analysis.................................76 3.5.5.1TheoryCorroboration....................76 3.5.5.2NumericalResults......................76 3.6Summary....................................79 4ENERGY-INTEGRATIONDETECTIONFORPPMRECEIVERS........81 4.1ChapterContributions.............................81 4.2PreviousWork.................................82 4.3Energy-IntegrationDetection.........................82 4.3.1Motivation................................82 4.3.2BitDecision...............................83 4.3.3Example.................................86 4.4ProbabilityofBit-ErrorforEID.........................88 4.4.1BitDecision...............................88 4.4.2ProbabilityofBit-Error.........................89 4.4.3ModiedProbabilityofBit-Error....................91 4.4.4EnergyScalingFactors.........................92 4.5Simulation...................................94 6
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4.6Analysis.....................................94 4.6.1TheoryCorroboration.........................94 4.6.2Bit-ErrorRate..............................95 4.6.3IntegrationTime............................95 4.6.4SignalBandwidth............................97 4.7Summary....................................98 5COGNITIVEPHY-MACCOOPERATIVEPROTOCOL..............100 5.1ChapterContributions.............................101 5.2PreviousWork.................................101 5.3SystemModel.................................102 5.3.1NetworkandSignalModel.......................102 5.3.2ModulationandDemodulationSchemes...............103 5.3.3OptimalIntegrationTime........................104 5.3.4CarrierSenseMultipleAccesswithCollisionAvoidance......105 5.4ChannelEstimation..............................107 5.4.1SignalandEnergyModel.......................107 5.4.2EnergyDifference...........................109 5.4.3EstimationoftheEnergyScalingFactor...............109 5.4.4AchievinganOptimalTransmissionDataRate............111 5.5UWBCooperativePHY-MACProtocol....................113 5.5.1ReceiverArchitectureforChannelEstimation............113 5.5.2CooperativePHY-MACProtocol....................114 5.5.3PHYandMACFrameFormats.....................116 5.6SimulationSetup................................117 5.6.1NetworkSimulator...........................117 5.6.1.1 Node class..........................118 5.6.1.2 Channel class........................119 5.6.1.3Otherimportantclassesandfunctions...........119 5.6.2SimulationParametersandSetup...................120 5.7Analysis.....................................121 5.7.1MessageDeliveryRatio........................122 5.7.2AverageTransmissionTime......................123 5.7.3Throughput...............................125 6CONCLUSIONSANDFUTUREWORK......................126 APPENDIX ADERIVATIONOFTHEPROBABILITYOFBIT-ERRORFORPPM-EDRECEIVERS.......................................130 BDERIVATIONOFTHEPROBABILITYOFBIT-ERRORFORPPM-EIDRECEIVERS.......................................132 CMEANANDVARIANCEOF P i P j X 2 j FOR X j N )]TJ/F25 11.9552 Tf 5.48 -9.684 Td [( j 2 ...........134 7
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REFERENCES.......................................137 BIOGRAPHICALSKETCH................................146 8
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LISTOFTABLES Table page 2-1EIRPLimitsforIndoorandOutdoorUWBSystems................31 2-2Comparisonbetweencoherentandnon-coherentmodulationschemes....37 2-3WirelessapplicationsandtheirpotentialbenetsfromUWBtechnology....43 2-4PathlossparametersforUWBchannelsinresidentialandcommercialbuildings..........................................44 2-5ModelparametersforUWBmultipathchannels.................48 3-1ConstantvaluesfortheexponentialtgivenbyEquation3.........58 3-2Constantvaluesfor opt ...............................58 3-3ConstantvaluesfortheexponentialtgivenbyEquation3.........70 3-4Constantvaluesfor T w opt .............................71 3-5Constantvaluesfor T w opt whenISIisconsidered................74 3-6OptimalintegrationtimesfordifferentvaluesofsignalbandwidthandBER...75 4-1Constantvaluesfor b t ..............................92 4-2Constantvaluesfor 0 b t and 00 b t ........................93 5-1Simulationparameters...............................121 9
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LISTOFFIGURES Figure page 1-1Timelineofpopularcommercialshort-rangewirelesssystems..........21 2-1Exampleofmultipathpropagation.........................25 2-2Exampleofsmall-scaleandlarge-scalefading..................26 2-3ExampleofadditivewhiteGaussiannoise....................27 2-4Exampleofco-channelandadjacent-channelinterference............29 2-5Exampleofinter-symbolinterference........................29 2-6FCCspectralmaskforindoorandoutdoorUWBsystems.............31 2-7ComparisonofthetheoreticalchannelcapacitiesbetweenUWBandWi-Fi systems........................................32 2-8ExampleofUWBlowinterferencewithnarrowbandandwidebandsignals...33 2-9ExampleoftheUWBrobustnessagainstmultipathpropagation........34 2-10ExamplesofcoherentmodulationschemesforUWBcommunications.....38 2-11Examplesofnon-coherentmodulationschemesforUWBcommunications..40 2-12SomeUWBwirelessapplications..........................42 2-13PathlossforUWBchannelsinresidentialandcommercialbuildings......45 3-1GeneralarchitectureforEDreceivers.......................49 3-2SignalprocessingforaED-PPMreceiver....................52 3-3Powerspectraldensitiesofasquarepulse,Gaussianpulse,andAWGN....54 3-4Signalandnoiseenergyproleasafunctionofthereceiverbandwidth.....55 3-5PSDofthetransmittedsignalandACIsignals..................59 3-6Simulatorblockdiagram...............................62 3-7ComparisonbetweensimulationsandEquation3tovalidatethesimulator.64 3-8Comparisonbetweensimulations,Equation3,andEquation3.....65 3-9Required SNR bit toachievea BER =10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 ....................66 3-10Normalizedoptimalreceiverbandwidthversusthesignal's10 dB -bandwidth for T w =30 ns =1,and BER =10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(3 .......................67 10
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3-11Signalandnoiseenergyproleasafunctionofintegrationtime.........68 3-12Energyscalingfactor T w foreachUWBCMreportedin[28].........70 3-13IllustrationofISIandIFI..............................72 3-14Simulatorblockdiagram...............................74 3-15ComparisonofsimulationsandEquation3tovalidatethesimulator.....76 3-16ComparisonbetweensimulationsandthemodiedBERequationswith B = 2 GHz and T w =25,30,80,100 ns forCM1through4,respectively......77 3-17Required SNR bit toachievea BER =10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(5 for B =2 GHz .............78 3-18Optimalintegrationtime T w opt toachieve BER =10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 ..............78 3-19Required SNR bit toachieve BER =10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 ......................79 4-1Exampleoftheactualandoptimalprobabilitiesofbit-error P e forradiosoperatinginCM1andCM2.............................84 4-2GeneralblockdiagramforanEIDreceiver.....................86 4-3Exampleofabinarylogic1demodulatedusingEDandEID..........87 4-4EnergyscalingfactorsforUWBchannels.....................93 4-5SimulatorBlockDiagram..............................94 4-6ComparisonbetweensimulationresultsandthederivedBERequationfor EIDreceivers....................................95 4-7Probabilityofbit-errorforEDandEIDforCM1through4and B =2 GHz ..96 4-8Required SNR bit forEDandEIDtoachievea BER =10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 for B =2 GHz andCM1through4.................................97 4-9Required SNR bit forEDandEIDtoachieve BER =10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(3 ............98 5-1Exampleofawirelessad-hocnetwork.......................103 5-2IllustrationoftheCSMA-CAprotocol........................106 5-3Signalprocessingoftheproposedchannelestimation..............111 5-4Accuracyoftheenergyscalingfactorestimationasmoresymbolsareused..112 5-5PPMEDreceiverarchitecturewiththeproposedchannelestimation......114 5-6CognitivePHY-MACprotocolsummary.......................115 5-7FrameformatforeachMPDU............................117 11
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5-8FrameformatofthePLDU..............................117 5-9Diagramsofthetwomainclassesusedbythenetworksimulator........118 5-10Messagedeliveryratioasafunctionofathemessagearrivalrateandb thenumberofnodesinthenetwork........................122 5-11Averagetransmissiontimeasafunctionofathemessagearrivalrateand bthenumberofnodesinthenetwork......................124 5-12Throughputasafunctionofathemessagearrivalrateandbthenumber ofnodesinthenetwork...............................125 12
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LISTOFABBREVIATIONSANDVARIABLES Abbreviations ACIAdjacent-channelinterference, page28 ACKAcknowledgementpacket, page107 ADCAnalog-to-Digitalconverter, page54 AICAkaikeInformationCriterion, page45 ASKAmplitudeshiftkeying, page39 AWGNAdditivewhiteGaussiannoise, page27 BCHBose-Chaudhuri-Hocquenghemcodingalgorithm, page118 BERBit-errorrate, page36 BOKBi-orthogonalkeying, page41 BPFBand-passlter, page29 BPSKBinaryphaseshiftkeying, page37 CA-MACCognitiveautonomousMACprotocol, page102 CCICo-channelinterference, page28 CCTChannelcodingtheorem, page27 CIRChannelimpulseresponse, page46 CLTCentrallimittheorem, page28 CMChannelmodel, page47 CPLNC-MACCooperativePHYlayernetworkcodingMACprotocol, page101 CRCcyclicredundancycheck, page116 CSMACarriersensemultipleaccess, page105 CSMA-CACSMAwithcollisionavoidance, page105 CTSClear-to-sendpacket, page105 DATADatapacket, page107 DCFDistributedcoordinationfunction, page105 DCMDual-carriermodulation, page41 13
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DIFSDCFinter-framespacing, page106 DPSKDifferentialPSK, page41 EDEnergydetection, page21 EIDEnergy-integrationdetection, page81 EIRPEquivalentisotropicallyradiatedpower, page30 ESDEnergyspectraldensity, page56 FCCFederalCommunicationsCommission, page21 FSKFrequencyshiftkeying, page39 HDRHighdatarate, page32 HLDUHigherlayerdataunit, page119 i.i.dIndependentandidenticallydistributed, page47 IEEEInstituteofElectricalandElectronicsEngineers, page20 IFIInter-frameinterference, page51 IFSInter-framespacing, page106 ISIInter-symbolinterference, page28 JRJamresistance, page35 LNALow-noiseamplier, page54 LOSLineofsight, page25 MAMultipleaccess, page35 MACMediumaccesscontrolsublayer, page21 MPDUMACprotocoldataunit, page116 MUIMulti-userinterference, page102 NAVNetworkallocationvector, page106 NLOSNon-LOS, page33 OOKOn-offkeying, page39 OPSMOrthogonalpulse-shapemodulation, page38 PGProcessinggain, page34 14
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PHYPhysicallayer, page21 PLDUPHYlayerdataunit, page116 PPMPulse-positionmodulation, page21 PSDPowerspectraldensity, page27 PSKPhaseshiftkeying, page37 PSMPulse-shapemodulation, page38 QoSQualityofservice, page106 QPSKQuadraturephaseshiftkeying, page37 RFRadiofrequency, page30 RFIDRadio-frequencyidentication, page20 RTSRequest-to-sendpacket, page105 RxReceiver, page25 SIFSShortinter-framespacing, page106 SINRSignal-to-interference-and-noiseratio, page72 SIRSignal-to-interferenceratio, page35 SNRSignal-to-noiseratio, page32 std.dev.Standarddeviation, page44 T-RTransmitter-receiver, page25 TRTransmittedreference, page41 TxTransmitter, page25 UWBUltra-Wideband, page21 WBANWirelessbodyareanetworks, page20 WLANWirelesslocalareanetworks, page20 WPANWirelesspersonalareanetworks, page20 WSNWirelesssensornetworks, page20 Variables Channelspacingnormalizedtothe B 10 dB oftheTxsignal, page60 15
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B Receiverbandwidth, page67 B 10 dB Signal10 dB -bandwidth, page28 B f Fractionalbandwidth, page30 Receiverbandwidthnormalizedtothe B 10 dB oftheTxsignal, page55 opt Optimal page57 C Shannon'schannelcapacity, page32 d 0 Referencedistance, page43 E 0 Noiseenergy, page67 E b Energyperbit, page53 E i Interferenceenergy, page59 f c Centerfrequency, page28 f ch Channelfrequencyseparation, page28 f s Samplingfrequency, page27 PL Pathlossexponent, page43 I 0 InterferencePSDconstant, page59 N 0 NoisePSDconstant, page27 P 0 Noisepower, page27 P b Averagepowerperbit, page67 P ED Probabilityofbit-errorforEDreceiversusingPPM, page53 P EID Probabilityofbit-errorforEIDreceiversusingPPM, page90 PL Pathloss, page44 PL 0 Pathlossatthereferencedistance d 0 page43 PL Averagepathloss, page43 SNR bit SNRperbit, page57 T c Chipdurationsameaspulsewidth, page34 T p Pulsetimewidth, page56 T s Symbolperiod, page34 16
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t s Samplingperiod, page27 T w Integrationwindowlengthorintegrationtime, page52 T w opt Optimal T w page69 X PL Shadowingparameterforthelog-normalpathlossmodel, page44 17
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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy ACOGNITIVEPHY-MACCOOPERATIVEPROTOCOLFORLOW-POWER SHORT-RANGEWIRELESSAD-HOCNETWORKSUSINGUWBPPMRADIOS By JoseM.Almodovar-Faria May2014 Chair:JaniseMcNair Major:ElectricalandComputerEngineering Nowadayslow-powershort-rangewirelessad-hocnetworksarebecomingmore popularasthedemandforwirelessapplicationssuchassensorandpersonalarea networkscontinuetogrow.Recently,inparticularsincetheFederalCommunications Commissionapprovalin2002,ultra-widebandUWBcommunicationshavebeen proposedasaviableandefcientalternativetoimplementshort-rangewirelessapplications.Forthepastdecade,numerousinvestigationsandresearchworkshave beendoneinordertoemployUWBtechnologyinwirelessapplicationsthathavebeen traditionallyimplementedwithconventionalnarrowbandtechnologies.Thevastrangeof benetsofferedbyUWBmakesit,inmanycases,anidealsolutionwhenimplementing wirelessradiosandnetworks.Low-poweroperation,low-complexityandlow-costradio architectures,andhighdataratesareamongthemanyadvantagesofUWB.Inmost short-rangewirelessad-hocnetworks,low-poweroperationaswellasmultipleaccess controlMACiscrucialinthenetworkdesign. Pulse-positionmodulationPPMisawell-knowndigitalmodulationscheme thatwhenusedinUWBradioscanachievesimplelow-costarchitecturesandmore importantlyaverylow-poweroperationwhileofferingrelativelygooddataratesand bit-errorrateBERperformance.TheDCFfunctiondescribedbytheIEEE802.11 WLANstandardisusedquiteoftenastheMACprotocolwhenimplementingwireless networksingeneralandhasproventobeefcientformanyapplications.Thisdoctoral 18
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dissertationpresentsanewcognitiveandcooperativeprotocolbetweenthephysical PHYlayerandtheMACsublayerforwirelessad-hocnetworksusingPPMUWB radios.Byacognitiveestimationofthewirelesschannelandthecooperationbetween theMACandPHYlayers,thecognitiveprotocolcandynamicallyadjustthetransmission dataratebetweentwonodesoptimizingtheircommunication.Simulationsshowthatthe protocolimprovestheoverallnetworkperformanceintermsofmessagedeliveryratio andaveragetransmissiondelay. 19
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CHAPTER1 INTRODUCTION Inthelastthreedecades,asthewirelesscommunicationsindustryhasadvanced, wehaveseenagreatincreaseinthedevelopmentofnotonlylong-rangeandmediumrangewirelesscommunicationse.g.radioandtelevisionbroadcasts,satellitecommunicationsandcellularnetworksamongothersbutinshort-rangewirelesssystems aswell.Forthelast15years,wirelesssystemsinvolvingradio-frequencyidentication RFID,wirelesssensornetworksWSN,wirelesslocalareanetworksWLAN,personalareanetworksWPANandbodyareanetworksWBANhavebeenincreasingly developedtomeetthedemandsofourtechnology-hungrysociety.Thesesystemsare usedinmanyoftoday'swirelessapplicationssuchasmobiledevices,wirelessrouters, wirelessaudioandvideosystems,advancedremotecontrolling,andmuchmore. Figure1-1showsatimelineofsomepopularshort-rangewirelessapplicationsthat havebeencommercializedoverthelastsixdecades.Untilearly1990s,therewerefew commercialapplicationsforshort-rangesystemse.g.remotecontrolsRCs,cordless phonesandfewotherapplications.Atthetime,mostofthewirelessapplications commerciallyavailablefocusedonmediumandlong-rangecommunications.However, thankstotheresearchdoneduringthe1970sandearly1980s[61],therstWLAN productsstartedtoappearattheendofthe1980s.By1997,theoriginalversionofthe IEEE 1 802.11standardforWLANwasnalizedandwithitcamearapiddevelopment ofthistechnologyforresidentialandcommercialusee.g.Wi-Firouters.OthershortrangesystemssuchasWPANandWBANstartedaroundtheideaofWLANandhave extendedinthelastdecadetonumerousothersystemssuchasWSNandRFID.Today, thesesystemshaveaverywiderangeofapplicationssuchasbluetoothinmobile 1 IEEEstandsforInstituteofElectricalandElectronicsEngineers 20
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Figure1-1:Timelineofpopularcommercialshort-rangewirelesssystems devicesandremotecontrollers,high-speedwirelessrouters,RFIDtags,andbody implantablesensorstomentionjustafew. Recently,inparticularsincetheFederalCommunicationsCommissionFCCapprovalin2002,ultra-widebandUWBcommunicationshavebeenproposedasaviable andefcientalternativetoimplementshort-rangewirelessapplications.Thus,forthe lastdecade,researchandnumerousinvestigationshavebeendoneinwhichtheconventionalnarrowbandcommunicationsarebeingsubstitutedbyUWBcommunications. ThismainlyduetothewiderangeofbenetsofferedbyUWBcommunicationsincluding low-poweroperation,low-complexityandlow-costradioarchitectures,andhighdata ratesamongseveralothers. Inthisdoctoraldissertation,non-coherentUWBradiosusingpulse-positionmodulationPPMandenergy-detectionEDdemodulationarestudiedandoptimized.In addition,amodicationtotheEDtechniqueisproposedanddiscussedindetail.Based ontheextensivestudyandthetheorydeveloped,anewcognitiveandcooperativeprotocolinvolvingthephysicalPHYlayerandthemediumaccesscontrolMACsublayer isintroduced. Therestofthisdoctoraldissertationisdividedin5additionalchapters.Chapters 2,3,and4correspondtotheworkdoneonUWBPPMradios.Chapter2,provides aliteratureoverviewofUWBcommunicationsalongwiththeexplanationofseveral 21
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keyconceptsdirectlyrelatedtothediscussionthroughoutthisdocument.Chapter3 discussesindetailEDanditsoptimalreceiverbandwidthandoptimalintegrationtime inthepresencenoiseandcertaininterferencesources.Thetheorypresentedinthis chapteristhebaseforthechannelestimationthatwillbeusedforthecognitiveand cooperativeprotocol.Chapter4presentsamodicationmadetotheEDdemodulation techniquepresentedinChapter3thatimprovesthereceiverperformance.Thismodicationalongwiththeoriginaldemodulationmethodwillbeusedintheimplementationof thenewprotocolpresentedinChapter5.Inthischapter,thecognitiveandcooperative PHY-MACprotocolispresented,discussedandanalyzed.Finally,conclusionsare presentedinChapter6.Thischapteralsoprovidesabriefsummaryofthefuturework. 22
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CHAPTER2 BACKGROUNDANDMOTIVATION TheeldofUWBwirelesscommunicationshasbeenrapidlygrowinginthepast decadesinceitsFCCapprovalin2002.ThewidevarietyofadvantagesthatUWB offershasmotivatedasignicantinteresttowarditsdevelopmentandapplicationtoa vastrangeofwirelessapplicationsincludingmediumandlongrangecommunications [30,90].However,atleast80%ofUWBcommercialapplicationsareenvisionedtobe short-rangewirelesscommunications[38].Althoughtheconceptspresentedinthis chapterfocusonshort-rangewirelesscommunications,theyarestillvalidforpotential applicationsinthemedium-rangeandeveninthelong-rangedomainofUWBwireless communications. 2.1ChapterContributions ThischapterprovidesaliteratureoverviewofUWBcommunications.Itpresents thekeyconcepts,benets,andchallengesofUWBsignalingaswellasitsapplications andtechnologies.Inaddition,areviewofUWBchannelmodelingisofferedincludinga characterizationofthechannelmodelsproposedbytheIEEEP802.15.3ataskgroup. 2.2HistoryoftheDevelopmentofUWBCommunications UWBcommunicationsemploynarrowpulsesinordertoachievelargebandwidths and,therefore,itsearlynamewasimpulsecommunicationsthetermUWBbecame popularduringthe1990s.Therstexperimentswithnarrowpulsescanbetracedback tothelatethe19 th centurywhenHeinrichHertzexperimentedwithsparkdischarges [42]toverifyMaxwell'sequationsonelectromagnetictheory.TheequipmentHertz usedisprobablytherstimpulseradioinhistory.Afewyearslater,GuglielmoMarconi's experimentsusingspark-gaptransmissionsexpandedHertz'sworkanddemonstrated itspracticalapplication:wirelesscommunications[8]. IronicallyMarconi,knowntodayastheinventorofradio,wasusingUWBcommunicationsforitsradioapplicationsbyemployingspark-gaptransmissions.Infact,forabout 23
