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Iterative Partially Coherent Demodulation and Its Application to Frequency Shift Key(Fsk) Modulated Signals

Permanent Link: http://ufdc.ufl.edu/UFE0044936/00001

Material Information

Title: Iterative Partially Coherent Demodulation and Its Application to Frequency Shift Key(Fsk) Modulated Signals
Physical Description: 1 online resource (94 p.)
Language: english
Creator: Adeladan, Oluwatosin A
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: channel -- cpfsk -- cross -- decoder -- demodulation -- fhss -- fsk -- iterative -- layer -- mac -- multiple -- partially -- phy -- refine -- throughput -- tikhonov -- users -- viterbi
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Demodulation schemes for information transmitted over communication channels are broadly classified into coherent or non-coherent schemes. For non-coherent demodulation, the knowledge of the channel is not available and the transmitted symbols are demodulated in its absence. For coherent demodulation, the channel is estimated and its influence is accounted for in demodulation. In cases where the channel estimate is poor, using this estimate for coherent demodulation can degrade the performance of the system. Partially coherent demodulation was introduced by Viterbi in 1965 as a way of exploiting the statistical information of the phase error with the goal of designing and implementing a better detector. However, not much work has been done in this area since its introduction. In particular, although iterative detection and decoding techniques are widely proposed for use in receivers, techniques to refine phase estimates and use these noisy phase estimates through partially coherent demodulation have not been considered prior to the work described in this dissertation. In this dissertation, we explore the use of partially coherent detection in conjunction with iterative channel estimation and demodulation in different channel scenarios. We show performance gains in terms of improved error rates, reduced error floor, and increased multi-user capability. We present results that show that these improvements translate to the MAC layer. We also present a new cross-layer technique that exploits information in the physical layer to optimize the aggregate system throughput in the MAC layer.
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.
Statement of Responsibility: by Oluwatosin A Adeladan.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Shea, John M.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044936:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044936/00001

Material Information

Title: Iterative Partially Coherent Demodulation and Its Application to Frequency Shift Key(Fsk) Modulated Signals
Physical Description: 1 online resource (94 p.)
Language: english
Creator: Adeladan, Oluwatosin A
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: channel -- cpfsk -- cross -- decoder -- demodulation -- fhss -- fsk -- iterative -- layer -- mac -- multiple -- partially -- phy -- refine -- throughput -- tikhonov -- users -- viterbi
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Demodulation schemes for information transmitted over communication channels are broadly classified into coherent or non-coherent schemes. For non-coherent demodulation, the knowledge of the channel is not available and the transmitted symbols are demodulated in its absence. For coherent demodulation, the channel is estimated and its influence is accounted for in demodulation. In cases where the channel estimate is poor, using this estimate for coherent demodulation can degrade the performance of the system. Partially coherent demodulation was introduced by Viterbi in 1965 as a way of exploiting the statistical information of the phase error with the goal of designing and implementing a better detector. However, not much work has been done in this area since its introduction. In particular, although iterative detection and decoding techniques are widely proposed for use in receivers, techniques to refine phase estimates and use these noisy phase estimates through partially coherent demodulation have not been considered prior to the work described in this dissertation. In this dissertation, we explore the use of partially coherent detection in conjunction with iterative channel estimation and demodulation in different channel scenarios. We show performance gains in terms of improved error rates, reduced error floor, and increased multi-user capability. We present results that show that these improvements translate to the MAC layer. We also present a new cross-layer technique that exploits information in the physical layer to optimize the aggregate system throughput in the MAC layer.
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.
Statement of Responsibility: by Oluwatosin A Adeladan.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Shea, John M.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044936:00001


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ITERATIVEPARTIALLYCOHERENTDEMODULATIONANDITSAPPLICATIONTO FREQUENCYSHIFTKEYFSKMODULATEDSIGNALS By OLUWATOSINA.ADELADAN ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2012

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c 2012OluwatosinA.Adeladan 2

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ToJesusChrist,myparentsandsiblings,andtomyAduke 3

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ACKNOWLEDGMENTS IwillliketothankDr.JohnM.Sheaforhismentorship,patienceandguidance.Iwill alsoliketothankmyparentsandsiblingsfortheirprayersandsupportovertheyears. Finally,iwillliketothankAdukeforherloveandunderstandingduringthisphaseofour lives. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS..................................4 LISTOFTABLES......................................7 LISTOFFIGURES.....................................8 ABSTRACT.........................................10 CHAPTER 1INTRODUCTION...................................11 2INTERFERENCEMITIGATIONWITHPARTIALLYCOHERENTDEMODULATION INASLOWFREQUENCY-HOPPINGSPREAD-SPECTRUMSYSTEM....15 2.1IntroductionofInterferenceMitigationwithPartiallyCoherentDemodulation inaSlowFHSSSystem............................15 2.2SystemModel.................................15 2.3ChannelEstimation..............................18 2.3.1ExpectationMaximizationEMAlgorithm..............18 2.3.2CoherenceParameterEstimation...................20 2.3.3InitialChannelEstimation.......................25 2.3.3.1Theoneinterferercase...................25 2.3.3.2Themultipleinterferercase.................26 2.4SoftDemodulatorandDecoder........................27 2.5PerformanceResults..............................33 2.6Summary....................................40 3MULTIPLE-ACCESSINTERFERENCEMITIGATIONANDITERATIVEDEMODULATION OFCPFSKINASYNCHRONOUSSLOWFHSSSYSTEMS...........43 3.1IntroductionofMultiple-AccessInterferenceMitigationandIterativeDemodulation ofCPFSKinAsynchronousSlowFHSSSystems..............43 3.2SystemModel.................................43 3.3ParameterEstimation.............................49 3.3.1ChannelEstimatorDesiredUser..................49 3.3.2TimingOffsetEstimatorInterferingUser..............50 3.3.3InterferingChannelEstimation....................51 3.4SoftDemodulator................................51 3.5SimulationResults...............................52 3.6Summary....................................56 4ITERATIVECHANNELESTIMATIONANDPARTIALLYCOHERENTDEMODULATION OFCPFSKINTIME-SELECTIVEFADINGCHANNELS.............59 5

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4.1IntroductionofIterativeChannelEstimationandPartiallyCoherentDemodulation ofCPFSKinTime-SelectiveFadingChannels................59 4.2SystemModel.................................59 4.3ChannelEstimation..............................63 4.3.1InitialChannelEstimation.......................63 4.3.2IterativeChannelEstimation......................65 4.4SimulationResults...............................66 4.5Summary....................................69 5LINK-LAYERTHROUGHPUTOFFREQUENCY-HOPPINGSYSTEMSWITH INTERFERENCEMITIGATION...........................72 5.1IntroductionofLink-LayerThroughputofFrequency-HoppingSystems withInterferenceMitigation..........................72 5.2SystemModel.................................72 5.3ThroughputAnalysis..............................74 5.4Cross-LayerProtocol..............................79 5.5ResultsandDiscussion............................80 5.6Summary....................................84 6CONCLUSIONS...................................87 REFERENCES.......................................89 BIOGRAPHICALSKETCH................................94 6

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LISTOFTABLES Table page 2-1SelectedvaluesofSNRandcorresponding ...................25 5-1Selectednumberofusersandcorrespondingblockerrorrates.........73 5-2Comparisonofthemaximumachievablethroughputforbothcases.......76 5-3Throughputcomparisontable............................84 7

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LISTOFFIGURES Figure page 2-1Systemmodel....................................16 2-2Graphofthecoherenceparameter vs.SNR E= 2 .............24 2-3Interferencepatterns................................27 2-4TrellisusedintheBCJRalgorithmforthesoftdemodulator............28 2-5Blockerrorratevs. E b =N 0 fortwouserscontendingontenfrequencybands inaRayleighchannelwithSIR= 0 dB.........................34 2-6Blockerrorratevs.SIRfortwouserscontendingontenfrequencybandsin aRayleighchannelwith E b =N 0 =20 dB.......................35 2-7Performanceoverselectednumberofiterations,SIR= 0 dB............36 2-8Evolutionof acrossiterationsforselecteddwellintervals............37 2-9Blockerrorratevs.numberofusers, E b =N 0 =24 dB,SIR= 0 dB.........38 2-10Maximumnumberofusersthatcanbesupportedforatargeterrorrateof 10 )]TJ/F26 7.9701 Tf 6.586 0 Td [(2 inasysteminwhichuserscontendover 100 frequencybandsatSIR= 0 dB..........................................39 2-11Blockerrorratevs. E b =N 0 fortwouserscontendingontenfrequencybands inaRayleighchannelwithSIR= 0 dB:Channelvarianceestimationcase.....41 2-12Blockerrorratevs.numberofusers, E b =N 0 =24 dB,SIR= 0 dB:channelvariance estimationcase....................................42 3-1Systemmodel.....................................44 3-2Structureofadwellinterval. P and N denotesetsofpilotandnullsymbols, respectively......................................45 3-3Trellisandtransitionsforaselectedstate......................53 3-4Comparisonofschemesfor E b =N 0 =24 dBacrossarangeofPartial-Band Interferencevalues..................................54 3-5Comparisonofschemesfor E b =I 0 t =5 dBacrossarangeof E b =N 0 .......56 3-6Comparisonofschemesfor E b =I 0 t =0 dBacrossarangeof E b =N 0 .......57 3-7Comparisonofschemesfor E b =I 0 t =0 dBand E b =N 0 =24 dB..........58 4-1Systemmodel....................................60 8

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4-2Comparisonofdemodulationschemesfor F s T s =0 : 005 ..............67 4-3Comparisonofdemodulationschemesfor F s T s =0 : 01 ..............68 4-4Comparisonofdemodulationschemesfor F s T s =0 : 02 ..............69 4-5Comparisonofdemodulationschemesfor F s T s =0 : 04 ..............70 4-6Blockerrorratevs. E b =N 0 forvaryingnumberofiterationsand F s T s =0 : 005 ..71 5-1Throughputasafunctionofthetransmissionprobabilityforanetworkconsisting of50users.......................................75 5-2Throughputasafunctionofthetransmissionprobabilityforanetworkconsisting of100users......................................75 5-3Throughputasafunctionofthetransmissionprobabilityforanetworkconsisting of150users......................................76 5-4Throughputasafunctionofthetransmissionprobabilityforanetworkconsisting of200users......................................77 5-5Throughputasafunctionofthetransmissionprobabilityforanetworkconsisting of250users......................................77 5-6Optimaltransmissionprobabilityasafunctionofthenumberofusersinthe system.........................................78 5-7Throughputevolutionovertime, N =50 users...................81 5-8Evolutionofaveragetransmissionprobabilityovertime, N =50 users......81 5-9Throughputevolutionovertime, N =100 users..................82 5-10Evolutionofaveragetransmissionprobabilityovertime, N =100 users.....82 5-11Throughputevolutionovertime, N =150 users..................83 5-12Evolutionofaveragetransmissionprobabilityovertime, N =150 users.....83 5-13Throughputevolutionovertime, N =200 users..................84 5-14Evolutionofaveragetransmissionprobabilityovertime, N =200 users.....85 5-15Throughputevolutionovertime, N =250 users..................85 5-16Evolutionofaveragetransmissionprobabilityovertime, N =250 users.....86 9

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AbstractofdissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy ITERATIVEPARTIALLYCOHERENTDEMODULATIONANDITSAPPLICATIONTO FREQUENCYSHIFTKEYFSKMODULATEDSIGNALS By OluwatosinA.Adeladan December2012 Chair:JohnM.Shea Major:ElectricalandComputerEngineering Demodulationschemesforinformationtransmittedovercommunicationchannels arebroadlyclassiedintocoherentornon-coherentschemes.Fornon-coherent demodulation,theknowledgeofthechannelisnotavailableandthetransmitted symbolsaredemodulatedinitsabsence.Forcoherentdemodulation,thechannel isestimatedanditsinuenceisaccountedforindemodulation.Incaseswherethe channelestimateispoor,usingthisestimateforcoherentdemodulationcandegrade theperformanceofthesystem.Partiallycoherentdemodulationwasintroducedby Viterbiin1965asawayofexploitingthestatisticalinformationofthephaseerrorwith thegoalofdesigningandimplementingabetterdetector.However,notmuchworkhas beendoneinthisareasinceitsintroduction.Inparticular,althoughiterativedetection anddecodingtechniquesarewidelyproposedforuseinreceivers,techniquestorene phaseestimatesandusethesenoisyphaseestimatesthroughpartiallycoherent demodulationhavenotbeenconsideredpriortotheworkdescribedinthisdissertation. Inthisdissertation,weexploretheuseofpartiallycoherentdetectioninconjunctionwith iterativechannelestimationanddemodulationindifferentchannelscenarios.Weshow performancegainsintermsofimprovederrorrates,reducederroroor,andincreased multi-usercapability.Wepresentresultsthatshowthattheseimprovementstranslateto theMAClayer.Wealsopresentanewcross-layertechniquethatexploitsinformationin thephysicallayertooptimizetheaggregatesystemthroughputintheMAClayer. 10

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CHAPTER1 INTRODUCTION Therapidlyincreasingdeploymentofwirelesstechnologiesforbothmilitary andnon-militaryapplicationsnecessitatetheabilitytocommunicateinincreasingly challengingenvironments.Thegoaloflivinginafullyconnectedworldhasincreased thedemandfornitechannelresources.Ithasalsomeantthatdeviceshavetobeable tocommunicateinhighlydynamicchannelscausedbyfading. FrequencyhoppingspreadspectrumFHSSisonetechnologyusedtoprovide robustnessagainstmultipleaccessinterferenceMAIandjamming.InslowFHSS systems,thepackettobetransmittedisdividedintodifferentsegmentsandeach segmentistransmittedinadifferentfrequencychannelaccordingtoapseudo-random hoppingpattern.TheaimofthisapproachistoproviderobustnesstoMAIbyenabling signalstohopoutoffrequencychannelsthatareimpairedbyinterferenceorslow frequency-selectivefading.However,whenthehoppingpatternsofdifferenttransmitters arenotorthogonal,packetsfromdifferenttransmitterscollideatthereceiverwhenthey occupythesamefrequencybandatthesametime.Thiseventisknownasahit[1,2]. anditseverelylimitsthemulti-usercapabilityofthesystem. MostpreviousworkonMAImitigationinFHSSsystemsfocusesonfastFHSS communicationinwhicheachsymbolissentovermultiplefrequencies[38].In[911], jointdetectionofsymbolshavebeenconsideredfortheslowFHSScase.Inallof thepreviouswork,ithasbeenassumedthatthehoppingpatternsandtimingofthe otherusersareknownatthereceiver.Ithasalsobeenassumedthatthereceivercan simultaneouslydemodulatethesignalsatallthecarrierfrequencies,thusrequiringa verywidebandreceiver.Theseassumptionsproducescomplexitythatprohibitstheiruse inad-hocnetworkssuchasinthemilitarySINCGARS[12]andHaveQuicksystems. Mostoftheworkthathavebeendoneonimprovingtheperformanceoffrequency 11

