Effective Channel Estimation and Efficient Symbol Detection for Multi-Input Multi-Output Underwater Acoustic Communications

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Title:
Effective Channel Estimation and Efficient Symbol Detection for Multi-Input Multi-Output Underwater Acoustic Communications
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english
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Ling,Jun
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University of Florida
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Doctorate ( Ph.D.)
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University of Florida
Degree Disciplines:
Electrical and Computer Engineering
Committee Chair:
Li, Jian
Committee Members:
Sun, Yijun
Lin, Jenshan
Cattafesta III, Louis N

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Subjects / Keywords:
acoustic -- channel -- multi -- symbol
Electrical and Computer Engineering -- Dissertations, Academic -- UF
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Electrical and Computer Engineering thesis, Ph.D.
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Abstract:
Achieving reliable underwater acoustic communications (UAC) has long been recognized as a challenging problem owing to the scarce bandwidth available and the reverberant spread in both time and frequency domains. To pursue high data rates, we consider a multi-input multi-output (MIMO) UAC system, and our focus is placed on two main issues regarding a MIMO UAC system: 1) channel estimation, which involves the design of the training sequences and the development of a reliable channel estimation algorithm, and 2) symbol detection, which requires interference cancelation schemes due to simultaneous transmission from multiple transducers. To enhance channel estimation performance, we present a cyclic approach for designing training sequences with good auto- and cross-correlation properties, and a channel estimation algorithm called the iterative adaptive approach (IAA). Sparse channel estimates can be obtained by combining IAA with the Bayesian information criterion (BIC). Moreover, we present sparse learning via iterative minimization (SLIM) and demonstrate that SLIM gives similar performance to IAA but at a much lower computational cost. Furthermore, an extension of the SLIM algorithm is introduced to estimate the sparse and frequency modulated acoustic channels. The extended algorithm is referred to as generalization of SLIM (GoSLIM). Regarding symbol detection, a linear minimum mean-squared error based detection scheme, called RELAX-BLAST, which is a combination of vertical Bell Labs layered space-time (V-BLAST) algorithm and the cyclic principle of the RELAX algorithm, is presented and it is shown that RELAX-BLAST outperforms V-BLAST. We show that RELAX-BLAST can be implemented efficiently by making use of the conjugate gradient method and diagonalization properties of circulant matrices. This fast implementation approach requires only simple fast Fourier transform operations and facilitates parallel implementations. The effectiveness of the proposed MIMO schemes is verified by both computer simulations and experimental results obtained by analyzing the measurements acquired in multiple in-water experiments.
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Statement of Responsibility:
by Jun Ling.
Thesis:
Thesis (Ph.D.)--University of Florida, 2011.
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Adviser: Li, Jian.

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EFFECTIVECHANNELESTIMATIONANDEFFICIENTSYMBOLDETECTIONFORMULTI-INPUTMULTI-OUTPUTUNDERWATERACOUSTICCOMMUNICATIONSByJUNLINGADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2011

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c2011JunLing 2

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ACKNOWLEDGMENTS Foremost,Iwouldliketorecognizemyadvisor,Dr.JianLioftheElectricalEngineeringDepartment,forherexcellentguidance,whole-hearteddedication,andcontinuousencouragementthroughoutmyPh.D.training.Ifeelextremelyluckytobeinvolvedintheunderwateracousticcommunicationprojectandhaveherasasourceofwisdom,skills,andencourages.Withoutherhelp,thisdissertationwouldnothavebeenpossible.IfurthermoreacknowledgeDr.MagnusNordenvaadofLuleaUniversityoftechnology,whoseconstantassistanceandconstructivecommentsonmyworkhavecertainlymademeintoabetterthinkerandengineer.IalsowouldliketomakespecialreferencetoDr.JamesPreisigofWoodsHoleOceanographicInstitution,forhishelponexperimentaldatacollection.IrecognizemycommitteemembersattheUniversityofFlorida:Dr.YijunSun,Dr.JenshanLin,andDr.LouisN.CattafestaIII.Theirtimeandeffortstowardsmydissertationanddefensehavebeengreatlyappreciated.Last,butnotleast,IthankmyfamilyandmyfriendsintheSpectralAnalysisLaboratory.Theirencouragementhasinspiredmeateverylevelofmygraduatestudies. 3

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 3 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 10 CHAPTER 1INTRODUCTION ................................... 12 1.1ChallengesofUnderwaterAcousticCommunications(UAC) ........ 12 1.2ExistingUACSchemes ............................ 16 1.3DissertationOutline .............................. 19 1.4Notation .................................... 20 2ENHANCEDCHANNELESTIMATIONANDSYMBOLDETECTIONFORHIGHSPEEDMULTI-INPUTMULTI-OUTPUT(MIMO)UAC .............. 26 2.1SystemOutline ................................. 28 2.2ChannelEstimation .............................. 29 2.2.1ProblemFormulation .......................... 29 2.2.1.1Training-directedmode ................... 30 2.2.1.2Decision-directedmode ................... 31 2.2.2TrainingSequenceDesign ....................... 31 2.2.3ChannelEstimationAlgorithm ..................... 33 2.2.3.1Iterativeadaptiveapproach(IAA) .............. 34 2.2.3.2IAAwiththeBayesianinformationcriterion ........ 36 2.2.3.3IAAwithRELAX ....................... 37 2.2.3.4Complexityanalysis ..................... 38 2.3SymbolDetection ................................ 38 2.3.1ProblemFormulation .......................... 38 2.3.2TheLinearMinimumMean-SquaredError(LMMSE)Filter ..... 39 2.3.3DetectionSchemes ........................... 40 2.3.3.1Linearcombinatorialnulling ................. 40 2.3.3.2CLEAN-BLAST ........................ 41 2.3.3.3RELAX-BLAST ........................ 41 2.4NumericalandExperimentalResults ..................... 42 2.4.1Simulations ............................... 42 2.4.1.1Channelestimationperformance .............. 42 2.4.1.2Symboldetectionperformance ............... 43 2.4.2RACE08In-WaterExperimentationResults ............. 44 4

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3ONBAYESIANCHANNELESTIMATIONANDFASTFOURIERTRANSFORMBASEDSYMBOLDETECTIONINMIMOUAC .................. 55 3.1SystemOutline ................................. 56 3.2ChannelEstimation .............................. 57 3.2.1Training-DirectedMode ........................ 57 3.2.2ChannelEstimationAlgorithm .................... 58 3.2.3AutomaticSelectionofChannelTapNumber ............ 61 3.2.4Decision-DirectedMode ........................ 63 3.3SymbolDetection ................................ 63 3.3.1DetectionScheme ........................... 63 3.3.2EfcientLMMSEFiltering ....................... 65 3.4NumericalandExperimentalResults ..................... 68 3.4.1Simulations ............................... 68 3.4.1.1Channelestimation ..................... 68 3.4.1.2Symboldetection ...................... 69 3.4.2SPACE08In-WaterExperimentationResults ............. 70 3.4.2.1Experimentalspecications ................. 70 3.4.2.2Ambientnoiseanalysis ................... 71 3.4.2.3Channellengthselection .................. 72 3.4.2.4Stoppingcriterionfortheconjugategradientmethod ... 72 3.4.2.5Codedbiterrorrateperformance .............. 73 4MIMOUACOVERSPARSEANDFREQUENCYMODULATEDACOUSTICCHANNELS ...................................... 86 4.1ChannelEstimation .............................. 88 4.1.1Training-DirectedMode ........................ 88 4.1.2Decision-DirectedMode ........................ 90 4.1.3ChannelEstimationAlgorithm ..................... 91 4.2SymbolDetection ................................ 93 4.2.1ProblemFormulation .......................... 93 4.2.2PhaseCompensation ......................... 93 4.2.3AlamoutiDiversityScheme ...................... 94 4.3NumericalandExperimentalResults ..................... 97 4.3.1SimulationofChannelEstimationPerformance ........... 97 4.3.2WHOI09In-WaterExperimentationResults ............. 101 4.3.2.1Experimentspecics ..................... 101 4.3.2.2PerformanceoftheAlamouticodingscheme ....... 102 4.3.2.3Performanceoftransmitting2pairsofAlamouticodes .. 105 4.3.3ACOMM10In-WaterExperimentationResults ............ 106 4.3.3.1Experimentspecics ..................... 106 4.3.3.2PerformanceoftheMIMOBLASTscheme ........ 106 5

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5FUTUREWORK ................................... 118 5.1MIMOUAC:AnApplicationPointofView .................. 118 5.1.1DataRate ................................ 118 5.1.2Real-TimeImplementation ....................... 120 5.2MultiuserUACSystems ............................ 121 5.2.1Frequency-DivisionMultipleAccess .................. 122 5.2.2Time-DivisionMultipleAccess ..................... 123 5.2.3Code-DivisionMultipleAccess .................... 124 REFERENCES ....................................... 129 BIOGRAPHICALSKETCH ................................ 137 6