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20yearsafterHertz'srstexperiments,thiswasthedominanttechnology[37]forthe earlyresearchinwirelesscommunications.Later,mainlyduetothelackofappropriate hardwareforpulse-basedmodulationanddemodulationaswellaswidebandinterferencemitigationtechniques,sinusoidalwavesbecametheleadingformofwireless communications.Itwasnotuntilthelate1960sandearly1970sthatpulse-basedcommunicationsresurfacedwiththepioneeringcontributionsofresearcherslikeHenning Harmuth,PaulVanEtten,andGeraldRoss[7].HarmuthpublicationspresentedthebasicreceiverandtransmitterdesignforUWBwhileVanEtten'sexperimentsinUWBradar systemsresultedinthedevelopmentofthebasicconceptsforUWBantennas.In1971, Rossledapatentonthetransmissionandreceptionofpulsesignalswithoutdistortion [68]andin1973itbecametherstUSpatentawardedforUWBcommunications. ForthenexttwodecadesafterRoss'patent,UWBwasmostlyusedbythemilitary incommunications,radar,sensing,andnicheapplications[18].Inthe1990s,afew startupcompaniesinparticular,TimeDomainCompanyTDC[80]stageda movementtowardthecommercializationofUWBsystemswhich,afteryearsofmuch opposition,culminatedwithitsapprovalbytheFCCinAprilof2002.Afewmonths later,thePulsOnchipsetfromTDCbecametherstUWBcommunicationsproduct certiedbytheFCC.Sincethen,UWBhasbeenamajorresearchareainwireless communicationsasevidencedbythenumerousarticlesandbookspublishedinthelast 10years. 2.3KeyConceptsinWirelessCommunications Thissectionbrieydenesafewkeyconceptsinwirelesscommunicationsthatare relevanttothediscussionthatwillbedevelopedinsubsequentchapters.Thesekey conceptsare:small-scalefading,large-scalefading,noise,andinterference. 2.3.1MultipathandSmall-ScaleFading Aradiosignalthatistransmittedthroughawirelesschanneltravelsthroughmultiple pathsbeforereachingthereceiver'santenna.Thisphenomenaiscalledmultipath 24
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aMultiplepropagationpaths bTransmittedandreceivedsignals Figure2-1:Exampleofmultipathpropagation propagation,orsimplymultipath,andisthecauseoftherapidamplitudeuctuations thattheradiosignalundergoesoverashortperiodoftime,i.e.shortdistance.Figure 2-1ashowsanexampleofmultiplesignalpaths.ThedirectpathfromtransmitterTx toreceiverRxiscalledtheline-of-sightLOSpathanditisusuallythedominant multipathcomponentofthereceivedradiosignal. Small-scalefadingdescribestheeffectscausedbymultipathpropagationandother factorssuchasthesignalbandwidthandreceivermotionrelativetothetransmitter. Themostimportanteffectsdescribedbysmall-scalefadingare:timedispersiondueto multipathpropagationdelays,rapidchangesinsignalstrengthandpolarity,andrandom frequencymodulationduetoDopplershifts. 1 Figure2-1bshowsanexampleofthese effectsonatransmittedpulse.Ascanbeseen,thereceivedpulsehasbeendispersed intimewithadecreasingaveragesignalstrengthandchangesinfrequencyandpolarity. 2.3.2PathLossandLarge-ScaleFading Small-scalefadingdescribestherapidchangesinsignalstrengthovershort transmitter-receiverT-Rseparationdistances.Large-scalefading,incontrast,describesthemeansignalstrengthattenuationoverlongerT-Rseparationdistances,i.e. 1 Whenatransmitterandareceiveraremovingrelativetoeachother,thefrequency ofthereceivedsignalchangesbasedontheirmotion.Thisphenomenonisknownas theDopplereffectorDopplershift. 25
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aLinearScale bLogarithmicScale Figure2-2:Exampleofsmall-scaleandlarge-scalefading longerperiodsoftimes.Figure2-2ashowsanexampleofsignalstrengthvariations asafunctionofT-Rdistanceillustratingtherapidsmall-scalefadingandtheslower large-scalefading.Thegurealsoshowsthatthemeansignalstrengthi.e.large-scale fadingattenuatesexponentiallyastheT-Rdistanceincreases.Forthisreasonaswell astosimplifyrelatedcalculations,thesignalstrengthattenuationisoftendescribedin logarithmicscalesasshowninFigure2-2b. Inwirelesscommunications,thesignalstrengthattenuationiscommonlyreferred toaspathloss.Sincethesignalattenuatesmoreandmoreasittravelsfurtheralongits wirelesspath,thepathlossincreaseswithlargerT-Rdistances.Pathlossisveryuseful whendeningthatradiocoverageareaofatransmitter. 2 2.3.3Noise Thereareseveraltypesofnoisee.g.shotnoise,burstnoise,Browniannoisebut themostcommonwhenitcomestowirelesscommunicationsisthermalnoise.This 2 Theradiocoverageareareferstohowfarareceivercanbefromthetransmitterso thatthereceivedsignalstrengthislargeenoughtobedetected. 26
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aTimeDomain bFrequencyDomain Figure2-3:ExampleofadditivewhiteGaussiannoise unavoidablephenomenonisarandomprocesscausedbythermalmotionsofelectrons inanyconductingmaterialandhasthreemainproperties: 1.Itisanadditiveprocessbecauseareceivedsignalcanberepresentedbythesum ofthetransmittedsignalandthenoisesignal. 2.IthasaconstantpowerspectraldensityPSDforallfrequenciesi.e.white noise. 3 3.Itfollowsazero-meanGaussiandistributionwithnitevariance 2 equaltothe averagenoisepower P 0 Hence,thermalnoiseisoftencalledadditivewhiteGaussiannoiseAWGN.Figure23ashowsanexampleofAWGNwhenusingasamplingperiod t s =1 = f s ,where f s isthe samplingfrequency.Figure2-3b,ontheotherhand,showsAWGNinthefrequency domain,thatis,aatspectrumwithaPSDof N 0 = 2. 4 AWGNisfundamentalintheunderstandingofwirelesscommunications.Abasic theoremofInformationTheoryistheChannelCodingTheoremCCT[14]fromwhich 3 AsignalwithconstantPSDforallfrequenciesiscalledwhitenoiseinanalogyto whitelightwhichcoversallwavelengths. 4 ThePSDconstantvalueforAWGNis N 0 forallfrequenciespositiveandnegative. However,real-worlddevicesonlyusethepositivehalfofthespectrum.Therefore, N 0 = 2 isusedinstead. 27
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canbeconcludedthattheworst-casebackgroundnoiseinwirelesschannelsisAWGN [50,76]asitminimizesthechannelinformationcapacity.Furthermore,recently,ithas beensuggestedthatAWGNisalsotheworst-caseadditivenoiseinwirelessnetworks ingeneral[76,77].Intuitively,itmakessensetheuseofAWGNtomodelallnoisesince, inmanycases,thecombinednoisesourcesshouldapproachaGaussianrandom distributionbytheCentralLimitTheoremCLT. 2.3.4Interference Interferencecanbedenedasanyunwantedsignalfromanexternalsourcethat altersordisruptstheintendedsignal.Inwirelesscommunicationsthereisawiderange ofinterferencesignals,orjustinterferers,thataretakenintoaccountwhendesigning wirelesssystems.Broadlyspeaking,interferenceinwirelesscommunicationscanbe dividedin: 1.Co-channelinterferenceCCI:thefrequencybandschannelsoftheinterferer andtheintendedsignaloverlap. 2.Adjacent-channelinterferenceACI:theinterfererisataneighboringchanneland partofitsenergyisleakedintothefrequencybandoftheintendedsignal 3.Inter-symbolinterferenceISI:apreviousintendedsignalinterfereswiththe currentintendedsignalduetothetimedispersioncausedbymultipathpropagation seesection2.3.1. Figure2-4ashowsanexampleofCCIforasignalwithcenterfrequency f c .Inthis example,thefrequencybandsoftheinterferencesignalsoverlapwiththefrequency bandoftheintendedsignal,i.e.thechannelfrequencyseparation f ch 5 islessthan the10 dB -bandwidthofthesignal B 10 dB 6 Similarly,Figure2-4bshowsanexample ofACIwhich,incontrasttoCCI, f ch isgreaterorequalthan B 10 dB .Inbothgures,the 5 Thechannelfrequencyseparationisthefrequencyspacingbetweenthecenterfrequenciesoftwochannels. 6 Inwirelesscommunications,thefrequencybandofasignalisusuallydeterminedby its10 dB -bandwidth B 10 dB ,i.e.thefrequencybandinwhichthesignal'sPSDfalls10 dB fromitshighestpoint. 28
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aCo-channelinterferenceCCI bAdjacent-channelinterferenceACI Figure2-4:Exampleofco-channelandadjacent-channelinterference dashedyellowlinesrepresentanon-idealband-passlterBPF.Ontheotherhand,an exampleofISIisillustratedinFigure2-5.Thisexampleshowsthewirelesstransmission oftwosymbols. 7 Asseeninthegure,therstreceivedsymbolinterfereswiththe secondsinceitstimedispersionduetomultipathpropagationislargerthanthesymbol period. aTransmittedSignal bReceivedSignal Figure2-5:Exampleofinter-symbolinterference 7 Indigitalcommunications,asymbolisasignalmodulatedtorepresentoneormore logicbits. 29
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2.4UWBDenitions TheFCCnalruleonUWBTransmissionsystemsdenesaUWBtransmitter as anintentionalradiator 8 thatatanypointintime,hasafractionalbandwidthequal toorgreaterthan0.20orhasaUWBbandwidthequaltoorgreaterthan500MHz, regardlessofthefractionalbandwidth [26].Inthisdenition,thefractionalbandwidth B f is B f = f H )]TJ/F49 11.9552 Tf 11.955 0 Td [(f L = f c where f c = f H + f L = 2isthecenterfrequencyand f H and f L are,respectively,theupper andlowerboundariesofthe3 dB -bandwidth 9 ofthetransmittedsignal. Inadditiontothebandwidthrequirement,theFCCalsodenesamaximumtransmissionpower.ThepowerlimitsfortheequivalentisotropicallyradiatedpowerEIRP 10 ofindoorandoutdoorUWBsystemswhenmeasuredatadistanceof3 m witha bandwidthresolutionof1 MHz aretabulatedinTable2-1. TheFCCalsosetsapowerlimitforunintentionalradiators. 11 Forfrequencies above960 MHz ,thistypeofradiatorscannotexceedanelectriceldstrengthof 500 V = m measuredataT-Rseparationdistanceof3 m overa1 MHz frequencyband [25].TocomparethislimittotheUWBEIRPlimit,theconversionequationgivenby[12] 8 IntentionalradiatorsaredevicesthatgenerateradiofrequencyRFenergyonpurposesuchaswirelesstransmitters,imagingsensors,andgroundpenetratingradars amongmanyothers. 9 The3 dB -bandwidthofasignalisthefrequencybandinwhichitsPSDfalls3 dB fromthehighestpoint. 10 EIRP,asdenedbytheFCC,referstothehighestsignalpowerstrengthmeasured at3 m fromthesourceatanyfrequencyandinanydirection. 11 UnintentionalradiatorsaredevicesnotdesignedtoemitRFenergyonpurposesuch asdigitalelectronics,electricchargers,andaudioampliersamongmanyothers. 30
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Table2-1:EIRPLimitsforIndoorandOutdoorUWBSystems FrequencyRange MHz IndoorEIRP dBm = MHz OutdoorEIRP dBm = MHz 960 )]TJ/F22 11.9552 Tf 14.612 0 Td [(1610 )]TJ/F22 11.9552 Tf 9.298 0 Td [(75.3 )]TJ/F22 11.9552 Tf 9.298 0 Td [(75.3 1610 )]TJ/F22 11.9552 Tf 14.612 0 Td [(1990 )]TJ/F22 11.9552 Tf 9.298 0 Td [(53.3 )]TJ/F22 11.9552 Tf 9.298 0 Td [(63.3 1990 )]TJ/F22 11.9552 Tf 14.612 0 Td [(3100 )]TJ/F22 11.9552 Tf 9.298 0 Td [(51.3 )]TJ/F22 11.9552 Tf 9.298 0 Td [(61.3 3100 )]TJ/F22 11.9552 Tf 14.611 0 Td [(10600 )]TJ/F22 11.9552 Tf 9.298 0 Td [(41.3 )]TJ/F22 11.9552 Tf 9.298 0 Td [(41.3 Above10600 )]TJ/F22 11.9552 Tf 9.298 0 Td [(51.3 )]TJ/F22 11.9552 Tf 9.298 0 Td [(61.3 Figure2-6:FCCspectralmaskforindoorandoutdoorUWBsystems. P rad =4 d 2 rad E 2 rad = Z 0 canbeused.Inthiscase,thedistancefromthemeasurementlocationtotheradiator is d rad =3 m ,theelectriceldstrengthfromtheradiatoris E rad =500 V = m andthe characteristicimpedanceoffreespaceis Z 0 =120 .Withthesevalues,theradiated powerlimitforunintentionalradiatorsis P rad 75 nW )]TJ/F22 11.9552 Tf 21.918 0 Td [(41.3 dBm per1 MHz .Thislimit isoftencalledthenoiseoorandisshowninFigure2-6alongwiththeFCCspectral maskforindoorandoutdoorUWBtransmitters.Fromthegure,itisevidentthatthe bestfrequenciestooperateUWBsystemsrangefrom3.1 GHz to10.6 GHz wherethe EIRPlimitisthehighest. 31
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Figure2-7:ComparisonofthetheoreticalchannelcapacitiesbetweenUWBandWi-Fi systems. 2.5UWBBenets UWBtechnologyoffersseveraladvantagesoverthetraditionalnarrowbandtechnologies.Amongthese,thekeybenetscanbesummarizedas:highdatarateHDR, lowsignal-to-noiseratioSNRoperation,lowinterference,multipathrobustness,high interferencerejection,andlow-cost,low-complexity,andlow-energyarchitectures. 2.5.1HDRandLowSNROperation TheCCTstatesthatinformationcanbetransmittedatanydatarate R thatdoesnot exceedthechannelcapacity C [14],i.e. R C .Thiscapacityisgivenbythewell-known formuladerivedbyShannonin1948[75] C = B log 2 1+ SNR where B isthetransmissionbandwidthandSNRisthesignal-to-noiseratio.From Equation2,itisclearthatUWBsystemshavethepotentialtoachieveHDRdueto theirlargetransmissionbandwidth.ThisisillustratedinFigure2-7whichshowsthe theoreticalchannelcapacityasafunctionofSNRforanUWBsystemwith B =500 MHz andcurrentWi-Fisystems.Fromthegure,itiseasytoseethatevenatlowvaluesof SNR,UWBsystemscanstillofferrelativelylargedataratesasaresultofthetheirlarge 32
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Figure2-8:ExampleofUWBlowinterferencewithnarrowbandandwidebandsignals. bandwidth.Forinstance,intheory,theUWBsystem B =500 MHz with SNR =0.5 dB hasthesamechannelcapacitythanWi-Fi802.11ac B =80 MHz at SNR =20 dB 2.5.2LowInterference Asexplainedinsection2.4,theEIRPlimitforUWBradiosis )]TJ/F22 11.9552 Tf 9.299 0 Td [(41.3 dBm = MHz which isthenoiseoor.Duetothispowerlimitandlargebandwidth,UWBsignalsappearas regularchannelnoisetotraditionalnarrowbandandwidebandradiosoperatinginthe samefrequencyband,thatis,UWBsignalsproduceverylowinterferencetoin-band radios.ThisisillustratedinFigure2-8. 2.5.3MultipathRobustness UWBpulseshaveaveryshortduration.ThismakesUWBsystemslesssensitive tomultipathpropagationthannarrowbandsystemsthatusewiderpulses.Thereason isthatthepulsepropagatingthroughanon-LOSNLOSpathhasaverysmallwindow ofopportunitytocollidewiththepulsepropagatingthroughtheLOSpathwhichcauses signaldegradation[58]. Toillustratethisconcept,anexampleisshowninFigure2-9.Letusassumethat atransmittedpulsepropagatesonlythroughaLOSpathandaNLOSpathasshown inFigure2-9awithtraveldistancesof10 m and11 m ,respectively.Then,assuminga propagationspeedequaltothespeedoflight c =3 10 8 m = s ,thesignalpropagating 33
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aPropagationpaths bArrivaltimeprole Figure2-9:ExampleoftheUWBrobustnessagainstmultipathpropagation throughtheLOSpatharrivesatthereceiverafter33.3 ns whiletheNLOSsignalarrives 3.3 ns later.ThewidepulserepresentinganarrowbandsignalinFigure2-9bhas atimedurationlargerthanthedifferenceinthearrivaltimesofthemultipathsignals whichcausesacollision.Incontrast,thenarrowpulseinthesamegurehasasmaller durationthan3.3 ns andthusnocollisionoccurs. 2.5.4HighInterferenceRejection Anapproximatemeasureforthecapabilityofasystemtorejectinterferenceis theprocessinggainPG.HigherPGresultsingreaterabilitytosuppressin-band interference[66].AcommonwaytodenePGis PG = R c R s = T s T c where R c =1 = T c isthechiprate T c isthechipdurationorpulsewidthand R s =1 = T s is thesymbolrate T s isthesymbolperiod.InUWBsystems,verynarrowpulsesareused inordertogeneratelargesignalbandwidthsand,hence, T c isverysmallincomparison to T s .Consequently,the T s = T c ratio,sometimescalledthespreadingfactor,isusually quitelarge. 34
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InmultipleaccessMAapplications,inparticular,highPGisdesiredsincethe dominantinterferencecomesfromin-bandsignals.ThejamresistanceJR 12 margin offersameasureofhowcapableasystemiswhenrejectingin-bandinterferenceand canbedenedas[95] JR = PG )]TJ/F49 11.9552 Tf 11.955 0 Td [(SIR min [ dB ] where SIR min istheminimumsignal-to-interferenceratioSIRrequiredtomeetadesiredsystemperformance.Clearly,UWBisanattractivetechnologyforMAapplications sinceitcanprovidehighPGresultinginahighresistancetonarrowbandinterference signals. 2.5.5Low-Cost,Low-Complexity,andLow-EnergyArchitectures ThelowtransmissionpowerandverylargesignalbandwidthofUWBradiosbring advantagesinthehardwareimplementationsuchassmallantennasandotherpassive elements,relativelysimplearchitectures,andlow-energyoperation. Thehighfrequencyband.1 )]TJ/F22 11.9552 Tf 12.713 0 Td [(10.6 GHz allocatedforUWBresultsinsignals withsmallwavelengths.This,inturn,helpsreducingthesizeofantennassinceitis typicallyproportionaltothesignalwavelength.Inaddition,passiveelementssuchas inductorsandcapacitorsusedmainlyforimpedancematchingandresonancearealso reducedinsizeduetotheUWBhighfrequencyband. 13 Havingsmallerantennasand passiveelementssignicantlyreducethesizeofUWBintegratedcircuitsresultingina considerablereductioninthecostofmanufacturing. 12 Althoughthetermjammingnowadaysisusuallyusedtorefertoanintentional attemptofdisruptingacommunication,inthepast,itwasoftenusedasasynonymto in-bandinterference.Thus,JRcanbeinterpretedasinterferenceresistance. 13 Circuitsdesignedforhigherfrequenciesneedsmallervaluesofinductance L and capacitance C astheresonancefrequencyisproportionalto1 = p L C 35
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Thepulse-basedtransmissionofUWBsystemsallowsforlow-complexityarchitectures.Forinstance,pulsescanbegenerateddirectlyintheUWBfrequencyband withoutrequiringfrequencytranslation[84].Thiseliminatestheneedofanoscillator forfrequencyup-conversionreducingthenthecomplexityofthetransmitterandits energyconsumption.Similarly,inthereceiverend,oscillatorsfordown-conversioncan beomittedbyemployingnon-coherentmodulationschemessuchasenergy-detection discussedindetailinChapter3.Inaddition,theFCClimitof )]TJ/F22 11.9552 Tf 9.299 0 Td [(41.3 dBm = MHz onthe EIRPofUWBradiosimpliesaverylowpowertransmissionwhichreducestheneedof powerampliersinthetransmitterarchitectures. Ingeneral,thelowtransmissionpowerandthepotentiallowcomplexityofUWB radiosresultinlow-energyandlow-costsystems.Theseaddtothelistofbenetsthat makeUWBaveryattractivetechnologyforshort-rangewirelesscommunications. 2.6CommonDigitalModulationSchemesForUWBRadios ThissectionbrieydiscussesseveralbasicmodulationschemesusedinUWB digitalsystems.Thesecanbedividedintwomaingroups:coherentandnon-coherent modulation.Coherentmodulationexploitsthephaseandshapeofthecarriersignal inordertotransmitinformation.Non-coherentmodulation,incontrast,usesonlythe instantaneouspowerofthesignaleliminatingtheneedforcoherentcarrierrecovery[86]. Bothcoherentandnon-coherentmodulationtechniqueshaveadvantagesover eachotherseeTable2-2andchoosingoneovertheotherwillstronglydependonthe targetapplication.Forinstance,intermsofdatarateandbit-errorrateBER,coherent modulationschemeswilltypicallyprovideabettersystemperformance[67].However, non-coherentmodulationschemesrequirelessenergytooperateandcanberealized withrelativelysimplerarchitecturesmainlyduetothefactthatnocoherentcarrier recoveryisneeded. 36
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Table2-2:Comparisonbetweencoherentandnon-coherentmodulationschemes ParameterCoherentNon-coherent CarrierRecoveryYesNo EnergyperbitHigherLower DataRateHigherLower BERLowerHigher ComplexityHigherLower 2.6.1CoherentModulationSchemes Indigitalradios,phaseshiftkeyingPSKisacommonlyusedcoherentmodulation technique.Asitsnamesuggests,thephaseofthesignalcarriesthedigitalinformation. APSKsignalcanbemodeledas s i t = t cos 2 f c t + i where t istheenvelopeofthesignal, f c isthecenterfrequency, i isthephaseof thesignalcorrespondingtothe i th modulationstateofasinglesymbol.Forinstance, thepopularbinary-PSKBPSKschemeusestwophases,i.e. 1 =0and 2 = torepresentabinarybit.Forthesephasevalues, s 1 t = t cos 2 f c t and s 2 t = )]TJ/F49 11.9552 Tf 9.298 0 Td [(s 1 t 14 ThisisshowninFigure2-10where s 1 t and s 2 t representabinary logic0and1,respectively. Quadrature-PSKQPSKisanothercommondigitalmodulationschemeemployed inUWBsystems.ItfollowsthesameprincipleasBPSKbutitusesfourdistinctphases, i.e. 1 =0, 2 = = 2, 3 = ,and 4 =3 = 2,torepresentfourmodulationstates,thatis,a 2-bitsymbol. 14 For 1 =0and 2 = ,thesignalsrepresentingthebinarystatesand1areoppositeinsignand,hence,BPSKissometimesinterpretedasASKorPSM. 37
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Figure2-10:ExamplesofcoherentmodulationschemesforUWBcommunications AlthoughlesscommonthanPSK,pulse-shapemodulationPSMisacoherent schemethathasbeenproposedforUWBcommunications[24,43,52].Thismodulation method,insteadofsignalphasesasinPSK,usesdifferentpulseshapestorepresent eachmodulationstateofthesymboltobetransmitted.Orthogonal-PSMOPSMisa typicalwayofimplementingthistypeofmodulationscheme[40,89].Itutilizespulses thatareorthogonaltoeachother.AnexampleofOPSMisshowninFigure2-10. 2.6.2Non-CoherentModulationSchemes Inmanycases,coherentdigitalmodulationschemesderivedfromconventional narrowbandsystemse.g.BPSKandQPSKarenotfeasibletoimplementlow-power UWBradios[86].Thishasledresearcherstoshifttowardsnon-coherentschemesdue tothepotentialofverylow-powerradioimplementations. Pulse-positionmodulationPPM,probablythemostcommonmodulationtechnique foundintheUWBliterature[37],usesthepositionintimeofapulsetorepresentthe modulationstatesofthesymboltobetransmitted.WithPPM,apulseislocatedin 38
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oneoftwotimeslotstorepresenteachmodulationstateor1ofa1-bitsymbol.An exampleofPPMisshowninFigure2-11a. AnothercommonandverysimplemodulationschemeusedforUWBcommunicationsison-offkeyingOOK.Withthismodulationtechnique,apulseanditsabsence areusedtorepresenteachmodulationstateofabinarybit.AnexampleofOOKis illustratedinFigure2-11a. Althoughlessfrequent,othernon-coherentmodulationschemesforUWBthat canbefoundintheliteraturearefrequencyshiftkeyingFSK[65,78]andamplitude shiftkeyingASK[53].FSKusesdifferentcenterfrequenciestorepresenttwoormore modulationstates.Figure2-11bshowsanexamplefora1-bitsymbolinwhichthe lowerfrequencyrepresentsabinarylogic0whilethehigherfrequencyrepresentsa logic1. WithASK,theinformationismodulatedintheamplitudeofthesignal,thatis,each amplitudevaluerepresentamodulationstate.AlthoughASKisnotcommonlyinUWB applications,itisworthmentioningasOOKandevenBPSKcanbeconsideredASK.To illustratethis,lettheASKsignals s 0 t and s 1 t representabinarylogic0andlogic1, respectively,where s i t = 8 > > < > > : i cos 2 f c t ,0 t t p 0, otherwise f c isthecenterfrequencyand i isthesignalamplitudecorrespondingtothe i th modulationstateinthiscase,0or1.If 0 =0and 0 =1,thenASKresemblesOOK. Ontheotherhand,if 0 = )]TJ/F22 11.9552 Tf 9.299 0 Td [(1and 1 =1,thenASKappearsasBPSK. 2.6.3OtherCoherentandNon-CoherentModulationSchemes Overthelastdecade,severalmodulationschemeshavebeendevelopedfor UWBcommunicationsinordertoachievehigherdataratesandimprovetheBER performance.Thesegobeyondthescopeofthediscussioninthiswork.Nevertheless, 39
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aMostcommonschemes bOtherschemes Figure2-11:Examplesofnon-coherentmodulationschemesforUWBcommunications 40