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hoppingsystemsinadhocnetworkshasfocusedoninterferencemitigationbyerasing symbolsthathavebeeninvolvedinahit[1315]. In[16],Viterbicharacterizedtheprobabilitydensityfunctionpdfofthephase errorarisingfromaphase-lockedloopPLL.Theresultingpdf,knownhastheTikhonov density,hasbeenrecentlyappliedinthecontextofpartiallycoherentdemodulation toproblemssuchasderivingtherightstrategiesfordecisionfusioninlargesensor networks[17],multipathdiversitycombiningrulesforRAKEreceiversindirectsequence spreadspectrumDSSS[18]andphaseshiftkeymodulatedsystemsaffectedby intersymbolinterferenceISI[19].In[20],partiallycoherentreceiverarchitectures werederivedforquadratureamplitudemodulatedQAMsystemsthatshowincreased performanceinbiterrorratesoverarangeofsignal-to-noiseratioswhencomparedto coherentdemodulation. In[21,22],anexpectationmaximizationEMbasedalgorithmisusedforchannel estimationandsignaldetectioninthepresenceofMAIforasystememployingBinary FrequencyShiftKeyingBFSK.Thisiterativealgorithmusesnoncoherentdemodulation andtakesadvantageofthewaythatthesymbolsoftheinterferinganddesireduserare partiallyexposedwhenfrequencyshiftkeyingisusedandthesymbolsfromdifferent usersarriveasynchronouslyatthereceiver.InChapter2ofthisDissertation,webuild uponthismodelbymakingproperuseofthesoftoutputsofthedecoderaftereach iterationtoimprovethechannelestimatesofthedesireduser.Wealsointroducethe coherenceparameterandshowitsderivationandapplicationtopartiallycoherent demodulation.Wedevelopaninterferencemitigationschemeforthecaseofatmost onestronginterfererineachdwellintervalandweassumethatthecomplexchannel gainoftheinterferingusercanbeeasilyestimated.Weshowthatbyusingpartially coherentdemodulation[2325]withinaniterativereceiverprocessinwhichthephase estimateofthedesireduserisrened,signicantperformancegainsareachievedin termsofblockerrorratesandthemulti-usercapabilityofthesystem. 12

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ContinuousphasefrequencyshiftkeyingCPFSKisattractiveasamodulation techniquebecauseitallowsforamoreefcientuseofthebandwidthresourceofthe systemthantraditionalFSK[23,26].However,CPFSKisnotveryrobusttochannel interferencebecauseoftheinherentmemoryinthesystem.Inpreviousworkon FHSSsystemsthatuseCPFSKmodulation,themultiple-accessinterferenceMAI isdisregardedessentiallytreatingitasnoise,whichisshowntoworkwellwhenthe signal-to-interferenceratioishigh[27,28].InChapter3,weconsidertheproblemof interferencemitigationinanFHSSsystemswithnon-orthogonalspreadingsequences employingBinaryContinuousPhaseFrequencyShiftKeyingBCPFSK.Wedevelopan iterativeinterferencemitigationschemeforaslowFHSSsystememployingBCPFSK andusethecoherenceparameterinchannelestimation.Thisschemeaddressesthe difcultyposedbythenon-memorylessnatureofthemodulationwhenitcomesto estimatingthechannelparametersoftheinterferinguser.Inparticular,becauseofthe continuousphaserequirementofCPFSK,thisschemeisdevelopedwiththeassumption thatonlytheamplitudeofthechannelofthedesiredusercanbeestimated. ToenablecoherentdemodulationofCPFSKinafrequencynon-selectivetime varyingchannel,pilotsymbolsareperiodicallyinsertedintothesymbolsequence inordertotrackthechannel.ThepilotinsertionratesarespeciedbytheNyquist Samplingtheoremanddependsonthefadingrateofthechannel[29].InChapter4, weexploretheuseofsparserpilotsymbolspacingandpilotinsertionratesthatare signicantlylowerthantheratesspeciedbyNyquistandperformiterativechannel estimationanddemodulationbasedonqualityofthechannelestimates.Weshow thattheadaptivenatureofthepartiallycoherentdemodulationschemeallowsfor performancethatisbetterthaneithercoherentornoncoherentdemodulationformost fadingscenarios. InChapter5,westudytheperformanceimprovementthatisgainedonthelink layerbyusinginterferencemitigationatthephysicallayer.Wealsopresentanewcross 13

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layerapproachthatuseslocalestimatesateachnodetodynamicallyadapteachnode's transmissionprobabilitytoenabletheentiresystemtooperateatclosetoitsmaximum achievablethroughput. Finally,wepresentconclusionsinChapter6. 14

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CHAPTER2 INTERFERENCEMITIGATIONWITHPARTIALLYCOHERENTDEMODULATIONINA SLOWFREQUENCY-HOPPINGSPREAD-SPECTRUMSYSTEM 2.1IntroductionofInterferenceMitigationwithPartiallyCoherentDemodulation inaSlowFHSSSystem In[21,22],anexpectationmaximizationEMbasedalgorithmforchannel estimationandsignaldetectioninthepresenceofMAIwaspresentedforasystem employingBinaryFrequencyShiftKeyingBFSK.Thealgorithmiteratesamongthree stages:parameterestimation,interferenceanddesiredmodulationsymbolestimation softdemodulation,anderrorcorrectionanddecodingstages.Inthischapter,werevise theparameterestimationstagetomakebetteruseoftheoutputofthesoftdecoder inestimatingtheparametersofthedesireduser.Wealsointroduceacoherence parameterthatwillbeusedforpartiallycoherentdemodulationinthesoftdemodulation stage.Weshowhowtheperformanceofthesystemcanbesignicantlyimprovedby usingpartiallycoherentdemodulation[23,30].Becausetheperformanceofthesystem alsodependsheavilyontheimpactofthedwellintervalshitbyMAI,weinvestigatethe effectofmodelingtheinterferenceasGaussianandestimatingitsvarianceacrossthe dwellinterval.Weshowthatthechannelvarianceestimateisalsoimpactedbyanyerror inthephaseestimate,andupdatingthelikelihoodsbasedontheestimatedchannel variancecanthusreducethegainsfrompartiallycoherentdemodulation. Therestofthischapterisorganizedasfollows.InSection2.2,wepresentthe systemandinterferencemodels.InSection2.3,wepresentthechannelestimation strategyusingtheEMalgorithm.Weexplainhowdemodulationisperformedin Section2.4.PerformanceresultsarepresentedanddiscussedinSection2.5and thechapterisconcludedinSection2.6. 2.2SystemModel ThesystemmodeltobeconsideredisillustratedinFig.2-1.Weconsidera multiusersystemwitheachuseremployingBFSK.Ateachuser,theinformationis 15

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encoded,interleavedandpackedintoaframeoflength L codedbits.Theframeisthen dividedinto D dwellintervalsoflength L=D andpassedthroughthemodulator.Each symbolisthenmodulatedwithfrequencies f 0 and f 1 ifthecorrespondingbitis 0 and 1 respectively.Thesymbolsineachdwellintervalarethenmodulatedontoacarrier accordingtoapseudo-randomfrequency-hoppingscheme.Multipleaccessinterference Figure2-1.Systemmodel occursbecausethehoppingpatternsoftheusersarenotorthogonal.Wedesignan interferencemitigationschemebasedonthemostlikelyscenario,inwhichthereisone stronginterfererinourdwellintervalofinterest.Weconsiderafrequency-selective Rayleighfadingchannel,whichwemodelasablockfadingchannelwithamplitudes andphasesthatareconstantovereachdwellintervalbutareindependentacrossdwell intervals. Atthereceiver,thesignalisdehoppedandpassedthroughabankofmatched lters.Theoutputofthematchedlterischaracterizedby y 0 k = a 1 )]TJ/F53 11.9552 Tf 11.955 0 Td [(x k e j 1 + a 2 g k e j 2 + n 0 ; 16

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and y 1 k = a 1 x k e j 1 + a 2 h k e j 2 + n 1 ; where A 1 = a 1 e j 1 and A 2 = a 2 e j 2 arethecomplex-valuedprocesseschannelgains. Also, isthesymbol-timeoffsetbetweentheinterferingsymbolanddesiredsymbol, and g k and h k arethecontributionsoftheinterferencesignaltothedesiredsignal atsymbol k ,whicharedenedas g k = T I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 + 1 )]TJ/F53 11.9552 Tf 14.184 8.088 Td [( T I k ; and h k = T I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1+ 1 )]TJ/F53 11.9552 Tf 14.185 8.088 Td [( T I k )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 : Here I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 and I k arevaluesforconsecutiveinterferencesymbolsand I k = )]TJ/F15 11.9552 Tf 9.299 0 Td [(1 ifno interferenceispresent. Ifwedene y = y 0 1 ;y 1 1 ;y 0 2 ;y 1 2 ;:::;y 0 N ;y 1 N ; = a 1 ;a 2 ; 1 ; 2 ; ; x = x 0 1 ;x 1 1 ;x 0 2 ;x 1 2 ;:::;x 0 N ;x 1 N ; and I = I 1 ;I 2 ;I 3 ;:::;I N ; then,theprobabilitylikelihoodfunctionof y given x and I isgivenby p y 0 k ;y 1 k j x ; I ; = 1 4 2 4 exp )]TJ/F15 11.9552 Tf 19.936 8.088 Td [(1 2 2 y 0 k )]TJ/F53 11.9552 Tf 11.956 0 Td [(a 1 )]TJ/F53 11.9552 Tf 11.955 0 Td [(x k e j 1 )]TJ/F53 11.9552 Tf 11.956 0 Td [(a 2 g k e j 2 2 exp )]TJ/F15 11.9552 Tf 19.936 8.088 Td [(1 2 2 y 1 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(a 1 x k e j 1 + a 2 h k e j 2 2 : 17

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2.3ChannelEstimation 2.3.1ExpectationMaximizationEMAlgorithm Thechannelparameters, ,areestimatediterativelyusingtheEMalgorithm.We treatthesymbolsofthedesireduserandtheinterferinguserastheunobservedlatent data.Thealgorithmupdatestheestimatefromtheequation, n = argmax Q ; n )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 ; where Q ; n )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 isBaum'sauxiliaryfunction,givenby Q ; 0 = E [ log p y ; x ; I j j y ; 0 ]= E [ log p y j j y ; 0 ]+ E [ log p x j j y ; 0 ]+ E [ log p I j j y ; 0 ] Since I and x areassumedtobeindependentofourchannelparameters,2 canbewrittenas Q ; 0 = C )]TJ/F15 11.9552 Tf 15.535 8.088 Td [(1 N N X k =1 X x k ;I k )]TJ/F21 5.9776 Tf 5.756 0 Td [(1 ;I k 1 2 2 y 0 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(a 1 )]TJ/F53 11.9552 Tf 11.955 0 Td [(x k e j 1 )]TJ/F53 11.9552 Tf 11.955 0 Td [(a 2 g k e j 2 2 + y 1 k )]TJ/F53 11.9552 Tf 11.956 0 Td [(a 1 x k e j 1 + a 2 h k e j 2 2 p x k j y k ; 0 p I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 ;I k j y k ; 0 i ; where C isthecombinationofallparametersthatareindependentof ;assuch,only thesecondtermisusefulformaximization.Also.let Q k ; 0 = X x k ;I k )]TJ/F21 5.9776 Tf 5.756 0 Td [(1 ;I k 1 2 2 y 0 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(a 1 )]TJ/F53 11.9552 Tf 11.955 0 Td [(x k e j 1 )]TJ/F53 11.9552 Tf 11.955 0 Td [(a 2 g k e j 2 2 + y 1 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(a 1 x k e j 1 + a 2 h k e j 2 2 p x k j y k ; 0 p I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 ;I k j y k ; 0 i and Q ; 0 = N X k =1 Q k ; 0 : 18

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Tondthechannelparametersthatmaximize2,wedenethegradientoperator r x = x u + j x v for x = u + jv .Thelocallyoptimalvalueof k canbefoundbysolvingthe followingsetofequations r A 1 Q k ; 0 =0 ; and r A 2 Q k ; 0 =0 : Solving2and2producesthefollowingsetoflinearequations 1 ^ A 1 k + 2 ^ A 2 k = 1 ; and 3 ^ A 1 k + 4 ^ A 2 k = 2 : where 1 =1 ; 2 = X x k X I k )]TJ/F21 5.9776 Tf 5.756 0 Td [(1 X I k f [ )]TJ/F53 11.9552 Tf 11.955 0 Td [(x k g k + x k h k ] p x k j y ; 0 p I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 ;I k j y ; 0 g ; 3 = 2 ; 4 = X I k )]TJ/F21 5.9776 Tf 5.756 0 Td [(1 X I k g k 2 + h k 2 p I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 ;I k j y ; 0 ; 1 = X x k )]TJ/F53 11.9552 Tf 11.955 0 Td [(x k y 0 k + x k y 1 k p x k j y ; 0 ; and 2 = X I k )]TJ/F21 5.9776 Tf 5.756 0 Td [(1 X I k g k y 0 k + h k y 1 k p I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 ;I k j y ; 0 : Wecanrewrite2and2inmatrixformas ^ A k = : From2,alltheelementsof aregreaterthanorequaltozero.Itthenfollows thatthedeterminantof denoted j j! 0 as 2 ; 4 0 .Thisisthespecialcasefor whichithasbeendeterminedthattherearenointerferencecomponentsinthesame branchasthedesireduserforthatparticularsymbol.Here, ^ A 1 k = 1 19