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LISTOFTABLES Table page 1-1Thecomparisonofkeysystemparameters. .................... 14 2-1Iterativeadaptiveapproach(IAA) .......................... 35 2-2IAAwiththeBayesianinformationcriterion. .................... 36 2-3IAAwithRELAX. ................................... 37 2-4Biterrorrate(BER)forL=200. ........................... 46 2-5BERforL=400. ................................... 47 3-1TheconjugategradientmethodforRELAX-BLAST. ................ 67 3-2200mperformanceofusingsparselearningviaiterativeminimization(SLIM). 75 3-31kmperformanceofusingSLIM. .......................... 75 3-460mperformanceofusingSLIM. .......................... 75 3-5200mperformanceofusingleasesquares(LS). ................. 76 3-61kmperformanceofusingLS. ........................... 76 3-760mperformanceofusingLS. ........................... 76 4-1BERperformanceoftheAlamoutidiversityscheme. ............... 104 4-2BERperformanceinsystemsequippedwith1transmitterand2receivers. ... 104 4-3BERperformanceoftransmitting2pairsofAlamouticodes. ........... 105 7

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LISTOFFIGURES Figure page 1-1Anunmannedunderwatervehicle. ......................... 22 1-2TheGulfofMexicooilspill. ............................. 22 1-3Absorptioncoefcientversusfrequency. ...................... 23 1-4Longchannelimpulseresponse(CIR). ....................... 23 1-5Scatteringfunctionsobtainedattwodifferentunderwateracousticconditions. 24 1-6NormalizedCIRevolutionoverapproximatelya1minperiod. .......... 25 2-1Thestructureofasingledatapackage. ...................... 48 2-2AnNMunderwateracousticcommunication(UAC)system. ......... 49 2-3ThemodulusofthesimulatedCIRs. ........................ 50 2-4Meansquarederrors(MSEs)oftheCIRestimates. ................ 51 2-5Thebiterrorrates(BERs)fora412UACsystem. ............... 52 2-6ThemodulusoftheCIRestimates. ......................... 53 2-7Thechanneltrackingprocedure. .......................... 54 3-1Thestructureofasingledatapacket. ....................... 78 3-2AnNMUACsystem. ............................... 78 3-3ThemodulusofthesimulatedCIRs. ........................ 79 3-4MSEsoftheCIRestimates. ............................. 79 3-5ThecodedBERsfora412MIMOsystem. ................... 80 3-6SPACE08meteorologicaldata. ........................... 81 3-7NormalizedCIRevolutionoverapproximatelya1minperiod. .......... 82 3-8Spectralestimationofthereceivedmeasurements. ................ 83 3-9Theplotofn(r)versusthechanneltaps. ..................... 84 3-10TheimpactoftCGontheaveragenumberofiterationsrequiredbytheconjugategradientmethod. ................................... 85 3-11Thechanneltrackingprocedure. .......................... 85 3-12Datapacketstructure. ................................ 85 8

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4-1TheAlamoutidiversityscheme. ........................... 110 4-2ThemodulusofthesimulatedCIRs. ........................ 110 4-3TheMSEsoftheCIRestimatesandtheDopplerfrequencyestimates. ..... 111 4-4EvolutionsoftheCIRs. ................................ 112 4-5EvolutionsoftheestimatedDopplerfrequencies. ................. 112 4-6ThestructureofthetransmittedsymbolsfortheAlamoutischeme. ....... 113 4-7CIRevolutions. .................................... 113 4-8EvolutionsoftheestimatedDopplerfrequencies. ................. 114 4-9Sourceinformationcontainedinthetransmittedpackage. ............ 115 4-10Thestructureofthetransmittedsymbols. ..................... 116 4-11TheimpactofcodedBERonthequalityoftherecoveredmascotimages. ... 117 4-12Recoveredmascotimageusingsparselearningviaiterativeminimization. ... 117 5-18-PSKconstellation. ................................. 126 5-216-QAMconstellation. ................................ 126 5-3Frequency-divisionmultipleaccess. ........................ 127 5-4Time-divisionmultipleaccess. ............................ 127 5-5Code-divisionmultipleaccess. ........................... 128 9

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyEFFECTIVECHANNELESTIMATIONANDEFFICIENTSYMBOLDETECTIONFORMULTI-INPUTMULTI-OUTPUTUNDERWATERACOUSTICCOMMUNICATIONSByJunLingAugust2011Chair:JianLiMajor:ElectricalandComputerEngineering Achievingreliableunderwateracousticcommunications(UAC)haslongbeenrecognizedasachallengingproblemowingtothescarcebandwidthavailableandthereverberantspreadinbothtimeandfrequencydomains.Topursuehighdatarates,weconsideramulti-inputmulti-output(MIMO)UACsystem,andourfocusisplacedontwomainissuesregardingaMIMOUACsystem:1)channelestimation,whichinvolvesthedesignofthetrainingsequencesandthedevelopmentofareliablechannelestimationalgorithm,and2)symboldetection,whichrequiresinterferencecancelationschemesduetosimultaneoustransmissionfrommultipletransducers. Toenhancechannelestimationperformance,wepresentacyclicapproachfordesigningtrainingsequenceswithgoodauto-andcross-correlationproperties,andachannelestimationalgorithmcalledtheiterativeadaptiveapproach(IAA).SparsechannelestimatescanbeobtainedbycombiningIAAwiththeBayesianinformationcriterion(BIC).Moreover,wepresentsparselearningviaiterativeminimization(SLIM)anddemonstratethatSLIMgivessimilarperformancetoIAAbutatamuchlowercomputationalcost.Furthermore,anextensionoftheSLIMalgorithmisintroducedtoestimatethesparseandfrequencymodulatedacousticchannels.TheextendedalgorithmisreferredtoasgeneralizationofSLIM(GoSLIM).Regardingsymboldetection,alinearminimummean-squarederrorbaseddetectionscheme,calledRELAX-BLAST,whichisacombinationofverticalBellLabslayeredspace-time 10

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(V-BLAST)algorithmandthecyclicprincipleoftheRELAXalgorithm,ispresentedanditisshownthatRELAX-BLASToutperformsV-BLAST.WeshowthatRELAX-BLASTcanbeimplementedefcientlybymakinguseoftheconjugategradientmethodanddiagonalizationpropertiesofcirculantmatrices.ThisfastimplementationapproachrequiresonlysimplefastFouriertransformoperationsandfacilitatesparallelimplementations.TheeffectivenessoftheproposedMIMOschemesisveriedbybothcomputersimulationsandexperimentalresultsobtainedbyanalyzingthemeasurementsacquiredinmultiplein-waterexperiments. 11

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CHAPTER1INTRODUCTION Earthisawaterplanet:approximately71%ofitssurfaceiscoveredbywater.Despitecountlessattemptstoexplorethisvastmysteriousunderwaterfrontierthroughouthumanhistory,themajorityoftheoceanbodystillremainsunexplored.Theadvancesoverthelastseveraldecadesinhardwareandcommunicationtechniqueshaveledtoarecentexcitementinunderwateractivities,includingenvironmentalmonitoring,commercialorresearchexploration,andharborprotection.Forthesetasks,preferablesystemsinvolvethedeploymentofunderwatersensorsortheemploymentofunmannedunderwatervehicles(UUVs).(Figure 1-1 showsaUUV.)Asaconsequence,theestablishmentofunderwateracousticcommunications(UAC)iscriticaltoensurereliabledataexchangeamongthesefreeunderwaternodes,whichmakesitpossibletofurthercoordinatethem.Forexample,hadreliableUACtechniquesbeeninuse,UUVswouldhavebeenemployedtocontroltheoilspillintheGulfofMexicoinApril2010(Figure 1-2 ). Sincewaterisnotamediumsuitableforpropagatingelectromagneticwaves,UAChastorelyonacousticwavestotransmitsignals.Incontrasttoradiocommunications,whichhavealreadymadesignicantimpactsuponeverydaylife,thedevelopmentofUACisstillintheresearchstagemainlyduetotheuniquechallengesimposedbytheunderwaterenvironment.FourmajorchallengeswillbeelaboratedinSection 1.1 ,alongwithanexplanationofwhyitisdifculttoachievereliableUAC.Section 1.2 brieyreviewstheexistingUACschemes.Section 1.3 presentstheoutlineofthisdissertation.Section 1.4 liststhenotationsusedthroughoutthisdissertation. 1.1ChallengesofUnderwaterAcousticCommunications(UAC) Tohelpunderstandtheuniquechallengesposedbytheunderwaterenvironment,Table 1-1 contrastskeysystemparametersemployedbythewirelesslocalareanetwork(WLAN)standardforradiocommunications[ 87 ]andseveralrecentlyconducted 12