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afewofthemarementionednextwithreferencesthatthereadermaylookupforfurther information. Inthenon-coherenttechniquesdomain,transmitted-referenceTRsignaling [45,69]isanoftenusedtechniquetoachieveanon-coherentphasecomparisonof thecarriersignalatthereceiver.SimilartoPSKschemes,itusesthephaseofthe carriersignaltomodulatebinaryinformation.However,incontrasttoPSK,areference signalsometimescalledsignaltemplateistransmittedalongwiththesignalcarrying theinformation.Atthereceiver,thesignalscanbecorrelatedtoperformthephase comparisoneliminatingtheneedforcoherentcarrierrecovery. Anothermodulationschemeabletocomparephasesusinganon-coherentdemodulationisdifferential-PSKDPSK[11,44]. 15 Withthismodulationtechnique, theinformationismodulatedusingthedifferenceinphasesofthecarriersignal.At thereceiver,similartoTRsignaling,thecurrentsignalandtheprevioussignalcanbe correlatedtodeterminethechangeinphaseand,hence,demodulatethesignal. Inthecoherenttechniquesdomain,someinterestingmodulationschemesare bi-orthogonalkeyingBOK[59]andtherecentlyproposeddual-carriermodulation DCM[70].SimilartoOPSM,BOKutilizesdifferentpulseshapestomodulatebinary information.However,thesetofpulsesarebi-orthogonaltoeachotherratherthan orthogonalasinOPSM.Ontheotherhand,DCMusestwoQPSKsymbolsanda dual-frequencycarriertomodulatethebinaryinformation. 2.7UWBApplications ThevastbenetsofferedbyUWBcommunicationsqualifythistechnologyasa promisingalternativetoexistingandfutureshort-rangewirelessapplications.Asshown inFigure2-12,UWBcanbeusedtoimplementavarietyoftoday'swirelesstechnologies 15 ForPSK,bothcoherent[19]andnon-coherent[44]implementationscanbefoundin literature. 41
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Figure2-12:SomeUWBwirelessapplications. suchasWSN,WBAN,WPAN,RFID,andradiolocalizationsystems.Table2-3shows someofthesewirelesstechnologiesandhowtheycanmainlybenetfromtheUWB advantagesdiscussedinsection2.5.Forinstance,WBANandRFIDrequiresimple architecturesthatconsumelowenergyandproduceverysmallinterferencetoother wirelesssystems.Therefore,theybenetmainlyfromthelowenergyoperation,low complexity,andlowinterferencethatUWBcommunicationsoffer. UWBtechnologyhasbeenusedinthelastfewyearstorealizewirelesssystems thatweretraditionallyaccomplishedwithnarrowbandsometimeswithwideband communications.ThisdemonstratethefeasibilityofUWBasthealternativetechnology tocurrentwirelesssystems.TakeforexampleHDRwirelesssystemse.g.Wi-Fi.In [97,98],twoUWBtransceiversarereportedtoachievedataratesofupto400 Mbps whichisfarmorethanthe150 Mbps offeredbythepopular802.11 n Wi-Fistandardand closetothe450 Mbps offeredbytherecent802.11 ac standard.Similarly,in[5,17], [32,83],[33,62],and[81,96]seeTable2-3wirelessradioswereimplementedfor WSN,WBAN,RFID,andpositioningsystems,respectively,demonstratingtheability ofUWBcommunicationstobeanalternativetocurrenttechnologyindifferentwireless applications. 42
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Table2-3:WirelessapplicationsandtheirpotentialbenetsfromUWBtechnology Application Examples in Literature Low Energy HDR Low SNR Multipath Robustness High PG Low Complexity Low Interference WSN[5,17] WBAN[32,83] RFID[33,62] WPAN[97,98] Localization[81,96] 2.8UWBChannelModeling 2.8.1Large-ScalePathLossforIndoorUWBChannels Wirelesspropagationmodelsoftenuseanalyticalexpressionsorttingcurvesto recreateempiricaldatameasuredindifferentenvironments.Indoorpropagationmodels inparticularhavebeenextensivelystudiedovertheyearsandcanbefrequentlyfound intheliteraturee.g.[21,35,79,93].Allofthemagreethattheaveragereceivedpower decreasesexponentiallywithdistance.Therefore,theaveragepathloss PL canbe approximatedbythelog-distancemodelgivenby[66] PL d = PL 0 +10 PL log 10 d = d 0 [ dB ] anditiscommonlyusedtoestimatetheaveragepathlossasafunctionofdistance d InEquation2, d 0 isthereferencedistanceusuallychosenas1or3meters, PL 0 is thepathlossat d 0 ,and PL isthepathlossexponentwhichindicatestheslopeofthe averageincreaseinpathloss. Oneproblemwiththelog-distancepathlossmodelisthatitdoesnottakeinto accountthattheenvironmentalclutterdiffersfromonelocationtoanotherresultingin differentpathlossesevenwhentheT-Rseparationdistanceisthesame.Thisphenomenonisoftencalledshadowingorlog-normalshadowing.Empiricalobservations 43
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Table2-4:PathlossparametersforUWBchannelsinresidentialandcommercialbuildings ResidentialCommercial ParameterLOSNLOSLOSNLOS d 0 m 1111 PL 0 dB 45.950.343.747.3 PL dB 2.013.122.072.95 X PL std.dev., dB 3.023.82.34.1 haveshownthatthepathlosshasarandomcomponentandfollowsalog-normaldistribution[15].Thus,thepathloss PL forindoorenvironmentsisbetterrepresentedbythe log-normalshadowingmodeldescribedby PL d = PL 0 +10 PL log 10 d = d 0 + X PL [ dB ] where X PL isazero-meanGaussianrandomvariablewithstandarddeviationstd. dev. thatmodelstheshadowingeffect.UsingEquation2,anUWBindoorpath lossmodelforresidentialandcommercialbuildingswaspresentedin[35].Table2-4 showsthevaluesofthemodelparameters PL 0 PL d 0 ,and X PL forLOSandNLOS measurementsinresidentialandcommercialbuildings. Thislog-normalshadowingmodelusingthevaluesinTable2-4isillustratedin Figure2-13.Figure2-13ashows PL asafunctionofT-Rseparationdistancein residentialbuildingsforbothLOSandNLOS.Similarly,Figure2-13balsoshows PL butthistimeusingtheparametersvaluesforcommercialbuildings.Inbothgures,the solidlinesrepresenttheaveragepathloss PL andthedashedlinesenclosethe98% condence-intervalregioni.e. 2.33 2.8.2Small-ScaleFadingModelforIndoorUWBMultipathChannels Incontrasttonarrowbandsystems,inUWBsystemsthesamplingperiodismuch smallerdueitswidebandnatureand,hence,thenumberofresolvablemultipath 44
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aResidential bCommercial Figure2-13:PathlossforUWBchannelsinresidentialandcommercialbuildings componentswithinthisperiodistoosmalltojustifyitsapproximationundertheCLT. Therefore,itisoftenarguedthatRayleighandRicefading 16 arenotgoodsmall-scale fadingmodelsforUWBwirelesschannels.Despiteofthisargument,thereareempirical measurementsthatsupporttheRayleigh[60]andRice[48]distributionstomodelUWB multipathfadingscenarios.Furthermore,accordingto[74],theAkaikeInformation CriterionAIC[2]supportsRayleighandRiceamplitudedistributionstoadequately modeltheUWBchannelsmeasuredbytheauthors. AlthoughtherearemeasurementsthatsupportRayleighandRicedistributionsto modelsmall-scalefadingforsomeUWBscenarios,extensiveworkcanbefoundinthe literatureusingotherdistributionstomodelUWBchannelsmoreaccurately.Someof thesedistributionsareNakagami[13],Weibull[36],andlog-normal[29].Amongthese, themostcommonlyfoundinliteratureisthelog-normaldistributionprobablybecause itistheoneadoptedbytheIEEEP802.15.3ataskgroupinits2003nalreport[27]. 16 Fornarrowbandsystems,RayleighandRiceareprobablythemostcommonlyused distributionstomodelsmall-scalefading. 45
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Therefore,tomodelmultipathfading,theIEEEP802.15modelisusedinthisworkandit ispresentednext. TheIEEEP802.15.3amodelisderivedfromtheSaleh-Valenzuelamodel[72]with minormodications.Itconsistsofthediscrete-timechannelimpulseresponseCIR givenby h i t = X i L X l =0 K X k =0 i k l )]TJ/F49 11.9552 Tf 5.48 -9.684 Td [(t )]TJ/F49 11.9552 Tf 11.955 0 Td [(T i l )]TJ/F25 11.9552 Tf 11.955 0 Td [( i k l where i k l arethemultipathgaincoefcients, T i l isthedelayofthe l th cluster, i k l isthedelayofthe k th multipathcomponentrelativetothe l th clusterarrivaltime T i l isthedeltafunction, 17 i referstothe i th realization, L isthetotalnumberof clusters,and K isthenumberofraysmultipathcomponentswithinthe l th cluster.The randomvariable X i representsshadowingandfollowsalog-normaldistributionsuchthat 20 log 10 j X i j N )]TJ/F22 11.9552 Tf 5.479 -9.684 Td [(0, 2 X 18 or,equivalently, j X i j =10 n X = 20 where n X N )]TJ/F22 11.9552 Tf 5.479 -9.684 Td [(0, 2 X .Themultipathgaincoefcientsaredenedas k l = p k l j l k l j = p k l Y k l where p k l isequiprobable 1toaccountforsignalinversionduetoreections, l representsthefadingassociatedwiththe l th cluster,and k l modelsthefadingassociatedwiththe k th rayofthe l th cluster.InEquation2, j l k l j followsalog-normal 17 TheDiracdeltafunction t )]TJ/F49 11.9552 Tf 11.956 0 Td [(t 0 canbeinformallydenedasafunctionthatis zeroeverywhereexceptat t = t 0 withintegralofoneoverallrealnumberswhichimpliesthat t )]TJ/F49 11.9552 Tf 11.955 0 Td [(t 0 = 1 at t = t 0 .However,inelectricalengineeringitissometimesused as t )]TJ/F49 11.9552 Tf 11.955 0 Td [(t 0 =1for t = t 0 andzerootherwise.ThisisthecaseforEquation2. 18 N )]TJ/F25 11.9552 Tf 5.479 -9.684 Td [( 2 isthecommonnotationforanormalGaussianrandomvariablewith mean andvariance 2 46
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distributionsuchthat20 log 10 j l k l j N )]TJ/F25 11.9552 Tf 5.48 -9.684 Td [( k l 2 1 + 2 2 or Y k l = j l k l j =10 k l + n 1 + n 2 = 20 where n 1 N )]TJ/F22 11.9552 Tf 5.479 -9.684 Td [(0, 2 1 and n 2 N )]TJ/F22 11.9552 Tf 5.48 -9.684 Td [(0, 2 2 areindependentrandomvariablescorrespondingtothefadingoneachclusterandray,respectively,and k l = 10 [ ln 0 )]TJ/F49 11.9552 Tf 11.955 0 Td [(T l = )]TJ/F23 11.9552 Tf 8.98 0 Td [()]TJ/F25 11.9552 Tf 11.956 0 Td [( k l = ] ln 10 )]TJ/F22 11.9552 Tf 13.151 8.847 Td [(ln 10 )]TJ/F25 11.9552 Tf 5.479 -9.684 Td [( 2 1 + 2 2 20 InEquation2, 0 isthemeanenergyoftherstpathoftherstclusterand )]TJ/F22 11.9552 Tf 9.647 0 Td [(and aremodelparameters.Theexcessdelayofthe l th cluster T l withclusterarrivalrate canbemodeledas T l = T l )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 + n T ,1 2 + n T ,2 2 for l =1,2,..., L ,where [ n T ,1 n T ,2 ] N 0, 2 )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 areindependentandidentically distributedi.i.dnormalrandomvariablesand T 0 =0forLOSchannelsor T 0 = n T ,1 2 + n T ,2 2 forNLOS.Similarly,thedelayofthe k th multipathcomponentwithinthe l th cluster k l withrayarrivalrate canbemodeledas k l = k )]TJ/F22 7.9701 Tf 6.587 0 Td [(1, l + n ,1 2 + n ,2 2 for k =1,2,..., K ,where [ n ,1 n ,2 ] N 0, 2 )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 arei.i.dnormalrandomvariables and 0, l =0bydenitionsinceitisrelativetothecluster,i.e.therstrayofthe l th cluster arrivesattime T l Basedontheequationspresentedinthissection,Table2-5showsallthenecessary parameterstomodelCIRsforthefourUWBchannelscenariospresentedintheIEEE P802.15.3ataskgroupreport[27].ThechannelmodelCM1isbasedonLOSchannel measurementswithaT-Rdistancebetween0and4 m .CM2andCM3correspond toNLOSmeasurementsatT-Rdistancesof0 )]TJ/F22 11.9552 Tf 12.612 0 Td [(4 m and4 )]TJ/F22 11.9552 Tf 12.612 0 Td [(10 m ,respectively,and CM4wasgeneratedtorepresentanextremeNLOSmultipathchannel.Thesechannel 47
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Table2-5:ModelparametersforUWBmultipathchannels ParameterCM1CM2CM3CM4 x dB 3.00003.00003.00003.0000 1 dB 3.39413.39413.39413.3941 2 dB 3.39413.39413.39413.3941 )]TJ/F22 11.9552 Tf 86.462 0 Td [(7.10005.500014.000024.0000 4.30006.70007.900012.0000 nsec )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 0.02330.40000.06670.0667 nsec )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 2.50000.50002.10002.1000 modelsareparticularlyimportantwhenoptimizingEDradiosaswillbediscussedin Chapter3. 48
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CHAPTER3 OPTIMIZATIONOFENERGY-DETECTIONPPMRECEIVERS Forlowcomplexity,lowcost,andverylowpowerwirelessapplications,noncoherentmodulationschemesareinmostcasesthebestsolutionasexplainedin section2.6.Non-coherentarchitecturesareoftenimplementedusingPPMtomodulate thebinaryinformationtobetransmitted.TodemodulateaPPMsignal,awell-known techniqueisenergydetectionED.InmanypracticalapplicationsfoundintheUWB literaturee.g.[16,17,34,47,51,92,97],EDisfrequentlychosenasthedemodulation techniquemainlybecausethereceiverarchitectureisrelativelysimpletoimplementand offersusuallyoffersverylow-poweroperation. WithPPMbrieyintroducedinsubsection2.6.2,apulseistransmittedinone oftwotimewindowstorepresentabinarylogic1or0.Therefore,todemodulatethe receivedsignalitisnecessarytodetermineinwhichwindowthepulsewastransmitted in.Todothis,withED,theenergyineachwindowiscalculatedandcompared.Then, thepulseisassumedtobetransmittedinthewindowwiththehighestenergy.Figure 3-1showsthegeneralarchitectureofEDreceivers.Asshown,afterchannelselection andamplication,thetransmittedsignalissquaredandintegratedinordertodetermine itsenergy.Abitdecisionisthencarriedoutbycomparingtheenergiesinthetwotime windowsalsoknownasintegrationwindows. Duetoitsbasicprincipleofenergycomparison,EDreceiversareverysensitiveto channelnoisei.e.anincreaseinnoiseenergyincreasestheprobabilityofbit-error. Figure3-1:GeneralarchitectureforEDreceivers 49
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AssuminganAWGNchannel,thenoiseenergyvarieslinearlywiththelengthofthe integrationwindowandthelterbandwidthduetoitsconstantPSD.Hence,theBPF bandwidthandtheintegrationtimeofthereceiverplayavitalroleinthereceiver's performanceandtheymustbecarefullychoseninordertominimizetheBERi.e. probabilityofbit-error. 3.1ChapterContributions Inthischapter,theeffectsofreducingthereceiver'sbandwidthandintegration timearediscussedandgeneralequationstodeterminethetheiroptimalvaluesare derived.Asdiscussedinsubsection3.2,theseequationsareofspecialinterestfor bothsystemdesignandpotentialcognitiveradios.Furthermore,differentinterference sources,namelyACI,ISI,andIFI,aretakenintoconsiderationtoaccuratelypredictthe optimaloptimalbandwidthandintegrationtimeofPPM-EDreceiversinrealisticwireless scenarios. 3.2Previouswork Therehasbeenpreviousworktoshowthereareoptimalbandwidthsandintegration timesthatminimizethebit-errorsinducedatthereceiverbyUWB.In[88]and[20],the well-knownBERequationforPPMEDreceiversisusedtographicallyshowthatthere existsoptimalreceiverbandwidthsandoptimalintegrationtimes,respectively.In[71], theauthorsproposedanadaptiveEDreceiverand,onceagain,graphicallydemonstrate theoptimalintegrationinterval. Thepreviousworkhasbeenabletodemonstratetheexistenceofoptimalvaluesfor thereceiverbandwidthandintegrationtime.However,itfailstoprovidegeneralclosedformequationsthataccuratelypredicttheseoptimalvaluesasafunctionofsystem parameterssuchasthebandwidthofthetransmittedsignalandthetargetBER.Such generalequationswouldbeagreatadvantageforsystemdesignerssince,otherwise, ndingtheoptimalvaluestimecouldleadtospendvaluabletimerunningsimulationsor writingcodetosolveBERequationsnumerically. 50
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Generalequationsforoptimalbandwidthsandintegrationtimesnotonlyfacilitate thedesignprocessbuttheymayalsobebenecialinPPMcognitiveradios.Forinstance,aPPMsystemthatadjuststhereceiverbandwidthand/orintegrationtimeto theoptimalvaluebasedonparameterssuchasthesignalbandwidthorthetargetBER wouldspendlessprocessingpowerbyhavingbuilt-inequationsinsteadofalgorithmsto numericallyndtheoptimalvalue. Inadditiontothelackofclosed-formequationsfortheoptimalbandwidthsandintegrationtimes,thepreviousworkdoesnottakeintoaccountinterference.Inparticular, mainlyduetothemultipathfading,ISIandIFI 1 cannotbeignoredwhendeterminingthe optimalintegrationtime.Ontheotherhand,ACIbecomesmorerelevantwhenthereare multipletransmissionchannelsrelativelyclosetoeachother.Inthiscase,ACIcannotbe ignoredwhenndingtheoptimalreceiverbandwidth. 3.3Energy-DetectionDemodulationforPPM WhenusingPPM,abinarybitismodulatedbytransmittingapulseinoneoftwo integrationwindows.Forinstance,inFigure3-2a,apulseistransmittedintherst integrationwindowtorepresentabinarylogic1.Apulseinthesecondwindowwould haverepresentedalogic0.Assumethat p t isthetransmittedpulse, h t istheCIR, and n t isabbrefAWGN.Then,thereceivedsignalseeFigure3-2bcanbeexpressed as s t = p t h t + n t where representstheconvolutionoftwofunctions.WithenergydetectionED demodulation,thereceivedsignal s t issquaredandintegratedtodeterminethetotal energyineachwindowandthebitdecisionismadebycomparingtheseenergies,i.e. 1 Atthispoint,inter-frameinterferenceIFIhasnotbeenintroducedyet.Itwillbe explainedinsection3.5. 51
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aTransmittedsignalbinarylogic1 bReceivedsignalwithAWGN cReceivedsignalaftersquaring dReceivedsignalaftersquaring andintegrationi.e.signalenergy Figure3-2:SignalprocessingforaED-PPMreceiver E 1 = T w 0 [ s t + n t ] 2 dt 1 ? 0 E 2 = 2 T w T w [ s t + n t ] 2 dt where T w istheintegrationtime.Figure3-2cshowsthereceivedsignalafterself-mixing, i.e. [ s t + n t ] 2 .Finally,Figure3-2dshowstheintegrationofthesquaredsignalsin eachintegrationwindow,i.e.theenergiesin E 1 and E 2 .Notethat E 1 < E 2 whichresults inanerrorsincethepulsewastransmittedintherstintegrationwindow.Thisisa bit-errorcausedbyAWGNandanexampleofthepreviousargumentthatEDreceivers areverysensitivetonoise. 52
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3.3.1ProbabilityofBit-Error InthepreviousexampleFigure3-2,abit-erroroccurredbecausetheenergyin thesecondintegrationwindow E 2 washigherthantheenergyintherstwindow E 1 andthepulsewastransmittedintherstwindow.Consequently,ifthesameexampleis used,theprobabilityofbit-erroris P ED = P E 1 E 2 = P E 1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(E 2 0 .Theexpression tocalculatethisprobabilityisderivedin[64]andsummarizedinAppendixAforthe convenienceofthereader. IfthereceivedsignalissampledattheNyquistrate 2 andthenumberofsamples ineachintegrationwindowissufcientlylargeormoresamplesaccordingto[20] then,byemployingtheCLT, P ED canbeapproximatedby P ED Q 0 B @ E b = N 0 p 2 B T w +2 E b = N 0 1 C A where E b istheenergyperbit, E b = N 0 isoftencalledtheSNR-per-bit, B isthesignal bandwidth, T w istheintegrationtime,and Q x =1 = p 2 1 x exp )]TJ/F49 10.9091 Tf 8.485 0 Td [(u 2 = 2 du isthewell-knownQ-function. 3.4OptimalReceiverBandwidth Whendesigningwirelessradios,thereceiverbandwidthi.e.BPFbandwidthis typicallychosentobethe10 dB -bandwidthofthetransmissionsignal[4].However, inmostcases,thisbandwidthisnottheoptimalvalue.Typically,theoptimalreceiver bandwidthissmallerthanthe10 dB -bandwidthofthesignalaswillbeshownlaterinthis chapter.Furthermore,asmallerreceiverbandwidthrelaxesthespecicationsonthe 2 TheNyquistrateistheminimumsamplingrateforwhichthesampledsignalretains allthepropertiesoftheoriginalsignal. 53
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receivercircuitse.g.LNAbandwidth,ADCsampleratewhilereducingtheintegration ofnoiseenergyintothesystem. 3.4.1EffectofReceiverBandwidthReduction Intheintroductionofthischapter,theimportanceoftheBPFwasmotivated basedonthefactthatEDreceiversareverysensitivetonoise.Thus,theimpact ofnoiseonreceiver'sBERperformancecanbereducedbymaximizingtheSNR. ThiscanbeinferredfromEquation3since E b = N 0 isproportionaltoSNR,i.e.SNR = E b = N 0 B T w )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 .BycarefullychoosingtheBPFbandwidth,theSNRcanbe maximized.Toillustratethis,let SNR = P s )]TJ/F45 11.9552 Tf 11.955 0 Td [( P s P n )]TJ/F45 11.9552 Tf 11.955 0 Td [( P n = P s P n 0 B @ 1 )]TJ/F45 11.9552 Tf 11.955 0 Td [( P s = P s 1 )]TJ/F45 11.9552 Tf 11.955 0 Td [( P n = P n 1 C A where,asshowninFigure3-3, P s and P n arethereductioninsignalandnoise power,respectively,and P s and P n arethenominalsignalandnoisepowerwhenthe receiverbandwidthisequaltothe10 dB -bandwidthofthetransmittedsignal. AstheBPFbandwidthisdecreasedfromthe10 dB -bandwidth,thenumerator ofequation3decreasesataslowerratethanthedenominator,i.e. P s = P s < P n = P n .Hence,theSNRincreasesuntil P s = P s isnolongersmallerthan P n = P n .The Figure3-3:Powerspectraldensitiesofasquarepulse,Gaussianpulse,andAWGN 54
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Figure3-4:Signalandnoiseenergyproleasafunctionofthereceiverbandwidth maximumvalueforSNRisachievedwhentheratesofchange P s = P s and P n = P n are equal.ThiscanbegraphicallyseeninFigure3-4.Bothsignalandnoisepowerincrease asthereceiverbandwidthincreases;however, P s = P s < P n = P n remainstrueuntilthe slopei.e.rateofchangeofthesignalpowerisequaltotheslopeofthenoiseenergy, i.e. P s = P s = P n = P n .Atthispoint,theSNRismaximized. 3.4.2ModiedProbabilityofBit-ErrorandOptimalReceiverBandwidth Inthissubsection,Equation3ismodiedtoincludetheeffectofreducingthe BPFbandwidth.Forconvenienceandcomparisonpurposes,thereceiverbandwidth isnormalizedtothecommonlyused10 dB -bandwidthofthetransmittedsignal,i.e. = f = B 10 dB where f istheBPFbandwidth.Furthermore,squarepulsesareusedas thetransmittedsignalsincetheyaretypicallyusedintheimplementationofUWBradios mainlyduetothesimplicitytogeneratethem.Nevertheless,theresultsaresimilarfor otherpulseshapessuchasGaussiansincethePSDofaGaussianpulseiscomparable tothatofasquarepulseinsidethe10 dB -bandwidthlessthan3%ofpowerdifference asshowninFigure3-3. 55
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3.4.2.1ProbabilityofBit-ErrorandReceiverBandwidth TheFouriertransformofasquarepulseisgivenbythe sinc function V T p f = T p sin )]TJ/F25 11.9552 Tf 5.479 -9.684 Td [( T p f T p f where T p pulsetimewidth.TheESDisgivenby S E f = V T p f 2 .Then,integrating S E f overarangeoffrequenciesgivesthetotalenergyofthesignaloverthatrange. Thus,thepulseenergyi.e.energyperbitbasedontheBPFbandwidth f is E b f = f = 2 )]TJ/F46 7.9701 Tf 6.586 0 Td [( f = 2 S E f df =2 f = 2 )]TJ/F46 7.9701 Tf 6.587 0 Td [( f = 2 T p sin )]TJ/F25 11.9552 Tf 5.479 -9.683 Td [( T p f T p f 2 df E b f =2 cos )]TJ/F25 11.9552 Tf 5.48 -9.684 Td [( T p f + T p f Si )]TJ/F25 11.9552 Tf 5.48 -9.684 Td [( T p f )]TJ/F22 11.9552 Tf 11.955 0 Td [(1 2 f where Si x = x 0 sin t = t dt .The10 dB -bandwidthofthetransmittedsignalcan becalculatedusingtheTaylorseriesofa sinc functionwhichyieldsthefollowing approximation B 10 dB 1.476 = T p Withthisapproximationandthepreviouslydened = f = B 10 dB ,Equation3 becomes E b =2 cos 1.476 + T p f Si 1.476 )]TJ/F22 11.9552 Tf 11.955 0 Td [(1 2 B 10 dB Toaccountforthereductioninthedetectedsignalenergyduetoareceiverbandwidth reduction,anenergyscalingfactorcanbedenedas = E b = E b =1 56