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Theestimateof A 1 overaparticulardwellintervalisgivenby ^ A 1 = N X k =1 ^ A 1 k : Wealsogenerateestimatesofthevariance, c ,of ^ A 1 .Theestimateoftheoffset betweenthedesiredandinterferinguserisgivenby r Q ; 0 =0 ; whosesolutionisoftheform 1 T = 2 )]TJ/F53 11.9552 Tf 11.955 0 Td [( 3 ; and 1 = X k X I k )]TJ/F21 5.9776 Tf 5.757 0 Td [(1 X I k j A 2 j 2 I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 )]TJ/F53 11.9552 Tf 11.955 0 Td [( I k 2 + I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 )]TJ/F53 11.9552 Tf 11.956 0 Td [( I k )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 p I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 ;I k j y ; 0 ; 2 = X k X I k )]TJ/F21 5.9776 Tf 5.756 0 Td [(1 X I k X x k Re A 2 I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 )]TJ/F53 11.9552 Tf 11.955 0 Td [( I k y 0 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 1 )]TJ/F53 11.9552 Tf 11.955 0 Td [(x k + Re A 2 I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 )]TJ/F53 11.9552 Tf 11.955 0 Td [( I k )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 y 1 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 1 x k p x k j y ; 0 p I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 ;I k j y ; 0 ; 3 = X k X I k )]TJ/F21 5.9776 Tf 5.757 0 Td [(1 X I k j A 2 j 2 [ I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 )]TJ/F53 11.9552 Tf 11.955 0 Td [( I k I k + I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 )]TJ/F53 11.9552 Tf 11.955 0 Td [( I k )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 I k )]TJ/F15 11.9552 Tf 11.955 0 Td [(1] p I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 ;I k j y ; 0 : 2.3.2CoherenceParameterEstimation Givenestimatesofthevariance, c ,of ^ A ,wemapbetweentheSNR j A 1 j 2 = 2 c and coherenceparameter, ,usingthefollowingapproach.Considerareceivedsignal whoselowpassIandQcomponents, y I and y Q ,havebeencorruptedbyuncorrelated Gaussiannoisewithvariance n ,itfollowsthatwecanwritethejointpdfofboth componentsas p y I ;y Q = 1 2 2 exp )]TJ/F15 11.9552 Tf 10.494 8.087 Td [( y I )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 1 I p E 2 + y Q )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 1 Q p E 2 2 2 ; 20

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where A 1 I p E and A 1 Q p E arethein-phaseandquadraturechanneleffectsnormalized bythesymbolenergy.Ifwedene Y = q y 2 I + y 2 Q and =arctan y Q y I : Itfollowsthataftersomesubstitutionthatthejointpdfofthemagnitude, Y ,andphase, ,isgivenby p Y; = Y 2 2 n exp )]TJ/F53 11.9552 Tf 10.494 8.088 Td [(Y 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(2 Y j A 1 j cos A )]TJ/F53 11.9552 Tf 11.955 0 Td [( p E + j A 1 j 2 E 2 2 n ; wherethe = A )]TJ/F53 11.9552 Tf 11.955 0 Td [( isthephaseerror. Foreaseofexposition,letusdene = j A 1 j 2 E ,itthenfollowsthatwecanwritethe marginalpdfofthephaseas Z 1 0 p Y; dY = 1 2 2 exp )]TJ/F53 11.9552 Tf 15.806 8.088 Td [( 2 2 Z 1 0 Y exp 2 Y cos )]TJ/F53 11.9552 Tf 11.955 0 Td [(Y 2 2 2 dY: Aftersomemanipulations,wecanexpress2as p = 1 2 2 exp )]TJ/F53 11.9552 Tf 15.806 8.088 Td [( 2 2 exp 2 cos 2 2 2 Z 1 0 cos exp )]TJ/F15 11.9552 Tf 10.494 8.088 Td [( Y )]TJ/F53 11.9552 Tf 11.955 0 Td [( cos 2 2 2 dY + Z 1 0 Y )]TJ/F53 11.9552 Tf 11.955 0 Td [( cos exp )]TJ/F15 11.9552 Tf 10.494 8.088 Td [( Y )]TJ/F53 11.9552 Tf 11.955 0 Td [( cos 2 2 2 dY : Ifwedene u = Y )]TJ/F27 7.9701 Tf 6.586 0 Td [( cos 2 2 2 andapplythischangeofvariabletothesecondintegral term,weget p = 1 2 2 exp )]TJ/F53 11.9552 Tf 13.441 8.088 Td [( 2 2 2 exp 2 cos 2 2 2 Z 1 0 cos exp )]TJ/F15 11.9552 Tf 10.494 8.088 Td [( Y )]TJ/F53 11.9552 Tf 11.955 0 Td [( cos 2 2 2 dY + Z 1 2 cos 2 = 2 exp )]TJ/F53 11.9552 Tf 9.298 0 Td [(u du : 21

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Thisexpressionreducesto p =exp )]TJ/F53 11.9552 Tf 13.44 8.088 Td [( 2 2 2 exp 2 cos 2 2 2 cos p 2 2 Z 1 0 1 p 2 2 exp )]TJ/F15 11.9552 Tf 10.494 8.088 Td [( Y )]TJ/F53 11.9552 Tf 11.955 0 Td [( cos 2 2 2 dY + 1 2 2 exp )]TJ/F53 11.9552 Tf 10.494 8.088 Td [( 2 cos 2 2 2 : ExpandingandwritingintermsoftheQ-function,weget p = cos p 2 2 exp )]TJ/F53 11.9552 Tf 13.44 8.088 Td [( 2 2 2 exp 2 cos 2 2 2 1 )]TJ/F53 11.9552 Tf 11.956 0 Td [(Q cos + 1 2 2 exp )]TJ/F53 11.9552 Tf 13.441 8.088 Td [( 2 2 2 : Usingthefactthat Q x exp )]TJ/F53 11.9552 Tf 9.298 0 Td [(x 2 = 2 forlargevaluesof x ,wecanre-write2 as p cos p 2 2 exp )]TJ/F53 11.9552 Tf 13.441 8.088 Td [( 2 2 2 exp 2 cos 2 2 2 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [(exp )]TJ/F53 11.9552 Tf 10.494 8.088 Td [( 2 cos 2 2 2 + 1 2 2 exp )]TJ/F53 11.9552 Tf 13.44 8.088 Td [( 2 2 2 : ThesecondtermgoestozeroforhighSNRs,sothatwehave p cos p 2 2 exp )]TJ/F53 11.9552 Tf 13.44 8.087 Td [( 2 2 2 exp 2 cos 2 2 2 : Thiscanbere-writtenas p cos p 2 2 exp 2 2 2 )]TJ/F15 11.9552 Tf 5.479 -9.683 Td [(cos 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 Forlarge 2 = 2 ,thedensityisconcentratedaroundzeroforwhich cos =1 ,so,we canre-writetheexpressionas p p 2 2 exp )]TJ/F53 11.9552 Tf 13.44 8.088 Td [( 2 2 2 sin 2 : ThisistheTikhonovdensitypresentedin2[16,23]athighSNRs.Let denote therandomchannelphase,theprobabilitydensityfunctionfor is p j ^ = exp cos 2 I 0 ; j j 22

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where I 0 isthemodiedBesselfunctionoftherstorder. Forlargevaluesof ,theBesselfunctioninthedenominatorcanbeapproximated as I 0 exp p 2 ; and2canbemodiedtoproduce p = exp cos 2 I 0 p exp cos )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 p 2 = p exp )]TJ/F54 11.9552 Tf 5.48 -9.683 Td [()]TJ/F15 11.9552 Tf 9.298 0 Td [(2 sin 2 = 2 p 2 Thepdfisconcentratedaround =0 forlargevaluesof .Inthiscase, sin 2 = 2 sin 2 = 4 .Theresultingexpressionisgivenby p = p exp )]TJ/F54 11.9552 Tf 5.479 -9.684 Td [()]TJ/F26 7.9701 Tf 10.494 4.707 Td [(1 2 sin 2 p 2 : ComparingEquation2andEquation2,itisquitestraightforwardtoseethe equivalence.Also, = 2 = 2 forhighsignaltonoiseratios. Wecanalsoseefrom2thatwhen iszero,theresultingprobabilitydensity functionpdfdegeneratestoauniformdistribution,whichcorrespondstononcoherent detection.Ontheotherhand,theexpressionbecomesadeltafunctionas !1 ,which correspondstocoherentdetection. Let = 1 ; 2 ;:::; N anddene k = k )]TJ/F15 11.9552 Tf 14.568 3.155 Td [(^ ; 1 k N .Itthenfollowsthatthe jointpdfof given andthe k 'sisgivenby p j ^ ; = N Y k =1 exp cos k 2 I 0 ; j k j : 23

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TheMaximum-LikelihoodMLestimateof satises d d N Y k =1 exp cos k 2 I 0 =0 : [2 I 0 ] N N X k =1 cos k exp N X k =1 cos k # )]TJ/F15 11.9552 Tf 11.956 0 Td [(exp N X k =1 cos k # N N I 0 N )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 I 1 =0 : Aftersomesimplication,wegetthattheMLestimateof satises 1 N N X k =1 cos k = I 1 I 0 : WeutilizeanempiricalapproachtomapbetweentheparametersoftheGaussian channelandthecoherenceparameter intheTikhonovdistributionusing2.We generate N =10 8 channelrealizationsforeachvalueofSNRwithknownsymbols inordertoinvestigatetherelationshipbetweentheSNRofthechannelandthe coherenceparameter.Thesevalueswerecompiledandstoredinatable.Fig.2-2 showsthisrelationshipforalimitedrangeofSNRvalues.Table2-1givesusvaluesof thecoherenceparameteratselectedpoints. Figure2-2.Graphofthecoherenceparameter vs.SNR E= 2 24

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Table2-1.SelectedvaluesofSNRandcorresponding SNR E= 2 Coherenceparameter 200199.5512 10099.5072 2019.4182 109.2941 54.4061 11.3514 2.3.3InitialChannelEstimation 2.3.3.1Theoneinterferercase Duetotheabsenceoftherequiredprobabilitiesatthebeginningoftheiteration process,wegeneratelocalestimatesof A 1 foreachsymbolinthedwellinterval accordingto ^ A 1 k = y 0 k + y 1 k : Withtheselocalestimates,weattempttoreducetheeffectoftheinterfererbyobserving themedianofthelocalestimateswithinadwellintervalandsettingourestimateof A 1 to thismedian.Additionally,wealsoestimatethevarianceofthechannel,withthepurpose ofquantifyingthequalityofourestimateandthechannel,usingthemedianasthede factomean. Theadditionof K nullsymbolsatthebeginningandendofthedwellintervalassists intheestimationoftheinterferinguserparameters. K nullsymbolsarealsoinsertedin puncturedpositionswithintheframe.Thedecisionstatisticofanullsymbolcontaining interferencecanbewrittenas z 0 k = A 2 g k + n 0 ; and z 1 k = A 2 h k + n 1 ; 1 k K: 25

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Themaximumlikelihoodestimateof A 2 isderivedforasetof K nullbitsbymaximizing J A 2 = log P z 0 1 ;z 1 1 ;z 0 2 ;z 1 2 ;z 0 3 ;z 1 3 ;:::;z 0 K ;z 1 K j I; = C 1 )]TJ/F15 11.9552 Tf 17.277 8.087 Td [(1 N 0 K X k =1 z 0 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 g k 2 + z 1 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 h k 2 ; whosesolutionis ^ A 2 = P K k =1 z 0 k g k + z 1 k h k P K k =1 g 2 k + h 2 k : Sincewehavenopriorinformationaboutthecontributionsoftheinterfererintherst iteration,weset h k = g k = 1 2 ,sothatourestimatebecomes ^ A 2 = 1 K K X k =1 )]TJ/F53 11.9552 Tf 5.479 -9.684 Td [(z 0 k + z 1 k : Weuse2togeneratethreeestimatesof A 2 usingtheleft,rightandthe randomnullbits.Wechoosetheestimatethathasthemaximumamplitudeandusethis astheestimateofthechannelparameterofourinterferer. 2.3.3.2Themultipleinterferercase SinceitiswidelyunderstoodthattheEMalgorithmisverysensitivetoinitial conditions,obtainingthebestpossibleinitialchannelestimateisofutmostimportance. Iftherearemorethanoneinterfererinadwellinterval,thentheestimatesofthe parametersoftheinterferenceshouldvaryoverthedwellinterval.Consideracase wherewehave 100 userscontendingover 100 frequencybands.Theprobabilitythata particulardwellintervalwillbehitbymorethanoneinterfereris 0 : 2605 ,whichimplies thatmorethanaquarterofdwellintervalswillbehitbymorethanoneinterferer. Forthesedwellintervals,ourassumptionofaconstantinterferencegaininadwell intervaldoesnothold.Todealwiththisscenario,wederivethechannelestimateby followingthesesteps 1.Wederivetwoestimatesoftheinterferersusingtheleftandrightnullbits. 26

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2.Usingboththeleftandtherightnullbits,wegeneratetwoestimatesofthe desiredusergainusingtherst K symbolsaftertheleftnullbitsandthelast K symbols beforetherightnullbits.Wealsogeneratevarianceestimatesforbothcases. 3.Wechoosetheestimateofthedesireduser'schannelgainwiththeleast varianceandsubtractitfromthereceivedsymbolstogiveestimatesoftheinterference ateachsymbolposition. 4.Becausetheseestimatesarepronetobenoisy,wepassthestreamof estimatesthroughamovingaverageltertoestimatethechannelparameterofthe interferinguserateachsymbolposition. 2.4SoftDemodulatorandDecoder Inthissection,wepresentatrellisbasedalgorithmthatisusedtocalculatethe probabilitiesofthedesiredandinterferingsymbolsthatareusedbythechannel estimationpresentedinthelastsectionaswellastheerror-correctiondecoder.The softdemodulatorutilizesextrinsicinformationfedbackfromthedecoderthesymbol probabilitiesaswellasintrinsicinformationthatitgeneratesfromthetrellis.Thetrellis Figure2-3.Interferencepatterns 27

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isdesignedtobeabletohandleatleastonestronginterfererineachdwellinterval. Whenadwellintervalishitbyinterferencefromasingleuser,theresultinginterference canbeclassiedasttingoneofthreepatterns.Thedwellintervalcouldbebehitfrom theleft,theright,orbothsidesFig.2-3.Also,becauseoftheasynchronousnature ofthetransmission,adesiredsymbolthathasbeenhitmaycontaininterferencefrom twoconsecutivesymbolsfromtheinterferingsignal.Werefertotheearlierandlater symbolsastheleft-andright-interferingsymbols,respectively. Figure2-4.TrellisusedintheBCJRalgorithmforthesoftdemodulator. 28