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in-waterUACexperiments.Theexperimentalspecicsofthefourin-waterUACexperimentsmentioned,namelyRACE08,SPACE08,WHOI09,andACOMM10,willbefurtherelaboratedinthesubsequentchapters,alongwithadetailedsummaryoftheexperimentalresults. Oneofthedeningcharacteristicsofanacousticchannelisthattheabsorptionoftheunderwatermediumincreasesasthesignalfrequencyincreases[ 76 ].TherelationshipbetweenabsorptioncoefcientandfrequencyisshowninFigure 1-3 .Oneobservesthatduetosevereabsorption(orstrongsignalattenuation),theoutputpowerofasignalfrequencymodulatedat180kHzwillreducebyalmost50dBover1kmpropagation.Asaconsequence,thepowerofthereceivedsignalinresponsetothe180kHztransmittedsignalcouldbetooweaktoensurereliableUACatanyreasonabledistance.Tomitigatethepowerabsorption,practicalUACsystemsadoptrelativelylowcarrierfrequencyandlimitedsignalbandwidth,overwhichthefrequencyresponseisrelativelyat[ 76 ].ThisexplainswhythebandwidthandcarrierfrequencyinUACaresosmallcomparedtothoseemployedbyWLAN(Table 1-1 ).Roughlyspeaking,thebandwidthofthetransmittedsignalequalsthesymbolrate.Thelimitedbandwidthavailable,therefore,imposesanupperboundontheattainablesymbolrateinconventionalsingle-inputsystems.Toovercomethisrestriction,throughsimultaneoustransmissionusingmultipletransmitters,multi-inputmulti-output(MIMO)systemsofferincreaseddataratescomparedtotheirsingle-inputcounterparts[ 84 ].AdetailedstudyofMIMOUACsystems,thedesignofthesimultaneouslytransmittedsequenceset,andthedevelopmentofeffectivechannelestimationalgorithmsandefcientsymboldetectionschemes,formsthefocusofthisdissertation. Inashallowwaterenvironment,duetothereectionsfromboththesurfaceandbottom,thetransmittedsignalcanreachthereceivinghydrophoneviadifferentpropagationpathsatdifferentdelays[ 55 ].Figure 1-4A illustratesanacousticchannelcharacterizedbythreemultipaths,namelyadirectpath(orprincipalarrival),asurface 13

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Table1-1. ThecomparisonofkeysystemparametersemployedinUACandWLAN. RACE08SPACE08WHOI09ACOMM10WLAN Averagedelayspreadontheorderof10ms500nsPropagationspeed1500m/s3108m/sBandwidth3.9kHz10kHz8kHz4kHz20MHzCarrierfrequency12kHz13kHz30kHz20kHz5.2GHzCoherencetime(insymbols)103105 14

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reection,andabottomreection.Theempiricalunderwaterchannel,ofcourse,ismuchmorecomplexthanthissimplemodelbyallowingformorereectioncombinations,includingsurface-bottomreection,bottom-surfacereection,andsoon[ 55 ].Multipathpropagation,coupledwiththerelativelylowvelocityofacousticwavescomparedtoelectromagneticwaves,leadstoalargespreadindelay,asshowninTable 1-1 .Thedifferenceinthepropagationtimebetweentheearliestandlatestarrivals(countingthepathswithsignicantpowersonly)couldspantenstohundredsofsymbolperiods,whichtranslatesintolongchannelimpulseresponse(CIR)andsevereinter-symbolinterference(ISI)atthereceiverside.AtypicalCIRestimatedinanempiricalunderwaterenvironmentisshowninFigure 1-4B ,where80channeltapsareconsidered.BesidestheISI,MIMOtransmissionfurtherintroducessevereinterferencefromallothertransmitters,whichsignicantlycomplicatesthestructureofthereceiverandmakesdifculttheextractionofthedesiredsymbolsfromanygiventransmitter. Acousticchannelsarewellknownasdoublespreadingchannels.Thatis,besidesthespreadinginthetimedomain(i.e.,thelongdelayspread,aspreviouslyremarked),theacousticchannelalsospreadsinthefrequencydomain,notably,theDopplereffects[ 6 55 ].ThepresenceoftheDopplereffects,owingtotherelativemotionsbetweenthetransmittersandreceiverplatformsandthedynamicunderwatermedium,inducesafrequency-dependentphaseshifttothetransmittedsymbolsorevensignalscaling(i.e.,signalcompressingorstretching).ADoppler-inducedphaseshiftorsignalscalingimpairsthereliabilityofUAC,especiallyinthecaseofaphase-coherentdetectionscheme.Apreferabletoolforcharacterizingadoublespreadingchannelisthescatteringfunction,whichdecouplestheacousticchannelintoabankofpathsthatexperiencedifferentdelaysandDopplerfrequencies[ 43 ].Figure 1-5 showstwoscatteringfunctionsobtainedintwodifferentseaconditions.Figure 1-5A showsthatbelowfrozensurfaceoftheArcticOcean,boththedirectpathat5msdelayandthesurfacereectionat10msdelayarecenteredat0Hz.Thisobservationsuggeststhattheunderlyingacoustic 15

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channelsuffersfromnegligibleDopplerspreading,andtherefore,thechannelcanbereasonablymodeledasanISIchannel(i.e.,spreadingindelayonly).Incontrast,intheBahamasonawindyday,Figure 1-5B demonstratesthatboththedirectpathandthesurfacereectionexperiencesignicantDopplershifts.Mostnotably,thespanoftheDopplerfrequencyexperiencedbythesurfacereectionsexceeds10Hz.Inthisscenario,theDopplerspreadingcannotbeignored,andtheunderlyingchannelisindeeddoublespreading. Ontopofthescarcebandwidthavailableanddoublespreading,theunderwateracousticchannelisalsotime-varyinginnature.ByliningupaseriesofCIRsestimatedataregularperiod(every38.4msinthisexample),Figure 1-6 showstheevolutionofthenormalizedCIRoverapproximatelyaone-minuteperiod.TheCIRestimateatthe0sreferencetimeisshowninFigure 1-4B .OneobservesfromFigure 1-6 thatthechanneltaps,especiallythosecorrespondingtosurface-interactivepathsafter5msdelay,experiencesignicantvariationsovertime.Comparedtoradiofrequencywirelesscommunications,thehighlytime-varyingnatureoftheacousticenvironmentpermitsarelativelyshortcoherencetimewithrespecttothesymbolperiod(Table 1-1 ),duringwhichthechannelcanbereasonablyassumedtobestationary[ 98 ].Thisisreferredtoastheblock-fadingassumptioninthecommunicationsregime[ 7 ].(Actually,theblock-fadingmodelassumesablock-wiseindependentchannel,whileinanempiricalacousticenvironmentthechannelsbetweensuccessiveblockscouldbecorrelated.Inparticular,theeffectivenessofsingle-carrierUACreliesheavilyonsuchcorrelations,aswewillshowinthisdissertation.) 1.2ExistingUACSchemes Datingbacktothe1970s,earlyresearchattemptsemployedanalogsystems,essentiallysophisticatedloudspeakers,toexploretheapplicabilityofUAC.ThesepreliminaryUACsystemswereawkward,andtheresultingperformancewaseasilyaffectedbytheunderwaterconditions.Bytakingadvantageofdigitalmodulation 16

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overanalogmodulation(suchaspowerfulerrorcorrectiontechniquesandresistancetochannelimpairments),thenextgenerationofUACsystems,featuringdigitalcommunicationtechniques,gainedpopularityinthelate1980s.Backthen,withlimitedhardwareperformanceandinadequateknowledgeaboutaccurateacousticchannelmodeling,researchersbelievedthatcoherentUAC,suchasphase-shiftkeying(PSK)[ 57 ],waspracticallyunfeasibleowingtothemajorchallengesimposedbytheacousticenvironment(Section 1.1 ).Asaconsequence,incoherentstrategies,suchasfrequency-shiftkeying(FSK)[ 57 ],drewalotofinterestinstead[ 4 20 ].Althoughimmunetodoublespreading,FSKisnotadesirablemodulationschemefromaspectrumefciencypointofview:atanytime,onlyasmallportionoftheavailablebandwidthisused,leadingtoadataratelowerthanthatwhichwouldbeachievedbyothersystemsmakingfulluseoftheavailablebandwidth.Itwasnotuntiltheemploymentofthephaselockedloop(PLL)methodology[ 3 29 ]inunderwaterapplicationsthatphase-coherentUWAcommunicationsbecamepossible[ 14 15 74 ]. WhilePLLisgenerallysuccessfulinmitigatingtheeffectsofDopplerspreading,thedelayspreadcanbeaccountedforbyeitherthedecisionfeedbackequalizer(DFE)[ 56 73 ]orthepassive-phaseconjugate(PPC)[ 13 ]methods.AdetailedtreatmentalongsidewithperformancecomparisonsofDFEandPPCispresentedbyYang[ 94 95 ].InpracticalUWAsystems,thecouplingofDFEandPLLhasfoundgreatsuccess[ 73 74 ]andalmostbecameastandard[ 31 ].Inpractice,theltercoefcientsinvolvedinDFEareupdatedbyadaptiveapproachessuchasthewell-knownrecursiveleastsquares(RLS)ortheleastmeansquare(LMS)algorithms[ 19 30 74 ].TheprinciplebehindPPCismatchedltering:whenCIRisconvolvedwithitstime-reversedandconjugatedversionateachreceiverandaddedup,thesummationapproachesadeltafunction[ 96 ].Thiscompensatesforthechanneleffectsinthereceivedsignal.Obviously,theperformanceofsuchanapproachreliesheavilyontheaccuracyoftheCIRestimate,especiallywhenonlyfewreceiversexist.Takingonestepfurtherbeyond 17

