Citation
A Cognitive PHY-MAC Cooperative Protocol for Low-Power Short-Range Wireless Ad-Hoc Networks Using UWB PPM Radios

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Title:
A Cognitive PHY-MAC Cooperative Protocol for Low-Power Short-Range Wireless Ad-Hoc Networks Using UWB PPM Radios
Creator:
Almodovar-Faria, Jose M
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (146 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Electrical and Computer Engineering
Committee Chair:
MCNAIR,JANISE Y
Committee Co-Chair:
LATCHMAN,HANIPH A
Committee Members:
LI,XIAOLIN
NEWMAN,RICHARD E
Graduation Date:
5/3/2014

Subjects

Subjects / Keywords:
Approximation ( jstor )
Bandwidth ( jstor )
Demodulation ( jstor )
Mathematical constants ( jstor )
Radio ( jstor )
Random variables ( jstor )
Receivers ( jstor )
Signals ( jstor )
Simulations ( jstor )
Supernova remnants ( jstor )
Electrical and Computer Engineering -- Dissertations, Academic -- UF
ad-hoc -- bandwidth -- cognitive -- communications -- cooperative -- cross-layer -- energy-detection -- energy-integration-detection -- integration-time -- mac -- networks -- optimization -- phy -- pulse-position-modulation -- ultra-wideband -- wireless
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Electrical and Computer Engineering thesis, Ph.D.

Notes

Abstract:
Nowadays low-power short-range wireless ad-hoc networks are becoming more popular as the demand for wireless applications such as sensor and personal area networks continue to grow. Recently, in particular since the Federal Communications Commission approval in 2002, ultra-wideband (UWB) communications have been proposed as a viable and efficient alternative to implement short-range wireless applications. For the past decade, numerous investigations and research works have been done in order to employ UWB technology in wireless applications that have been traditionally implemented with conventional narrowband technologies. The vast range of benefits offered by UWB makes it, in many cases, an ideal solution when implementing wireless radios and networks. Low-power operation, low-complexity and low-cost radio architectures, and high data rates are among the many advantages of UWB. In most short-range wireless ad-hoc networks, low-power operation as well as multiple access control (MAC) is crucial in the network design. Pulse-position modulation (PPM) is a well-known digital modulation scheme that when used in UWB radios can achieve simple low-cost architectures and more importantly a very low-power operation while offering relatively good data rates and bit-error rate (BER) performance. The DCF function described by the IEEE 802.11 WLAN standard is used quite often as the MAC protocol when implementing wireless networks in general and has proven to be efficient for many applications. This doctoral dissertation presents a new cognitive and cooperative protocol between the physical (PHY) layer and the MAC sublayer for wireless ad-hoc networks using PPM UWB radios. By a cognitive estimation of the wireless channel and the cooperation between the MAC and PHY layers, the cognitive protocol can dynamically adjust the transmission data rate between two nodes optimizing their communication. Simulations show that the protocol improves the overall network performance in terms of message delivery ratio and average transmission delay. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: MCNAIR,JANISE Y.
Local:
Co-adviser: LATCHMAN,HANIPH A.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2014-11-30
Statement of Responsibility:
by Jose M Almodovar-Faria.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Embargo Date:
11/30/2014
Resource Identifier:
907294911 ( OCLC )
Classification:
LD1780 2014 ( lcc )

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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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