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andincorporatedintoEquation3.Then,theprobabilityofbit-errorcanberewrittenas P ED Q 0 B @ E b = N 0 p 2 T w B 10 dB +2 E b = N 0 1 C A andsolvingitfor E b = N 0 givestherequiredSNR-per-bit SNR bit toachievecertain BERperformance SNR bit = E b N 0 = K 2 0 B B @ 1+ v u u t 1+ 2 T w B 10 dB K 2 1 C C A where K = Q )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 P ED = Q )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 BER and Q )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 istheinverseQ-function.Equation3 canbeusedtoobtainanoptimalbandwidthaswillbeshownnext. 3.4.2.2OptimalReceiverBandwidth Theoptimalreceiverbandwidth opt isthevalueof thatminimizesEquation3, i.e.minimizestherequired SNR bit .Hence, opt = Solve 2 6 4 @ @ [ SNR bit =0 ] 3 7 5 Equation3cannotbesolvedexplicitlymainlyduetothecomplexityofthescaling factor andthesquarerootterm.Thus,toobtainasolutionfor opt ,approximations for p 1+2 T w B 10 dB = K 2 and areneeded.Formathematicalsimplicity,a non-linearleast-squareregressionisusedwiththeexponentialt y i = a i + b i exp c i + d i x where x istheregressionparameteri.e.theindependentvariable, a i b i c i d i are constants,and i identiesthedesiredapproximation,i.e. i =1refersto p 1+ X where X =2 T w B 10 dB = K 2 and i =2to .Thevaluesfortheconstantsareshown 57
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Table3-1:ConstantvaluesfortheexponentialtgivenbyEquation3 i Approximation Term Regression Parameter a i b i c i d i 1 X 104.82 )]TJ/F22 11.9552 Tf 9.298 0 Td [(0.661.73 )]TJ/F22 11.9552 Tf 9.299 0 Td [(0.089 1 p 1+ X 10 X 5010.78 )]TJ/F22 11.9552 Tf 9.298 0 Td [(1.351.89 )]TJ/F22 11.9552 Tf 9.299 0 Td [(0.018 50 X 25022.90 )]TJ/F22 11.9552 Tf 9.299 0 Td [(11.770.49 )]TJ/F22 11.9552 Tf 9.299 0 Td [(0.004 2 0.3 < 11.138 )]TJ/F22 11.9552 Tf 9.298 0 Td [(0.102.60 )]TJ/F22 11.9552 Tf 9.298 0 Td [(2.35 Table3-2:Constantvaluesfor opt Range A B C D 1 M 100.77567.517.11.355 10 M 500.76650.019.50.350 50 M 2500.742120.033.00.100 inTable3-1.Now,usingEquation3toestimateEquation3givesthefollowing approximation SNR bit K 2 1+ a 1 + b 1 exp c 1 + d 1 M a 2 + b 2 exp c 2 + d 2 where M =2 T w B 10 dB = K 2 .Equation3canbeusedtosolveEquation3.Taking itsderivativeandthensolvingfor givestheoptimalnormalizedbandwidth opt which canbeapproximatedby opt = A + ln )]TJ/F49 11.9552 Tf 5.479 -9.684 Td [(B = M C + D M TheconstantsinEquation3aresummarizedinTable3-2forthreedifferent rangesof M andamaximumerroroflessthan1%. 3.4.3Adjacent-ChannelInterference Theanalysisinthissectionassumessquarepulsesastheinterferencesignal.The ideabehindthisanalysisistogainabetterunderstandingonhowtheBPFbandwidth 58
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changestheBERperformanceofaPPMEDreceiverinthepresenceofothertransmitterswithsimilarsignalsbutoperatinginadjacentchannels,therefore,producingACI 3.4.3.1EffectofACIontheReceiverPerformance SincetheFCCapprovalforUWBwirelesssystems,severalpapersrelatedtoUWB -specicinterferencehavebeenpublishedandamongthemare[28,31,49,57,87]. Differentapproachestomodelin-bandUWBinterferencecanbefoundinliterature. However,manyofthemagreeinaGaussianapproximationmodele.g.[28,57,87]. Consequently,hereACIistreatedasAWGNandmodeledwithaatpowerspectrum. Figure3-5showsthespectrumofthetransmittedsignal,theBPF,theACIsignals, andtheinterferencePSD I 0 .Theshadedregionrepresentstheinterferenceenergy E i Tocalculatethisenergy,Equation3canbeusedwithdifferentintegrationlimits.Then, E i f ch f = f ch + f = 2 f ch )]TJ/F46 7.9701 Tf 6.587 0 Td [( f = 2 T p sin )]TJ/F25 11.9552 Tf 5.48 -9.684 Td [( T p f T p f 2 df where f ch isthefrequencyspacebetweenthetransmittedsignalandtheinterference signali.e.channelspacingand f istheBPFbandwidthseeFigure3-5.Again, forconvenience, f ch and f arenormalizedtothe10 dB -bandwidthofthesignal,i.e. Figure3-5:PSDofthetransmittedsignalandACIsignals 59
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= f ch = B 10 dB and = f = B 10 dB .Then,bysolving3,theACIenergycanbe expressedas E i = cos c 1 1 + cos c 2 2 + c [ Si c 1 + Si c 2 ] )]TJ/F22 11.9552 Tf 17.159 11.835 Td [(2 1 2 2 B 10 dB where c =1.476 1 = )]TJ/F22 11.9552 Tf 12.124 0 Td [(2 ,and 1 = +2 .Now,recalltheassumptionofat powerspectrumforACI.Then,theinterferencespectraldensityisgivenby I 0 = P i = f where P i istheinterferenceaveragepowerand,forasingle1-sidedadjacentinterferer, itcanbeapproximatedby P i = E i = T s where T s =2 T w .Therefore,thespectral densityofmultiple2-sidedadjacentinterfererscanbewrittenas I 0 = 2 T w B 10 dB m X k =1 E i k k where m isthetotalnumberof2-sidedinterfererse.g. m =1inFigure3-5and k = E b =1 = E i 0,1 istheSIRofthe k th 2-sidedinterferer. ToaccountforACI,aneffective SNR bit ,i.e. E b = N 0 eff ,canbeusedinEquation3 3.SincetheinterferenceismodeledbyaGaussianapproximationasmotivatedearlier, theeffective SNR bit canbeexpressedas E b = N 0 eff = E b = N 0 + I 0 whichisoftencalled thesignal-to-interference-and-noiseratioabbrSINRSignal-to-interference-and-noise ratio.Here, N 0 = E b = E b = N 0 I 0 = I 0 ,and E b E b =1 .Thus, 0 B @ E b N 0 1 C A eff = 2 6 4 1 E b = N 0 + I 0 E b =1 3 7 5 )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 Bysubstituting E b = N 0 for E b = N 0 eff toaccountforACI,Equation3canberewritten as 60
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P ED Q 0 B B B B B B B B B B @ 2 6 4 1 E b = N 0 + I 0 E b =1 3 7 5 )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 v u u u u t 2 T w B 10 dB +2 2 6 4 1 E b = N 0 + I 0 E b =1 3 7 5 )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 1 C C C C C C C C C C A andsolvedfor E b = N 0 whichyieldstherequired SNR bit asafunctionofthereceiver bandwidth andthechannelspacing ,i.e. SNR bit = 2 6 4 K 2 1+ p 1+2 T w B 10 dB = K 2 )]TJ/F22 11.9552 Tf 39.639 11.834 Td [(1 SIR bit 3 7 5 )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 where SIR bit = E b =1 = I 0 3.4.3.2AnApproximationfortheOptimalReceiverBandwidthinthePresenceof ACI Equation3canonlybesolvednumericallyduetoitscomplexity.However, byfollowingtheapproachinsubsection3.4.2.2andmakingsomeassumptions,an expressionfor opt canbeobtained.Inthiscase,theassumptionsareasfollows: 1.Onlytherst2-sidedACIissignicanti.e. m =1andithasaunitarySIRi.e. 1 =1. 2.UsingtheexponentialtgivenbyEquation3, E i 1 2 [ exp 3.35+3.85 1 )]TJ/F22 11.9552 Tf 11.955 0 Td [(exp 3.35+3.85 2 ] 3.TheACIsignalhasthesamebandwidthasthetransmittedsignal. Fortheseassumptions,theoptimalbandwidthcanbecalculatedbyusingtheexpressionfor SNR bit giveninEquation3andsolvingEquation3.Thisyieldsthe followingapproximation 61
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Figure3-6:Simulatorblockdiagram opt A + ln )]TJ/F49 11.9552 Tf 5.479 -9.684 Td [(B = M )]TJ/F30 11.9552 Tf 11.955 9.684 Td [()]TJ/F49 11.9552 Tf 5.479 -9.684 Td [(E = ln )]TJ/F49 11.9552 Tf 5.479 -9.684 Td [(F = C + M D where A B C D aregiveninTable3-2, E =5.20, F =0.89,and10 M < 50. Recallthat M =2 T w B 10 dB = K 2 3.4.4SimulationSetupandValidation Tosupportandcorroboratethetheorydevelopedinthissection,asimulatorfora PPM-EDreceiverwasbuiltinMATLAB R .Itssetupisdiscussednextfollowedbythe simulationsruntovalidatethatitisproperlyworking. 3.4.4.1Setup Figure3-6showsthesimulatorblockdiagram.Ithasthreemajorparts:modulation, channelmodeling,demodulation. Inthemodulationpart,streamofbinarybitsarerandomlygenerated.Theseare thenmodulatedandup-convertedusingPPMandsquarepulsesasthetransmission signal. Tosimulatethewirelesschannel,thechannelmodelingpartaddsAWGNandACI tothetransmittedsignalasfollows: 62
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1.AWGN:Since E b = N 0 isspecied,then N 0 canbecalculatedifthe E b isknown. Itcanbecalculatedbysquaringandintegratingthemodulatedsignalforonebit. Thus, N 0 = E b E b = N 0 = 1 E b = N 0 N X i =1 s 2 i where s i isthe i th sampleofthereceivedsignaland N =2 T w B 10 dB isthetotal numberofsamples.Theone-sidednoiseaveragepowercanbecalculatedas P 0 = N 0 2 f s = f s 2 E b = N 0 N X i =1 s 2 i Finally,thenoisesignalisrealizedbygenerating N randomvaluesthatare normally-distributedwithzero-meanandvariance 2 = P 0 2.ACI:Togenerateinterference,anotherstreamofrandombitsisgenerated, modulated,andup-convertedtoanadjacentchannel.TheamplitudeoftheACI signalsarescaledusingthespeciedSIR,denedas k inEquation3,such thatthefollowingequationissatised N X i =1 s 2 i = 1 N X i =1 I 2 i where I i isthe i th sampleoftheACIsignal. Finally,thedemodulationpartsimulatesthesignalprocessingattheEDreceiver.The receivedsignalisrstltered,thensquaredandintegratedoverperiodsof T w .Each pairofintegrationwindowsisthencomparedandabitdecisionismadebasedonthe highestenergy. 3.4.4.2Validation Tovalidatethesimulator,severalsimulationswereruntocomparetheresultswith thewell-knownBERexpressiongivenbyEquation3.Figure3-7showsthesimulated 63
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Figure3-7:ComparisonbetweensimulationsandEquation3tovalidatethesimulator BERcurvesfortwosignalbandwidths GHz and2 GHz andanintegrationtimeof 30 ns alongwiththeidealcurvesobtainedusingEquation3.Thesimulatedvalues closelyagreewiththeidealvalues.Hence,thesimulatorcanpredictwithaccuracythe BERperformanceforaPPM-EDreceiveranditwillbeusednexttocorroboratethe theorydevelopedthroughoutthissection. 3.4.5Analysis 3.4.5.1TheoryCorroboration ThemainequationsderivedinthissectionareEquation3andEquation3 22whichareexpressionstocalculatetheBERofaPPM-EDreceiverasafunction ofitsbandwidth.Equation3doesnottakeintoaccountACIwhileEquation3 considersACIundercertainassumptionsasstatedinsubsection3.4.3.2.Theother importantequationsareEquation3,Equation3,Equation3,andEquation 3.ThesearejustalgebraicmanipulationsofEquation3andEquation3. Thus,tocorroboratethetheorydeveloped,itissufcienttoverifythatEquation3 andEquation3hold.Figure3-8ashowsaplotofBERfortheidealvaluesobtained usingEquation3andtheresultsfromthesimulationsfor =1.Itcanbeseenthat 64
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aNoACI,Equation 3 bACIwith =0.8 ,Equation 3 Figure3-8:Comparisonbetweensimulations,Equation3,andEquation3 Equation3yieldsvaluesthatareveryclosetothosesimulatedand,therefore,it holds.Similarly,Figure3-8bcorroboratesEquation3. 3.4.5.2NumericalResults Designersinwirelesscommunicationsuselinkbudgetswhenimplementing wirelessradios.Animportantparameterforthelinkbudgetisthe SNR bit or E b = N 0 requiredtoobtainadesiredBER.ThisvaluecanbecalculatedwithEquation3and Equation3asafunctionofreceiverbandwidth,desiredBERand,inthecaseof Equation3,interferencefrequencyspacing.Figure3-9showstherequired E b = N 0 as afunctionofthenormalizedreceiverbandwidth toachieveaBERof10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 .Notethat thelowestvalueof E b = N 0 correspondstotheoptimalreceiverbandwidth.However,a smallerreceiverbandwidthcanprovidehardwareadvantagese.g.lowersamplingrate, lowerpowerconsumptionataminimalcostintherequired E b = N 0 .Forinstance,fora 1 GHz signal,thereceiverbandwidthcouldbereducedbyhalfi.e. =0.5withaloss in E b = N 0 oflessthan1 dB .Ifthesystemcantoleratethisdegradation,thebenetsfor thesystemmaybesignicante.g.halfthesamplingrate,lowerpowerconsumption, betterinputmatching. 65
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Figure3-9:Required SNR bit toachievea BER =10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 FromFigure3-9,itisalsoclearthatthisoptimalreceiverbandwidthisafunction ofthesignal's10 dB -bandwidth B 10 dB .Equation3isanaccurateapproximationfor thenormalizedoptimalreceiverbandwidth opt anditisplottedagainst B 10 dB inFigure 3-10.Notethathavingalargersignalbandwidthincreasesthesavingsinreceiver bandwidth.Inotherwords,theoptimalreceiverbandwidthbecomessmallerwithrespect tothesignalbandwidthrecall = f = B 10 dB asthelatterincreases. 3.5OptimalIntegrationTime AnED-PPMreceiveressentiallysquaresandintegratesthereceivedsignalto determineitsenergyintwotimewindows.Then,bycomparingbothenergies,abit decisionismade.Asdiscussedbefore,thisprincipleofenergydetectionmakesthe receivermorevulnerabletonoiseand,sinceboththesignalandnoiseenergiesare proportionaltotheintegrationtime, T w mustbecarefullychosensothattheBERcan beminimized. 3.5.1EffectofIntegrationTimeduetoMultipathFading Theenergyofatransmittedpulseisspreadintimeduetotheeffectofmultipath fading.Thus,todetectthepulseenergy,thereceivedsignalmustbeintegratedfor asignicantlylargertimethanthepulsewidth.Alargerintegrationtimeallowsthe 66
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Figure3-10:Normalizedoptimalreceiverbandwidthversusthesignal's10 dB bandwidthfor T w =30 ns =1,and BER =10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 detectionofmostofthesignalenergy E b ,however,italsointegratesmorenoise energy E 0 intothesystemwhichdegradesitsBERperformance.Hence,bycarefully choosingtheintegrationtime,theSNRcanbemaximizedjustlikechoosingtheoptimal receiverbandwidthasdiscussedinsection3.4. ToshowtheconceptofSNRmaximizationletSNR= P b = P 0 ,where P b and P 0 aretheaveragepowerofthetransmittedsignalandnoise,respectively.Since E b = P b T w and E 0 = P 0 T w =2 N 0 B T w where B isthereceiverbandwidth, 3 then SNR= E b = E 0 .Figure3-11shows E b and E 0 asafunctionof T w .As T w increases both E b and E 0 increasebutatdifferentrates.Whentheincreaserateslopeof E b becomessmallerthantheconstantslopeof E 0 ,theSNRreachesitsmaximum. 3 Thefocusofthissectionistheintegrationtime T w and,hence,thereceiverbandwidthisassumedtobe B = B 10 dB 67
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Figure3-11:Signalandnoiseenergyproleasafunctionofintegrationtime 3.5.2ModiedProbabilityofBit-ErrorandOptimalIntegrationTime Followingtheapproachusedinsection3.4forthereceiverbandwidth,inthis subsectionascalingfactorfor E b isemployedtomodifyEquation3.Themodied equationisthenusedtoderivetheoptimalintegrationtime. 3.5.2.1ProbabilityofBit-ErrorandIntegrationTime Thereceivedsignal s t canberepresentedbytheconvolutionoftheCIR h t and thetransmittedpulse p t ,i.e. s t = h t p t Then,theenergyofthereceivedsignalasafunctionofintegrationtimecanbecalculatedas E b T w = T w 0 s 2 t dt = f s T w X i s 2 i = f s where s i isthevalueofthe i th sampleofthereceivedsignal s t f s isthesampling frequencyand T w istheintegrationtime.NormalizingEquation3tothetotalenergy ofthetransmittedsignal,i.e. E b T w 1 ,givestheenergyscalingfactor T w = E b T w E b 1 68
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ToobtainthemodiedBERexpression,thisfactorcanbeappliedtoEquation3.The newexpressionfortheprobabilityofbit-errorthataccountsfortheenergyspreadofthe signalis P ED T w Q T w E b = N 0 p 2 T w B +2 T w E b = N 0 SolvingEquation3for E b = N 0 givesthe SNR bit requiredtoachieveagivenBER,i.e. SNR bit T w = E b N 0 = K 2 T w 1+ r 1+ 2 T w B K 2 where K = Q )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 BER 3.5.2.2OptimalIntegrationTime ForgivenvaluesofBERandsignalbandwidth B ,Equation3predictsthe required SNR bit asafunctionoftheintegrationtime.Thus,byminimizing SNR bit T w theoptimalintegrationwindow T w opt canbeobtained,i.e. T w opt = Solve @ @ T w [ SNR bit T w ] =0, T w Sincethescalingfactor T w isobtainednumericallyusingtheUWBchannelmodeling presentedinsubsection2.8.2and T w appearsinthesquareroottermofEquation3 33,thereisnoexplicitsolutionforEquation3.Followingtheapproachinsubsection 3.4.2.2,approximationsfor p 1+2 T w B = K 2 and T w areemployedtogetthe solutionofEquation3.Theseapproximationsareobtainedusinganon-linear regressionwithanexponentialt Y j = a j + b j exp )]TJ/F49 11.9552 Tf 5.479 -9.684 Td [(c j + d j X j where j identiestheapproximationparameteri.e. Y 1 T w and Y 2 p 1+ Z where Z =2 T w B = K 2 X j istheindependentvariableinthiscase T w or Z ,and a j b j c j 69
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Table3-3:ConstantvaluesfortheexponentialtgivenbyEquation335 j Approximation Term Regression Parameter a j b j c j d j 1 Z < 104.82-0.661.73-0.089 1 p 1+ Z 10 Z < 5010.78-1.351.89-0.018 50 Z < 30022.90-11.770.49-0.004 2 T w < 30CM10.993-0.1222.04-0.178 2 T w 8 T w < 42CM21.025-0.1292.371-0.094 21 T w < 102CM31.035-0.1122.517-0.037 30 T w < 147CM41.028-0.0812.847-0.027 Figure3-12:Energyscalingfactor T w foreachUWBCMreportedin[28] d j areconstantssummarizedinTable3-3foreachchannelmodelCMpresentedin subsection2.8.2. Figure3-12plotstheenergyscalingfactor T w withtheircorrespondingexponentialts.Asshown,Equation3yieldsaccurateapproximations < 1%oferror.Thus, itisusedtoestimateEquation3,i.e. SNR bit T w canbeapproximatedby SNR bit K 2 1+ a 2 + b 2 exp c 2 + d 2 M T w a 1 + b 1 exp c 1 + d 1 T w where M = B = K 2 .Theoptimalintegrationtime T w opt canbedeterminedusingthis approximationinEquation3.Thesolutionthenyields 70
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Table3-4:Constantvaluesfor T w opt RangeCM A w B w 10 9 C w D w 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(9 0.1 M < 118.8013.400.581.90 0.1 M < 1221.9023.500.462.30 0.1 M < 1353.1036.500.281.60 0.1 M < 1473.1036.400.231.50 1 M < 3017.2022.661.000.215 1 M < 30220.4021.350.950.250 1 M < 30350.7049.950.660.260 1 M < 30469.9055.000.600.190 T w opt A w + ln B w = M C w + M D w where T w opt isgiveninnanosecondsandthevaluesofconstants A w B w C w D w for eachCMcanbefoundinTable3-4. 3.5.3Inter-SymbolandInter-FrameInterference ISIandIFIareinheriteffectsofmultipathfadingand,hence,shouldnotbeignored particularlywhenoptimizingaED-PPMwirelesssystem.Thus,thissubsectiontakes intoaccounttheireffect. 3.5.3.1EffectofISIandIFIontheReceiverPerformance ISIandIFIcanbeapproximatedasGaussianusingthecentrallimittheorem whenthenumberofchannelrealizationsandsuccessivebitsaresufcientlylarge [1].Therefore,hereISIandIFIaretreatedasAWGN.Furthermore,theyaretakenas awholesothatthetotalinterferenceenergyistheenergyofbothISIandIFIasitis explainednext. Figure3-13showstwoUWBpulsesundermultipathfadingandtransmittedin differentintegrationwindows.InFigure3-13a,thesignalenergy E b isthatwithinthe rstintegrationwindow,theIFIisthesignalinthesecondintegrationwindowwithin thesamesymbolperiod,andtheISIistheremainingsignalthatinterfereswiththenext symbol.Figure3-13bshowsapulsetransmittedinthesecondintegrationwindow. 71
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aPulseintherstwindow bPulseinthesecondwindow Figure3-13:IllustrationofISIandIFI Notethat,inthiscase,thereisnoIFI,i.e.theentireexcesssignalinterfereswiththe nextsymbol.Foralargenumberoftransmittedbitsthatcanrandomlybeinanyofthe twointegrationwindows,ISIandIFIcanbeaveragedtogethertodeterminethetotal interferencesimulationscorroboratethisassumption.Consequently,fromnowon, bothinterferencesareaddressedonlyasISIforsimplicityanditstotalenergycanbe calculatedas E i T w = 1 0 S Rx 2 t dt )]TJ/F39 11.9552 Tf 11.956 16.273 Td [( T w 0 S Rx 2 t dt which,byusingEquation3,isthesameas E i T w = E b 1 )]TJ/F49 11.9552 Tf 12.054 0 Td [(E b T w where E b 1 is justthetotalbitenergy.RecallingtheassumptionoftheGaussianapproximationforISI [1],theaverageinterferencespectraldensitycanbeestimatedas I 0 T w = E b 1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(E b T w 2 T w B = E b 1 [ 1 )]TJ/F25 11.9552 Tf 11.955 0 Td [( T w ] 2 T w B Then,toaccountforISI,aneffective SNR bit ,i.e. E b = N 0 eff ,canbeappliedtoEquation 3.Thiseffective SNR bit includestheenergyscalingfactor T w aswellas I 0 T w and canbeexpressedas E b = N 0 eff = T w E b = N 0 + I 0 .Theratio E b = N 0 + I 0 isoften calledthesignal-to-interference-and-noiseratioperbitSINR-per-bit.Thus, E b = N 0 eff 72
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isessentiallytheSINR-per-bitwiththeexceptionthatthescalingfactor T w hasbeen included.Now,let N 0 = E 1 = E b = N 0 and I 0 T w = E 1 [1 )]TJ/F25 11.9552 Tf 12.015 0 Td [( T w ] = T w B .Then, theeffective SNR bit canbeexpressedas E b = N 0 eff = T w 1 E b = N 0 + [ 1 )]TJ/F25 11.9552 Tf 11.955 0 Td [( T w ] 2 T w B )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 Bysubstituting E b = N o eff for E b = N o ,Equation3andEquation3canberespectivelyrewrittenas P ED T w Q E b = N 0 eff p 2 T w B +2 E b = N 0 eff and SNR bit T w = T w = K 2 1+ p 1+2 T w B = K 2 )]TJ/F22 11.9552 Tf 13.15 8.088 Td [(1 )]TJ/F25 11.9552 Tf 11.955 0 Td [( T w 2 T w B # )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 3.5.3.2OptimalIntegrationTime TheoptimalintegrationtimecanbeobtainedbyoptimizingEquation32which hasnoexplicitsolutionasexplainedinSection3.5.2.2.Thus,onceagain,exponential tsareusedresultinginthesameapproximationgivenbyEquation3,i.e. T w opt A w + ln B w = M = C w + M D w ,however,withdifferentconstantvalues.Thesecanbefound intable3-5.Forconvenience,Table3-6shows T w opt forseveralsignalbandwidthsand threedifferentvaluesofBER. 3.5.4SimulationSetupandValidation Tocorroborateandsupporttheequationsderivedinthissection,asimulatorsimilar totheonepresentedinsubsection3.4.4wasbuiltinMATLAB R .Thissectionbriey describesitsimplementationandvalidation. 3.5.4.1Setup Thesimulator'sblockdiagramisshowninFigure3-14.Justasthesimulator presentedinsubsection3.4.4,itcomprisesthreemainparts:modulation,channel 73