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theclassiccouplingofDFEwithPLL,YangpresentsahybridstructurecombiningtheadvantageofPPCwithasinglechannelDFE[ 97 ],andintroducesaDopplershiftremovalmodulebeforefeedingthesignalstotheDFE[ 99 ]. Aspreviouslyremarked,theemploymentofMIMOschemesisleveragedbytheneedforachievinghigherdataratesinUAC.Thepricewehavetopayisthatsevereinterferencefromallothertransmittersmustbemitigatedwhiledetectingthesignalfromanygiventransmitter[ 84 ].Asaconsequence,accuratechannelestimationandsymboldetectiontechniques,thatareabletoovercomethechallengesoftheunderwaterenvironmentaswellasthedestructiveinterferences,arerequired.DuetoitsimportanceinincreasingdataratesinUACsystems,severalapproacheshavebeenproposedintheliterature.Theminimummean-squarederror(MMSE)basedlinearcombinatorialnulling(LCN)[ 11 ]detectionschemewasconsideredin[ 66 ].AMIMOreceptionschemeusingtwolayersofequalizationwaspresentedin[ 23 ]andcomparedwiththeMIMOdecisionfeedbackequalizer(MIMO-DFE)[ 72 ].Amajordrawbackoftheequalizerstructuresuggestedin[ 23 ]isitscomputationalcomplexity.Aspatialmodulationscheme,whichassumesthataccuratechannelestimatesarereadilyavailableatthetransmitterside,waspresentedin[ 32 ].Inmostunderwaterenvironments,suchaschemeisthoughdifculttoimplementprimarilysincethechannelcharacteristicsvarytoorapidlytoallowforfeedbackinformation.Whenchannelcoding[ 57 ]isused,iterativeequalizationtechniques,forinstance,Turboequalization[ 12 ],canbeusedtoachievegoodperformancebyexchangingsoftinformationbetweenequalizersanddecoders[ 53 59 ].However,iterativeequalizationtechniquesalsosufferfromhighcomputationalcomplexity.Asanalternativetotheaforementionedtimedomainprocessingmethods,[ 36 ]presentsafrequencydomainorthogonalfrequency-divisionmultiplexing(OFDM)approachforMIMOUACpurposes.OFDMsystemsare,however,generallynotpreferablefromanamplierefciencypointofviewduetohighpeak-to-average-powerratio[ 51 ]andunimodular(unitmodulus)sequences 18

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arefavoredinstead.Furthermore,thehighlytime-varyingnatureoftheUACchannelposesinter-channelinterferenceissuesinmulti-carrierapproaches. Thisdissertationfocusesonsingle-carriertransmissionscheme.WeprovidethoroughinvestigationofaMIMOUACsystembyprovidingadetailedtreatmentofeverystepinvolvedfromdatatransmissionatthetransmittertosymboldetectionatthereceiver.Thisisdonebypresentingapproachesfordesigningwell-structuredtrainingsequenceset,effectivechannelestimationmethodsandefcientdetectionschemes.BothsimulationandexperimentalresultsvalidatetheutilityoftheproposedoverallschemeforMIMOUAC. 1.3DissertationOutline InChapter 2 ,twokeyissuesregardingthedesignofaMIMOUACsystem,namelychannelestimationandsymboldetection,areaddressed.Toenhancechannelestimationperformance,acyclicapproachfordesigningtrainingsequencesetandachannelestimationalgorithmcalledtheiterativeadaptiveapproach(IAA)arepresented.SparsechannelestimatescanbeobtainedbycombiningIAAwiththeBayesianinformationcriterion(BIC).Moreover,theRELAXalgorithmcanbeusedtoimprovetheIAAwithBICestimatesfurther.Regardingsymboldetection,alinearMMSEbaseddetectionscheme,calledRELAX-BLAST,whichisacombinationofverticalBellLabslayeredspace-time(V-BLAST)algorithmandthecyclicprincipleoftheRELAXalgorithm,ispresentedanditisshownthatRELAX-BLASToutperformsV-BLAST.BothsimulatedandRACE08experimentalresultsareprovidedtovalidatetheproposedMIMOscheme. Chapter 3 addressestheoverallefciencyoftheMIMOUACreceptionschemes.Specically,anefcientuserparameterfreeBayesianapproach,referredtoassparselearningviaiterativeminimization(SLIM),ispresented.SLIMprovidesgoodchannelestimationperformancealongwithreducedcomputationalcomplexitycomparedtoIAA.Moreover,RELAX-BLASTisimplementedefcientlybymakinguseofthe 19

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conjugategradientmethodanddiagonalizationpropertiesofcirculantmatrices.TheproposedalgorithmrequiresonlysimplefastFouriertransformoperationsandfacilitatesparallelimplementations.SPACE08experimentalresultsshowthattheproposedMIMOUACschemescanenjoyalmosterror-freeperformanceevenundersevereoceanenvironments. TheMIMOUACschemespresentedinChapters 2 and 3 aredevelopedforISIacousticchannels,i.e.,theunderlyingchannelsareassumedtospreadinthetimedomainbutnotinthefrequencydomain(Section 1.1 ).InChapter 4 ,weincorporateDopplereffectsbydealingwithMIMOUACoversparseacousticchannelssufferingfrombothISIandfrequencymodulations,e.g.,motion-inducedDopplershifts.AnextensionofSLIMispresentedtoestimatethesparseandfrequencymodulatedacousticchannels.TheextendedalgorithmisreferredtoasgeneralizationofSLIM(GoSLIM).Moreover,Chapter 4 considerschannelequalizationandsymboldetectionforvariousMIMOtransmissionschemes,includingbothspace-timeblockcodingandspatialmultiplexing,underthechallengingchannelconditions.Theeffectivenessoftheproposedapproachesisdemonstratedusingin-waterexperimentalmeasurementsrecentlyacquiredduringWHOI09andACOMM10experiments. Chapter 5 elaboratesthefuturework.Inthischapter,ourfocusisshiftedfromresearchideadevelopmenttoconcretesystemimplementationbycriticizingtheexistingMIMOUACschemesfromanapplicationpointofview.Moreover,wealsoprovideavisionforthefutureofUACbydiscussingthepossibilitiesandchallengesofemployingmultiusertechniquesintheunderwaterenvironments. 1.4Notation Wehereinlistthemathematicalnotationusedthroughoutthisdissertation.kk2denotestheEuclideannormofavector,jjjjFdenotestheFrobeniusmatrixnorm,andjjisthemodulus.()isthecomplexconjugateofascalar,()Tand()Hdenotethetransposeandconjugatetranspose,respectively,ofamatrixorvector.E()denotesthe 20

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expectedvalue,Idenotestheidentitymatrixofappropriatedimensionand^xdenotestheestimateofx.diag(v)representsadiagonalmatrixinwhichtheelementsofvareonthediagonal.TheithcolumnofamatrixXiswrittenasxi.Re()representstherealcomponentofacomplex-valuedvectorofmatrix.Othermathematicalsymbolsaredenedaftertheirrstappearance. 21

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Figure1-1. Anunmannedunderwatervehicle(UUV).CopyrightimagecourtesyofWoodsHoleOceanographicInstitution. A B Figure1-2. A)TheburningDeepwaterHorizonoilplatformafteramassiveexplosionintheGulfofMexicoonApril20,2010.B)TheGulfofMexicoonMay6,2010.CopyrightimagescourtesyoftheNewYorkTimes. 22

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Figure1-3. Absorptioncoefcientversusfrequency.Copyrightimagecourtesyof[ 76 ]. A B Figure1-4. A)Anunderwateracousticchannelwith3multipaths.B)Apracticalchannelimpulseresponse(CIR)with80channeltaps. 23

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A B Figure1-5. Scatteringfunctionsobtainedattwodifferentunderwateracousticconditions.A)Arcticenvironmentwithfrozenseasurface.B)BahamaIslandsonawindyday.Thecontoursarein3-dBincrements.Copyrightimagecourtesyof[ 32 ]. 24

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Figure1-6. NormalizedCIRevolutionoverapproximatelya1minperiod. 25

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CHAPTER2ENHANCEDCHANNELESTIMATIONANDSYMBOLDETECTIONFORHIGHSPEEDMULTI-INPUTMULTI-OUTPUTUAC ThischapterfocusesonthevariousaspectsofusingaMIMOacousticcommunicationssysteminanunderwaterenvironmentwheredelayspreadispresent.Theproblemwasdividedintotwomainparts:i)channelestimation,whichinvolvesthedesignofthetrainingsequencesandthedesignofthealgorithmtoestimatethechannelcoefcientsusingthetrainingsequencesorpreviouslydetectedsymbolsandii)symboldetection.Ingeneral,theveryrsttaskofthereceiveristoconductatraining-directedchannelestimation[ 43 74 ].Toachievegoodperformance,bothwell-structuredtrainingsequencesandasignalprocessingmethodologythatcanestimatetheCIRaccuratelyusingthedesignedtrainingsequencesarerequired.Inaddition,toaddressthetime-varyingnatureoftheunderwateracousticchannel,thedecision-directedchannelestimationisperformedregularlyusingthedetectedsymbols[ 43 74 ].Therefore,thechannelestimationalgorithmshouldbeabletoworkwellbothintraining-anddecision-directedmodes. ForpracticalISIchannelsencounteredinUAC,sequenceswithgoodauto-andcross-correlationpropertiesinsteadarerequired[ 90 93 ].Earlyresearchhasfocusedonbinarytrainingsequences[ 16 93 ]duetopracticalconcernsandsimplicity.Lateron,theuseofpolyphasetrainingsequenceswasproposed,wherethepossiblephasevalueswereconnedtoapredenedniteset[ 90 ].Itisobviouslyadvantageoustoallowthephasevaluestobecontinuous.Thecyclicapproach(CA)presentedbyLiet.al.[ 40 41 ]forprobingsequencedesignenjoyssuperiorperformanceovertheaforementionedmethodsbyallowingcontinuousphasevalueswhilestillbeingcomputationallytractable.ThetrainingsequencesdesignedusingtheCAmethodologypossessgoodauto-andcross-correlationpropertiesasdesiredforMIMOchannelestimationincommunications[ 40 41 ]. 26