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Fig.2-4givesapictorialrepresentationofthetrellisused.Thetrellisstartsinstates S 0 S 1 ,or S X .Whenthedesiredframeishitfromtheleft,thetrellisstartsinstates S 0 or S 1 withthesubscriptsrepresentingthevalueoftheleft-interferingsymbol.Thetrellis startsfrom S X ifthedwellintervalhasnotbeenhitfromtheleft.Onceinstates S 0 or S 1 ,thetrelliscantransitiontoeitherstate S 0 or S 1 ,dependingonthevalueofthenext interferencesymbol,ortostate M 1 whentheinterferencefromtheleftterminates.There are 2 K states M 1 ;M 2 ;:::;M 2 K usedtoenforcethepresenceof 2 K nullsymbolsbetween dwellintervals. State M 2 K transitionstostates E 0 or E 1 ifthedwellintervalishitfromtherightor state E X ifthereisnointerferencefromtheright.Ifthereisnohitfromtheleft,state S X alsotransitionsto E 0 or E 1 ifthereisahitfromtheright.Intotal,thetrelliscontains 2 K +6 states. Thebranchinputtothetrellisistheinterferencesymbolwhichtakesitsvaluefrom theset f 0 ; 1 ;X g whichrepresentinterferencevalue 0 ,interferencevalue 1 ,andno interference.Theinputtransitionsthetrellisintooneofthestateswhosesubscriptisthe inputvalue.Forexample,aninputvalueof 0 transitionsthetrellisintostates S 0 or E 0 ;an inputof 1 tostates S 1 or E 1 ;andaninputof X toeither S X E X oroneoftheother 2 K states. Weusethetrellistocalculatetheprobabilitiesofthedesiredandinterfering symbolsusingtheBCJRalgorithm.Thebranchmetricconnectingstate s 0 attime k )]TJ/F15 11.9552 Tf 12.198 0 Td [(1 to s attime k isgivenby k s 0 ;s = p y 0 k ;y 1 k ;s k = s j s k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 = s 0 = p y 0 k ;y 1 k j s k = s;s k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 = s 0 p s k = s j s k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 = s 0 = X x k p y 0 k ;y 1 k j I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 s k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 ;I k s k ;x k p x k p s k = s j s k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 = s 0 : Here, I l s l =0 if s l 2f E 0 ;S 0 g I l s l =1 if s l 2f E 1 ;S 1 g and I l s l = )]TJ/F15 11.9552 Tf 9.298 0 Td [(1 if s l isinanyof theother 2 K +2 states.Fortherstroundofdemodulationanddecoding p x k =0 : 5 29

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Oncethedecodingisperformed,thisextrinsicinformationisfedbackfromtheMAP decoderoftheerrorcorrectingcode. Theprobabilitymeasure, p y 0 k ;y 1 k j I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 s k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 ;I k s k ;x k ,isderivedbyintegrating 2over 1 .Fornoncoherentdemodulation,inwhichweassumethatwehaveno knowledgeofthechannelphaseofthedesireduser,wehave p )]TJ/F53 11.9552 Tf 5.48 -9.683 Td [(y 0 k ;y 1 k j I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 s k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 ;I k s k ;x k = l = exp )]TJ/F15 11.9552 Tf 16.402 8.088 Td [(1 2 2 )]TJ/F54 11.9552 Tf 5.48 -9.684 Td [(j y 0 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 g k j 2 + j y 1 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 h k j 2 + j A 1 j 2 I 0 j A 1 j 2 j y l )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 H k ;l j ; where I 0 isthemodiedBesselfunctionoftherstkind. Forcoherentdemodulation,inwhichweassumethatwehavefullknowledgeofthe channelphaseofthedesireduser,theprobabilitymeasureisgivenby p )]TJ/F53 11.9552 Tf 5.48 -9.684 Td [(y 0 k ;y 1 k j I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 s k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 ;I k s k ;x k = l = exp )]TJ/F15 11.9552 Tf 16.402 8.088 Td [(1 2 2 )]TJ/F54 11.9552 Tf 5.48 -9.683 Td [(j y 0 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 g k j 2 + j y 1 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 h k j 2 + j A 2 j 2 exp Re f A 1 [ y l )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 H k ;l ] g 2 : Finally,forthepartiallycoherentdemodulation,inwhichthephaseofthedesired userismodeledasaTikhonovrandomvariablewithcoherenceparameter, ,evaluating 2over2yields p )]TJ/F53 11.9552 Tf 5.48 -9.684 Td [(y 0 k ;y 1 k j I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 s k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 ;I k s k ;x k = l = exp )]TJ/F15 11.9552 Tf 16.402 8.088 Td [(1 2 2 )]TJ/F54 11.9552 Tf 5.48 -9.684 Td [(j y 0 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 g k j 2 + j y 1 k )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 h k j 2 + j A 2 j 2 I 0 j A 1 j 2 q R 2 + I 2 ; 30

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where R =Re[ y l )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 H k ;l ]+ 2 j A 1 j cos 1 and I =Im[ y l )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 H k ;l ]+ 2 j A 1 j sin 1 : Wepresenttheaprioriprobabilitiesofthetransitionbetweenthestates, p s k = s j s k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 = s 0 ,derivedin[22].Theresultsconrmtheintuitivereasoningthatthe probabilitiesofsymbolsbeinginaparticulartypeofhitarenotequallylikelyandare afunctionoftime, k .Inotherwords,theleftmostbitsinaredwellintervalaremuch morelikelytobeinterferedwithbyahitthatoccursontheleft.Forthedifferentstate transitions,theprobabilitiesaregivenby p s k = S j j s k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 = S i = 1 2 1 )]TJ/F15 11.9552 Tf 29.303 8.088 Td [(1 N D )]TJ/F53 11.9552 Tf 11.955 0 Td [(k ;i;j 2 0 ; 1 p s k = M 1 j s k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 = S i = 1 N D )]TJ/F53 11.9552 Tf 11.955 0 Td [(k ;i 2 0 ; 1 ; p s k = M i +1 j s k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 = M i =1 ;i 2f 1 ; 2 ;:::; 2 M g ; p s k = E X j s k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 = M 2 M =1 )]TJ/F15 11.9552 Tf 14.826 8.088 Td [(1 F ; p s k = E i j s k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 = M 2 M = 1 2 F ;i 2 0 ; 1 ; p s k = E j j s k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 = E i = 1 2 ;i;j 2 0 ; 1 ; p s k = S X j s k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 = S X = 8 > > < > > : 1 )]TJ/F26 7.9701 Tf 49.774 4.707 Td [(1 F N D +2 M )]TJ/F27 7.9701 Tf 6.587 0 Td [(N D )]TJ/F27 7.9701 Tf 6.587 0 Td [(k ; 0 k 2 M 1 )]TJ/F26 7.9701 Tf 52.984 4.708 Td [(1 F N D +2 M )]TJ/F26 7.9701 Tf 6.587 0 Td [( k )]TJ/F26 7.9701 Tf 6.586 0 Td [(2 M ; 2 M k N D ; p s k +1 = E i j s k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 = S X = 8 > > < > > : 1 2 1 F N D +2 M )]TJ/F27 7.9701 Tf 6.586 0 Td [(N D )]TJ/F27 7.9701 Tf 6.586 0 Td [(k ; 0 k 2 M 1 2 1 F N D +2 M )]TJ/F26 7.9701 Tf 6.586 0 Td [( k )]TJ/F26 7.9701 Tf 6.587 0 Td [(2 M ; 2 M k N D i 2 0 ; 1 : 31

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Givenknowledgethebranchmetric, s 0 ;s ,theforwardandbackwardlooking probabilities, s and s 0 aregiven[31]by k +1 s = X s 0 k s 0 k +1 s 0 ;s ; and k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 s 0 = X s k s k s 0 ;s : Theinitialvaluesof and aretheprobabilitiesthatthetrellisstartsorendsateach initialorterminalstate.Theseprobabilitiesaregivenby 0 s = S i = 1 2 F N D N D +2 M ;i 2 0 ; 1 ; 0 s = S X =1 )]TJ/F15 11.9552 Tf 14.826 8.087 Td [(1 F N D N D +2 M ; N D s = S i =0 ;i;j 2 0 ; 1 ; N D s = E X = 1 F 1 )]TJ/F15 11.9552 Tf 14.826 8.088 Td [(1 F N D )]TJ/F15 11.9552 Tf 11.955 0 Td [(2 M N D +2 M ; N D s = M i = 1 F N D +2 M ; N D s = E i = 1 2 F N D N D +2 M ;i 2 0 ; 1 ; and N D s = S X = 1 F 1 )]TJ/F15 11.9552 Tf 14.826 8.087 Td [(1 F F N D +2 M )]TJ/F15 11.9552 Tf 11.955 0 Td [( N D )]TJ/F15 11.9552 Tf 11.955 0 Td [(2 M N D +2 M ; : Giventhesevalues,thejointaposterioriprobabilityforconsecutiveinterference symbolsisgivenby p I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 ;I k j y = C X U f I k )]TJ/F21 5.9776 Tf 5.756 0 Td [(1 ;I k g k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 s 0 k s 0 ;s k s ; where I k 2f X; 0 ; 1 g and U f I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 ;I k g isthesetofallstatetransitionsthathave I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 ;I k as theirbranchoutputs.Also, C isaprobabilitynormalizationconstant. 32

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Giventhisinformation,wecangeneratethelikelihoodfunctionofthereceived metricgiventheinterferenceandthetransmittedsymbolas p y 0 k ;y 1 k j x k = X I k )]TJ/F21 5.9776 Tf 5.756 0 Td [(1 X I k p y 0 k ;y 1 k j x k ;I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 ;I k p I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 ;I k ; wherewehaveapproximated p I k )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 ;I k by p I k )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 ;I k j y Theoutputofthesoftdemodulatoristhelog-likelihoodratiothatcombinesthis informationwiththeextrinsicinformationprovidedbythedecoder.Thelog-likelihood ratioiscalculatedas LLR x k = log p y 0 k ;y 1 k j x k =0 p y 0 k ;y 1 k j x k =1 + log p x k =0 p x k =1 : Also,wepresentresults,motivatedin ?? ,wherewereplacethenoisevariancein 2,2and2withtheestimatedchannelvariance. 2.5PerformanceResults Weevaluatedtheperformanceofourreceiverusingcomputersimulations. 1000 encodedbitsareinterleavedandtransmittedover 10 frequencybands.Informationbits areencodedusingarate 1 = 2 convolutionalcodeofconstraintlength 7 ofmaximum freedistanceandinterleavedusingapseudo-randomchannelinterleaverbefore transmission.Thechannelparameters A 1 and A 2 aremodeledascomplexGaussian randomvariablesthatareconstantwithinadwellintervalandindependentamong dwellintervals.Thetimeoffsetbetweenusers, ,isuniformlydistributedon ;T ] .We assumethatalltheparametersotherthanthedesireduser'stimingareunknownatthe receiver,andwecomparetheperformanceofasystememployingpartiallycoherent demodulationtoonesutilizingcoherentandnoncoherentdemodulation. Werstconsiderasysteminwhicheachdwellintervalexperiencesinterference fromatmostoneuser.Forthisscenario,weconsiderasimplesystemcontaining twouserscontendingovertenfrequencybands.Fig.2-5showsacomparisoninthe performanceofpartiallycoherentdemodulationandthemoretraditionalcoherentand 33

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non-coherentapproaches.Weseefromthegurethatpartiallycoherentdemodulation performsaswellorbetterthanbothoftheotherdemodulationschemesforallvalues of E b =N 0 .Wealsoseethatatlow E b =N 0 ,ourapproachisabletoadaptandget performancethatcloselymatchesthatprovidedbyfullycoherentdemodulation,butas thechannelbecomeslessnoisy,weseeasubstantialdropintheerroroorcompared tocoherentdemodulationaboutanorderofmagnitude. Figure2-5.Blockerrorratevs. E b =N 0 fortwouserscontendingontenfrequencybands inaRayleighchannelwithSIR= 0 dB. Next,weconsiderhowthestrengthoftheinterferenceaffectsperformance. Weconsidera 2 )]TJ/F76 11.9552 Tf 9.299 0 Td [(usersystemwithtenfrequencybandsavailablefortransmission andaxed E b =N 0 =20 dB.Fig.2-6presentstheblockerrorrateasafunctionof 34

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thesignal-to-interferenceratio.Weseethatwegetabouta 3 dBgainacrossall SIR'scomparedtothenoncoherentcaseandatleast 2 dBimprovementforthe coherentcase.Wealsoobservethepresenceofanerroroorthatseverelyaffects theperformancewhenusingcoherentdemodulationinthisenvironment. Figure2-6.Blockerrorratevs.SIRfortwouserscontendingontenfrequencybandsin aRayleighchannelwith E b =N 0 =20 dB. Fig.2-7showstheblockerrorratesasafunctionof E b =N 0 atselectednumbersof iterations.Thereislittleperformancetobegainedafter 12 iterations.Wealsopresent theevolutionof acrossiterationsinFig.2-8.Weseeevidenceofimprovementinthe channelestimateastheiterationprogresses.InFig.2-9andFig.2-10,weconsider 35

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Figure2-7.Performanceoverselectednumberofiterations,SIR= 0 dB. 36

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Figure2-8.Evolutionof acrossiterationsforselecteddwellintervals. 37

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amorerealisticsysteminwhichmultipleuserscontendover 100 frequencybands. Fig.2-9presentstheblockerrorrateasafunctionofthenumberofusers.Wecan seethattheperformancecurvesforcoherentandnoncoherentdemodulationarevery similar.However,forasystemusingpartiallycoherentdemodulationinthisscenario, wegetabouta 40% improvementinthenumberofusersthatcanbesupportedata targeterrorrateof 10 )]TJ/F26 7.9701 Tf 6.586 0 Td [(2 .ForFig.2-10,weconsiderasystemoperationatSIR= 0 dB Figure2-9.Blockerrorratevs.numberofusers, E b =N 0 =24 dB,SIR= 0 dB. andinvestigatethemaximumnumberofusersthatcanbesupportedateach E b =N 0 ata targeterrorrateof 10 )]TJ/F26 7.9701 Tf 6.586 0 Td [(2 .Weseethatpartiallycoherentdemodulationoutperformsthe betterofthecomparisoncasesacrossall E b =N 0 bysupportingupto 44% moreusers. 38

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Figure2-10.Maximumnumberofusersthatcanbesupportedforatargeterrorrateof 10 )]TJ/F26 7.9701 Tf 6.586 0 Td [(2 inasysteminwhichuserscontendover 100 frequencybandsatSIR= 0 dB 39