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Table3-5:Constantvaluesfor T w opt whenISIisconsidered RangeCM A w B w C w D w 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(9 0.1 M < 1111.0619.70.3981.130 0.1 M < 1224.2023.90.3050.988 0.1 M < 1356.7861.70.1920.730 0.1 M < 1477.6750.10.1500.628 1 M < 3018.0330.60.7360.040 1 M < 30220.9560.90.6290.115 1 M < 30351.8739.60.3440.057 1 M < 30471.2850.00.3000.054 Figure3-14:Simulatorblockdiagram modeling,anddemodulation.Themaindifferenceisthatheremultipathfadingis modeledandACIandlteringarenotincludedasthemainfocusinthissectionisthe integrationtimeandnotthereceiverbandwidth. Tosimulatethewirelesschannel,thechannelmodelingpartincludeAWGNand multipathfadingasfollows: 1.AWGN:Similartotheprevioussimulator,Equation3canbeusedtocalculate thenoisepower P 0 .Then,thenoisesignalisisrealizedbygeneratingrandom valuesthatarenormally-distributedwithzero-meanandvariance 2 = P 0 74
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Table3-6:OptimalintegrationtimesfordifferentvaluesofsignalbandwidthandBER Bandwidth BER OptimalIntegrationTime T w opt nsec GHz CM 1 CM 2 CM 3 CM 4 0.510 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 21.2037.4980.54106.27 1.010 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 18.2233.4573.2797.13 2.010 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 15.4829.8366.8189.25 4.010 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 13.4127.1662.1383.72 7.010 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 11.8525.6259.5880.59 0.510 )]TJ/F22 7.9701 Tf 6.586 0 Td [(4 22.7539.6184.35111.14 1.010 )]TJ/F22 7.9701 Tf 6.586 0 Td [(4 19.8135.6077.13101.95 2.010 )]TJ/F22 7.9701 Tf 6.586 0 Td [(4 16.8831.6770.0893.21 4.010 )]TJ/F22 7.9701 Tf 6.586 0 Td [(4 14.4228.4564.3886.36 7.010 )]TJ/F22 7.9701 Tf 6.586 0 Td [(4 12.4226.4561.0082.28 0.510 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 23.8441.1187.03114.60 1.010 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 20.9937.2180.03105.62 2.010 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 18.0133.1872.7796.51 4.010 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 15.3129.6066.4288.78 7.010 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 13.6227.4262.6084.26 2.MultipathFading:TheCIRisgeneratedusingthemultipathmodelpresentedin subsection2.8.2.Then,theconvolutionofthemodulatedsignaland the CIRis carriedout. 3.5.4.2Validation Tovalidatethesimulator,simulationresultsarecomparedtothewell-knownBER expressionforaED-PPMreceiver,Equation3.Figure3-15showsBERcurves obtainedusingboththesimulatorandEquation3fora2 GHz signalandthree differentintegrationtimes.Ascanbeseen,thesimulatorpredictswithaccuracytheBER performanceoftheED-PPMreceiver.Thus,itisusednexttocorroboratetheequations derivedinthissection. 75
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Figure3-15:ComparisonofsimulationsandEquation3tovalidatethesimulator 3.5.5Analysis 3.5.5.1TheoryCorroboration ThemainequationsderivedinthissectionareEquation3,Equation3, andEquation3.TheseareobtainedbyalgebraicmanipulationfromEquation 3andEquation3.Therefore,verifyingthatthesetwoequationsholdmustbe sufcienttocorroboratethattherestoftheequationsholdaswell.InFigure3-16a, theidealvaluesobtainedfromEquation3andthesimulationresultsareplotted forcomparison.Asillustrated,theBERcurvescloselyagreewhichcorroboratethat Equation3holds.Likewise,Figure3-16bcorroboratesEquation3. 3.5.5.2NumericalResults Whendesigningwirelesssystems,animportantparameterofthelinkbudgetis theSNR-per-bit E b = N 0 requiredbythesystemtoyieldcertainprobabilityofbit-error. Equation3andEquation3canbeusedtocalculatethisvalueasafunctionof thesystemparametersi.e.signalbandwidth,integrationtime.IncontrasttoEquation 3,Equation3takesintoaccountISI.AnexampleispresentedinFigure3-17 whichshowstwoplots.Therst,Figure3-17a,correspondstothe E b = N 0 requiredto 76
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aNoISI,Equation 3 bISI,Equation 3 Figure3-16:ComparisonbetweensimulationsandthemodiedBERequationswith B =2 GHz and T w =25,30,80,100 ns forCM1through4,respectively achievea BER =10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(5 whennoISIisconsideredwhileinthesecond,Figure3-17b, ISIistakenintoaccount.Thelowestvaluesof E b = N 0 determinetheoptimalintegration timeswhicharemarkedwitharrowsinthegure.However,ifthesystemcantolerate certaindegradationinperformance,theintegrationtimecanbedecreasedbelowits optimalvalue.Forinstance,forCM3,theoptimalintegrationtimeisaround72 nsec with E b = N 0 =20 dB .Ifthesystemcantoleratea1 dB degradationin E b = N 0 ,the integrationtimecanbereducedto41 nsec .Thisreductioncouldeasilytranslateinto valuablesystembenetssuchaslowerpowerconsumptionandhigherdatarate. FromFigure3-17,itisevidentthattheISIincreasestheoptimalintegrationtime. ThisisbecauseinordertoreducetheISIeffecttheintegrationwindowsmustbelarger comparedtothecasewhereISIisignored.ThisisalsoshowninFigure3-18wherethe optimalintegrationtimeforeachCMwithandwithoutISIisplottedasafunctionofthe signalbandwidth.Ingeneral,theintegrationtimeissignicantlylargerwhenconsidering ISImeaningthatitseffectonthesystemperformancecannotbeneglected. 77
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aNoISI bISI Figure3-17:Required SNR bit toachievea BER =10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(5 for B =2 GHz Figure3-18:Optimalintegrationtime T w opt toachieve BER =10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 78
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Figure3-19:Required SNR bit toachieve BER =10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 Figure3-18alsoshowsthattheoptimalintegrationtimedecreasesasthesignal bandwidthincreases.Thisisduetothefactthatalargerbandwidthincreasesthenoise powerrecall P 0 =2 N 0 B and,consequently,thenoiseenergy.Thus,toaccountfor largernoiseenergy,areductionintheintegrationwindowisnecessary.However,the reductionhastobesmallenoughtokeeptheeffectofISIatanacceptablelevel. Nevertheless,thatreductioninintegrationtimeasthesignalbandwidthincreases comesatacost.Figure3-19showstheSNR-per-bitrequiredtoachieveaBERof10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(5 whentheintegrationtimeischosentobetheoptimalvalue.Asillustrated,increasing thesignalbandwidthdegradestheoverallsystemperformancei.e.ahigher SNR bit is necessarytoachievethesameBER.Again,herethe SNR bit performancetrade-offcan beenseen.Forinstance,inthiscaseifthesystemcouldtoleratea1 dB degradation intherequired SNR bit ,thesignalbandwidthcouldbealmostdoubledresultingina potentialincreaseindatarate. 3.6Summary Thischapterpresentedthederivationofanalyticalexpressionstodetermine optimalvaluesforthereceiverbandwidthandintegrationtimeforED-PPMradios.The 79
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discussionandanalysisdevelopedincludedtheeffectofthreeinterferencesources:ACI fortheoptimalbandwidth,andISIandIFIfortheoptimalintegrationtime. TheseequationsareveryconvenientwhendesigningED-PPMreceiversforUWB wirelesschannels.Furthermore,ifthechannelcanbeestimatedspecically T w then theequationsmightbeusefulincognitiveradiostodynamicallyadjusttheintegration time. 80
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CHAPTER4 ENERGY-INTEGRATIONDETECTIONFORPPMRECEIVERS AsexplainedinChapter3,EDreceiversareverysensitivetonoise,thatis,they aremorevulnerabletonoisethancoherentdemodulationtechniquese.g.BPSK. Therefore,thesizeoftheintegrationwindowi.e.integrationtimeisacrucialdesign parametersinceitisdirectlyproportionaltothesignalandnoiseenergycapturedfrom thechannel[3]. PreviousworkshaveinvestigateddifferentapproachestoimprovetheBERperformanceofEDreceivers.In[3,20,71],theauthorsshowthatthereisanoptimal integrationtimetominimizetheprobabilityofbit-errori.e.BER.InChapter3,equationsforthisoptimalintegrationtimewerederived.However,theusefulnessofthese equationsreliesonagoodapproximationofthemultipathfadingchannel.Furthermore, evenifthechannelapproximationsaregood,theyareonlyvalidforcertainchannel conditions.Therefore,aradiooptimizedforcertainchannelconditionswillshowasignificantdegradationifitoperatesunderdifferentenvironments.Toreducethisdegradation, inthischapter,energy-integrationdetectionEIDisproposedandcomparedtoEDto showitsadvantages. 4.1ChapterContributions Inthischapter,ademodulationtechniqueEIDbasedontheintegrationofthe receivedsignalenergyratherthanthesignalenergyaloneisproposed.Effectively, itissimilartoaweightedEDdemodulationusinglineardecreasingweightsineach sampleofthereceivedsignalbutdoesnotincreasesignicantlythecomplexityofthe receiverandyetreducestheBERincomparisontoED.Thisisdemonstratedbythe BERequationderivedlaterinthechapterandcorroboratedbysimulations. 81
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4.2PreviousWork TherehasbeenpreviousworkaimingtoimproveEDreceiversbyapplyingweights toeachsampleofthereceivedsignal[56,82].ApplyingweightstothereceivedsignalrequiresaprioriknowledgeoftheCIRinordertoaccuratelydeterminetheweight magnitudeforeachsamplesothatsamplescarryinghigherenergyhaveincreased detectability.Ontheotherhand,iftheweightsaredynamicallydeterminedbyperformingachannelestimation[82],aconsiderableamountofsignalprocessingisneeded, increasingthecomplexityofthereceiverand,hence,itspowerconsumption.Thus,in applicationswherearchitecturesimplicityandverylow-poweroperationarerequired, thisapproachmightnotbeaviablesolution. 4.3Energy-IntegrationDetection 4.3.1Motivation Whentransmittingasignaloverawirelesschannel,themultipathfadingeffectively spreadsitsenergyovertimeseethereceivedsignalinFigure3-2.Thus,toavoidIFI andISIseesubsection3.5.3,theintegrationtimeofanEDreceivermustbelarge enoughtocapturemostofthesignalenergy.Thistimeisoftendeterminedbased ontheworst-casemultipathscenario.Forinstance,in[54,99,85],integrationtimes between30 nsec and50 nsec areusedsincetheyaregoodapproximationsforED receiverstocaptureatleast99%ofthesignalenergyinworst-casemultipathscenarios duringshort-rangecommunicationsinLOSandNLOSchannels,respectively.Typically, designingforworst-casemultipathscenariosresultsinintegrationtimesthatare signicantlylargerthanthoserequiredintheaverage-casemultipathscenario. FromEquation3,itiseasytoseethattheprobabilityofbit-error P ED increases astheintegrationtime T w increasessincetheQ-functionisastrictlydecreasing function.Therefore,anEDreceiverdesignedforworst-casemultipathscenariosi.e. larger T w experiencesaperformancedegradationwhenitoperatesinaverage-case multipathscenarios.InChapter3,itwasshownthatthereisanoptimalintegration 82
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timethatminimizesthe SNR bit toachievecertainprobabilityoferror.Thisoptimal integrationtimeisobtainedbyassumingthereceiverwilloperateunderoneoftheUWB channelmodelsdescribedintheIEEEP802.15workinggroupreport[28].Forinstance, theoptimalintegrationtimeforanEDreceivertoachievea BER =10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 withasignal bandwidthof2 GHz isaround18 nsec and33 nsec forCM1andCM2,respectively. IfareceiverdesignedforCM1operatesinawirelesschannelsimilartothechannel approximatedbyCM2quadrantIandIIofFigure4-1,thenitsprobabilityoferror increasestoapproximately20 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 ,whichrepresentsasignicantdegradationwhen comparedtotheoriginalgoalof BER =10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(5 .Ontheotherhand,ifareceiverdesigned forCM2operatesinachannelapproximatedbyCM1quadrantIIIandIVofFigure 4-1,thenithasthesameprobabilityofbit-errorbuthasthepotentialtobereducedto about10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(7 becausetheintegrationtimecouldbedecreasedto18 nsec Ingeneral,asystemdesignedtooperateinagivenwirelesschannelwillshowa considerabledegradationinitsactualorpotentialprobabilityofbit-errorwhenitoperates inadifferentchannel.Hence,forasystemthatrequiresproperfunctionalityindifferent typesofchannelsoravaryingchannel,itisdesirabletoatleastreducetheinherent performancedegradationcausedbylargerintegrationtimes.Tothateffect,EIDis proposedandshowinsection4.6thatithasasmallerperformancedegradationrate thanED. 4.3.2BitDecision Assumethatabinarylogic1hasbeenmodulatedusingPPMi.e.apulseis transmittedintherstintegrationwindowandtransmittedoverawirelesschannel. Then,thereceivedsignalintherstandsecondwindowcanbeexpressedby X i = i + n i Y i = m i 83
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Figure4-1:Exampleoftheactualandoptimalprobabilitiesofbit-error P e forradios operatinginCM1andCM2. respectively,where i isthe i th sampleofthereceivedpulse, n i and m i representAWGN ineachintegrationwindow, i =1,2,..., N and N = f s T w isthenumberofsamplesper window.TodemodulatethesignalusingED,itisnecessarytocalculatetheenergyin bothwindows,i.e. E X N = 1 = f s P i X 2 i and E Y = 1 = f s P i Y 2 i .Thebitdecisionisthen givenby E X N 1 ? 0 E Y N Notethat E X N = P X N T w = P X N N = f s where P X N istheexpectedaverage powerintherstintegrationwindow.Similarly, E Y = P Y N N = f s .Hence,thecondition giveninEquation4isequivalentto P X N ? P Y N .Itisknownthattheexpected averagepowerofarandomprocessisgivenbytheexpectationofthesumofitssquare [41].Inthiscase,thatis P X N = E N X i =1 i + n i 2 # 84
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P Y N = E N X i =1 m i 2 # where E [ ] representstheexpectedvalue.Since s i and n i areindependentprocesses and n i hasmeanzeroforall i ,then E [ s i n i ] =0and P X N = E N X i =1 2 i # + E N X i =1 n 2 i # = P N + P n N where P N and P n N aretheexpectedaveragepowerofthereceivedsignaland noiseintherstintegrationwindow,respectively.Thus,thebitdecisionbasedonEDis P N 1 ? 0 [ P m N )]TJ/F49 11.9552 Tf 11.955 0 Td [(P n N ] where P m N = P Y N istheexpectedaveragepowerofnoiseinthesecondintegration window. FortheproposedEID,thebitdecisionisbasedonthecomparisonoftheintegration ofthesignalenergy,i.e. N X i E X i ? N X i E Y i where E X i = P X i i = f s and E Y i = P Y i i = f s .Thus,thenewbit-decisionconditionin termsofaveragepowercanbedenedas P i i P X i ? P i i P Y i andisequivalentto N X i =1 i P i 1 ? 0 N X i =1 i [ P m i )]TJ/F49 11.9552 Tf 11.955 0 Td [(P n i ] If P m )]TJ/F49 7.9701 Tf 6.586 0 Td [(n i = P m i )]TJ/F49 11.9552 Tf 12.042 0 Td [(P n i ,thenthebitdecisionsgivenbytheconditionsinEquation4 andEquation4simplifyto 85
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Figure4-2:GeneralblockdiagramforanEIDreceiver. P N )]TJ/F49 11.9552 Tf 11.955 0 Td [(P m )]TJ/F49 7.9701 Tf 6.587 0 Td [(n N 1 ? 0 0 N X i =1 i P i )]TJ/F49 11.9552 Tf 11.955 0 Td [(P m )]TJ/F49 7.9701 Tf 6.587 0 Td [(n i 1 ? 0 0 respectively.Notethat,sincethechannelthermalconditionsarenotlikelytochange signicantlyinshortperiodsoftimee.g.2 T w ,theexpectedaveragepowerofnoise inbothwindowsisapproximatelythesame,i.e. P n i P m i ,and P m )]TJ/F49 7.9701 Tf 6.586 0 Td [(n i 0.Then, inaverage,Equation4canbeexpectedtobeastrongerconditionthanEquation 4since P i i P i > P N andshouldresultinalowerprobabilityoferror.Figure 4-2showsablockdiagramofthesignalprocessingcarriedoutbyanEIDreceiverto makeabitdecision.Asillustrated,aftersquaringself-mix,thesignalisintegrated twicecumulative-sumandsumineachintegrationwindow.Then,thehighestvalue determinesinwhichwindowthepulsewastransmitted,thatisabitdecisionismade. 4.3.3Example InthispartweshowanexampleofthesignalprocessingdonebybothEDandEID receivers.Onceagain,itisassumedthatapulsewastransmittedintherstintegration windowrepresentingabinarylogic1.Figure4-3ashowsthereceivedsignalincluding 86
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aReceivedsignal bSignalenergy cEnergyintegration Figure4-3:Exampleofabinarylogic1demodulatedusingEDandEID noiseAWGNassuminga SNR bit atthereceiver'santennaof3 dB ,i.e. E b = N 0 =3 dB Figure4-3bshowstheintegrationcumulative-sumofthesquaredsignal,i.e. E X i = 1 = f s i X j =1 X 2 j = 1 = f s i X j =1 )]TJ/F25 11.9552 Tf 5.48 -9.684 Td [( j + n j 2 E Y i = 1 = f s i X j =1 Y 2 j = 1 = f s i X j =1 m 2 j = f s AnEDreceiverwouldhavedemodulatedthissignalasabinarylogic0since E X N < E Y N or,inwords,theenergyinthesecondintegrationwindowmarkedas E m inthe gureishigherthantheenergyintherstwindow.Clearly,thisisabit-errorsincethe transmittedbitwasalogic1andnotalogic0. ThebitdecisionbasedonEIDinvolvestheintegrationofenergyineachwindow whichisgivenby I X i = 1 = f s 2 i X j =1 E X j I Y i = 1 = f s 2 i X j =1 E Y j 87
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fortherstandsecondintegrationwindows,respectively.Then,thebitdecisionforEID is I X N ? I Y N whichdemodulatesthesignaltoabinarylogic1since I X N > I Y N ascanbeseeninFigure4-3dwhere I X N ismarkedas I m Inthiscase,thepreviousargumentofEquation4beingastrongercondition thanEquation4holds,i.e.thecommonEDproducedabit-errorwhiletheEIDdid not.Atthispoint,itisprobablyworthmentioningagainthatEquation4isastronger conditionthanEquation4inaverage.Therefore,therewillbeindividualbitdecisions inwhichEDoutperformsEID.However,ingeneral,EIDperformsbetterthanED.To comparetheirperformances,werstmustcalculatetheprobabilityofbit-errorforEID whichisdoneinthenextsection. 4.4ProbabilityofBit-ErrorforEID Inthissection,theequationfortheprobabilityofbit-errorofEIDispresented.First theconditionrequiredtomakeabitdecisionsshownfollowedbythederivationofthe probabilityofbit-erroranditsmodiedversiontoincludethemultipathfadingeffect. 4.4.1BitDecision Asbefore,let n i and m i bethenoiseintherstandsecondintegrationwindows, respectively,and i bethetransmittedpulseatthereceiver'santennafor i =1,2,..., N where N =2 B T w isthetotalnumberofsamplesineachintegrationwindowassuming theNyquistsamplingrate 1 isused.Recallthat m i and n i areassumedtobeAWGN and,hence, X i and Y i areGaussianrandomvariableswithmeans i and0,respectively. Both X i and Y i areassumedtohavethesamevariance 2 sincethenoiseaverage powerisnotlikelytochangeoversmallperiodsoftimee.g.2 T w .Inshort,wehave X i N )]TJ/F25 11.9552 Tf 5.48 -9.684 Td [( i 2 and Y i N )]TJ/F22 11.9552 Tf 5.48 -9.684 Td [(0, 2 1 TheNyquistrateistheminimumsamplingrateforwhichthesampledsignalretains allthepropertiesoftheoriginalsignal. 88
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AsdiscussedintheprevioussectionandshownintheblockdiagramofFigure4-2, thedemodulationbasedonEIDrstcarriesoutthesquaringself-mixandintegration cumulative-sumofthereceivedsignalineachwindowjustlikethecommonED demodulation.Then,theresultingsignals, E X i and E Y i ,areintegratedonceagain andcomparedtoeachotherinordertomakeabitdecision,i.e. N X i =1 E X i 1 ? 0 N X i =1 E Y i Withsimplealgebraicmanipulation,itcanbeshownthat N X i =1 E X i = N X i =1 i X j =1 X 2 i = N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i X 2 i andthenEquation4canbeexpressedas N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i X 2 i 1 ? 0 N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i Y 2 i Notethat N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i X 2 i isjustthesquareofthesignalweightedby N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i which decreaseslinearlyas i increases.Inotherwords,thesignalsampleswillhavelower weightsastimepasseswhichmakessensesincetheamplitudeofthereceivedsignalin averagedecreaseswithtimeduetomultipathfading.Also,notethat P i N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i X 2 i and P i N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i Y 2 i followachi-squaredistributionsince X i and Y i areGaussian randomvariables.Hence,thebitdecisionisjustthecomparisonoftwochi-square randomvariablessimilartotheEDdemodulation.Theprobabilityofbit-errorofthis comparisonisdiscussednext. 4.4.2ProbabilityofBit-Error Recallthat X i N )]TJ/F25 11.9552 Tf 5.479 -9.684 Td [( i 2 and Y i N )]TJ/F22 11.9552 Tf 5.479 -9.684 Td [(0, 2 andlet 89
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V = N X i =1 i X j =1 X 2 j = N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i X 2 i W = N X i =1 i X j =1 Y 2 j = N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.956 0 Td [(i Y 2 i sothattheconditionforabitdecisiongivenbyEquation4canbeexpressedas V ? W .Hence,abit-erroroccurswhen V W and,consequently,theprobabilityof bit-erroris P EID = P V W .ThisprobabilityisderivedinAppendixBandforlarge N it canbeapproximatedby P EID Q 0 B @ s 2 = 2 2 p N 0 + s 2 = 2 1 C A where s 2 = N X i =1 i X j =1 2 j N 0 N 3 3 + 1 2 N X i =1 i X j =1 j X k =1 2 k and Q istheQ-functionasdenedbyEquation3.Notethattheenergyoftherst i samplesofthereceivedsignalis E b i = 1 = f s P i j =1 2 j and 2 = N 0 f s = 2.Therefore,the probabilityofbit-error P EID canbeexpressedas P EID Q 0 B @ E 0 b = N 0 q 2 B T w 3 = 3+2 )]TJ/F22 11.9552 Tf 5.48 -9.684 Td [(2 E 00 b )]TJ/F49 11.9552 Tf 11.956 0 Td [(E 0 b = N 0 1 C A where E 0 b = f s P N i =1 E b i and E 00 b = f 2 s P N i =1 P i j =1 E b i .Theprobabilityoferroris commonlyexpressedasafunctionof E b = N 0 .NextweslightlymodifyEquation4in ordertoexpressitintermsof E b = N 0 andtakeintoaccountthemultipathfadingeffect. 90