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ThesecondphaseofchannelestimationinvolvesthedesignofthealgorithmthatwillestimatetheCIRusingthetrainingsequences(orthepreviouslydetectedsymbols)andthereceivedmeasurements.Toaddressthesparsityoftheacousticchannel[ 5 33 73 75 ],threeimportantsparsitybasedtechniqueshavebeenusedforunderwaterchannelestimation,namelythematchingpursuit(MP)algorithm,theorthogonalMP(OMP)algorithm[ 52 ],andtheleastsquaresMPalgorithm(LSMP)[ 8 10 42 43 50 52 ].Thesemethods,however,involveuserparameterthatisdifculttodetermine,andtheirperformancemightdegradesignicantlydependingonthestructureofthematrixrelatingtheunknownstothemeasurements.Toaddresstheseproblems,wepresentauserparameter-freenonparametriciterativeadaptiveapproach(IAA)[ 100 ]forestimatingtheCIRaccuratelyevenwhenthetrainingsequencesarearbitraryandshortinlength.ThedominantchanneltapestimatesofIAAcanbeusedinaBayesianinformationcriterion(BIC)[ 63 70 ]todecidewhichtapstoretainandwhichonestodiscard.Thiscombinedmethod,calledIAAwithBIC,resultsinsparsechannelestimates.Furtherimprovementsinperformancecanbeachievedbyinitializingthelaststepofthecyclicandrelaxation-basedRELAX[ 38 39 ]algorithmviatheIAAwithBICsparseestimates. FollowingtheestimationoftheCIRisthedesignofthedetectionschemeforextractingthepayloadsymbolsfromthemeasurements.Weusealinearminimummean-squarederror(LMMSE)basedlterforsignaldetection.TwoimportantmethodsforapplyingtheLMMSEltercoefcientstothemeasurementsarethelinearcombinatorialnulling[ 11 ]andverticalBellLabsLayeredSpace-Time(V-BLAST)algorithms[ 92 ].Itisinterestingtonotethatthesetwoapproachesresembletheclassicalperiodogram[ 69 88 ]andtheCLEAN[ 27 ]methodsusedinspectralestimationapplications.BeinginspiredfromtheimprovementsofRELAXovertheperiodogramandCLEAN[ 69 ],weproposetheRELAX-BLASTdetectionalgorithm,whichisacombinationofV-BLAST 27

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andthecyclicprincipleofRELAXasthenamesuggests,andshowthatitoutperformsV-BLAST. Therestofthischapterisorganizedasfollows.Section 2.1 outlinesthesystemcongurationanddescribesthedatapackagestructure.Section 2.2 formulatestheproblemofCIRestimation,describestheCAmethodfortrainingsequencedesignandpresentstheIAAalgorithmtogetherwiththeBICandRELAXextensions.Next,thesymboldetectionproblemisanalyzedinSection 2.3 andtheLMMSEbasedRELAX-BLASTdetectionschemeisproposed.BothsimulatedandexperimentalresultsarepresentedinSection 2.4 .Theseadatawasgatheredintherescheduledacousticcommunicationsexperiment(RACE08),whichwasconductedbytheWoodsHoleOceanographicInstitution(WHOI)inNarragansettBay. 2.1SystemOutline ConsideranNMMIMOUACsystemequippedwithNtransmittransducersandMreceivetransducers.Theindividualdatastreamsofeachtransmitteraresymbolalignedandaresentsimultaneously.ThedatastreamsofeachtransmitterconsistofsuccessivedatapackagesoftheformshowninFigure 2-1 .ThedatapackagesstartwithatrainingsequenceoflengthPwhichisfollowedbyasilentgap,thepayloadsequenceandanothersilentgap.Duringthegapintervals,nosignalistransmittedinordertopreventtheinner-packageISI(Gap1)betweenthetrainingandpayloadsymbolsandtheinter-packageISI(Gap2)betweentwoconsecutivepackages.Thepayloadsequence,whichhaslengthQ(Q>Pingeneral),istheestimationtargetandeachpayloadsymbolisdrawnfromaquadraturePSK(QPSK)constellationmodulatedwithGraycode[ 57 ].ThefourconstellationpointsoftheQPSKsymbols,i.e.,fej(2n)]TJ /F9 7.97 Tf 6.59 0 Td[(1) 4g4n=1,lieontheunitcircle.Suchaconstellationisdesirableinpracticeduetoitsunitmodulus.Thesamepracticalconstraintsrequirethetrainingsymbolstohaveunitmodulusaswellbutnorestrictionisimposedontheirphasevalues. 28

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Inwhatfollows,ourconsiderationisalwaysconnedtoonedatapackageoftheformgiveninFigure 2-1 .Letxn(t)denotethetthsymbolinthepackagesentbythenthtransmitterandletym(t)denotethetthsymbolinthepackagereceivedbythemthreceiver,wheren=1,...,N,m=1,...,M,t=1,...,T,andTisthetotalsymbollengthofasingletransmittedpackage.Wedonotgointothedetailsofthesamplingandsynchronizationproceduresandassumethatsuchoperationshavealreadybeenemployedandthesampledcomplexbasebandsignalsareavailableatthereceiver. Figure 2-2 showstheNMMIMOsystemstructurethatwewillusethroughoutthechapter.Thesourcebitsareencoded,QPSKmodulated,interleavedanddemultiplexedfortransmissionfrommultipletransducers.Arandominterleaverisusedinordertoavoidbursterrors,whichoccurwhenthechannelbehavesbadlyatcertainintervalsoftime[ 57 ].Afterthesignalshavebeenreceivedbythereceivearray,theprocessingconsistsoftwosteps:estimatingtheCIR(intraining-ordecision-directedmode)anddetectingthesymbolsbyusingtheestimatedCIR.Oncethesymbolshavebeendetected,theyaremultiplexed,deinterleavedandthenfedintoaViterbidecodertorecoverthesourcebits.Wenowdiscussthechannelestimationproblem. 2.2ChannelEstimation 2.2.1ProblemFormulation Inthetraining-directedmode,aninitialCIRestimateisobtainedbyusingthetrainingsequencessentatthebeginningofeachpackagewhereasinthedecision-directedmode,thepreviouslydetectedsymbolsareusedtoupdatethemostrecentCIRestimate.Howfrequentlythechannelestimatehastobeupdateddependsonthechannelcharacteristics.Foranonstationarychannel(relativetothetotallengthoftherstgapandthepayloadsequence),theCIRhastobeupdatedfrequentlywhereasforastationarychannel,theinitialCIRestimatemightyieldsufcientperformancefordetectingtheentirepayloadsequence. 29

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2.2.1.1Training-directedmode Themeasurementvectoratthemthreceivercanbewrittenas: ym=NXn=1~Xnhn,m+em(2) form=1,...,M,where ym=[ym(1),...,ym(P+R)]TJ /F4 11.955 Tf 11.96 0 Td[(1)]T, (2) hn,m=[hn,m(1),...,hn,m(R)]T, (2) Thevectorhn,mheredenotestheCIRbetweenthenthtransmitterandthemthreceiveranditcontainsRchanneltaps, ~Xn=266666666664xn(1)...0......xn(P)xn(1)......0...xn(P)377777777775, (2) where~Xn2C(P+R)]TJ /F9 7.97 Tf 6.58 0 Td[(1)Rcontainsthenthtrainingsequenceandhenceisknown,andemisadditivenoise(thermalorhardwarerelatednoise)atthemthreceiver.( 2 )canberewrittenas: ym=Xhm+em,(2) whereX=[~X1~XN]andhm=[hT1,mhTN,m]T.Thetraining-directedchannelestimationproblemthenreducestoestimatinghmfromthemeasurementsymandknownX.Itisassumedthatthechannelisstationaryoverthelengthofym.InordertoestimateallthechannelsfortheNMMIMOsystem,( 2 )hastobesolvedform=1,...,M,i.e.,Mtimes.NotethatXdoesnotdependonm. 30