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Theresultsforthecasewherethenoisevarianceisreplacedbythechannel varianceisshowninFig.2-11andFig.2-12Weseethatthisapproachprovides superiorinterferencemitigationcapabilityacrossall Eb=N 0 .WealsoseeinFig.2-12that farmoreusersaresupportedwhencomparedtothecaseofnointerferencemitigation. Inparticular,weseeanimprovementofmorethan 100% inthenumberofusersthatcan besupportedatatargeterrorrateof 10 )]TJ/F26 7.9701 Tf 6.586 0 Td [(2 forthecoherentandpartiallycoherentcases. However,wealsoseethatpartiallycoherentdoesnotprovideasignicantperformance gainovercoherentdemodulationbecauseinthecoherentdemodulator,theerrorsin thereferencephaseresultinadditionalnoisethatcanbetreatedasapproximately Gaussian. 2.6Summary Inthissection,wehaveusedpartiallycoherentdemodulationtoimprovethe performanceofaninterferencemitigatingreceiver.Wequantiedourlevelofcondence intheestimateoftheparametersofthedesireduserandwehaveusedthisnew quantitytoaidindemodulation.Wehaveshownthatthisiterativepartiallycoherent demodulationapproachprovidesmorerobustnesstointerference.Wehavealsoshown substantialgainsinthemultiple-accesscapabilityofthesystem.Finally,wehaveshown thatadditionalperformancegainscanbeachievedwhenthethermalnoisevarianceis replacedbytheestimatedchannelvarianceduringdemodulation. 40

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Figure2-11.Blockerrorratevs. E b =N 0 fortwouserscontendingontenfrequency bandsinaRayleighchannelwithSIR= 0 dB:Channelvarianceestimation case. 41

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Figure2-12.Blockerrorratevs.numberofusers, E b =N 0 =24 dB,SIR= 0 dB:channel varianceestimationcase. 42

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CHAPTER3 MULTIPLE-ACCESSINTERFERENCEMITIGATIONANDITERATIVE DEMODULATIONOFCPFSKINASYNCHRONOUSSLOWFHSSSYSTEMS 3.1IntroductionofMultiple-AccessInterferenceMitigationandIterative DemodulationofCPFSKinAsynchronousSlowFHSSSystems TheissueofMAImitigationinCPFSK-modulatedFHSSsystemisamore challengingonebecauseCPFSKisnotamemorylessmodulationscheme.The traditionalapproachtodealingwithMAIinthissysteminvolvestreatingtheinterference asnoise.Thisapproachhasbeenshowntoworkwellifthesignal-to-interferenceratio ishigh[27,28].However,thisapproachdoesnotworkwellforlowsignal-to-interference ratio.Thisisbecauseitdisregardsthefactthatforthemostlikelyscenarioofonestrong interfererinadwellinterval,thereisastructuretotheinterferencecontainedinthat interval. Inthischapter,weexploitthestructureoftheinterferencewiththegoalofdesigning amorerobustsystem.Weshowperformancegainsintermsoftheblockerrorrate andmulti-accesscapabilityofthesystem.Therestofthechapterisarrangedas follows.InSection3.2,weintroducethesystemmodelandderivethechannellikelihood fordemodulationofCPFSK.InSection3.3,wedescribehowtheparametersofthe channelisestimated,andinSection3.4,wegiveanexplanationonhowdemodulation isperformed.PerformanceresultsfromsimulationsarepresentedinSection3.5,and thechapterisconcludedinSection3.6. 3.2SystemModel ThesystemmodelconsideredinthischapterisillustratedinFig.3-1.Weconsider aFHSSsystemwithmultipleuserstransmittingsimultaneously.Thetransmittersare identical,butthefrequencyhoppingpatternsvaryfromoneusertotheother.Datais convolutionallycoded,andthesymbolsattheoutputoftheencoderareinterleavedand packedintoaframeofxedlength.Thesebitsarethendividedintosegmentof D data bitsandmodulatedusingCPFSK.Ineachdwellinterval,the D databitsaretransmitted 43

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alongwith P pilotsymbolsand N nullsymbolsoneachsideofthedatasymbols,as showninFig.3-2.Duringthenullsymbols,notransmissionoccurs,whichallowsthe receivertodetectandestimatethepresenceofMAI. Figure3-1.Systemmodel. Let q denotetheinputsequencetothemodulatorforaparticulardwellinterval.For M-aryCPFSK,theentriesof q arechosenfromthealphabetset Q = f 0 ; 1 ;:::;M )]TJ/F15 11.9552 Tf 12.311 0 Td [(1 g Forthe i thsymbolin q ,themodulatedsignal x i t ischosenasthe q i th signalinthe set S = f s k t ;k =0 ; 1 ;:::;M )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 g ,where s k t = 1 p T exp jh k )]TJ/F15 11.9552 Tf 11.955 0 Td [( M )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 t T s ;t 2 [0 ;T s : Here h isthemodulationindexand T s isthesymbolduration.Inordertomaintain continuousphasetransitionsbetweenconsecutivesymbols,thisphaseisaccumulated as i +1 = i + q i )]TJ/F15 11.9552 Tf 11.956 0 Td [( M )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 h: 44

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Figure3-2.Structureofadwellinterval. P and N denotesetsofpilotandnullsymbols, respectively. Forsimplicity,inthischapter,wefocusonthebinarycase M =2 ,althoughour techniquescanbeappliedforother M TheresultingCPFSKsymbolsaremodulatedontoacarrieraccordingtothe slowfrequency-hoppingscheme.Thechannelisdividedinto F frequencybands.A pseudo-randomhoppingsequenceisusedtochooseacarrierfrequencyforeach dwellinterval.Allthesymbolsinaparticulardwellintervalarethentransmittedat thesamecarrierfrequency.Becausethehoppingpatternsofdifferentusersarenot orthogonal,MAIoccurswhenmultipleuserstransmitatthesametimeonthesame carrierfrequency.Thesignalsarriveatthereceiverwithrandomamplitudesandphases. Thechannelisaslowfrequency-selectiveRayleighfadingchannel.Wemodelthisusing blockfadinginwhichtheamplitudeandphaseareconstantovereachdwellintervalbut varyfromonedwellintervaltoanother. Atthereceiver,thereceivedsignalisdehoppedandpassedthroughabank of M pairsofmatchedlterwithonepairmatchedtothein-phaseandquadrature componentsofeachfrequencytone.Weassumethatthereceivercanachieveperfect timingforthedesiredsignal 1 .However,anyinterferingsignalsareasynchronoustothe desiredsignal.Asinthepreviouschapter,wedesigntheinterferencemitigationscheme basedonthepresenceofonestronginterferinguser,andthereceivermustdetectand obtaintiminginformationfortheinterferenceinanydwellintervalforwhichthereisMAI. 1 Ifitcannotobtaingoodtiminginformationforthedesiredsignal,thenitwillhaveno possibilityofrecoveringit. 45

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Consideradesiredsymbolthatisreceivedinthepresenceofaninterferingsignal forwhichthesymbolboundariesare secondsdelayedwithrespecttothesymbol boundariesofthedesiredsignal,i.e 0 T s .Afteritismatchedlteredandsampled, thereceivedsignalcanbewritteninvectorformas y = A 1 x e j + A 2 I + n ; where A 1 = a 1 e j 1 and A 2 = a 2 e j 2 arethecomplexchannelgainsofthedesiredand interferinguser,respectively.Here, I isan M by 2 matrixwhoserows, I k ,modelthe effectofinterferenceinthematchedlterand modelsthephasesoftheinterference symbols.Sincetheinterferenceisasynchronous,theoutputofthematchedlters areassociatedwithtwoconsecutiveinterferingsymbols.Eachelementof y canbe representedas y k = A 1 x k e j + A 2 I k + n k ; where x k = Z T s 0 x t s k t dt; n k = Z T s 0 n t s k t dt; I k = Z 0 s m t )]TJ/F53 11.9552 Tf 11.956 0 Td [( + T s s k t dt; Z T s s n t )]TJ/F53 11.9552 Tf 11.955 0 Td [( s k t dt ; = e j i )]TJ/F21 5.9776 Tf 5.756 0 Td [(1 ;e j i 0 ; and s m t ;s n t 2S ; 8 m;n 2f 0 ; 1 g .ThenoisevectorisGaussianwithacovariance matrix R = E [ nn H ] whoseentriesaregivenby r k;i =Sinc i )]TJ/F53 11.9552 Tf 11.955 0 Td [(k h e j i )]TJ/F27 7.9701 Tf 6.586 0 Td [(k h ; 46

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where Sinc x = 8 > > < > > : 1 if x =0 sin x x otherwise. Itthenfollowsthatthematrix I isoftheform 2 6 4 I 1 ; 1 ;I 1 ; 2 I 2 ; 1 ;I 2 ; 2 3 7 5 ; sincethereareatmosttwointerferencesymbolsinadesiredsymbolinterval.Consider theoutputofthematchedlterfor s k t inthepresenceofconsecutiveinterference symbols s m t and s n t .Thentheinterferencetermsaregivenby I k; 1 = 8 > > > > > > < > > > > > > : 0 ; if s m t =0 T s exp )]TJ/F27 7.9701 Tf 10.494 5.699 Td [(ih )]TJ/F26 7.9701 Tf 6.586 0 Td [(1+2 k T s + T s ; if m = k i exp ih )]TJ/F21 5.9776 Tf 5.756 0 Td [(1+2 m T s )]TJ/F22 5.9776 Tf 5.756 0 Td [( T s )]TJ/F26 7.9701 Tf 6.587 0 Td [(exp ih )]TJ/F21 5.9776 Tf 5.756 0 Td [(1+2 m T s + )]TJ/F21 5.9776 Tf 5.756 0 Td [(2 k T s 2 h )]TJ/F27 7.9701 Tf 6.586 0 Td [(k + m ; if m 6 = k and I k; 2 = 8 > > > > > > < > > > > > > : 0 ; if s m t =0 1 )]TJ/F27 7.9701 Tf 15.272 4.707 Td [( T s exp ih )]TJ/F26 7.9701 Tf 6.587 0 Td [(2 k T s ; if n = k )]TJ/F27 7.9701 Tf 10.494 7.828 Td [(i exp )]TJ/F22 5.9776 Tf 7.782 4.024 Td [(ih )]TJ/F21 5.9776 Tf 5.757 0 Td [(1+2 k T s )]TJ/F26 7.9701 Tf 6.587 0 Td [(exp )]TJ/F22 5.9776 Tf 7.782 4.024 Td [(ih kT s )]TJ/F21 5.9776 Tf 5.756 0 Td [(2 nT s )]TJ/F22 5.9776 Tf 5.756 0 Td [( +2 n T s 2 h k )]TJ/F27 7.9701 Tf 6.587 0 Td [(n ; if n 6 = k: Tosimplifythenotation,wedenethechannelparametervector = f a 1 ;a 2 ; 1 ; 2 ; g Theprobabilitydensityfunctionof y given x I ,and is p y j x ; I ; = 1 M det R exp )]TJ/F15 11.9552 Tf 9.299 0 Td [( y )]TJ/F53 11.9552 Tf 11.956 0 Td [(A 1 x e j )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 2 I H R )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 y )]TJ/F53 11.9552 Tf 11.955 0 Td [(A 1 x e j + A 2 I : 47

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Theexponentialterminthedensityfunctioncanbewrittenas )]TJ/F15 11.9552 Tf 11.955 0 Td [( y H R n )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 y )]TJ/F15 11.9552 Tf 11.955 0 Td [(2Re A 1 e j yR n )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 x )]TJ/F15 11.9552 Tf 11.955 0 Td [(2Re A 2 y H R n )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 I + j A 1 j 2 x H R n )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 x +2Re A 1 A 2 e )]TJ/F27 7.9701 Tf 6.587 0 Td [(j x H R n )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 I + j A 2 j 2 H I H R n )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 I : Dene K = 1 2 2 R n .When x t = s v t x isthe v th columnof K .Then3becomes )]TJ/F90 11.9552 Tf 9.299 0 Td [(y H K )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 y +2Re A 2 y H K )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 I 2 2 )]TJ 13.151 8.088 Td [(j A 1 j 2 )-222(j A 2 j 2 H I H K )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 I 2 2 + 2Re A 1 e j y v )]TJ/F15 11.9552 Tf 11.955 0 Td [(2Re A 1 A 2 e )]TJ/F27 7.9701 Tf 6.586 0 Td [(j I v 2 2 : Here, I v isdenedasthe v th elementoftheproductof I and .Dene ^ y v = y v and ^ I v = I v Theuseofpilotsymbolswhoseinducedphasesareknown apriori atthereceiver allowsforchannelestimationofthedesireduseratthereceiver.So,givenestimates ofthechannelparametersofthedesireduser,wecanintegrate3overtheuniform randomvariable 2 toyield exp )]TJ/F90 11.9552 Tf 9.298 0 Td [(y H K )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 y )-222(j A 1 j 2 +2Re A 1 e j y v 2 2 )]TJ 10.494 8.088 Td [(j A 2 j 2 H I H K )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 I 2 2 I 0 j A 2 j 2 q 2 r + 2 i where r =Re y H KI )]TJ/F15 11.9552 Tf 11.955 0 Td [(Re A 1 e )]TJ/F27 7.9701 Tf 6.587 0 Td [(j I v ; i =Im y H KI )]TJ/F15 11.9552 Tf 11.955 0 Td [(Im A 1 e )]TJ/F27 7.9701 Tf 6.586 0 Td [(j I v ; and I 0 isthezerothordermodiedBesselfunctionoftherstkind. 48

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3.3ParameterEstimation Theparametersofthedesiredandinterferingusersmustbeestimatedbefore interferencemitigationcanbeperformedusingthesoftdemodulationschemedescribed inSection3.4.Theuser'schannelparametersareestimatedusingthepilotsymbols atthebeginningandendofeachdwellinterval.Thereliabilityoftheestimatesfrom eachsetofpilotsymbolsisdeterminedandusedindecidingwhichsettouseforthe desireduser'schannelestimateandwhichsetofnullsymbolstouseinestimatingthe parametersoftheinterferinguser.Next,wecomputetherelativetimingoffsetofthe interferinguserbyusingthenullsymbolsindwellintervalscontaininginterference. Oncewehaveanestimateofthesymboloffset,weusethisestimatetocalculatethe magnitudeoftheinterferenceineachdwellinterval. 3.3.1ChannelEstimatorDesiredUser TomaintainthecontinuousphaserequirementofCPFSK,agroupof P pilot symbolsareinsertedafterthe M nullsymbolsandanothergroupisinsertedafterthe datablock.Weestimatetheparametersofthedesireduserusingthepilotsymbols.In particular,weperformthisestimateassumingthatatleastoneofthetwosetsofpilot symbolshavenotbeeninterferedwith.Sincethepilotsymbolsarepositionedonboth sidesofthedatablock,wegeneratetwoestimatesof A 1 andchoosetheestimatethat providesthebestreliability,assuggestedbyacoherenceparameter.Foreachpilot symbol,thelocalestimateforthechannelisgivenby ^ A 1 k = w T k y k e )]TJ/F27 7.9701 Tf 6.586 0 Td [(j k ; where k isapilotsymbolpositionthatisamemberofacontiguousgroupof P pilot symbolsthatankthedatablockontheleftorrightand T denotesthetranspose 49