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4.4.3ModiedProbabilityofBit-Error Letthereceivedsignal i bethecontinuousfunctionoftime t suchthat 1 = f s P i j =1 2 j = t 0 2 d where i = f s t =2 B t assumingagain f s istheNyquistsampling rate.Then,thesignalenergyasafunctionoftimeisgivenby E b t = t 0 2 d Furthermore,denetheenergyscalingfactor b t suchthat E b t = b t E b where E b = E b 1 = 1 0 2 d isthetotalenergyofthereceivedpulse,i.e. b t = E b t E b 1 = E b t E b Then,thevalues E 0 b and E 00 b inEquation4canbeexpressedas E 0 b = f s T w 0 E b d =2 B E b T w 0 b d E 00 b = f 2 s T w 0 t 0 E b d dt =4 B 2 E b T w 0 t 0 b d dt If E 0 b = E b 0 b T w and E 00 b = E b 00 b T w where 0 b T w =2 B T w 0 b d 00 b T w = 2 B 2 T w 0 t 0 b d dt thentheprobabilityofbit-error P EID giveninEquation4canberewrittenas P EID Q 0 B @ 0 b T w E b = N 0 q 2 B T w 3 = 3+2 2 00 b T w )]TJ/F25 11.9552 Tf 11.955 0 Td [( 0 b T w E b = N 0 1 C A 91
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Table4-1:Constantvaluesfor b t ModelRange* nsec ab )]TJ/F23 11.9552 Tf 5.479 -9.684 Td [( 10 9 sec )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 CM1 T w > 5 )]TJ/F22 11.9552 Tf 9.298 0 Td [(0.9353 )]TJ/F22 11.9552 Tf 9.299 0 Td [(0.1832 CM2 T w > 13 )]TJ/F22 11.9552 Tf 9.299 0 Td [(1.6221 )]TJ/F22 11.9552 Tf 9.299 0 Td [(0.1207 CM3 T w > 40 )]TJ/F22 11.9552 Tf 9.299 0 Td [(2.4567 )]TJ/F22 11.9552 Tf 9.299 0 Td [(0.0651 CM4 T w > 50 )]TJ/F22 11.9552 Tf 9.299 0 Td [(1.8616 )]TJ/F22 11.9552 Tf 9.299 0 Td [(0.0389 *Constantsareaccurate < 1%errorinthespeciedtimerange and,hence,Equation4hasbeenmodiedtobeexpressedintermsof E b = N 0 .Next, thescalingfactors 0 b T w and 00 b T w arecharacterizedbasedontheIEEEP802.15 UWBchannelmodels. 4.4.4EnergyScalingFactors SincebothEDandEIDreceiversonlydealwiththeenergyofthesignalandnotits phase,theonlyinteresthereisinhowmuchofthetotalenergycanbecapturedbythe receiverasafunctionoftime.Thus,thereceivedsignal t isnormalizedsothatits totalenergy is 1whichistheconventionusedin[3,20,39],i.e. 0 t = t = s 1 0 2 d where t = p t h t p t isthereceivedpulse, h t istheCIRand represents theconvolutionofbothfunctions.Wecanuse 0 t tocalculatetheenergyscalingfactor b t denedbyEquation4,i.e. b t = t 0 0 2 d .Next,employingtheMATLAB R codeprovidedintheIEEEP802.15workinggroupreport[28],CIRrealizationsare generated,convolvedwith p t ,andaveragedinordertodetermine b t whichfollows anexponential-likecurve.Thenanon-linearregressionwithanexponentialtiscarried outtoapproximatetheenergyscalingfactoras b t 1+ a exp b t where a and b areconstantswithspecicvaluesforeachchannelmodelandare summarizedinTable4-1. 92
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a b t b 0 b t c 00 b t Figure4-4:EnergyscalingfactorsforUWBchannels Table4-2:Constantvaluesfor 0 b t and 00 b t ModelRange* nsec C 1 )]TJ/F23 11.9552 Tf 5.479 -9.683 Td [( 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(9 sec C 2 )]TJ/F23 11.9552 Tf 5.48 -9.683 Td [( 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(18 sec 2 C 3 )]TJ/F23 11.9552 Tf 5.479 -9.683 Td [( 10 9 sec )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 CM1 T w > 55.003 )]TJ/F22 11.9552 Tf 9.298 0 Td [(27.792 )]TJ/F22 11.9552 Tf 9.299 0 Td [(0.1832 CM2 T w > 1511.061 )]TJ/F22 11.9552 Tf 9.298 0 Td [(98.971 )]TJ/F22 11.9552 Tf 9.299 0 Td [(0.1207 CM3 T w > 4025.421 )]TJ/F22 11.9552 Tf 9.299 0 Td [(467.307 )]TJ/F22 11.9552 Tf 9.299 0 Td [(0.0651 CM4 T w > 5037.328 )]TJ/F22 11.9552 Tf 9.298 0 Td [(1046.800 )]TJ/F22 11.9552 Tf 9.299 0 Td [(0.0389 *Constantsareaccurate < 2%errorinthespeciedtimerange Figure4-4ashows b t usingEquation4andtheIEEEP802.15MATLAB R model.Asshowninthegure,theexponentialtyieldsaccurateapproximationswith lessthan1%oferrorwithinthetimerangespeciedinTable4-1. UsingEquation4,Equation4andEquation4canbeapproximatedas 0 b t 2 B t 2 6 4 1+ C 1 t exp C 3 t )]TJ/F22 10.9091 Tf 10.909 0 Td [(1 3 7 5 00 b t 2 B t 2 2 6 4 1 2 )]TJ/F49 10.9091 Tf 12.105 10.982 Td [(C 1 t + C 2 t 2 exp C 3 t )]TJ/F22 10.9091 Tf 10.909 0 Td [(1 3 7 5 wheretheconstants C 1 C 2 ,and C 3 aresummarizedinTable4-2.Figure4-4band Figure4-4cshow 0 b t and 00 b t ,respectively,usingtheirexponentialapproximations, i.e.Equation4andEquation4,andtheIEEEP802.15model.Onceagain,from thegures,itcanbeseenthattheexponentialtsyieldaccurateapproximationsless than2%oferrorwithinthetimerangespeciedinTable4-2. 93
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Figure4-5:SimulatorBlockDiagram 4.5Simulation Tocorroborateandsupportthederivedequationfortheprobabilityofbit-errorof anUWBreceiver,asimulatorwasbuiltusingMATLAB R .Itsblockdiagramisshownin Figure4-5anditisessentiallythesameastheonepresentedandvalidatedinSection 3.5.4.TheonlydifferenceisthatwhensimulatingEIDadoubleintegrationiscarriedout. 4.6Analysis 4.6.1TheoryCorroboration Tocorroboratethetheorypresentedinsection4.4.3,simulationsforeachone oftheIEEEP802.15UWBchannelmodelswererunandcomparedtoEquation4 31whichisthederivedequationfortheprobabilityofbit-errorofaEIDreceiver.The simulationparametersare B =2 GHz and T w =26,43,82,130 nsec forCM1through 4,respectively.Figure4-6showstheprobabilityofbit-errorBERcurvesobtainedwith boththesimulatorandEquation4.Ascanbeseenfromthegure,thetheoryand simulationscloselyagreewhichcorroboratesthederivedequation. 94
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Figure4-6:ComparisonbetweensimulationresultsandthederivedBERequationfor EIDreceivers 4.6.2Bit-ErrorRate Inthissection,thederivedprobabilityofbit-errorforEIDreceivers,Equation4 isusedalongwiththewell-knownBERexpressionforEDreceivers,Equation3,to comparebothdemodulationtechniquesandshowtheadvantagesofEIDoverED. Figure4-7comparestheperformancesofEDandEIDassumingasignalbandwidth B =2 GHz andintegrationtimes T w =26,43,82,130 nsec fortheCM1through4, respectively,allowingatleast99%ofthesignal'senergytobecaptured.Itisclearfrom thegurethatEIDoutperformsED.Onaverage,itperformsbetterbyapproximately 1.25 dB forthespeciedbandwidthandintegrationtimes.Thistranslatestoaround33% improvementintermsofthesignalenergyrequiredtoachievethesameperformance.In otherwords,anEIDreceiverrequiresapproximately33%lesssignalenergythananED receivertoachievethesameBERperformance. 4.6.3IntegrationTime Increasingtheintegrationtimealsoincreasesthetotalnoiseenergy E 0 detected bythereceiversinceinaverage E 0 = T w f s N 0 = 2.Thisincreaseinnoiseenergy degradesthereceiver'sperformance.ThisisshowninFigure4-8wheretherequired SNR bit toachievea BER =10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(3 isplottedasafunctionof T w for B =2 GHz .Asthe 95
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aCM1 T w =26 ns andCM2 T w =43 ns bCM3 T w =82 ns andCM4 T w =130 ns Figure4-7:Probabilityofbit-errorforEDandEIDforCM1through4and B =2 GHz integrationtimeincreasesbothEDandEIDreceiversrequireahigher SNR bit inorder toachievecertainBERperformanceinthiscase10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 .Thegurealsoshowsthe improvementofEIDoverEDsinceEIDalwaysrequiresalower SNR bit toachievethe sameperformance. Asmentionedinsubsection4.3.1,whendesigningthereceiver,theintegration timeisdeterminedbasedontheworst-casemultipathscenariotoensuretheproper operationofthesystem.Insubsection4.3.1,itwasarguedthatareceiverdesigned basedonaspecicwirelesschannelmodelwillshowaconsiderabledegradationin itsactualorpotentialBERperformancewhenitoperatesinadifferentchannel.This degradationisinherenttotheneedoflargerintegrationtimesand,althoughitcannotbe completelyeliminated,itwouldbedesirabletoatleastreduceit. Assumeforinstancethatareceiverisdesignedsothatitcanoperateinwireless channelsmodeledbyCM1through3.Theworst-casemultipathscenarioisgivenby CM3and,hence,theintegrationtimeischosentobe82 nsec sothatonaverage99% ofthesignalenergycanbecapturedbythereceiver.InFigure4-8a,itcanbeseen thatanEDreceiverwillexperienceadegradationofabout1.2 dB whencompared tothesamereceiverdesignedforachannelapproximatedbyCM2whichrequires 96
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aCM1and2 bCM3and4 Figure4-8:Required SNR bit forEDandEIDtoachievea BER =10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 for B =2 GHz andCM1through4 T w =42 nsec inordertocapture99%ofthesignalenergy.However,whenusingEID thisdegradationreducestoapproximately0.8 dB .ThiscanbeinferredfromFigure4-8, sincethedegradationratei.e.theslopeofthecurvesofEIDissmallerthanthatof ED.Hence,ingeneral,EIDreducestheperformancedegradationexperiencedbythe receiverwhenitoperatesinbetterchannelsthantheoneitwasoriginallydesignedfor. Furthermore,intheexampleabove,anEIDreceiverdesignedforCM3 T w = 82 nsec stillperformsbetterthananEDreceiverdesignedforCM2 T w =43 nsec asmarkedbythedashedhorizontallineinFigure4-8a.WhencomparedtotheED receiverdesignedforCM1 T w =26 nsec ,theperformanceoftheEDreceiver designedforCM3isaboutthesameeventhoughitsintegrationwindowisalmost3.2 timeslargeri.e. T w =82 nsec .Inthegure,thisismarkedbythesolidhorizontalline. 4.6.4SignalBandwidth Recallthattheaveragenoiseenergycapturedwithinanintegrationwindowis E 0 = T w f s N 0 = 2where f s =2 B .Thus, E 0 = T w B N 0 meaningthatthenoise energyisnotonlyhigherwhentheintegrationtimeisincreasedbutwhenthereceiver bandwidthisincreasedaswell.Consequently,thereceiver'sperformancedegradeswith increasingbandwidthjustaswithintegrationtimeasshownintheprevioussection.This 97
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aCM1 T w =26 ns andCM2 T w =43 ns bCM3 T w =82 ns andCM4 T w =130 ns Figure4-9:Required SNR bit forEDandEIDtoachieve BER =10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 isillustratedinFigure4-9wheretherequired SNR bit toachievea BER =10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(3 isplotted asafunctionof B using T w =26,43,82,130 nsec fortheCM1through4,respectively. ThegurealsoshowsonceagaintheimprovementofEIDoverEDsinceEIDalways requiresalower SNR bit toachievethesameperformance. Incontrasttowhathappenswithhigherintegrationtimes,increasingthesignal bandwidthhasapproximatelythesamedegradationratei.e.slopeofthecurves inFigure4-9forbothEDandEID.Thisisduetothefactthatchangingthesignal bandwidthdoesnotaffecttheratiobetweenthesignalenergycapturedin T w andthe totalsignalenergyi.e.theenergyscalingfactor b T w doesnotdependonreceiver bandwidth. 4.7Summary Energy-detectionEDisoftenusedasthedemodulationtechniquefornoncoherentPPMradiosmainlyduetoitssimplicityandpotentiallow-powerimplementation.Nonetheless,oneofitsmaindisadvantagesisitssensitivitytonoiseenergy.In priorpublicationstheapproachtothisproblemwastooptimizetheintegrationtimeor dynamicallyapplyweightstoeachsampleofthereceivedsignal.Inthecaseofthe integrationtimeoptimization,anEDreceiverwillsignicantlydegradeitsperformanceif itoperatesinwirelesschannelsdifferentfromtheoriginalchannelitwasdesignedfor. 98
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Inthecaseofusingdynamicweights,althoughitgreatlyimprovesitsperformance,it hasbeenshownthatthereceivercomplexityincreasessubstantiallyandmightnotbea viablesolutionwhenarchitecturesimplicityandlow-powerconsumptionisrequired. Inthischapter,thetheoryforademodulationtechniquebasedontheintegration ofenergyratherthanenergydetectionalonewaspresentedanddeveloped.The EIDtechniqueessentiallyaddsanadditionalintegratortothereceiverarchitecture, whichdoesnotrepresentasignicantincreaseinarchitecturecomplexitybutgivesa considerableimprovementoverED. ItwasalsoshownthatEIDnotonlyperformsbetterthanEDingeneral,butthat thedegradationitexperiencesduetoanincreaseofintegrationtimeissmallerthanthe degradationexperiencedbyanEDreceiverwiththesameincreaseinintegrationtime. Thisisparticularlyimportantsincethereceiverisusuallydesignedfortheworst-case multipathscenarioi.e.largerintegrationtimesmakingthereceivermissitspotential BERwhenoperatingunderbettermultipathscenarios.WithEID,thisdrawbackhas beenshowntobereduced. 99
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Chapter5 COGNITIVEPHY-MACCOOPERATIVEPROTOCOL ThewiderangeofbenetsthatUWBtechnologyoffers,makesitanattractive solutionforshort-rangewirelessnetworks[91].However,theintrinsiccharacteristicsof UWBchannelsposeseveralchallenges.OneofthemainchallengesinUWBwireless networksisdealingwithmultipathfading[9,10].Multipathfadingistheresultofa wirelesssignaltravelingthroughmultiplepaths.Duetothedifferentsignalpaths, multiplecopiesofthesamesignalarriveatthereceiverwithdifferentamplitudes, phasesanddelays.Intermsofenergy,multipathfadingeffectivelyspreadsovertime theenergyofthetransmittedsignal.Therefore,toaccountforthisenergyspread,the windowtoreceiveanUWBpulsemustbelargeenoughtocaptureitsenergy[3]. Alargerreceivingwindowresultsinasmallertransmissiondataratesincethepulse repetitionperiod,orinter-pulsespacing,islarger.Hence,worsechannelconditions, i.e.largerenergyspreading,requirelowertransmissiondatarates.Ingeneral,the transmissiondatarateofaUWBradiomustbedesignedtobelowenoughsothatthe radioisoperationalundertheworstchannelconditions[55].This,however,imposesthe samelowdatarateevenwhentheradioisoperatingunderbetterchannelconditions. Inaddition,ifdataratesarelow,thetransmissiontimeislargerandsoistheenergy spentbythereceiverasitscircuitrymustbekeptrunningforalongerperiodoftime[55]. Furthermore,thetransmissiondatarateand,consequently,thereceivingwindoware closelyrelatedtothebit-errorrateBERoftheUWBreceiver.Ifthereceivingwindow istoolargeortoosmalltheBERperformanceisdegraded.Previouswork[3,20,71] hasshownthat,dependingonthechannelconditions,thereisanoptimallengthforthe receivingwindowthatminimizestheBER. Inthischapter,theUCP-MACUWBcooperativePHY-MACprotocolshortforUWB CooperativePHY-MACprotocolisproposedanddiscussed.UCP-MACisacognitive andcooperativeprotocolbetweenthePHYandMAClayersthatdynamicallyoptimize 100
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thetransmissiondataratebasedonthechannelconditionsinordertoimprovethe communicationbetweenthetransmittingandreceivingnodes. ThedatarateoptimizationminimizestheBERofthereceiverandincreasesthe dataratewhentherearefavorablechannelconditions.Inadditiontotheenergysavings previouslymentioned,anincreaseddataratecombinedwithalowerBERimproves considerablythenetworkperformanceintermsoftransmissiontime,messagedelivery ratio,andthroughputaswediscusslater.Thisperformanceimprovementisprovenby simulationsobtainedfromanetworksimulatorbuiltinMATLAB R 5.1ChapterContributions Thecombinationofthealltheworkpresentedinpreviouschaptersledtotheidea anddesignoftheUCP-MACprotocoldiscussedinthischapter.Themaincontributions comprisethecognitivechannelestimationprocedureforUWBradiosusingPPM,the UCP-MACprotocolitself,andthenetworksimulatorbuiltinMATLAB R Toestimatethewirelesschannel,acognitiveestimationprocedurewasdeveloped andittakesadvantageofthesignalprocessingcarriedoutwhenreceivingapacket usingEDdemodulation.Withthischannelestimation,theoptimaldataratecanbe determined.TheUCP-MACprotocolthenallowsboththetransmitterandthereceiverto synchronizetheirtransmissiondataratestotheoptimalvaluemakingamoreefcient communication.Thisistestedusingthenetworksimulator.ItimplementsbothPHYand MAClayersaswellasUWBchannelmodelingandnetworktopologyinordertotestand analyzethecompleteprotocolinamorerealisticscenario. 5.2PreviousWork Often,whenusingrateadaptationtechniques,thetransmissiondatarateisadjustedasafunctionoftheSNRortheinterferencecreatedbyneighboringdevices[22]. Forinstance,in[6],theauthorproposedtheCooperativePHYlayernetworkcoding MACCPLNC-MACprotocolthatadjuststhedataratetotheShannon'smaximum channelcapacitybasedonthecurrentSNR.However,fortheimpulse-basedUWB,this 101
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approachisnotfeasiblesincethechannelcapacityisconstrainedbytheinter-pulse spacingrequiredduetomultipathfading[10].Ontheotherhand,in[63],theproposed Cognitive-AutonomousMACCA-MACprotocoladjuststhetransmissiondatarateto reducethemulti-userinterference 1 MUIcausedbyneighboringdeviceswhichshould improvethereceiver'sBER.However,thisapproachdoesnottakeintoaccountthatthe BERperformanceisnotonlyaffectedbyinterferencebutitalsodependsonthelength ofthereceivingwindowandoptimizingthislengthiscrucialinreducingBER. TheUCP-MACprotocolfocusesonminimizingtheBERbyutilizingtheoptimal datarate.RatherthancalculatingtheSNRtomaximizethetransmissiondatarate, UCP-MACminimizestheBERbycognitivelyndinganoptimaldatarate.Furthermore, whenchannelconditionsallowit,theoptimizationresultsinhigherdatarateswhichin turnreducesMUIsincepackettransmissionsarefasterand,therefore,devicesinthe networkinterferewitheachotherforalessamountoftime. 5.3SystemModel 5.3.1NetworkandSignalModel FortheUCP-MACprotocol,adecentralizednetworkstructureisconsidered.In particular,itisfocusedforshort-rangewirelessad-hocnetworksinwhichallnodeshave equalstatusand,atanygiventime,mayestablishacommunicationlinkwithanyother nodewithintransmissionrange.Figure5-1showsanexampleofawirelessad-hoc network.Insuchanetwork,thesignalreceivedbyanodecomprisesthetransmitted signalUWBpulses,AWGNandMUI.ForUWBwirelessnetworks,ithasbeenshown thatMUIcanbeapproximatedasMUI[94,23].Therefore,thesignalreceivedbyanode canbeexpressedas 1 Inawirelessnetwork,multi-userinterferencereferstotheinterferencesignalseen byanyreceivingnodeduetotransmissionsfromneighboringnodes. 102
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Figure5-1:Exampleofawirelessad-hocnetwork s t = p t h t + n t where representstheconvolutionoftwofunctions, p t isthetransmittedUWBpulse, h t isthechannelimpulseresponseCIR,and n t isAWGNincludesthechannel's thermalnoiseandMUI. 5.3.2ModulationandDemodulationSchemes AtthePHYlayer,theUCP-MACprotocolemploysPPMseeChapter3formodulation.RecallthatwithPPM,asymbolinthiscaseasinglebinarybitismodulated bytransmittingapulseinoneoftwointegrationwindows.Abinarylogic1ismodulated bytransmittingapulseintherstintegrationwindow.Abinarylogic0ismodulatedby transmittingapulseinthesecondwindow. TodemodulatethePPMsignal,EDorEIDcanbeused.WhenusingEDdiscussed inSection3.3,thereceivercomparesthesignalenergiesineachoftheintegration windows.Theintegrationwindowwiththehighestenergyrevealsthewindowinwhich thepulsesignalwastransmittedandabit-decisionisthenmade.Basedonthesignal denedbyEquation5,theenergyinanintegrationwindowisgivenby E k = t 0 + T w t 0 s 2 t dt 103
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where k 2 [ 1,2 ] identiestheintegrationwindow, T w istheintegrationtimei.e.the lengthofoneintegrationwindow, t 0 =0for k =1and t 0 = T w for k =2.If E 1 > E 2 thereceivedsignalisdemodulatedasabinarylogic1.If E 1 E 2 ,thereceivedsignalis demodulatedasabinarylogic0. Ontheotherhand,ifEIDseeSection4.3isused,thereceivercomparesthe integrationofenergyinsteadoftheenergyaloneasdonewithED.Then,thevalue calculatedineachintegrationwindowis E 0 k = t 0 + T w t 0 t t 0 s 2 d dt and,similartoED,if E 0 1 > E 0 2 thenthereceivedsignalisdemodulatedasabinarylogic1 whileif E 0 1 E 0 2 thenthereceivedsignalisdemodulatedasabinarylogic0. 5.3.3OptimalIntegrationTime TheBERequationsforbothEDandEIDwherepreviouslydiscussedinChapter3 andChapter4,respectively.Equation3yieldstheBERforEDwhileEquation4 givestheBERforEID.Solvingtheseequationsfor E b = N 0 givestheSNR-per-bitrequired toachievethetargetBERasafunctionofintegrationtime.ForED,thisrequiredSNR -per-bitcanbeexpressedas SNR ED bit T w = T w = K 2 1+ p 1+2 T w B = K 2 )]TJ/F22 11.9552 Tf 11.39 8.088 Td [(1 )]TJ/F25 11.9552 Tf 9.963 0 Td [( T w 2 T w B # )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 SNR EID bit T w = 2 6 6 4 0 T w 000 T w = K 2 1+ r 1+ [ 000 T w ] 2 h 2 T w B 3 = 3 i = K 2 )]TJ/F22 11.9552 Tf 11.39 8.088 Td [(1 )]TJ/F25 11.9552 Tf 9.963 0 Td [( T w 2 T w B 3 7 7 5 )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 where K = Q )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 BER istheinverseQ-functionseeEquation3, B isthereceiver's bandwidth, 104
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000 T w = h 2 00 b T w = 0 b T w )]TJ/F22 11.9552 Tf 11.955 0 Td [(1 i )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 00 b T w = 2 B 2 T w 0 t 0 b d dt 0 b T w =2 B T w 0 b d and istheenergyscalingfactor 2 denedbyEquation5.MinimizingEquations 5and5givestheoptimalintegrationtime T w opt forEDandEIDreceivers,respectively.Sincetheenergyscalingfactor T w dependsontheCIR,itmustbeestimatedin real-timeinordertoaccuratelypredict T w opt aschannelconditionsvaryovertime.An estimationprocedurefor T w willbeproposedinSection5.4. 5.3.4CarrierSenseMultipleAccesswithCollisionAvoidance AttheMAClayer,theUCP-MACprotocolemploysthecarriersensemultipleaccess CSMAwithcollisionavoidanceCSMA-CAprotocoldescribedforthedistributed coordinationfunctionDCFoftheIEEE802.11MACstandard[46].WithCSMA-CA ,thenodesinthewirelessnetworkcontendforthechannelusingtwocontrolpackets, namelyrequest-to-sendRTSandclear-to-sendCTS,tovirtuallysensethechannel beforetransmitting.Ifanodesensesthechannelasidlethenitisallowedtotransmit. Otherwise,thenoderemainssilenttoavoidcausingcollisionsinthenetwork. TheCSMA-CAprotocolisillustratedinFigure5-2.Assumeanetworkcomprises nodesA,B,C,andDwhereBandCarewithintransmissionrangeofbothAandDbut AandDcannotheareachother.ThisisshowninFigure5-2a.Nowsupposethatnode 2 Recallthattheenergyscalingfactor T w ,asdenedinSection3.5.2,isaratio representinghowmuchofthetotalsignalenergyiscapturedbythereceiverasafunctionoftheintegrationtime T w 105