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2.2.1.2Decision-directedmode Theprobleminthedecision-directedmodeisverysimilartothatofthetraining-directedmodeexceptthatnowthetrainingsymbolsarereplacedwiththepreviouslyestimatedpayloadsymbols.Accordingly,( 2 )and( 2 )canstillbeused,where ym=[ym(ti),...,ym(tf)]T,m=1,...,M,(2) containsthemeasurementsatthemthreceiverbelongtothetimeindexinterval[ti,tf],and ~Xn=266666664^xn(ti)^xn(ti)]TJ /F4 11.955 Tf 11.95 0 Td[(1)...^xn(ti)]TJ /F3 11.955 Tf 11.95 0 Td[(R+1)^xn(ti+1)^xn(ti)...^xn(ti)]TJ /F3 11.955 Tf 11.95 0 Td[(R+2).........^xn(tf)^xn(tf)]TJ /F4 11.955 Tf 11.95 0 Td[(1)...^xn(tf)]TJ /F3 11.955 Tf 11.96 0 Td[(R+1)377777775,n=1,...,N,(2) where^xn(ti)]TJ /F3 11.955 Tf 12.71 0 Td[(R+1)and^xn(tf)representtherstandthelastpreviouslyestimatedsymbols(someofthemcouldbetheknowntrainingsymbols),respectively,usedforupdatingthechannel.(Fornotationalsimplicity,~Xnisusedin( 2 )and( 2 )torepresenttwosimilarbutdifferentquantities,whichshouldbeclearfromthecontext.)Thedecision-directedchannelestimationproblemreducestoestimatinghmfromthemeasurementsymandthepreviouslydecodedsymbolsinX.Ontheonehand,itwouldbebenecialtokeepL,tf)]TJ /F3 11.955 Tf 12.16 0 Td[(ti+1(i.e.,thenumberofrowsof~Xn)largeforestimatingthechannelmoreaccuratelybutontheotherhand,forarapidlyvaryingchannel,Lmustbekeptsmallsothatthestationarityassumptionofthechanneloverthelengthofymholdsandsothatthechannelcanbeupdatedmorefrequently.Therefore,Lisatrade-offparameterwhichshouldbesetaccordingtotheexperimentalconditions. 2.2.2TrainingSequenceDesign Weusethealgorithmpresentedin[ 40 41 ]fordesigningtrainingsequencessuchthatXin( 2 )facilitatestheestimationoftheCIR.Itisdesirabletohavetrainingsymbolswithconstantmodulus,i.e.,thetrainingsymbolsshouldhavethefollowing 31

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genericform: xn(t)=ejn(t),t=1,...,P,n=1,...,N,(2) wheren(t)2[0,2)representsthephaseofthetthtrainingsymbolsentbythenthtransmitter.Ideally,ifXHX=PI(calledthepairwiseorthogonalityprinciple),thenthechannelestimatescanberecoveredperfectlybymatchedlteringinthenoiselesscase.However,pairwiseorthogonalityishardlyachievable,ifnotimpossible,inpractice[ 41 ].Instead,=kXHX)]TJ /F3 11.955 Tf 11.95 0 Td[(PIk2Fcanbemadesmall. LetUbeanarbitrarysemi-unitarymatrix(i.e.,UUH=I).Then, =kXHX)]TJ /F4 11.955 Tf 11.95 0 Td[((p PU)(p PUH)jj2F.(2) Minimizingcanthenbeformulatedinthefollowingrelated(butnotequivalent)way[ 41 ]: fn(t)g=argminfn(t)g,UHkX)]TJ 11.96 10.77 Td[(p PUHk2F,s.t.UUH=I.(2) ThisoptimizationproblemcanbesolvedefcientlybyusingtheCAmethod[ 41 81 ]whichguaranteesthatthecostfunctiondoesnotincreaseastheiterationsproceed.IntheCAmethod,Uisassumedgivenwhenestimatingfn(t)gandviceversa.Thisway,theoptimizationproblemissolvediterativelybydividingitintosimplersub-problems.WhenUHisxed,thesolutionto( 2 )hasthegenericform: =arg RXr=1zr!.(2) wherefzrgRr=1aregivennumbers.Forexample,whentheupdatetargetis1(1),zrrepresentsthe(r,r)thdiagonalentryofp PUH.Giventhephasesn(t),thesolutionto( 2 )isgivenbyUH=U~UH[ 28 41 ],where p PX=U)]TJ /F4 11.955 Tf 17.51 2.65 Td[(~UH(2) isthesingularvaluedecomposition(SVD)ofp PX(Uand~UHareunitarymatricesand)]TJ /F1 11.955 Tf -460.46 -23.91 Td[(isadiagonalmatrixwiththesingularvaluesofp PXonitsdiagonal). 32

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TheCAalgorithmisterminatedwhenthedifferenceofthecostfunction(denedin( 2 ))betweentwosucessiveiterationsdropsbelowacertainthreshold.FortheCAalgorithmtoshowgoodperformance,itisrecommendedthatPRandNR
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2.2.3.1Iterativeadaptiveapproach(IAA) Manyexistingweightedleastsquares(WLS)basedchannelestimationmethodologiesrequirethetuningofoneormoreuserparametersandtheirassumptionsontheCIRareingeneralnotvalidintheunderwaterscenario[ 34 83 ].Toaccountfortheseproblems,wepresentauserparameter-freeiterativeWLSbasedchannelestimationtechnique,calledIAA[ 100 ].IAAisanadaptiveandnonparametricalgorithm,anditdoesnotmakeanyexplicitassumptionsontheCIR.LetPbeanNRNRdiagonalmatrixwhosediagonalcontainsthesquaredabsolutevalueofeachchanneltap,i.e., Pr=jhrj2,r=1,...,NR.(2) wherePristherthdiagonalelementofPandhristherthelementofh.Thecovariancematrixofthenoiseandinterferencewithrespecttothetapofcurrentinteresthrcanbeexpressedas: Q(r)=R)]TJ /F3 11.955 Tf 11.96 0 Td[(PrxrxHr,(2) whereR,XPXH.Then,theWLScostfunctionisgivenby[ 37 67 69 ]: (y)]TJ /F3 11.955 Tf 11.95 0 Td[(hrxr)HQ)]TJ /F9 7.97 Tf 6.59 0 Td[(1(r)(y)]TJ /F3 11.955 Tf 11.96 0 Td[(hrxr).(2) Minimizing( 2 )withrespecttohryields ^hr=xHrQ)]TJ /F9 7.97 Tf 6.59 0 Td[(1(r)y xHrQ)]TJ /F9 7.97 Tf 6.59 0 Td[(1(r)xr.(2) Using( 2 )andthematrixinversionlemma,( 2 )canbewrittenas ^hr=xHrR)]TJ /F9 7.97 Tf 6.59 0 Td[(1y xHrR)]TJ /F9 7.97 Tf 6.58 0 Td[(1xr.(2) ThisavoidsthecomputationofQ)]TJ /F9 7.97 Tf 6.58 0 Td[(1(r)forNRtimesandonlyonematrixinversionisneededperiteration.IAAforchannelestimationissummarizedinTable 2-1 .SinceIAArequiresR,whichitselfdependsontheunknownchanneltaps,ithastobeimplementedasaniterativeapproach.Theinitializationisdonebyastandardmatched 34

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Table2-1. Iterativeadaptiveapproach(IAA) Pr=jxHryj2 (xHrxr)2,r=1,2,...,NRrepeatR=XPXH^hr=xHrR)]TJ /F16 5.978 Tf 5.75 0 Td[(1y xHrR)]TJ /F16 5.978 Tf 5.75 0 Td[(1xr,r=1,2,...,NRPr=j^hrj2,r=1,2,...,NRuntil(convergence) lter.OurempiricalexperienceisthatIAAdoesnotprovidesignicantimprovementsinperformanceafterabout15iterations.InIAA,PandhenceRareobtainedfromthechannelestimatesofthepreviousiterationandnotfromthemeasurementsyasdoneinconventionaladaptivelteringalgorithms. IfthecomputationofRbecomesproblematicduetonumericalill-conditioningduringtheiterations,aregularizationapproachcanbeused.IAAcanberegularizedbyconsideringanadditionalnoisetermseparatelyfromtheinterferencetermsintheexpressionforR: R=XPXH+,(2) whereisadiagonalmatrixwithunknownnoisepowersf2mgdym=1onitsdiagonal.IAAisthenimplementedinthesamewayasbeforeexceptthatnowthereareNR+dyratherthanNRunknowns.Consequently,f2mgcanbeestimatedby ^2m=jiHmR)]TJ /F9 7.97 Tf 6.59 0 Td[(1yj2 (iHmR)]TJ /F9 7.97 Tf 6.59 0 Td[(1im)2,m=1,...,dy,(2) ateachiteration,whereimisthemthcolumnofthedydyidentitymatrix.Sincethediagonalloadinglevelsarecalculatedautomatically,theapproachconservesthepracticalityofIAA.Settingf^mgdym=1tozerogivestheoriginalIAAalgorithm.canbeinitializedasallzeros. 35

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Table2-2. IAAwiththeBayesianinformationcriterion. P=f1,...,NRgI=f;g;=1;quit=0;BICold=1repeat~i=argmini2PIBICi()ifBIC~i()
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Table2-3. IAAwithRELAX. I:IndicesofthetapsselectedbyIAAwithBICK=jIj,i.e.,thenumberofselectedtapsrepeatfork=1,2,...,Kyk=y)]TJ /F17 11.955 Tf 11.96 8.96 Td[(PKi=1,i6=kxI(i)^hI(i)^hI(k)=xHI(k)yk=kxI(k)k22endforuntil(convergence) where=jIj+1,withjIjdenotingthesizeofI,iistheindexofthecurrenttapunderconsideration,and^hjistheIAAestimateofthejthelementofh,j2fI[ig.AfterBICisimplemented,theindicesofthesurvivingCIRtapscanbefoundinI.Allotherchanneltapsarethensettozero. 2.2.3.3IAAwithRELAX TheparametricandcyclicRELAXalgorithm[ 38 39 ]whichwasoriginallyproposedforspectralestimation,canbeusedtoimprovetheIAAwithBICresultsevenfurther.BecauseRELAXisparametric,itrequiresthenumberofsourcestobeknown.TheIAAwithBICresultcanbeusedtoestimatethenumberofsourcesandalsotoprovideinitialestimatesforthelaststepofRELAXasshowninTable 2-3 .NotethatI(k)denotesthekthelementinthesetI.TheideapresentedinTable 2-3 istoremovethecontributionfromallthecomponentsof^hotherthantheoneofcurrentinterest^hI(k)andthentoupdate^hI(k)intheminimumleastsquaressense.Thisprocedureisrepeateduntilthedifferenceofthecostfunctionky)]TJ /F12 11.955 Tf 9.92 0 Td[(X^hk22betweentwosuccessiveiterationsbecomeslessthanacertainthreshold.(Weusedathresholdof510)]TJ /F9 7.97 Tf 6.59 0 Td[(3inoursimulationsherein.)Forthebestperformance,itisrecommendedthatbeforeeachRELAXiteration,f^hkgbesortedbytheirmagnitudeindescendingorderandthecolumnsofXbepermutedaccordingly.Thisway,thetapwiththelargestmagnitudewillbeupdatedrst,thetapwiththesecondlargestmagnitudewillbeupdatednextandsoon. 37