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operation.Thevector w k isdenedas w ki = 8 > > < > > : 1 if x ki =1 0 ifotherwise, where y ki and w ki arethe i thelementsofvectors y k and w k respectively.Itthenfollows that ^ A 1 = 1 P P X k =0 ^ A 1 k ; foreachgroupofpilotsymbols. Itwasempiricallydeterminedthatiftheestimateof frombothsidesisgreater than 10 ,theestimatescanbecombinedinordertoprovidemoredatapointsfor estimation.Inthecasewhereonlyonesideisdeemedreliable,i.eitscoherence parameterisgreaterthan 10 ,onlythatsideisusedinestimation.Forthecasewhere bothsidesaredeemedunreliable,wechoosetheestimatefromthesidewithahigher coherenceparameter. 3.3.2TimingOffsetEstimatorInterferingUser Atthenullpositions,theamplitudeofthedesireduseriszero.Itthenfollowsfrom 3thattheprobabilityof y atthesesymbolpositionsisgivenby p y j x ; I ; nf 2 ; 1 ;a 1 g / exp )]TJ/F90 11.9552 Tf 9.299 0 Td [(y H K )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 y )-222(j A 2 j 2 H I H K )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 I 2 2 I 0 j A 2 j 2 y H KI ; where n representstheset-minusoperation. From3and3,wecanre-writetheinterferencematrix I tobeafunction oftheoffset, =T s ,insteadof .Themaximum-likelihoodMLestimatecannotbe derivedinanalyticalformfrom3,soweuseabrute-forcesearchbyquantizing thesearchspace.Weassumethattheoffsetisfromanitesetwhoseentriesare 50

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-spacedbetween 0 and 1 .Wethenevaluate3foreachoffsetvalueintheset acrossconsecutivenullsymbolsusingtheViterbialgorithm.Theinitialestimateof j A 2 j usedin3iscalculatedbytakingthesumofthemagnitudesofthematchedlter outputsateachnullpositionandtakingtheaverageacrossallthenullpositions. Theoffsetvaluethatprovidesthemostprobableinterferencesequenceischosen alongwithitscorrespondinginterferenceparameters.Atthispoint,wehavebothan estimatefortheoffsetandtheinterferencematrixateachsymbolposition. 3.3.3InterferingChannelEstimation From3,theoutputofthematchedlteratthenullpositionsisgivenby y = A 2 I + n Theinitialestimateof j A 2 j usedintherstiterationoftheoffsetestimationisderivedby takingtheaverageofthemagnitudesof y overallitselementsandoverbothleftand rightclustersofnullsymbols.Wedeterminewhethertousetheleftorrightestimates basedonthecoherenceparameter.Inotherwords,interferenceparametersare estimatedusingonlythesidewith low reliability. Forsubsequentiterations,itfollowsthatthelocalestimateoftheamplitudeofthe interferinguserateachnullsymbolpositioncanbewrittenas I y I I = ^ A 2 n Wederiveanestimatefor j A 2 j byaveragingthelocalestimates.Thisnewvalueis thenfedbackintotheoffsetestimationblockuntilitconverges. 3.4SoftDemodulator Initialdemodulationisperformedinthetraditionalway,wherewetreatthe interferenceasnoise.However,ifwefailtodecodetheframeafterasetnumberof iterations,weapplysoftdemodulationtoaidindetectingthedesiredsignalinthe presenceoftheMAI.Eachdwellintervalisdemodulatedusinga20-statetrellis, 51

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whereeachstateischaracterizedbyanorderedpairofasymbolphaseandaright edgeinterferingphaseofthedesiredsymbol.Ifweassumethatthesetofsymbol phasesisgivenby C = f 0 ; 0 : 5 ;; 1 : 5 g andthesetofinterferingphasesisgivenby D = f X; 0 ; 0 : 5 ;; 1 : 5 g ,then,theCartesianproduct, C D ,correspondstoallpossible states.Thecomponent X 2 D isusedtodenotethatnointerferenceispresent. Theinputtothetrellisisa2-tuplethatconsistsofanorderedpairfromthe Cartesianproductof R = f 0 ; 1 g and S = f X; 0 ; 1 g ,where R isthesetofallpossible valuesforthedesiredsymboland S isthesetofallpossibleinterferingsymbolvalues. Thenextstateofthetrellisisderivedbycalculatingitsstateattributes.Inparticular,the phasecontinuitypropertyofCPFSKisenforcedsothat, k +1 = k + r )]TJ/F15 11.9552 Tf 11.955 0 Td [( M )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 h;r 2 R; where k isthephaseofthedesireduseratthecurrentstate.Thesameformulais appliedtondingthenextinterferencephase.Thestatewiththesetwoattributesis chosenasthenextstate.Fig.3-3givesapictorialrepresentationifthetrellisandthe statetransitionsareshownforaselectedstate.Thebranchmetricforthetransitionis calculatedbyusing3andtheextrinsicinformationfromthedecoder.Itisgivenby LL v k +1 j v k =log[ p y j x ; I ; )-222(f 2 g ]+log[ p x k = r ] : Forthecasewherethedesireduser'schannelestimateisdeemedunreliable andthereareenoughdwellintervalswithreliableestimates,thesymbolswithinthe unreliabledwellintervalareerasedbeforebeingsenttothedecoder. 3.5SimulationResults Theperformanceoftheschemeprovidedinthischapterisexaminedandcompared tothecasewherethereceiverdoesnottrytomitigatetheeffectoftheinterference. Inoneofthecomparisoncases,weuseperfectestimatesoftheparametersofthe desireduserbutusecomputedestimatesfortheothercase.Weprovideresultsfora 52

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Figure3-3.Trellisandtransitionsforaselectedstate. proof-of-conceptsysteminwhichtwousersoccupytenfrequencybands.Thesystem usesaxedframesizeof 1000 encodedbits,whereencodedingisperformedwitha rate 1 = 2 convolutionalencoderwithconstraintlength 7 ofmaximumfreedistance.The encodedbitsareinterleavedusingapseudo-randombitinterleaverandtheframeis transmittedover 10 dwellintervals.Eachdwellintervalcontains N =5 nullsymbolsat thebeginningandendofthesub-frameand P =5 pilotsymbolsbeforeandafterthe dataframe.Ineffect,thenumberofsymboldurationscontainedineachdwellintervalis L =120 ,whereonly D =100 symboldurationscontaindatainformation. WeassumethateachdwellintervalexperiencesRayleighfading.Wemodel A 1 and A 2 ascircular-symmetriccomplexrandomvariablesthatareconstantovereach 53

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dwellintervalbutindependentamongdwellintervals. isuniformlydistributedon [0 ;T s Whenapplyingourscheme,weassumethatalltheparametersareunknownatthe receiverandneedtobeestimated.However,forourcomparisoncase,weassumethat theparametersofthedesireduserisknowna-prioriatthereceiver.Forourscheme, weattempttodecodewhilewedisregardtheinterferencefortherst 3 iterations.When decodingfails,then,weperformiterativeinterferencemitigationanddecoding. Figure3-4.Comparisonofschemesfor E b =N 0 =24 dBacrossarangeofPartial-Band Interferencevalues. Fig.3-4showstheperformanceofourschemecomparedtousingonlythe traditionalschemeintheregionofstrongMAI.Weseethatourschemesignicantly 54

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outperformsthecomparisoncaseforall E b =I 0 t SignaltoInterferenceratio 2 .Thisisdue tothefactthattheestimateoftheinterferenceparameterisverygoodathigh E b =N 0 andallowsaccuratesoftdemodulation.Theinterferencemitigationapproachachieves anapproximateorderofmagnitudeimprovementintheblockerrorratewhencompared tothesystemthatignoresinterferenceandhastoestimatethedesireduser'schannel. Foratargetrateof 10 )]TJ/F26 7.9701 Tf 6.587 0 Td [(2 ,wegetabouta 3 : 5 dBimprovementinthesystem'stolerance tointerferencecomparedtothecaseofperfectsideinformationand 5 dBforthecase wherethereceiverhastoestimatethechannelgainofthedesireduser. Fig.3-5comparesourapproachforaxed E b =I 0 t =5 dBoverarangeof E b =N 0 Weseeabouta 4 dBimprovementwhenweusetheestimatedsideinformationanda smallerimprovementwhenweuseperfectCSIforthesametargeterrorrateof 10 )]TJ/F26 7.9701 Tf 6.586 0 Td [(2 Theimportantthingtonotefromthisgraphisthereductionintheerroroorthatcomes fromusingourapproach. Fig.3-6showstheperformanceforxed E b =I 0 t =0 dB.Weseethatthetarget errorrateof 10 )]TJ/F26 7.9701 Tf 6.586 0 Td [(2 isunachievablewiththeschemethatdoesnotperforminterference mitigation,evenifperfectchannelestimatesareavailableforthedesireduser,butcan beachievedwithourapproach. Next,welookatamorerealisticcasewherewehaveseveraluserscontendingover 100 frequencybands.FromFig.3-7,weseeanincreaseinthenumberofusersthat canbesupportedatanygivenerrorrate.Foratargeterrorrateof 10 )]TJ/F26 7.9701 Tf 6.587 0 Td [(2 ,interference mitigationallowsforthesystemtosupport 18 userscomparedwith 4 forasystemusing thetraditionalapproach. 2 Here, I 0 t isdenedasthespectraldensitythatwouldexistiftheinterferencewere uniformlyspreadoverthedwellinterval 55

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Figure3-5.Comparisonofschemesfor E b =I 0 t =5 dBacrossarangeof E b =N 0 3.6Summary Inthischapter,wedevelopedaninterferencemitigationschemeforanFHSS systememployingCPFSK.Weexploitthestructureoftheinterferenceindemodulation andutilizereliabilityestimatesofthechannelinthedecodingprocess.Theparameters oftheinterferinguserareestimatedinaniterativemanner.Theresultsshowsignicant performanceimprovementoverthetraditionalscheme.Weobserveanapproximate order-of-magnitudeimprovementinblockerrorratefora 2 )]TJ/F76 11.9552 Tf 9.298 0 Td [(usersystemwhenoperating at E b =N 0 =24 dBforavarietyofinterferencelevels.Whenoperatingatanaverage E b =I 0 t of 5 dB,weobservedaperformancegainofapproximately 4 dBin E b =N 0 overthe traditionalschemeatablockerrorrateof 10 )]TJ/F26 7.9701 Tf 6.587 0 Td [(2 .Forasystemoperatingat E b =I 0 t =0 dB, 56

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Figure3-6.Comparisonofschemesfor E b =I 0 t =0 dBacrossarangeof E b =N 0 thiserrorrateisunachievableusingthetraditionalschemebutcanbeachievedusing ourinterferencemitigationscheme.Also,weshowthatinterferencemitigationallows foranincreaseofabout 350% inthenumberofusersthatcanbesupportedatatarget blockerrorrateof 10 )]TJ/F26 7.9701 Tf 6.587 0 Td [(2 forasystemthatconsistsofmultipleuserscontendingover 100 frequencybands. 57

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Figure3-7.Comparisonofschemesfor E b =I 0 t =0 dBand E b =N 0 =24 dB. 58

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CHAPTER4 ITERATIVECHANNELESTIMATIONANDPARTIALLYCOHERENTDEMODULATION OFCPFSKINTIME-SELECTIVEFADINGCHANNELS 4.1IntroductionofIterativeChannelEstimationandPartiallyCoherent DemodulationofCPFSKinTime-SelectiveFadingChannels Systemengineersfacethechallengeofhowtodesignsystemsthatoperateina verydynamicchannelenvironment.PilotsymbolassistedmodulationPSAMprovides awaytocontinuouslytrackthechannelbyusingembeddedknownsymbolsforchannel impulseresponsetracking[29,3436].Thepilotsymbolinsertionratedependson thefaderateofthechannelaspostulatedbyNyquist.Adaptivetechniqueslikethose proposedin[3739]requiresthatinformationaboutthefaderateareconstantlyfed backfromthereceivertothetransmitterinordertocontinuouslyoptimizethespacing betweenpilotsymbols.Whenthereisamismatchbetweenthisinsertionrateandthe actualfaderateofthechannel,theuseofthechannelgainsderivedfromthesepilot symbolsindemodulationcanadverselyaffectthesystem'sperformance. Inthischapter,weuseiterativepartiallycoherentdemodulationandchannel estimationtoaidindecodingforasystememployingCPFSK.Weexploretheuseof sparserpilotsymbolspacingandpilotinsertionratesthataresignicantlylowerthan theratesspeciedbyNyquist.Weshowthatforthesescenariostheadaptivenatureof thepartiallycoherentschemepresentedinthischapterallowsforperformancethatis asgoodorbetterthaneithercoherentorthenoncoherentdemodulationformostfading scenarios. 4.2SystemModel WeconsiderasystemthattransmitsusingcodedContinuous-PhaseFrequency ShiftKeyingCPFSKoveratimeselectivechannel.Thesystemmodelconsidered inthischapterisillustratedinFig.4-1.Asequence, f d j g ,of L databitsisencoded withaforwarderror-correctioncode.Theencodedbitsarethenpassedthroughan interleavertogenerateanewsequence f b j g ; 1 j L .Thisnewsequenceis 59

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thenmodulatedintoasequenceofCPFSKsymbolsandpilotsymbolareinserted. Duringmodulationandpilotsymbolinsertion,theinputsequenceisseparatedinto M groupsofcontiguousbits.Foreachbit, q i ; 1 i L=M ,ineachofthecontiguous bit-groups,acontinuoustimemodulatedsignal x i t ischosenasthe q th i signalfromthe set S = s m t ;m =0 ;:::;K )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 ,where K isthealphabetsizeand s m t = 1 p T s exp jh m )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 t T s ; where h isthemodulationindex.Inthischapter,forsimplicity,weconsider K =2 ,that Figure4-1.Systemmodel is,theBinary-CPFSKcasebutthisapproachcanalsobeextendedto K> 2 .Inorder tosatisfythecontinuousphaserequirementforCPFSK,thephaseofeachsymbolis accumulatedas i +1 = i + q i )]TJ/F15 11.9552 Tf 11.956 0 Td [( K )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 h: Attheendofeachbit-group,weinsertdata-dependentpilotsymbolsinorderto forcethephasetoapredeterminedphasestate.Gettingtheaccumulatedphaseto aknownphaseatthepilotsymbolrequirestheadditionofanumberofsymbolsthat 60