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aNetworktopology bPacketexchange Figure5-2:IllustrationoftheCSMA-CAprotocol AwantstotransmitdatatonodeB.Figure5-2bshowsthepacketexchangeunderthe CSMA-CAprotocol. TheprotocolstartswithnodeAsensingthechannelforaperiodoftimecalled DCFinter-framespacingDIFS. 3 AfteranidleDIFS,nodeAtransmitsaRTSpacketto nodeB.BothnodesBandCreceivethispacketastheyarewithintransmissionrange ofnodeA.SincethepacketisintendedfornodeB,nodeCsetsitsnetworkallocation vectorNAV,aninternaltimerindicatinghowlongthechannelwillbebusy,andstays silentforthatperiod.NodeBnowtransmitsaCTSpacketafterwaitingashortinterframespacingSIFSperiod.ThisCTSpacketisreceivedbynodesAandD.NodeD thensetsitsNAVandstayssilentfortheindicatedperiod.NodeAhasnowgainedthe 3 Inter-framespacingsIFSareperiodsoftimethatanodemustwaitbeforetransmittingapacket.Theycanbeusedforchannelsensinge.g.DIFSortoprovideenough timeforpropagationdelaysandinformationprocessinge.g.SIFS.Insomecases,they mightbealsousedtoprovidedifferentprioritylevelstoensurequalityofserviceQoS forcertaintransmissions. 106
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channeltotransmititsDATApacketsincenodesCandDwillremainsilent.NodeA nowtransmitstheDATApacket.ThisisreceivedbynodeBand,afterwaitingtheSIFS period,ittransmitsanacknowledgementACKpackettoletnodeAknowthatithas successfullyreceivedtheDATApacket.AftertheACKpacketisreceivedbynodeA, theircommunicationhassuccessfullynished. 5.4ChannelEstimation AsexplainedinSection5.3.2,todeterminetheoptimalintegrationtime T w opt ,the required SNR bit giveninEquations5and5mustbeminimized.However,todo that,theenergyscalingfactor T w ,mustbeestimatedrst.Recallthatthisfactoris theratioofhowmuchofthetotalsignalenergyhasbeenintegratedbythereceiverasa functionoftime.Inthissection,achannelestimationprocedurefor T w usingtheED techniqueisproposed. 5.4.1SignalandEnergyModel Assumethatalogic1hasbeenmodulatedusingPPM,i.e.thepulsesignalisplace intherstintegrationwindow,andtransmittedoverawirelesschannel.Thesamplesof thereceivedsignalintherstintegrationwindow X i andsecondintegrationwindow Y i canbeexpressedas X i = i + n i Y i = m i where i isthe i th sampleofthereceivedpulse, n i and m i representAWGNinthe channel,and i =1,2,..., N N = f s T w =2 B T w isthenumberofsamplesperwindow assumingtheNyquistsamplingrate f s =2 B isused.Theenergysamplesineach integrationwindowcanthenbeexpressedas 107
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E X i = 1 = f s i X j =1 X 2 j = 1 = f s i X j =1 )]TJ/F25 11.9552 Tf 5.48 -9.684 Td [( j + n j 2 E Y i = 1 = f s i X j =1 Y 2 j = 1 = f s i X j =1 )]TJ/F49 11.9552 Tf 5.48 -9.683 Td [(m j 2 Sincethenoisesamples n i and m i areassumedtobeAWGN,theycanberepresented asindependentandidenticallydistributedi.i.d.zero-meanGaussianrandomvariables withvariance 2 = N 0 f s = 2,i.e. n i N )]TJ/F22 11.9552 Tf 5.48 -9.684 Td [(0, 2 and m i N )]TJ/F22 11.9552 Tf 5.479 -9.684 Td [(0, 2 .Consequently, X i N )]TJ/F25 11.9552 Tf 5.479 -9.684 Td [( i 2 and Y i N )]TJ/F22 11.9552 Tf 5.48 -9.684 Td [(0, 2 arei.i.daswell.Atthispointisworthmentioningthat thevariancesof n i and m i canbeassumedtobethesameastheydependonthenoise spectraldensity N 0 whichinturndependsontemperature.Sincethetimebetween samplesisverysmallafractionofananosecond,thechangeintemperaturebetween themcanbeneglected. Now,notethat E X i and E Y i arethesummationofthesquareofGaussian randomvariableswhichareknowntofollowachi-squarerandomdistributionwith i degreesoffreedomandcentralityparameters s 2 X i = P i j =1 2 i and s 2 Y i =0,i.e. E X i 2 i )]TJ/F49 11.9552 Tf 5.479 -9.683 Td [(s 2 X i and E Y i 2 i 0 ,respectively.. Ingeneral,forachi-squarerandomvariablewith L degreesoffreedomandcentralityparameter s 2 ,themeanis L 2 + s 2 andthevarianceis2 N 4 +4 s 2 4 asshown in[64].Therefore,themeanandvariancefor E X i are E X i = i 2 + s 2 X i 2 E X i =2 i 4 +4 s 2 X i 2 whilefor E Y i ,since s 2 Y i =0,theseare E Y i = i 2 108
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2 E Y i =2 i 4 Now,thatwehaveanenergymodel,wecandevelopthechannelestimation proceduretoapproximatetheenergyscalingfactor.Thisestimationprocedureisbased ontheenergydifferenceofthetwointegrationwindows. 5.4.2EnergyDifference Followingtheenergymodeljustpresented,eachenergysampleintherstintegrationwindow E X i containsenergyfromthetransmittedpulseaswellasfrom noisewhile E Y i onlycontainsnoiseenergy.Intuitively,thedifference E X i )]TJ/F49 11.9552 Tf 12.579 0 Td [(E Y i shouldthenyieldinaveragethetransmittedpulseenergysincethetransmittedpulse andthenoiseinthechannelcanbeassumedtobeindependentprocessesandthe averagenoisepowerinbothintegrationwindowsisapproximatelythesameassuming anegligiblechangeintemperature. Toshowthisconcept,letusquicklygothroughthemath.Firstrecallthat X i and Y i arei.i.d.randomvariables.Hence, E X i and E Y i areindependentrandomvariables andthemeani.e.expectedvalueoftheirdifference E Z i = E X i )]TJ/F49 11.9552 Tf 11.955 0 Td [(E Y i isgivenby E Z i = E X i )]TJ/F25 11.9552 Tf 11.955 0 Td [( E Y i = s 2 X i where s 2 X i = P i j =1 2 i isthetransmittedpulseenergyaccumulateduptothe i th signal sample.Therefore,theexpectedvalueoftheenergydifference E Z i = E X i )]TJ/F49 11.9552 Tf 12.116 0 Td [(E Y i is theenergyfromthetransmittedpulse. 5.4.3EstimationoftheEnergyScalingFactor AsexplainedinSection5.3.2,theenergyscalingfactor representshowmuch ofthetotalenergyfromthetransmittedpulseisintegratedbythereceiverbasedon thelengthoftheintegrationwindow.Iftheenergysamplesofthetransmittedpulseare 109
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givenby s 2 X i = P i j =1 2 i aspreviouslydened,thentheenergyscalingfactoruptothe i th signalsampleofasinglesymbolcanbeexpressedastheratiogivenby i = s 2 X i s 2 X N where,asbefore, N = f s T w =2 B T w isthenumbersamplesineachintegration windowand s 2 X N isthetotalenergyofthetransmittedpulse.Now,recallthat s 2 X i is themeanof E X i )]TJ/F49 11.9552 Tf 12.321 0 Td [(E Y i asshowninEquation5.Similarly, s 2 X N isthemeanof E X N )]TJ/F49 11.9552 Tf 12.196 0 Td [(E Y N .Therefore,anestimationfortheenergyscalingfactorcanbeobtained usingthedifferenceoftheenergysamples,i.e. E X i )]TJ/F49 11.9552 Tf 11.959 0 Td [(E Y i ,ofasinglesymbol.Thisis illustratedinFigure5-3. Supposeagainthatalogic1,i.e.apulseistransmittedintherstintegration windowasshowninFigure5-3a.Thereceivedsignalduetomultipathfadingonly assumenoAWGNispresentfornowmaylookliketheoneinFigure5-3b.The resultingsignalaftersquaringandintegratingisshowninFigure5-3c.Asdenedby Equation5,normalizingthisresultingsignaltoitsmaximumvalueyieldstheenergy scalingfactor. Now,letusassumethatthesamepulseisreceivedbutnowinthepresenceof AWGN.Figure5-3dshowsthereceivednoisysignal.Aftersquaringandintegrating, theresultingsignalnowlookslikethatofFigure5-3e.Finally,takingtheenergy differencebetweentherstandsecondintegrationwindowsyieldsthesignalshown inFigure5-3fwhichisanapproximationoftheenergyofthereceivedpulsewithout AWGNshowninFigure5-3c. Wenotethatthisapproximationisnotveryaccurate.Ifmoreapproximationsare carriedoutwithdifferentsymbols,thentheiraverageyieldsamoreaccurateestimation. ThisisillustratedinFigure5-4wheretheUWBchannelmodelprovidedbytheIEEE P802.15.3areport[27]wasusedtogeneratetheCIRs.Increasingthenumberof symbols,20,50,150usedfortheestimation,increasesitsaccuracy. 110
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aTransmittedpulse dReceivedpulsewithnoise bReceivedpulse eEnergyofthereceivedpulsewithnoise cEnergyofthereceivedpulse fEnergydifference Figure5-3:Signalprocessingoftheproposedchannelestimation 5.4.4AchievinganOptimalTransmissionDataRate ForPPM-EDradios,thetransmissiondatarateisgivenby R data =1 = 2 T w since ittakestwointegrationwindowstotransmitasinglebit.Thenominalintegrationtime T w isdeterminedbytheworse-casemultipathscenario[55].Recallthattheenergyofthe transmittedpulseisspreadovertimeduetomultipathfading.Alargerenergyspreading correspondstoaworsemultipathscenarioandrequiresalarger T w sothatthereceiver canintegratemostoftheenergyfromthetransmittedpulse.Therefore,designers usuallychoosethenominal T w tobelargeenoughsothatthereceiverworksevenatthe worse-casemultipathscenario.However,oftenthereceiverwillbeoperatinginchannel conditionswherethenominal T w istoolargeresultinginaperformancedegradation 111
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a5 bits b20 bits c50 bits d150 bits Figure5-4:Accuracyoftheenergyscalingfactorestimationasmoresymbolsareused recallthatnoiseenergyisdirectlyproportionalto T w .Therefore,determiningthe optimalintegrationtime T w opt improvesthereceiverperformanceintermsofBERas demonstratedin[3]and,atthesametime,increasesthetransmissiondataratesince T w opt T w ,i.e. R data opt R data Intheworst-casescenario,thereceiverexhibitsitsoriginaldesignperformance andoperatesatthenominaldatarate.However,whenthechannelconditionsimprove sowillthereceiver'sBERperformanceandtransmissiondatarate.Forinstance,inthe exampleillustratedinSection5.4.3,ifthenominal T w ofanBERwas40 nsec andthe receivedSNR-per-bitis E b = N 0 =15 dB forasignalbandwidthof B =2 GHz ,theBER canbecalculatedusingEquation3yielding1.72 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(2 .However,afterestimating theenergyscalingfactor T w seeFigure5-4dandminimizingEquation5,the optimalintegrationtime T w opt isapproximately31 nsec withaBERof1.13 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(2 .This representsa34%improvementinBERanda29%increaseinthetransmissiondata rate. 112
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5.5UWBCooperativePHY-MACProtocol Aspreviouslymentioned,theUCP-MACprotocolproposedinthissectionemploysPPMmodulationandEDorEIDdemodulationatthePHYlayerandthemultiple accessmechanismoftheIEEE802.11CSMA-CAattheMAClayer.Themodulated symbolsbinarybitsofthecontrolpackets,RTSandCTS,areusedatthePHYlayer todeterminetheoptimalintegrationtimeofthereceivingandthetransmittingnodes. InformationontheoptimalintegrationtimeisthenexchangedusingtheMAClayersuch thateachnodeadaptsitsdatarateaccordingly. 5.5.1ReceiverArchitectureforChannelEstimation ApossiblereceiverimplementationforaPPM-EDradioemployingthechannel estimationtechniqueproposedinSection5.4.3isdepictedinFigure5-5.Thefront-end ofthereceivercorrespondstothegeneralarchitectureofaPPM-EDreceiverinwhich thereceivedsignalisltered,amplied,squaredandintegrated.Afterthisanalogsignal processing,theresultingsignalwhichrepresentstheenergyineachintegrationwindow isthenpassedthroughananalog-to-digitalA-to-Dconverter.Now,inthedigital domain,thebit-decisioncanbemadebycomparingtheenergyineachintegration window.Inaddition,thoseenergysignalsarealsousedfortheestimationoftheenergy scalingfactor ThechannelestimationblockinFigure5-5startswithtwodelaycomponentsthat accountforthetimeittakestomakethebit-decisioni.e.thedelayofthecomparator. Thisisbecausethebit-decisionmustbemadebeforethesignalprocessingforthe channelestimationinordertodeterminewhichintegrationwindowcontainsthetransmittedpulse.Recallthatapulseintherstintegrationwindowwasassumedfortheenergy modelpresentedinSection5.4.1andthustheenergyscalingfactorwasestimatedwith theenergydifference E X i )]TJ/F49 11.9552 Tf 12.076 0 Td [(E Y i ;however,ifthepulsewastransmittedinthesecond integrationwindow, E Y i )]TJ/F49 11.9552 Tf 10.814 0 Td [(E X i mustbeusedinstead.Theorderoftheintegrationwindowsisdonebythesecondcomponentcalledwindoworderintheblockdiagram.This 113
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Figure5-5:PPMEDreceiverarchitecturewiththeproposedchannelestimation componentisfollowedbyadigitalsubtractorandacomponenttonormalizetheenergy differencetoitsmaximumrecallthattheenergyscalingfactormustbebetween0to1. Afterthenormalization,theresultingsignalisanapproximationoftheenergyscaling factor.However,aspreviouslyexplained,multipleapproximationsmustbeaveragedto increasetheaccuracyoftheestimation.Therefore,theapproximationobtainedfrom eachreceivedsymbolisaccumulatedandthetotalisdividedbythenumberofsymbols L .Theresultingsignalisthenanaccurateestimationoftheenergyscalingfactorforthe currentchannelconditions. 5.5.2CooperativePHY-MACProtocol ThegeneralideaoftheproposedUCP-MACprotocolcanbeexplainedwith asimpleexample.SupposenodeAwantstotransmitdatatonodeB.Figure5-6 illustratesthegeneralstepsoftheircommunicationusingtheproposedprotocolwhich 114
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Figure5-6:CognitivePHY-MACprotocolsummary isbasedontheRTS/RTSmechanismoftheCSMA-CAprotocoldiscussedinSection 5.3.4. NodeAstartsbysensingthechannelduringtheDIFSperiod.Ifnothingisreceived duringthisperiod,nodeAassumesthechannelisidleandtransmitstheRTSpacketat thenominaldatarate R data =1 = 2 T w where T w isthenominalintegrationtime.While receivingtheRTSpacket,nodeBisestimatingtheenergyscalingfactor T w which willbeusedtodeterminetheoptimalintegrationtime T w opt .Onceithasnishedreceiving,nodeBcalculatesthe T w opt thatminimizesitsBERandsetsitsnewreceiving Rxdatarateto R data opt =1 = 2 T w opt .Then,nodeBpreparesandtransmitsthe CTSpacketwhichincludesthe T w opt thatitjustcalculated.NodeA,whilereceiving thisCTSpacket,alsoestimates T w andcalculatesitsown T w opt andincludeitin theDATApacket.Withthe T w opt receivedfromnodeBintheCTSpacket,nodeAsets itsthenewtransmittingTxdatarateto R data opt =1 = 2 T w opt .Atthispoint,both nodesaresynchronizedwiththesamedataratefortheexchangeoftheDATApacket. NodeAnowpreparesandtransmittheDATApacketthatincludesthedataframeand itsown T w opt .WhennodeBreceivestheDATApacket,itsetsthenewTxdatarate 115
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basedonthe T w opt receivedfromnodeA.Then,ittransmitstheACKpacketatthis newdataratewhichwillbereceivedbynodeA.AftertheexchangeoftheACKpacket, thecommunicationhassuccessfullynishedandbothnodesresettheirRxandTxdata ratestothenominalvalue R data =1 = 2 T w Insummary,theRTSandCTSpacketsarealwaystransmittedatthenominaldata rateand,inadditiontovirtuallysensingthechannel,theyarealsousedtodeterminethe optimaldataratesatwhichtheDATAandACKpacketswillbetransmitted.Oneofthe benetsobtainedwiththeproposedprotocolisthereducedprobabilityofbit-errorsfor theDATAandACKpacketssincetheyaretransmittedattheoptimaldatarate.Another benetistheincreaseindataraterecallthat R data opt R data allowingtheDATAand ACKpacketstobetransmittedfasterand,asaconsequence,thechannelisbusyfor lessamountoftime. Next,wedescribetheframeformatsfortheMAClayerpackets,orMACprotocol dataunitsMPDUsandthePHYlayerpacket,orPHYlayerdataunitPLDU. 5.5.3PHYandMACFrameFormats Figure5-7showstheframeformatsofthefourMPDUsRTS,CTS,DATA,ACK. ThesearesimilartothoseusedinIEEE802.11CSMA-CAprotocolexceptfortheeld reservedfortheoptimalintegrationtimeOptimal T w .TheIDeldidentiesthetype ofMPDURTS,CTS,DATA,orACK.TheDurationeldcontainsthetimeneededto nishthecommunicationandisusedbythereceivingnodetosetitsNAV.TheSource andDestinationeldsareusedtoidentifythenodeinitiatingthecommunicationand thenodeforwhichthepacketisintended,respectively.TheDataFrameeldcontains theinformationtobetransmittedwhiletheCRCeldisusedforerrordetectionusing thewell-knowncyclicredundancycheckCRC. ForthePHYlayer,theframeformatofitsPLDUisshowninFigure5-8.ThePHY preamblecomprisestheSYNCandSFDelds.Bothofthemcontainaspecicsequenceoflogic0sand1s.TheSYNCsequenceisusedforsynchronizationpurposes 116
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aRTS bCTS cDATA dACK Figure5-7:FrameformatforeachMPDU Figure5-8:FrameformatofthePLDU whiletheSFDisthestartframedelimiterandisusedtomarkthebeginningofthe PHYheader.ThisheadercontainstheFrameLengtheldandadedicatedCRC eldforerrordetection.TheframelengthreferstothelengthoftheCodedMPDUeld whichcontainstheMPDUfromtheMAClayerandcanbecodedfordifferentpurposes suchaserrorcorrection. 5.6SimulationSetup 5.6.1NetworkSimulator InordertotesttheproposedUCP-MACprotocol,acompletenetworksimulatorwas programmedinMATLAB R .Thesimulatorcontainsover30classesthatimplementeach oneofitsfunctionalities.Ageneraldiagramofthemainclasses, Node and Channel isshowninFigure5-9whereeachblockrepresentsaparentclass.The Node class implementsalltheprocessescarriedoutbyanodeinordertotransmitorreceivea message.Anodecomprisesthreecommunicationlayers:PHY,MAC,andahigher 117
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a Node class b Channel class Figure5-9:Diagramsofthetwomainclassesusedbythenetworksimulator layerprovidesthemessagesi.e.databitstobetransmitted.Ontheotherhand,the Channel classisusedtomodelthewirelesschannel,i.e.themediumthroughwhichthe transmittedsignalstravel. 5.6.1.1 Node class Toappropriatelysimulatethecognitiveprotocol,itisnecessarytofullyimplement bothPHYandMAClayersastheprotocolutilizesthecommunicationbetweenthem anditsmainfeature,integrationtimeoptimization,isbasedonthesignalprocessingof thereceivedsignal.ThePHYlayertakescareoferror-correctionandsignalmodulation whiletheMAClayerrunstheRTS/CTSmechanism. InthePHYlayer,theMPDUreceivedfromtheMAClayeriscodedforerrorcorrectionusingtheBose-Chaudhuri-HocquenghemBCHalgorithmwitha7 = 4 codingratiowhichhasbeenshowntobemoreenergy-efcientthanmostblockand convolutionalcodes[73].ThecodedMPDUalongwiththePHYheaderandpreamble makeupthePLDUaspreviouslyshowninFigure5-8.ThisPLDUisthenmodulated 118
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usingPPMandtheresultingsignalistransmitted.Theinverseoccurswhenasignalis received.ItisrstdemodulatedusingtheEDorEIDdemodulationtechnique.Atthis pointtheenergyscalingfactor T w isestimatedandforthecalculationoftheoptimal integrationtime T w opt .Thedemodulatedbitsarethenchecked.IfthePHYpreamble andheaderwerereceivedcorrectly,theremainingbitscorrespondingtothecoded MPDUaredecodedanderror-correctedbeforebeingsenttotheMAClayer. TheMAClayerrunstheUCP-MACprotocolwiththesupportofthePHYlayer. TheprotocolisexecutedforeachmessageintheMACbufferwhichinturnreceives messagesfromahigherlayer.Thismessagescanbecalledhigher-layerdataunits HLDUs.ForeachHLDUintheMACbuffer,RTS,CTS,DATA,andACKpacketsmust beexchangedtoachieveasuccessfultransmission. 5.6.1.2 Channel class Thisclassmodelsthechangesthatasignalundergoeswhiletravelingthrough thewirelessmedium,i.e.multipathfading,pathloss,interference,andadditivenoise. Tomodelmultipathfading,eachsignalisconvolutedwiththecorrespondingCIR generatedbytheMATLAB R modelprovidedbytheIEEEP802.15.3ataskgroupreport [27].Pathloss,ontheotherhand,ismodeledusingalog-normalshadowingmodel andtheparametersforUWBchannelsprovidedin[35].Interferenceismodeledby addingupallconvolutedsignalswiththeirrespectivepathlossesapplied.Finally, noiseismodeledbyaddingAWGNwithpowerspectraldensity N 0 = k B T K where k B =1.3806488 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(23 Joules = Kelvin istheBoltzmannconstantand T K isthe environmenttemperaturein Kelvins 5.6.1.3Otherimportantclassesandfunctions Inadditiontothe Node and Channel classes,therearetwoothermajorclasses usedinthesimulator: Topology and Messages .The Topology classcreatesthenetwork topologyandmodelsnodemobility.Thenodesarerandomlydistributedandmoved withinthenetworkarea.Ontheotherhand,the Messages classgeneratesrandomdata 119
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bitstosimulatetheHLDUsthataresenttotheMAClayerfortransmission.TheHLDU arrivaltimeismodeledasaPoissonprocesswitharrivalrate1 = sec )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 Thesimulatoralsousesseveralfunctionstoproperlywork.Amongthese,the mostmostimportantarethe RunSimulation and Results functions.Therstismainly aloopthatcontrolsthenetworktimebutisalsoresponsibleforhoweverythingis interconnected.Thesecondgoesthroughthesimulatorlogwhereallactionswere recordedduringthesimulationandcalculatesnetworkperformancemetricssuchas averagetransmissiontimeandmessagedeliveryratio.Thesemetricsareusedlaterto analyzeandcomparenetworkperformances. 5.6.2SimulationParametersandSetup Table5-1showstheparametersusedforthesimulationsrun.Thenumberof nodesandthemessagearrivalratewerevariedfrom5to30andfrom4to32 sec )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 respectively.Whenthearrivalratewasvaried,thenumberofnodeswassetto25. Whenthenumberofnodeswasvaried,thearrivalratewassetto20 sec )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 .Thenodes wererandomlyplacedwithinthenetworkareawhichhasdimensions5 5 5 meters Duringthesimulation,nodesmoverandomlywithinthenetworkareaataspeedof1 m = s ThebackoffalgorithmusedbytheMAClayerwhenapacketcollisionisdetectedis anexponentialalgorithminwhichthebackofftimeiscalculatedas t backoff = t backoffslot N slots where t backoffslot isthelengthofasinglebackofftimeslot, N slots isanumberrandomly chosenfromtheset [ 0,1,...,2 n )]TJ/F22 11.9552 Tf 11.955 0 Td [(1 ] ,and n istheretransmissionnumber.Forinstance, assumeanodeistransmittinganewmessageandapacketcollisionisdetected. Sincethenodewilltrytoretransmitforthersttime,then n =1andanumberfrom theset [ 0,1 ] israndomlychosen.Ifthenodeistryingtoretransmitforthesecondtime then n =2andthesetfromwhichanumberisrandomlychosenisnow [ 0,1,2,3 ] .If 120
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Table5-1:Simulationparameters ParameterValue NumberOfNodes5 )]TJ/F22 11.9552 Tf 14.612 0 Td [(30 NetworkDimensions m 5 5 5 NodeSpeed m = s 1 MessageArrivalRate1 = = s 4 )]TJ/F22 11.9552 Tf 14.612 0 Td [(32 Max.NumberofRetransmissions3 BackoffTimeSlot s 50 DIFS s 40 SIFS s 20 Temperature K 300 NominalIntegrationTime T w ns 100 PulseBandwidth GHz 2 TransmissionPower dBm )]TJ/F22 11.9552 Tf 9.298 0 Td [(8.3 LengthofMPDUFields bits ID4 Duration,Destination,Source,Optimal T w 16 Dataframe4000 CRC12 LengthofPLDUelds bits SYNC,SFD24,8 Framelength,CRC16,12 n =3,thesetis [ 0,1,2,3,...,7 ] andsoon.Theparametersfortheexponentialbackoff algorithmusedinthesimulationsarealsoshowninTable5-1. 5.7Analysis SeveralsimulationswereruninordertocomparetheperformanceoftheUCP-MAC protocol.Threeparametersareplottedinthissectionasafunctionofthemessage arrivalrateandthenumberofnodesinthenetwork.Boththearrivalrateandthe numberofnodeswerechosensincetheseeffectivelyincreasethenetworktrafc 4 givingabetterideaofhowtheprotocolbehaveswithincreasingtrafc. 4 Thetrafcinthenetworkincreasesasmoremessagesaresenteitherduetomore messagesbeingcreatedormorenodestransmitting. 121