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2.2.3.4Complexityanalysis TheinitializationstepofIAAhascomplexityO(2dy(NR)+3(NR))andeachIAAiterationhascomplexityO(d3y+(2d2y+3dy+2)(NR)).ThesecomplexitiesarecalculatedbycountingthemultiplicationanddivisionoperationsinTable 2-1 .Whendy>(NR),R)]TJ /F9 7.97 Tf 6.59 0 Td[(1canbecalculatedonlyonceattheinitializationstepofIAAandthenitcanbeupdatedwheneveryfPrgisestimatedusingtherank-1matrixinverseupdateformula[ 22 ].Thisway,thecomplexityofcomputingR)]TJ /F9 7.97 Tf 6.59 0 Td[(1reducestoO((d2y+3)(NR))ratherthanO(d3y)ateachIAAiteration.TheresultingcomplexityofIAAisthengivenbyO(d3y+(d2y+3dy+3)(NR))forinitializationandO((2d2y+2dy+5)(NR))perIAAiteration.ThecomplexityofIAAissmallerthanthoseofMPandLSMPwhendy(NR)andlargerwhendy>(NR)[ 43 ].However,thecomputationtimedoesnotdependonlyonthenumberofcomputationsbutratherisafunctionofthememoryaccesstime,theimplementationsoftwareandhardwareandthenumberofcomputationscombinedtogether.Notethattheregularization,BICandRELAXextensionswillbeappliedinallofournumericalexamplesandhenceforththiscombinedapproachwillsimplybereferredtoasIAA. 2.3SymbolDetection 2.3.1ProblemFormulation TreatingthetransmittedsymbolsastheunknownsinsteadoftheCIRsin( 2 ),themeasurementcanbeexpressedas[ 43 56 ]: ym=NXn=1^Hn,m_xn+em,m=1,...,M,(2) where^Hn,m2CR(2R)]TJ /F9 7.97 Tf 6.59 0 Td[(1)isgivenby ^Hn,m=266664^hn,m(R)...^hn,m(1)0............0^hn,m(R)...^hn,m(1)377775,n=1,...,N,m=1,...,M,(2) 38

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_xn=[xn(t0)]TJ /F3 11.955 Tf 11.95 0 Td[(R+1),...,xn(t0),...,xn(t0+R)]TJ /F4 11.955 Tf 11.95 0 Td[(1)]T,n=1,...,N,ym=[ym(t0),...,ym(t0+R)]TJ /F4 11.955 Tf 11.95 0 Td[(1)]T,m=1,...,M, (2) andt0representsthetimeindexcorrespondingtothepayloadsymbolofinterest.Notethatymrepresentsthemeasurementsin( 2 ),( 2 )and( 2 )sinceymrepresentsaportionofthereceivedsignalinanycase.However,theuseofymshouldbeclearfromthecontext.Stackingupallthemeasurements,( 2 )canbewrittenas 266664y1...yM377775=NXn=1266664^Hn,1...^Hn,M377775_xn+266664e1...eM377775,(2) or,equivalentlyas, ~y=NXn=1^Hn_xn+~e,(2) where~yand~e2CMR1,andf^HngNn=12CMR(2R)]TJ /F9 7.97 Tf 6.59 0 Td[(1).Thetransmittedsymbolsfxn(t0)gNn=1areestimatedusing~yin( 2 ).Whenestimatingfxn(t0+1)gNn=1,themeasurementvector~yisshiftedbyonesymbolduration,i.e.,t0isreplacedbyt0+1,andsoon.Notethatwhendetectingthesymbols,thechannelisassumedconstantsincethepreviouschannelupdate,whichallowsustotreatf^HngNn=1in( 2 )asknown. 2.3.2TheLinearMinimumMean-SquaredError(LMMSE)Filter Inthissection,webrieyreviewtheWienerlter[ 61 91 ],whichisoptimalintheMMSEsensewithrespecttoeachtransmittedsymbol,forsymboldetection.TheWienerlteriswidelyusedinthecommunicationliterature[ 49 54 92 ]andtheexpositionprovidedinthissectionisforthesakeofcompleteness.Thesteeringvectorcorrespondingtofxn(t0)gin( 2 )isgivenbysn,[^hTn,1^hTn,M]Twhere^hn,maretheestimatesofhn,mdenedin( 2 ).WeLetthesymbolofcurrentinterestbexn(t0).Then,theWienerlterforthissymbol,denotedasgn,canbederivedbysolving: fn=argminfE(jjfH~y)]TJ /F3 11.955 Tf 11.95 0 Td[(xn(t0)jj22).(2) 39

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Thesolutionto( 2 )is[ 61 91 ]: fn=R)]TJ /F9 7.97 Tf 6.58 0 Td[(1~y~yE(xHn(t0)~y),(2) whereR~y~yisthecovariancematrixof~y,i.e.,R~y~y=E)]TJ /F4 11.955 Tf 5.42 -9.68 Td[(~y~yH. Inthefollowing,itisassumedthatthepayloadsequencesarepairwiseuncorrelated,eachpayloadsequenceisuncorrelatedwiththenoise~e,thenoisehaszeromean,eachpayloadsymbolisindependentoftheotherpayloadsymbolsandeachpayloadsymbolhaszeromean.Byusingtheseassumptions,itiseasytoverifythat: R~y~y=~H~HH+R~e~e(2) where~H=[~H1,...,~HN]andE)]TJ /F3 11.955 Tf 5.48 -9.69 Td[(xHn(t0)~y=dn.( 2 )thenbecomes: fn=^H^HH+R~e~e)]TJ /F9 7.97 Tf 6.59 0 Td[(1sn(2) andthesoftestimateofthesymbolxn(t0)isgivenbyfHn~y.InourexperimentsweestimateR~e~efromtheresidualerrorobtainedduringthechannelestimationprocess,i.e.,usingem=ym)]TJ /F12 11.955 Tf 12.08 0 Td[(X^hm,m=1,...,M,in( 2 ).Sincedigitalcommunicationsrequirethereceivertomakeaharddecision,thenearestconstellationpointtofHn~yisselectedasthesymbolestimate. 2.3.3DetectionSchemes Inthefollowing,wewillconsiderthreeapproachesforapplyingtheltersffngtothemeasurements.Wewillnotetherelationsbetweentheapproachesproposedinthecommunicationsliteraturewiththoseinthespectralestimationareaandproposeanewschemeinspiredbythisrelationship. 2.3.3.1Linearcombinatorialnulling Inlinearcombinatorialnulling(LCN)[ 11 ],xn(t0)isdetectedusingfHn~yforn=1,...,Nseparatelywhereforeachn,othersymbolsaresimplytreatedasinterferences,i.e.,theestimationofxn(t0)hasnoeffectontheestimationofx~n(t0)(n6=~n).However, 40

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thisapproachshowspoorperformancewhenthechannelcoefcientsforeachtransmitterdiffersignicantlyinmagnitude.Forinstance,whenthechannelcoefcientsofthersttransmitterdominatealltheothers,thesymbolestimateforthersttransmitterwillberelativelyaccuratewhereasthesymbolssentfromtheothertransmitterswillbeburiedunderthecontributionfromthersttransmitterandhencetheywillbeestimatedinaccurately. 2.3.3.2CLEAN-BLAST Theideaofsequentialcancellationandnulling(SCN)canbeusedtoalleviatetheaforementioneddrawbackofLCN.Asthenameimplies,SCNrstdetectsthesymbolwiththestrongestchannelresponse.Then,thecontributionofthissymbolisremovedfromthemeasurements~y(andthecorrespondingcolumnsareremovedfrom~H)beforeestimatingtheothersymbols.ThisprocesscontinuesuntilalltheNsymbolsareestimated.Thesymbolwiththestrongestchannelcoefcientsisdetectedrstbecauseitcanbeestimatedmoreaccuratelythantheothersymbolswithweakerchannelcoefcients.Afterthedominantsymbolsaresubtractedfromthemeasurements,theweakersymbolscanbeestimatedmoreaccurately.Sequentialcancellation,fromtheviewpointoftheremainingsymbols,canberecognizedasinterferenceremoval.Eventually,whendetectingthesymbolwiththeweakestchannelcoefcients,nomoreinterferencesarepresent.ThedetectionalgorithmfeaturingSCNiscalledV-BLAST[ 92 ].Herein,wenamethealgorithmasCLEAN-BLASTtoemphasizeitsanalogytotheCLEANalgorithmusedinspectralestimation[ 64 ]. 2.3.3.3RELAX-BLAST Aswehavealreadypointedout,therelationshipbetweenLCNandCLEAN-BLASTisanalogoustothatoftheperiodogramandCLEAN[ 69 ].Inspectralestimation,RELAXisalsocalledSUPER-CLEAN[ 38 39 ]sinceitisarecursiveversionofCLEANbutwithmuchbetterperformance.BothV-BLASTandRELAX-BLASTtakeadvantageofsequentialinterferencecancellation(SIC)[ 84 ]Toachievesatisfactorydetection 41