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dependson h .Forourcase, 2 extrasymbolsarerequired,wherethelastsymbolisthe pilotsymbol. Thepilotbitsattheendofeachbit-groupprovidestheinitialphaseconditionforthe modulationofthenextbit-group.Thisisdoneuntiltheentireframeismodulated.Atthis point,wehave L +2 M symbolsintheframe. Let c t = ae j bethecomplexvalueprocessthatdescribesthebehaviorofthe channel.Sinceweareconsideringafrequencynon-selectiveatfadingchannel,we model c t asazeromeanlow-passGaussianprocess.Weassumethattherealand imaginarypartsof c t areindependentwithautocorrelation R c k = 1 2 J 0 F d T s k ; where J 0 isthezerothorderBesselfunctionoftherstkind, F d istherelativeDoppler betweentransmitter,andreceiverand T s isthesymbolduration. Atthereceiver, y k t = a k e j k p E s e j k x k t + n k t ; 1 k L +2 M;kT s t k +1 T s : Thissignalispassedthroughabankof K matchedlerstoproduce,invectornotation, y = ae j k + k p E s x + n : wheretheelementsofthevectors, y x ,and n canberepresentedas y m = ae j k + k p E s x m + n m x m = Z T s 0 x t s m t dt n m = Z T s 0 n t s m t dt 61

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Thenoisevector n isGaussianwithcovariancematrix, R n = E nn H .Theelementof R n aredenedintermsofthe sinc functionas r x;y = N 0 sinc x )]TJ/F53 11.9552 Tf 11.955 0 Td [(y h e j x )]TJ/F27 7.9701 Tf 6.587 0 Td [(y h : Ifweexpresstheprobabilityofthereceivedvector, y ,thatistheoutputofthe K matchedlters,intermsof x and a p E ,wegetthat p y j x ;:;a p E = 1 M det R n exp )]TJ/F15 11.9552 Tf 9.298 0 Td [( y )]TJ/F53 11.9552 Tf 11.955 0 Td [(a p E x e j + H R n )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 y )]TJ/F53 11.9552 Tf 11.955 0 Td [(a p E x e j + : Consideringjusttheexponent,wehave )]TJ/F15 11.9552 Tf 11.956 0 Td [( y H R n )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 y )]TJ/F53 11.9552 Tf 11.955 0 Td [(a 2 Ex H R n )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 y +2Re a p Ee )]TJ/F27 7.9701 Tf 6.587 0 Td [(j + x H R n )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 y : where Re istherealcomponentofthecomplex-valuedargument. Letusdenethenormalizedcovariancematrix, P = R n = 2 .Then,wecansee from4,thatwhen x t = s v t x isthe v th columnof P .So,given x = p v ,4 becomes, )]TJ/F15 11.9552 Tf 13.151 8.088 Td [( y H P )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 y + a 2 E x H P )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 y 2 2 )]TJ/F15 11.9552 Tf 13.15 8.088 Td [(Re ae )]TJ/F27 7.9701 Tf 6.586 0 Td [(j + x H P )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 y 2 : Fornoncoherentdemodulation,integrating4overtheuniformrandomvariable yields p y j x v ;:;a p E = 1 2 2 M det P exp )]TJ/F15 11.9552 Tf 10.494 8.088 Td [( y H P )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 y + a 2 E x H P )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 y 2 2 I 0 a p E 2 j y v j ; where I 0 isthezerothorderBesselfunctionoftherstkindand y v isthe v th columnof y 62

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Ifthechannelphaseisknown,wecanperformcoherentdemodulation,inwhich caseweget p y j x v ;:;a p E = 1 2 2 M det P exp )]TJ/F15 11.9552 Tf 10.494 8.088 Td [( y H P )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 y + a 2 E x H P )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 y 2 2 exp a p E 2 j y v j cos y v )]TJ/F53 11.9552 Tf 11.955 0 Td [( )]TJ/F53 11.9552 Tf 11.956 0 Td [( ; where y v referstotheangleattheoutputofthematchedltercorrespondingto x v Assumingwehaveanimperfectphaseestimateandacoherenceparameter, thatgivesusinformationaboutthequalityofthechannelphaseestimate, ,then,given theestimatesoftheotherparameters, = f x ;; ^ ;a p E g ,evaluating4overthe tikhonovdensitygivenin2yields p y j x v ;:;a p E = 1 M +1 2 M det P I 0 exp )]TJ/F15 11.9552 Tf 10.494 8.088 Td [( y H P )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 y + a 2 E x H P )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 y 2 2 I 0 a p E 2 q R 2 + I 2 ; where R = j y v j cos y v )]TJ/F53 11.9552 Tf 11.955 0 Td [( + 2 a p E cos ^ and I = j y v j sin y v )]TJ/F53 11.9552 Tf 11.955 0 Td [( + 2 a p E sin ^ : 4.3ChannelEstimation 4.3.1InitialChannelEstimation Atthisstage,theonlyinformationavailableforchannelestimationarethose providedbythepilotsymbols.Withtheknowledgeof k and x atthesepilotpositions, 63

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wecangeneratelocalestimatesofthechannelatthesepositions.Thatis ^ c p = w T p y p e )]TJ/F27 7.9701 Tf 6.586 0 Td [(j p ;p = f 1 ;Y +1 ; 2 Y +1 ;:::; M )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 Y +1 g : where p ispilotsymbolposition, Y isthepilotsymbolspacingand T denotesthe transposeoperation.Thevector w p isdenedas w pi = 8 > > < > > : 1 if x pi =1 0 ifotherwise, where x pi and w pi arethe ith elementofvectors x p and w p respectively. Next,wegenerateestimatesofthechannelatalltheothersymbolposition usingtheestimatesatthepilotpositions.Inparticular,wecalculatetheMinimum MeanSquaredErrorMMSEestimateof b k giventhechannelrealizationsatthepilot positions.Wecanexpressevery b k asalinearcombinationofthe c p 's.Mathematically, ^ b k = M )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 X p =1 h p ^ c p : Thesolutionto4decomposesto h = R )]TJ/F26 7.9701 Tf 6.586 0 Td [(1 r : where h =[ h 0 ;h 1 ;h 2 ;:::;h M )]TJ/F26 7.9701 Tf 6.587 0 Td [(1 ] T ; r =[ R c k )]TJ/F8 9.9626 Tf 9.963 0 Td [(1 ;R c k )]TJ/F11 9.9626 Tf 9.963 0 Td [(Y )]TJ/F8 9.9626 Tf 9.963 0 Td [(1 ;:::;R c k )]TJ/F8 9.9626 Tf 9.962 0 Td [( M )]TJ/F8 9.9626 Tf 9.963 0 Td [(1 Y )]TJ/F8 9.9626 Tf 9.963 0 Td [(1] T ; and R = 64

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0 B B B B B B B B B B @ R c R c Y :::R c M )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 Y R c Y R c :::R c M )]TJ/F15 11.9552 Tf 11.955 0 Td [(2 Y R c Y R c Y :::R c M )]TJ/F15 11.9552 Tf 11.955 0 Td [(3 Y :::::::::::: R c M )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 Y R c M )]TJ/F15 11.9552 Tf 11.955 0 Td [(2 Y :::R c 1 C C C C C C C C C C A Oncethechannelautocorrelation, R c ,isknown,thematrixinversionshownin 4onlyneedstobeperformedonceperpacket.Thelineargainsaregeneratedand appliedto4. Theevaluationof ^ c k andthecalculationofitsvariance ^ k willbeaddressedinthe nextsubsection. 4.3.2IterativeChannelEstimation Aftertherstroundofdemodulation,channelestimationcanberenedbyfeeding backhardsymboldecisions x andsymbolphasedecisions k .Armedwiththis knowledge,wecanrevisit4togeneratelocalestimatesofthechannelateach symbolposition.Specically,wecanwritethat ^ b k = w T k y k e )]TJ/F27 7.9701 Tf 6.586 0 Td [(j k ; 1 k L +2 M: where w k issimilarlydenedasin4. However,theestimatesproducedin4arenoisyestimates.Toreducethe amountofnoiseintheseestimates,wepassitthroughalter.ThebestlinearMMSE estimateofthechannelisgivenby ^ c k = b Q= 2 c X i = b Q= 2 c i b k )]TJ/F27 7.9701 Tf 6.587 0 Td [(i ; 1 k L +2 M: Here, Q istheltersizeandthe i 'saredenedasthecoefcientsofthelterderived bysolvingtheWiener-Hopfequationsgivenby b Q= 2 c X i = b Q= 2 c i R c [ k )]TJ/F53 11.9552 Tf 11.955 0 Td [(i ]+2 2 k = R c [ k ] : 65

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Theweightedvarianceiscalculatedby ^ k =0 : 5 V 1 V 2 1 )]TJ/F53 11.9552 Tf 11.956 0 Td [(V 2 b Q= 2 c X i = b Q= 2 c j i j b k )]TJ/F27 7.9701 Tf 6.586 0 Td [(i )]TJ/F15 11.9552 Tf 14.108 0 Td [(^ c k : Here, V 1 = P b Q= 2 c i = b Q= 2 c j i j and V 2 = P b Q= 2 c i = b Q= 2 c 2 i .Atablelook-upisperformedonthis valuetogeneratecorresponding 'sforallsymbolpositions. Coherentdecodingonlyoccurswhenthevarianceisequalto 0 .Thismeans thatthechannelisneitheraffectedbyfadingnorchannelnoise.Sincethissituation neverreallyoccursinpractice,ateachiteration,wedecidewhethertoperform coherentorpartiallycoherentdemodulationdependingontheoverallqualityofthe channelassuggestedbytheaverageofallthe ^ k .Ifthisaverageisgreaterthansome empirically-determinedthreshold,weusepartiallycoherentdemodulation,else,weuse coherentdemodulation.Inoursimulations,wefoundoutthatanormalizedvariance thresholdof 0 : 15 providesthebestresultacrossallfaderates. 4.4SimulationResults Theperformanceofthepartiallycoherenttechniquewasexaminedbysimulation andcomparedtothetraditionalcoherentandnoncoherenttechniques.Weevaluated thesystemforaxeddatalengthof 1000 encodedbits,whereencodingisperformed witharate 1 = 2 convolutionalencoderofconstraintlength 7 ofmaximumfreedistance. M =10 pilotsymbolsareplacedintheframeforchanneltrackingtoproduceapilot spacingof Y =100 Slowfadingisassumedandweevaluatethechannelperformancefornormalized faderates F d T s =0 : 005 F d T s =0 : 01 F d T s =0 : 02 ,and F d T s =0 : 04 .AccordingtoNyquist, thepilotinsertionratesforthesefaderatesshouldbe Y< 100 Y< 50 Y< 25 ,and Y< 12 : 5 respectively.Forallfaderates,thesizeoftheWienerlterusedinchannel estimationis Q =31 Sevendemodulationandchannelestimationiterationswereperformedandthe ViterbiAlgorithmwasusedtodemodulatetheframeonatrelliswiththedecoding 66

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metricsgivenby4and4forthecoherentandpartiallycoherentschemes respectively. Theinterestingthingtonotefromallthegurespresentedinthissectionisthe adaptivenatureofthepartiallycoherentscheme.InFigs.4-2and4-3,weseethat theperformanceofthepartiallycoherentschemelargelykeepsinstepwiththoseof thecoherentscheme.However,itoutperformsthecoherentschemeinthecaseof F d T s =0 : 01 forlarge E b =N 0 > 16 dB .Thisisbecauseatthesefadingrates,pilot symbolslargelytrackthevariationswithinthechannel,andthepartiallycoherent schemeassignshighcondencetothechannelphaseestimatesgeneratedinthe system. Figure4-2.Comparisonofdemodulationschemesfor F s T s =0 : 005 67

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Figure4-3.Comparisonofdemodulationschemesfor F s T s =0 : 01 Fig.4-4andFig.4-5telladifferentstory.Weobservethatforthesefaderates,the performanceofasystemapplyingthecoherentschemeisseverelydegraded.Thisis becausethepilotsymbolsnolongerprovidereliableestimationaboutthevariations inthechannel.Weobservethatfor F d T s =0 : 02 andblockerrorrateof 10 )]TJ/F26 7.9701 Tf 6.586 0 Td [(3 .partially coherentdemodulationoutperformsnoncoherentdemodulationbyabout 3 dB.This targeterrorratecannotbeachievedinasystemutilizingcoherentdemodulation.The partiallycoherentschemealsooffersaslightadvantageoverthenoncoherentscheme acrossall E b =N 0 for F d T s =0 : 04 .Wenoticethatatablockerrorrateof 10 )]TJ/F26 7.9701 Tf 6.586 0 Td [(2 ,thepartially 68

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Figure4-4.Comparisonofdemodulationschemesfor F s T s =0 : 02 coherentschemehasabouta 2 dBadvantageoverthenoncoherentscheme.Thiserror rateisunachievableusingcoherentdemodulation. Fig.4-6showstheblockerrorrateasafunctionof E b =N 0 forvaryingnumberof receiveriterationsinachannelwithaxedfaderateof FdTs =0 : 005 .Weobservethat iterativedemodulationprovidesanimprovementinperformancebecauseitallowsfor moreaccuratechannelestimates. 4.5Summary Inthischapter,wehaveshowntheperformanceimprovementthatisachievable throughtheuseofpartiallycoherentdemodulationinasystememployingbinary 69

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Figure4-5.Comparisonofdemodulationschemesfor F s T s =0 : 04 CPFSK.Wehavealsoshownthatwecanachieveperformancegainsofover 3 dB comparedwiththebestofeithernoncoherentorcoherentdemodulationforpilotsymbol insertionratesthataresparsecomparedtoNyquist. 70

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Figure4-6.Blockerrorratevs. E b =N 0 forvaryingnumberofiterationsand F s T s =0 : 005 71

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CHAPTER5 LINK-LAYERTHROUGHPUTOFFREQUENCY-HOPPINGSYSTEMSWITH INTERFERENCEMITIGATION 5.1IntroductionofLink-LayerThroughputofFrequency-HoppingSystemswith InterferenceMitigation Inthissection,weconsidertheimprovementthatisachievedinthedatalinklayer asaresultofinterferencemitigationonthephysicallayer.Wepresentasimplesystem modelandweusethistostudywhatinuencethisphysical-layerimprovementhason thelink-layerthroughput. Weconsiderhowinterferenceinformationcalculatedintheinterferencemitigation algorithmofeachnodecanbeusedtoestimateoftheaveragenumberofusersinthe systemduringaparticulartimeperiod.Thisknowledgeisusedtodevelopacross-layer protocolthatdynamicallyvariesthetransmissionprobabilityinordertomaximize aggregatesystemthroughput. 5.2SystemModel Weconsiderasysteminwhichradiosaredistributedrandomlyinspace.Consider agroupofradiosthatareuniformlydistributedwithinacircleofradius R .Weseekto evaluatetheaggregatesystemthroughputwhichisdenedastheaveragenumberof packetsreceivedperreceptionslot.Itisalsoassumedthatallthenodespossessthe sametransmitpower.Foratransmitteratadistance d ,thereceivedpowerisgivenby P RX = P TX C 0 a d ; where d 2f 0 ;R g C 0 isthepathlossgainatthereferencedistance d 0 isthepathloss exponentwhichisassumedtobe 2 forthisstudy,and a istheRayleighfadinggain. Fornodesuniformlydistributedwithinacircleofradius R ,theprobabilitydensity functionpdfofanypoint, d ,fromthecenterisgivenby f D d = 2 d R 2 ;d 2f 0 ;R g : 72