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a b Figure5-10:Messagedeliveryratioasafunctionofathemessagearrivalrateandb thenumberofnodesinthenetwork 5.7.1MessageDeliveryRatio Themessagedeliveryratioasapercentageiscalculatedas DR msgs = n msgs )]TJ/F49 11.9552 Tf 11.955 0 Td [(n drop n msgs 100 where n msgs isthetotalnumberofmessagestobetransmittedinthenetworkand n drop isthenumberofmessagesdroppedafterunsuccessfullyretransmittingforcertain amountoftimesinthiscase,3asshowninTable5-1.Ingeneral,anunsuccessful transmissionoccursduetouncorrectablebit-errors.Thesemainlyhappendueto transmissioncollisionsandnoiseinthewirelesschannel.Themessagedeliveryratio showsthepercentageofmessagesthataresuccessfullydelivered. Figure5-10showsthispercentageasafunctionofthemessagearrivalrateandthe numberofnodesinthenetwork.IncomparisontotheregularCSMA-CAprotocol,the UCP-MACprotocolsignicantlyimprovesthenumberofmessagesthataretransmitted successfullyinthenetworkasthetrafcincreases.Therearetwomainfactorsforthis improvement.TherstisthereductioninBERtheoptimalintegrationtime.Asmaller probabilityofbit-errorreducestheprobabilityofapacketerrorduetouncorrectable bit-errors.Thesecondfactoristheincreaseindatarateduetoasmallerintegration 122
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time.AfastertransmissionoftheDATAandACKpackets,reducesthetimeforwhichthe channelisbusywhichinturnreducestheprobabilityofcollisionsinthenetwork. Fromthegure,itisalsoclearthattheEIDdemodulationtechniqueperformsbetter thantheEDtechnique.Thisismostlyduetotheimprovementinbit-errorrateofEID overEDasdiscussedinChapter4. 5.7.2AverageTransmissionTime Thetransmissiontimeisdenedhereasthetotaltimeittakestosuccessfully nishthecommunicationbetweentwonodes.Thattimeismeasuredfromthemoment therstRTSpacketistransmitteduntiltheACKhasbeenreceived.Therefore,the minimumtransmissiontimeforamessagetobesuccessfullydeliveredoccurswhenno retransmissionsarerequiredandcanbecalculatedas t Tx min = t RTS + t CTS + t DATA + t ACK +3 t SIFS where t SIFS istheSIFStimeand t RTS t CTS t DATA ,and t ACK arethetimesrequiredto transmittheRTS,CTS,DAATA,andACKpackets,respectively.Whenthechannel conditionsarebetterthantheworst-casescenario, R data opt > R data whichreduces t DATA + t ACK resultinginasmallertransmissiontime.Thetotaltransmissiontimewhen retransmissionsarerequirediscalculatedasthetotaltimeittooktosuccessfullyreceive theACKpacketstartingfromthetimetherstRTSpacketwastransmitted.Therefore, thetransmissiontimeincreaseswiththenumberofretransmissions. Figure5-11showstheaveragetransmissiontimeofthenetworkasafunction ofmessagearrivalrateandnumberofnodes.Fromtheplotsiseasytoseethat asthetrafcinthenetworkincreases,theaveragetransmissiontimeincreasesas well.Thisisaconsequenceofanincreaseinthenumberofcollisionsyieldingmore retransmissionsand,hence,increasingtheaveragetransmissiontime.Thegure alsoshowstheimprovementoftheUCP-MACprotocolincomparisontotheregular CSMA-CAprotocol.Onceagain,thisimprovementismainlyrelatedtothereducedBER 123
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a b Figure5-11:Averagetransmissiontimeasafunctionofathemessagearrivalrateand bthenumberofnodesinthenetwork andtheincreaseddataratefortheDATAandACKpackets.Smallertransmissiontimes forthesepacketsreducethecommunicationtimebetweentwonodes.Inaddition,as previouslyexplained,thesetwofactorsreducetheprobabilityofretransmissions.With lowernumberofretransmissions,theaveragetransmissiontimeisreducedaswell recallthattransmissiontimeismeasuredfromtherstRTStransmitted. IncontrasttothemessagedeliveryratiodiscussedinSection5.7.1,heretheEID demodulationtechniqueperformsworsethantheEDtechniquewhenusingtheUCPMAC.ThemainreasonforthisbehavioristhattheoptimalintegrationtimeofEIDis higherthanthatofEDasdiscussedinChapter4.However,whenusingtheCSMA-CA protocol,EIDperformsbetterthanEDsinceitreducesthenumberofretransmissions causedbybit-errors. ApossiblesoultiontodecreasetheaveragetransmissiontimeofEIDistouse theoptimalintegrationtimecalculatedforED.Although,EIDwillnotbeoperatingat itsoptimalitshouldstillhaveasimilarorbetterBERperformancethanEDascanbe concludedfromtheanalysisdoneinChapter4,inparticular,fromFigure4-8.This possiblesolutionwillbestudiedandanalyzedinthefuture. 124
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a b Figure5-12:Throughputasafunctionofathemessagearrivalrateandbthenumberofnodesinthenetwork 5.7.3Throughput Throughput,oreffectivedatarate,canbedenedas R eff = l data t Tx where l data isthelengthofthedataframeinourcase,4000bitsand t Tx istheaverage transmissiontime.Figure5-12showsthecalculatedthroughputand,asexpected,it decaysasthetrafcinthenetworkincreasesduehighercollisionswhichtranslates intohighernumberofretransmissions.SincetheUCP-MACprotocol,inaverage, reducesthenumberofretransmissionsandincreasesthedatarateoftheDATAand ACKpackets,itoutperformstheregularCSMA-CAprotocolasdepictedinthegure. Figure5-12alsoshowsthatforthespecicsimulationparametersusedseeTable 5-1,theeffectivedatarateuctuatesfromabout4Mbpstolessthan100Kbpsas thetrafcinthenetworkincreases.Thisdegradationistheresultofhighernumberof retransmissionsmainlyduetoanincreaseinthenumberofcollisionsinthenetwork. 125
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Chapter6 CONCLUSIONSANDFUTUREWORK Forthelastthreedecades,asthewirelesscommunicationsindustryhasadvanced, therehasbeenagreatincreaseinthedevelopmentofnotonlylong-rangeandmediumrangewirelesscommunicationsbutinshort-rangewirelesssystemsaswell.ShortrangewirelessnetworkssuchasWLAN,WPAN,andWSNarewidelyusedintoday's technologyapplications.Inmanycasestheseapplicationshavealimitedpowersource andthusrequireverylow-powercommunicationstoextendtheirtimeofoperation. Recently,inparticularsincetheFCCapprovalin2002,UWBcommunicationshave attractedtheinterestofmanyresearchersasanalternativetechnologytoimplement low-powerwirelessapplications.UWBtechnologyoffersawiderangeofbenetsthat makesitaviablesolutionformanyshort-rangewirelesssystems.Amongthesebenets arelow-powertransmission,reducedinterference,lowcostandcomplexityinhardware, increasedrobustnessagainstmultipathfadingandrelativelyhighdatarates.Forthelast decade,researchandnumerousinvestigationshaveprovenUWBtobeanefcientand feasibletechnologyfordigitalcommunications. TheworkpresentedinthisdoctoraldissertationwasfocusedonUWBradiosusing PPMwhichisaverypopulardigitalmodulationtechniqueforverylow-powerwireless communications.Amongthecontributionsoftheworkdone,thekeycontributionisthe applicationofnon-coherentUWBradiosusingPPMtoanewcognitiveandcooperative protocolbetweenthePHYandMAClayers,i.e.theUCP-MACprotocol.Thisprotocol employsacognitivechannelestimationtechniquebasedonEDinthePHYlayerand amultipleaccessmechanismbasedontheCSMA-CAprotocolintheMAClayer. Theselayersexchangeinformationwitheachotherinordertooptimizethewireless communication. Previoustothedevelopmentofthetheorypresentedthroughoutthisdissertation, extensiveinvestigativeworkonUWBwasperformedandageneraloverviewalongwith 126
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keyconceptswerepresentedinChapter2.ThischapterincludedtheFCCdenitions andspecications,themainbenets,thecommonlyusedmodulationtechniques, andadescriptionofchannelmodelingforUWBwirelesscommunications.Fromthe discussioninthischapter,itwasclearthatnon-coherentPPMradiosareanexcellent choiceforapplicationsrequiringlow-powerandlow-complexityarchitectureswhichis thegeneralcaseoflow-powershort-rangead-hocwirelessnetworks.Themostpopular non-coherentdemodulationtechniqueforPPMisbasedonenergydetectionEDwhich isthebaseforthechannelestimationtechniqueusedbytheUCP-MAC. AmoredetaileddiscussiononEDreceiverswaspresentedinChapter3.Itwas shownthatforED-PPMreceiversthereisanoptimalbandwidthandanoptimalintegrationtimethatminimizestherequired SNR bit toachieveadesiredBER.Analytical equationstoapproximatetheseoptimalvalueswerederivedandpresentedtakinginto accountnon-idealitiessuchadjacent-channelinterferenceACI,inter-symbolinterferenceISI,andinter-frameIFI.Theseequations,corroboratedbysimulations,were usedtoanalyzetheeffectofmultipathfadingonED-PPMreceivers.Amongthendings, itwasshownthatincreasingthesignalbandwidthreducestheoptimalintegrationtime butdegradesthesystemperformanceintermsofBER.Inaddition,exampleswere brieydiscussedinshowingthatarelativelysmalldegradationin SNR bit canpotentiallyoffervaluablebenetssuchaslowerpowerconsumptionandhigherdatarates. Moreover,theequationsderivedarenotonlyusefulwhenunderstandingtheeffectsof multipathfadingbuttheyareconvenientwhendesigningED-PPMreceiversoperating inUWBchannels.Byusingthem,thedesignercaneasilychoosetheappropriateintegrationtimebasedonsystemparameterswithouttheneedofbuildingandrunning simulators. InChapter4,animprovementtothecommonEDtechniquewaspresented.The motivationwasbasedonthefactthatwhenapproximatingthebestintegrationtime,the optimizedreceiverwillbeoptimalonlyifitoperatesunderawirelesschannelsimilarto 127
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thechannelmodelusedforitsoptimization.Otherwise,thereceiverwillshowasignificantperformancedegradation.Toreducethisperformancedegradationexperienced byanoptimizedreceiveroperatingindifferentchannelconditions,theEIDtechnique wasintroducedandmathematicallyproved.AsdonefortheoptimizationofED-PPMreceiversinChapter3,analyticalequationswerederivedinordertounderstandtheeffect ofmultipathfadingonreceiversusingtheEIDdemodulationtechniqueandhowitimprovesthereceiver'sBERperformanceincomparisontotheEDtechnique.Simulations corroboratedtheequationsderivedwhichwereusedtonumericallycomparebothED andEIDtechniques.Theresultsshowedthat,althoughEIDisnotanoptimalsolution 1 itreducesconsiderablythedegradationexperiencedbyEDreceiverswhilekeepinga relativelysimplearchitecture.AnotherinterestndingwasthatEIDalsoreducesthe degradationinBERperformanceinherenttoanincreaseoftheintegrationtimewhen comparedtoED.Ontheotherhand,althoughEIDimprovesingeneraltheBERperformanceofthereceiver,themaindrawbackisthatitsoptimalintegrationtimeisusually higherthanthatofareceiveremployingtheEDtechnique.Thisisadisadvantagesince higherintegrationtimestranslateinaslowerbittransmission,i.e.smallertransmission datarates.Therefore,whendecidingbetweenEDandEIDtechniques,themaintradeoff isbetweentransmissionspeedandBER. InChapter5,achannelestimationmethodforPPMreceiverswaspresentedand discussedalongwiththenewUCP-MACprotocolwhichusesthischannelestimation inthePHYlayer.ItalsousesaMACmechanismbasedontheIEEE802.11DCF functiontooptimallyadjustthetransmissiondatarateinboththetransmittingandthe receivingnode.ThechannelestimationtechniqueisbasedonED,however,itcan beusedforbothEDandEIDtechniquessincetheyhavethesamereceiverfront-end 1 EIDisnotanoptimalsolutioninthesensethatitdoesnotcompletelyeliminatethe degradationofoptimizedreceiverswhenoperatingindifferentchannelconditions. 128
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architectureuptotherstintegrationstage.Usingthechannelestimation,anodecan calculateitsoptimalintegrationtimeand,hence,itsoptimaldatarate.Thisoptimaldata rateisthensharedbythetransmittingandthereceivingnodesinordertooptimize theircommunicationintermsoftransmissionspeedandareducedBER.Bothnodes exchangetheiroptimaldataratesthroughtheMAClayerprotocol.Then,theMAC layersofbothnodescommunicatewiththeirrespectivePHYlayersinordertoadjust theirtransmissiondataratesallowingthenodestosynchronizetheirtransmittingand receivingintegrationtimes.Bysimulatingthenewprotocol,itwasshownthatthe overallnetworkperformanceimprovesintermsoftheaveragetransmissiontimeand themessagedeliveryratio.Moreover,whenusingtheEIDdemodulationtechnique, themessagedeliveryratioimprovesfurther.However,theEDtechniqueyieldsa betteraveragetransmissiondelay.Therefore,atradeoffbetweendeliveryratioand throughputexistsandmustbestudiedinacase-by-casebasisdependingonthetypeof application. Futureworkworkwillincludeadditionalsimulationstohelpunderstandmorethe mentionedtradeoffandndotherareasandscenariosinwhichthethenewprotocol mayormaynotimprovetheoverallnetworkperformance.Improvementstotheprotocol willbeconsideredaswell.Forinstance,thechannelestimationtechniquemightbe furtherimprovedorevensubstitutedtoyieldmoreaccurateresultswhencalculating theoptimalintegrationtimes.Betteraccuracyinthiscalculationshouldyieldalower BERwhichreducestheprobabilityofapacketerror.Also,additionalimprovementsto theMAClayerprotocolcanbeinvestigatedinordertoadaptthecognitiveprotocolto certainapplications.Anexamplewouldbe,inverylow-powerorhightrafcnetworks, havingaschemeofidleperiodscouldreducetheenergyconsumptionandthecollisions producedbyhighnetworktrafc. 129
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AppendixA DERIVATIONOFTHEPROBABILITYOFBIT-ERRORFORPPM-EDRECEIVERS Let X i = i + n i and Y i = m i bethesignalsintherstandsecondintegration windows,respectively,for i =1,2,..., N .Here i represents i th sampleofthereceived signalpulseand m i and n i areindependentzero-meanGaussianrandomvariables withthesamevariances 2 representingAWGN.Theconditionforabitdecisionbased ontheenergy-detectionEDis N X i =1 X 2 i 1 ? 0 N X i =1 Y 2 i A Inthiscase,sincethepulseisintherstintegrationwindow,abit-erroroccursif P i X 2 i P i Y 2 i .Thus,weareinterestedintheprobability P )]TJ 5.479 -0.717 Td [(P i X 2 i P i Y 2 i .In[64], ithasbeenshownthat V = P N i =1 X 2 i followsthedistributionofanon-centralchi-square randomvariablewithacentralityparameter s 2 = P i 2 i and N degreesoffreedom,i.e. V 2 N )]TJ/F49 11.9552 Tf 5.48 -9.684 Td [(s 2 ,while W = P N i =1 X 2 i followsacentralchi-squarerandomvariablewith N degreesoffreedom,i.e. W 2 N 0 .Itwasalsoshownthattheprobabilityofbit-error P ED = P V W isgivenby P ED = 1 2 2 N )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 e s 2 = 2 N )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 X n =0 c n )]TJ/F49 11.9552 Tf 5.48 -9.684 Td [(s 2 = 2 n A where c n = 1 n N )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 )]TJ/F49 7.9701 Tf 6.587 0 Td [(n X k =0 )]TJ/F22 7.9701 Tf 5.48 -4.736 Td [(2 N )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 k A However,bytheCLT,if N issufcientlylarge, V and W canbeapproximatedaGaussianrandomvariables,i.e. V N )]TJ/F25 11.9552 Tf 5.48 -9.684 Td [( V 2 V and W N )]TJ/F25 11.9552 Tf 5.48 -9.684 Td [( W 2 W where V = N 2 + s 2 W = N 2 2 V =2 N 4 +4 s 2 2 ,and 2 W =2 N 4 asshownin[64].Hence,if welet Z = V )]TJ/F49 11.9552 Tf 12.302 0 Td [(W ,theprobabilityofbit-error P ED = P Z 0 canbeapproximatedby 130
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P ED Q Z = q 2 Z where Q referstotheQ-functiondenedbyEquation3and themeanandvarianceof Z are Z = V )]TJ/F25 11.9552 Tf 11.956 0 Td [( W = s 2 A Z = 2 V + 2 W =4 N 4 +4 s 2 2 A respectively.Now,assumingthesignalsinbothintegrationwindowsaresampledatthe Nyquistfrequency,thenumberofsamplesineachintegrationwindowis N =2 B T w where B isthebandwidthofthereceivedsignaland T w istheintegrationtimeineach window.Also,notethat s 2 = P i 2 i istheenergyofthereceivedsignal E b and 2 = N 0 = 2 where N 0 isthetwo-sidednoisespectraldensity.Therefore, P ED Q Z = q 2 Z can beexpressedintermsofthereceivedSNR-per-bit E b = N 0 ,bandwidth B ,andintegration time T w as P ED Q 0 B @ E b = N 0 p 2 B T w +2 E b = N 0 1 C A A whichyieldsaccurateresults < 5%errorfor B T w > 20[20]. 131
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AppendixB DERIVATIONOFTHEPROBABILITYOFBIT-ERRORFORPPM-EIDRECEIVERS AsinAppendixA,assume X i and Y i arethereceivedsignalsintherstandsecond integrationwindows,respectively.Then,theenergyintegrationineachwindowis V = N X i =1 i X j =1 X 2 j = N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i X 2 i B W = N X i =1 i X j =1 Y 2 j = N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.956 0 Td [(i Y 2 i B respectively,where X i N )]TJ/F25 11.9552 Tf 5.479 -9.684 Td [( i 2 and Y i N )]TJ/F22 11.9552 Tf 5.479 -9.684 Td [(0, 2 arestatisticallyindependentfor all i =1,2..., N .Hereweareinterestedinthe P V W = P V )]TJ/F49 11.9552 Tf 11.955 0 Td [(W 0 whichisthe probabilityofbit-error P e forabbrefEID.Toderiveanexpressionforthisprobabilitywe willneedthemeansandvariancesof V and W .InAppendixC,themeanandvariance of V arecalculatedtobe V = N 0 2 + E 0 N B 2 V =2 N 00 4 +4 h 2 E 00 N )]TJ/F49 11.9552 Tf 11.955 0 Td [(E 0 N i 2 B where N 0 = N N +1 = 2, N 00 = N N +1 2 N +1 = 6,and E 0 N and E 00 N aregivenby EquationsCandC,respectively.For W ,themeanandvariancesimplifyto W = N 0 2 B 2 W =2 N 00 4 B sincethemeanof Y i iszero,i.e. E 0 N = E 00 N =0.Ifwelet Z = V )]TJ/F49 11.9552 Tf 12.001 0 Td [(W ,thenmeanand varianceof Z are Z = V )]TJ/F25 11.9552 Tf 11.955 0 Td [( W and 2 Z = 2 V + 2 W ,i.e. 132
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Z = E 0 N B 2 Z =4 N 00 4 +4 h 2 E 00 N )]TJ/F49 11.9552 Tf 11.955 0 Td [(E 0 N i 2 B which,withsimplealgebraicmanipulation,canbeexpressedas Z = s 2 eff B 2 Z =4 N eff 4 +4 2 s 2 eff B where s 2 eff = E 0 N and N eff = N 00 +2 E 00 N )]TJ/F49 11.9552 Tf 11.955 0 Td [(E 0 N = 2 .NotethatEquationsB andBareinthesameformasEquationsAandAinAppendixA,respectively. Hence,theprobabilityofbit-error P EID = P Z 0 canbecalculatedusingEquation A.However,if N issufcientlylargethen N 00 N 3 = 3, Z N )]TJ/F25 11.9552 Tf 5.479 -9.684 Td [( Z 2 Z bytheCLT,and P EID = P Z 0 Q Z = q 2 Z ,i.e. P EID Q 0 B @ s 2 eff = 2 2 q N eff + s 2 eff = 2 1 C A B or,equivalently, P EID Q 0 B @ E 0 = 2 p N 3 = 3+2 2 E 00 )]TJ/F49 11.9552 Tf 11.955 0 Td [(E 0 = 2 1 C A B where Q istheQ-functionasdenedbyEquation3. 133
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AppendixC MEANANDVARIANCEOF P I P J X 2 J FOR X J N )]TJ/F25 11.9552 Tf 5.48 -9.684 Td [( J 2 Letusdenetherandomvariable V withmean V andvariance 2 V V = N X i =1 i X j =1 X 2 j = N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i X 2 i C where X 1 X 2 ,..., X N arestatisticallyindependentGaussianrandomvariableswith means i andvariances 2 i = 2 ,i.e. X i N )]TJ/F25 11.9552 Tf 5.48 -9.684 Td [( i 2 .Also,letusnowdenethefollowingGaussianrandomvariable Y i = p N +1 )]TJ/F49 11.9552 Tf 11.956 0 Td [(i X i where Y i N )]TJ/F23 11.9552 Tf 5.48 0.174 Td [(p N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i i N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i 2 suchthat V = N X i =1 Y 2 i C Itisclearthat V followsanon-centralchi-squarerandomvariablewith N degreesof freedomsince Y 1 Y 2 ,..., Y N areindependentGaussianrandomvariableswithnon-zero means.Then,themeanandvarianceof Y 2 i aregivenby[64] Y 2 i = 2 Y i + 2 Y i C 2 Y 2 i =2 4 Y i +4 2 Y i 2 Y i C respectively,where Y i = p N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i i and 2 Y i = N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i 2 .Since V = P i Y 2 i isthe sumofindependentrandomvariables,thenitsmean V canbecalculatedas V = N X i =1 Y 2 i = N X i =1 )]TJ/F25 11.9552 Tf 5.479 -9.684 Td [( 2 Y i + 2 Y i C V = 2 N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i + N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.956 0 Td [(i 2 i C andthevariance 2 V as 134
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2 V = N X i =1 2 Y 2 i = N X i =1 )]TJ/F22 11.9552 Tf 5.48 -9.684 Td [(2 4 Y i +4 2 Y i 2 Y i C 2 V =2 4 N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i 2 +4 2 N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i 2 2 i C Withsomealgebraicmanipulation,itcanbeshownthat N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i = N N +1 = 2C N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i 2 = N N +1 2 N +1 = 6C N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i 2 i = N X i =1 i X j =1 2 j C N X i =1 N +1 )]TJ/F49 11.9552 Tf 11.955 0 Td [(i 2 2 i =2 N X i =1 i X j =1 j X k =1 2 k )]TJ/F49 7.9701 Tf 17.405 14.944 Td [(N X i =1 i X j =1 2 j C and,hence,themeanandvarianceof V canbeexpressedas V = N 0 2 + N X i =1 i X j =1 2 j C 2 V =2 N 00 4 +4 2 4 2 N X i =1 i X j =1 j X k =1 2 k )]TJ/F49 7.9701 Tf 17.406 14.944 Td [(N X i =1 i X j =1 2 j 3 5 2 C respectively,where N 00 = N N +1 2 N +1 = 6and N 0 = N N +1 = 2.Furthermore, letusdene E i = i X j =1 2 j C E 0 i = i X j =1 j X k =1 2 k = i X j =1 E j C 135
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E 00 i = i X j =1 j X k =1 k X l =1 2 l = i X j =1 E 0 j C Then, V and 2 V canbesimpliedto V = N 0 2 + E 0 N C 2 V =2 N 00 4 +4 h 2 E 00 N )]TJ/F49 11.9552 Tf 11.955 0 Td [(E 0 N i 2 C 136
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BIOGRAPHICALSKETCH JoseM.Almodovar-FariareceivedhisB.S.degreeinElectricalEngineeringfrom theUniversityofPuertoRico-Mayaguezin2006,andM.S.degreesinElectricalEngineeringfromtheUniversityofMichigan-AnnArborin2008andfromtheUniversity ofFlorida-Gainesvillein2011.Inthespringof2014,hereceivedhisPh.D.degreein ElectricalandComputerEngineeringfromtheUniversityofFlorida.HisresearchinterestsincludeUWBwirelesscommunicationsandcognitiveradiosandnetworks. 146
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