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Ifwedeneanewvariable y = 1 d 2 ,wegetthat f Y y = 2 y 2 R 2 ;;d 2f R )]TJ/F26 7.9701 Tf 6.587 0 Td [(2 ; 1g : Also,since a isRayleighdistributedwithpdf f A a = a 2 exp )]TJ/F53 11.9552 Tf 13.889 8.087 Td [(a 2 2 2 ; wegetthattherandomvariable z = ay ,isdistributedaccordingto f Z z = z 2 R 2 r 2 ;z 2f 0 ; 1g : f Z z isthedistributionofthereceivedpower. Forvaryingnumberofusers, k ,wesimulatedthefadingandpathlosseffectsinthe presenceofadditiveGaussiannoise.Welookattwocases:oneforwhichweperform interferencemitigationandoneforwhichwedonot.Wegeneratecorrespondingblock errorratesforbothcasesinasystemthatconsistsof K userscontendingover F =100 frequencybandswithaverage E b =N 0 =24 dB .Selectedvaluesarepresentedin Table5-1. Table5-1.Selectednumberofusersandcorrespondingblockerrorrates. C 0 =0 : 9 R =3 d 0 ProbabilityofBlockError B ek NumberofUsers, k WithInterferenceMitigationWithoutInterferenceMitigation 10.00600.0061 20.00690.0107 40.01000.0225 60.01090.0358 80.01230.0491 200.03450.1576 400.09660.3668 600.19160.5605 800.29860.7002 1000.41870.8156 73

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5.3ThroughputAnalysis Giventheprobabilityofblockerror,wecanderivetheaveragesystemthroughput ofasystemconsistingof N nodes.Weassumethatallthenodesoperateinhalf-duplex mode.Wealsoassumethateachnodehasapacketavailablefortransmission.Inorder words,weoperateundersaturationconditions,inwhichthetransmissionqueueforeach nodeisalwaysassumedtobenon-empty.Weassumethateachnodeinthesystem transmitsinaslotwiththesameprobability p .Itfollowsthatthesystemthroughput, S denedasthenumberofnodesmultipliedbytheprobabilitythatapacketgeneratedby anynode, i ,withinan N -nodenetworkissuccessfullyreceivedbyitsintendedreceiver, j 2 N ,isgivenby S N;p = N N X k =1 N k p k +1 )]TJ/F53 11.9552 Tf 11.955 0 Td [(p N )]TJ/F27 7.9701 Tf 6.586 0 Td [(k +1 )]TJ/F53 11.9552 Tf 11.956 0 Td [(B ek J N;k ; where B ek istheprobabilityofblockerrorgiven k usersinthesystemand J N;k = k X m =1 1 m k m 1 N )]TJ/F53 11.9552 Tf 11.955 0 Td [(k m 1 )]TJ/F15 11.9552 Tf 26.086 8.088 Td [(1 N )]TJ/F53 11.9552 Tf 11.955 0 Td [(k k )]TJ/F27 7.9701 Tf 6.587 0 Td [(m 1 1 )]TJ/F77 11.9552 Tf 11.955 9.684 Td [()]TJ/F15 11.9552 Tf 5.48 -9.684 Td [(1 )]TJ/F26 7.9701 Tf 20.422 4.707 Td [(1 N )]TJ/F27 7.9701 Tf 6.586 0 Td [(k k istheprobabilitythatthereceiverisavailableforreception.Inparticular,itisassumed that,duetotheasynchronousnatureofpackettransmission,if n 2 N userstransmit tothesamereceiverwithinareceptioninterval,thereceiveronlyreceivesfromatmost onetransmitter.Wecomparethethroughputofthemitigationandnomitigationcases asafunctionof p forseveralvaluesof N inFig.5-1,5-2,5-3,5-4,and5-5.Weseethat interferencemitigationresultsinamarkedimprovementinthemaximumachievable throughputacrossallvaluesof N .Table5-3presentsthisimprovementacrossthe valuesof N consideredinthisstudy. 74

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Figure5-1.Throughputasafunctionofthetransmissionprobabilityforanetwork consistingof50users. Figure5-2.Throughputasafunctionofthetransmissionprobabilityforanetwork consistingof100users. 75

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Figure5-3.Throughputasafunctionofthetransmissionprobabilityforanetwork consistingof150users. Table5-2.Comparisonofthemaximumachievablethroughputforbothcases. MaximumAchievableThroughput S max N WithInterferenceMitigationWithoutInterferenceMitigation%Improvement 509.758.5614% 10018.2913.9231% 15025.0117.1546% 20030.2119.2157% 25034.2120.6066% Weseektochoosetheprobabilityoftransmission, p ,ofeachnodeinorderto maximizethesystemthroughput.MaximizingEquation5withrespectto p yields dS N;p dp = N X k =1 N;k p k )]TJ/F53 11.9552 Tf 11.955 0 Td [(p N )]TJ/F27 7.9701 Tf 6.586 0 Td [(k +1 J N;k )]TJ/F27 7.9701 Tf 16.804 14.944 Td [(N X k =1 N;k )]TJ/F53 11.9552 Tf 11.955 0 Td [(p N )]TJ/F27 7.9701 Tf 6.586 0 Td [(k p k +1 J N;k =0 ; where N;k =+ k N k )]TJ/F53 11.9552 Tf 11.955 0 Td [(B ek ; and 76

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Figure5-4.Throughputasafunctionofthetransmissionprobabilityforanetwork consistingof200users. Figure5-5.Throughputasafunctionofthetransmissionprobabilityforanetwork consistingof250users. 77

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N;k = N )]TJ/F53 11.9552 Tf 11.955 0 Td [(k +1 N k )]TJ/F53 11.9552 Tf 11.955 0 Td [(B ek : Thissolutioncanbederivednumerically. Givenanoptimal p ,foragivennetworkscenario,wecanemployasimplebackoff windowsystemwhereeachnodeoperatingindependentlyonitsownclock,randomly waitsforarandomintegerslottime t 2 ;W )]TJ/F15 11.9552 Tf 12.15 0 Td [(1 beforeittransmits.Accordingto[40], thebackoffwindowsize, W ,isgivenby W = 2 p )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 ; roundedtothenearestinteger.Thisguaranteesthatthesystemisoperatingatorclose toitsmaximumachievablethroughput.Theoptimaltransmissionprobability p forthe systembeingconsideredispresentedinFig.5-6. Figure5-6.Optimaltransmissionprobabilityasafunctionofthenumberofusersinthe system. 78

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5.4Cross-LayerProtocol From5,weseethatthederivationoftheoptimaltransmissionprobabilityis dependentonthenumberofusers, N .Thisisinformationthatisnotreadilyavailableat eachnodesincethenetworkmightchangefromtimetotime.However,wecanusethe observedinterferenceactivityateachnodetoderiveanestimateofthenumberofusers inthenetwork.Thisallowsustouseinformationderivedintheinterferencemitigation algorithmtomakedecisionsatthelinklayer. ConsiderthephysicallayersetupconsideredinChapter2.Eachnodetransmits aframetothereceiverover D =10 dwellintervals.Wealsoassumethatthenodes contendover F =100 frequencybands.Nullbitsareplacedontheleftandright sideoftheinformationtransmittedovereachdwellinterval.Duetotheasynchronous natureoftransmission,wehave 2 D observationsoftheinterferenceatthereceiver.We decidethatadwellintervalhasbeeninterferedwithiftheamplitudeobservedatthenull positionsontheleftor/andrightsideexceedsacertainthreshold. Given N a interferers,theprobabilitythatadwellintervalisdetectedtobehitfrom theleftorrightisgivenby Pr detectedhit = p = 1 )]TJ/F77 11.9552 Tf 11.955 16.857 Td [( 1 )]TJ/F15 11.9552 Tf 14.826 8.088 Td [(1 F N a )]TJ/F76 11.9552 Tf -341.483 -36.862 Td [(Here, )-278(= Pr z> .Forthisstudy,thethreshold, =0 : 1 Letusassumethatafter K observations,wehave K 0 K 1 ,and K 2 dwellintervals with 0 1 ,and 2 interferersrespectively.ItfollowsthattheMaximumLogLikelihood estimateof N a isgivenby d dN a p 2 K 2 p )]TJ/F15 11.9552 Tf 11.955 0 Td [(2 p 2 K 1 p 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(2 p +1 K 0 =0 ; whichyields a N a =1 )]TJ/F15 11.9552 Tf 35.915 8.088 Td [(2 K 2 + K 1 2\050 K 0 + K 1 + K 2 : Here, a = )]TJ/F15 11.9552 Tf 5.48 -9.684 Td [(1 )]TJ/F26 7.9701 Tf 14.301 4.707 Td [(1 F 79

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Theestimateofthenumberofactivenodesisgivenby ~ N a = 6 6 6 4 log 1 )]TJ/F26 7.9701 Tf 28.027 4.813 Td [(2 K 2 + K 1 2\050 K 0 + K 1 + K 2 log a +0 : 5 7 7 7 5 : 5.5ResultsandDiscussion InFigs.5-7,5-9,5-11,5-13,and5-15,wepresentresultsthatshowhowthe throughputevolvesaswedynamicallyvarythetransmissionprobabilitybasedonthis informationfordifferentsystemscenarios.Table5-3showsasummaryofhowwell thiscross-layerapproachperformswithregardstoachievingthemaximumsystem throughputineachscenario.Theperformanceoftheschemethatdynamicallyvaries thetransmissionprobabilityachievesathroughputthatiswithin 6 : 6% oftheoptimal valueforallvaluesof N considered. WealsopresentresultsinFigs.5-8,5-10,5-12,5-14,and5-16,thatshowthe evolutionoftheaveragetransmissionprobabilityacrossallthenodesovertime.The horizontallineshowstheoptimaltransmissionprobabilityineachscenario. 80

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Figure5-7.Throughputevolutionovertime, N =50 users. Figure5-8.Evolutionofaveragetransmissionprobabilityovertime, N =50 users. 81

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Figure5-9.Throughputevolutionovertime, N =100 users. Figure5-10.Evolutionofaveragetransmissionprobabilityovertime, N =100 users. 82

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Figure5-11.Throughputevolutionovertime, N =150 users. Figure5-12.Evolutionofaveragetransmissionprobabilityovertime, N =150 users. 83

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Figure5-13.Throughputevolutionovertime, N =200 users. Table5-3.Throughputcomparisontable. N MaximumAchievableThroughput S max SimulationThroughput%Difference 509.759.344.2% 10018.2917.394.9% 15025.0123.585.7% 20030.2128.515.6% 25034.2531.986.6% 5.6Summary Inthissection,weperformedastudythatshowedimprovementsinthroughputasa resultofinterferencemitigationinthephysicallayer.Wealsopresentanewtechnique thatuseslocalinformationaboutinterferenceateachreceivertoestimatethenumber ofusersoperatinginthesystematanyparticulartime.Weshowthatbyusingthis informationtomodifyitstransmissionprobability,wecangetperformancethatisclose tothemaximumachievablethroughput. 84

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Figure5-14.Evolutionofaveragetransmissionprobabilityovertime, N =200 users. Figure5-15.Throughputevolutionovertime, N =250 users. 85

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Figure5-16.Evolutionofaveragetransmissionprobabilityovertime, N =250 users. 86

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CHAPTER6 CONCLUSIONS InthisDissertation,wehavedevelopedtechniquesthatuseiterativepartially coherentdemodulationforsystemsoperatinginchannelswithmultipleaccess interferenceand/orchannelfading.InChapter2,weapplythisapproachtoan interferencemitigationschemeforuseinafrequency-hoppingspread-spectrumsystem thatusesfrequencyshiftkeymodulation.Weshowthatapplyingpartiallycoherent demodulationinaniterativemannercansignicantlyimprovetheperformanceofa systemintermsofblockerrorratesandthemulti-usercapabilityofthesystem.Wehave alsoshownthecalculationofacoherenceparameterthatservesasameasureofthe reliabilityofthechannelestimates. Next,weconsideredinterferencemitigationinasystemthatemploysfrequency hoppingwithcontinuous-phasefrequencyshiftkeying.Interferencemitigationforthis typeofsystempresentsauniquechallengebecausethemodulationisnotmemoryless. Wepresentedaiterativechannelestimationanddemodulationschemethatprovides performancegainsintermsoftheblockerrorratesandmulti-useraccesscapabilityof thesystem. Wehavealsoconsideredtheuseofiterativepartiallycoherentdemodulation inafrequencynon-selectivetimevaryingchannel.Weshowthatthisdemodulation approachisadaptivetochangingchannelconditions.Inparticular,weshowed performanceimprovementsinblockerrorrateswhenthepilotsymbolinsertionrate islowerthantheNyquistrate. Finally,weevaluatedtheeffectoftheseinterferencemitigationschemeson link-layerthroughputforasimpleslottedMACprotocol.Theresultsshowthatinterference mitigationsignicantlyimprovestheaggregatesystemthroughputforthefrequency hoppingsystems.Wehavealsopresentedanovelcross-layerapproachinwhichthe systemthroughputisapproximatelymaximizedbyadaptingeachnode'stransmission 87

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probabilitybasedoninformationitestimatesinthethephysicallayeraboutthenumber ofinterferersitobserveswhileitisinreceptionmode. 88

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BIOGRAPHICALSKETCH OluwatosinA.AdeladanreceivedtheB.S.inElectricalEngineeringdegreefrom theUniversityofAlabamaatBirminghamUABin2007andtheM.S.andPh.D. degreesinelectricalengineeringfromtheUniversityofFloridain2008and2012, respectively.Hiscurrentresearchinterestslieintheareaofcommunicationtheory appliedtoimprovingthemulti-usercapabilitiesofad-hocandsensornetworksaswell ascross-layerapproachestoimprovethroughputperformanceinfadingchannels. 94