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performance,thedetectionordershouldbechosencarefullyinaccordancewiththereceivedsignalpower.Thedetectionorderisdeterminedasfollows.Oncef^hn,mgisavailableforn=1,...,Nandm=1,...,M,thereceivedpowerforthenthtransmittedstream,denotedas(n),iscalculatedas(n)=PMm=1k^hn,mk2.Thereceiverrstdetectsthestreamassociatedwiththestrongestpoweramongf(n)gNn=1,followedbythedetectionofthestreamassociatedwiththesecondstrongestvalueandsoon. InthesamespiritasRELAX,RELAX-BLASTrstdetectsthesymbolwiththedominantchanneltapsandsubtractsitoutfrom~y.Then,itestimatesthenextdominantsymbolfromtheresiduesignal.UnlikeCLEAN-BLAST,however,whichatthistimeestimatesthethirdstrongestsymbol,RELAX-BLASTinsteadupdatesthetwoalreadydetectedsymbolsinaniterativemanneruntilthedifferenceoftheRELAX-BLASTestimatesbetweentwosuccessiveiterationsbecomeslessthanacertainthreshold.Oncethesetwosymbolsaresubtractedfromthemeasurementsandthethirdstrongestsymbolisestimated,thethreesymbolsareagainupdatedinaniterativemanneruntilallthethreeestimatesdonotimproveanymore.ThisprocessisrepeateduntilalltheNsymbolsaredetectedandupdated.Finally,notethatwhenN=1,i.e.,foraSIMOorSISOsystem,LCN,CLEAN-BLASTandRELAX-BLASTbecomeidenticalapproaches. 2.4NumericalandExperimentalResults InthissectionweevaluatetheperformanceoftheCAtrainingsequences,compareIAAwithMP,OMPandLSMPforchannelestimationandcompareCLEAN-BLASTwithRELAX-BLASTforsymboldetectionusingsimulationsand/ortheRACE08experimentalresults.Throughoutthissection,alltheCIRestimationalgorithmsarefollowedbyBICtoachievesparsity. 2.4.1Simulations 2.4.1.1Channelestimationperformance Tobeginwith,weconsidertheproblemofCIRestimationfora41multi-inputsingle-output(MISO)systemwithatime-invariantchannel.ThesimulatedCIR 42

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coefcientsresemblerealUWAconditionsencounteredintheRACE08experimentalmeasurements.Figure 2-3 showsthemodulusoftheCIRscorrespondingtothefourtransmitterswhereR=30delaytapsareconsidered.Giventhetrainingsymbols,thereceiveddatasamplesareconstructedusing( 2 ),wheree1isassumedtobeacircularlysymmetricindependentandidenticallydistributed(i.i.d.)complex-valuedGaussianrandomprocesswithmeanzeroandvariance2. Figure 2-4 showsthemeansquarederror(MSE)ofthechannelestimatesobtainedbyMP,OMP,LSMPandIAAwithtwodifferenttrainingsequences:QPSKtrainingandCAtraining.InQPSKtraining,eachtrainingsymbolisrandomlyselectedtobeoneofthefourQPSKconstellationpointswhereasinCAtrainingeachsymbolisselectedbyusingtheCAalgorithmdescribedinSection 2.2.2 .ThetrainingsequencelengthissetatP=128symbols.EachpointinFigure 2-4 isobtainedbyaveraging100Monte-Carlotrials.WeobservethatwhentheQPSKtrainingisused,IAAsignicantlyoutperformstheotherchannelestimationmethods.OMPandLSMPshowsimilarperformancewhereasMPshowstheworstperformance.Ontheotherhand,whentheCAtrainingsequencesareused,theperformancegapbetweenIAAandtheMPbasedchannelestimationalgorithmsdiminishesandallalgorithmsyieldverysimilarperformancealthoughIAAstillgivesthelowestMSE.Moreover,theperformanceofIAAisnotaffectedverymuchfromthecharacteristicsofthetrainingsequencesused.Thisisanadvantageovertheothermethodssinceinthedecision-directedmode,thechannelhastobeupdatedusingthepreviouslydecodedsymbols,whichdonothaveasgoodauto-andcross-correlationpropertiesasthespecicallydesignedtrainingsequences. 2.4.1.2Symboldetectionperformance Wenowevaluatethebiterrorrates(BER)ofCLEAN-BLASTandRELAX-BLASTfora412MIMOsystem.ThepackagestructureshowninFigure 2-1 isusedinthesimulationswithCAtrainingsequencesconsistingofP=512symbols,apayloadsequenceconsistingofQ=6000QPSKmodulatedsymbolsandtwogapsconsistingof 43

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80mutesymbolseach.IAAisusedforchannelestimation.Thedetectionorderforthealgorithmsis3,2,4,1(i.e.,thethirdchannelisassumedtohavethestrongestchannelresponseatallthereceiversandtherstchanneltheweakest).TheaverageBERsover100Monte-CarlotrialsareshownforthedatatransmittedfromallfourtransducersinFigure 2-5 .WeobservethatRELAX-BLASTshowsmuchbetterperformancethanCLEAN-BLASTaslongassevereerrorpropagationdoesnotexist.ThisresultissupportedbythefactthatsimilarperformanceimprovementsinspectralestimationareobtainedwhenRELAXisusedinsteadofCLEAN[ 38 39 ].Duetothisreason,wewilluseRELAX-BLASTwhenanalyzingtheRACE08datainthefollowing. 2.4.2RACE08In-WaterExperimentationResults Inthispart,weevaluateourproposedMIMOunderwatercommunicationsschemeusingtheRACE08experimentaldataset.RACE08wasconductedbyWHOIinNarragansettBay.Thewaterdepthsrangedfrom9to14mduringtheexperiments.Surfaceconditionswereprimarilywindblownchop.A424MIMOsystemwasusedintheexperiments.Theprimarytransmitterwaslocatedapproximately4mabovethebottomoftheoceanusingastationarytripod.Belowtheprimarytransmitter,asourcearrayconsistingof3transducerswasdeployedverticallywithaspacingof0.6mbetweentheelements.Thetopelementofthesourcearraywas1mbelowtheprimarysource.24receivingtransducersweremountedatarangeofapproximately400m.Receiversweredeployedverticallywithaspacingof0.05mbetweentheindividualelements.ThecarrierfrequencyandthebandwidthemployedintheRACE08experimentswere12kHzand3.9kHz,respectively. Thedatapacketthatwewillconsiderhereinisfromepoch\224.Someepochscouldnotbeevaluatedduetothesevereconditionsofsea.Amongthemanyepochsthatresultinreasonableperformance,epoch\224waschosenarbitrarily.ThepackagestructureshowninFigure 2-1 wasusedintheexperimentswithCAtrainingsequencesconsistingofP=512symbols,apayloadsequenceconsisting 44

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ofQ=2000QPSKmodulatedsymbolsandtwogapsconsistingof80mutesymbolseach.Thesymbolratewas3906.25symbolspersecond.ByapplyingQPSKmodulationandusing4transmitterssimultaneously,a31.25kbpsuncodedpayloaddataratewasachieved.Thecodingschemeweusedfortheexperimentswasa1/2convolutionalencoderwithconstraintlengthof5,andgeneratorpolynomials(10011)and(11011)[ 57 ].Thiscodingschemereducesthenetpayloadbitrateto15.63kbps. Theselectionofthenumberofdelaytaps,R,toconsiderisveryimportant.Avaluetoosmallwilllooseimportantchannelfeatureswhereasavaluetoolargewillcomplicatethereceiverandmayresultinoverttingaswellasincreasednoise.WefoundoutempiricallythatR=30yieldsreasonableresults.Figure 2-6 showsthemodulusofthetraining-directedIAAestimateoftheCIRatreceiver1.TheCIRsfortheotherreceivers,i.e.,f^hmg24m=2sharesimilarstructurewith^h1.AsshowninFigure 2-6 ,thedetectionordershouldbe2(strongestcoefcients),4,3and1(weakestcoefcients). ThechanneltrackingapproachwefollowissummarizedinFigure 2-7 .Intherststep,theCIRisestimatedusingthetrainingsequences.BasedontheinitialCIRestimate,therstL+50payloadsymbolsareobtainedusingRELAX-BLAST,whereLwasdenedafter( 2 ).Next,adecision-directedCIRestimationisdoneusingtherstLestimatedsymbols.ThereasonfornotusingalltheL+50estimatedsymbolswillbeexplainedshortly.WiththeupdatedCIR,startingfromthe(L)]TJ /F4 11.955 Tf 12.17 0 Td[(49)thsymbol,thesubsequentL+100symbolsaredetectedagainusingRELAX-BLAST.Thisprocessisrepeateduntilallthe2000payloadsymbolsaredetected.Figure 2-7 showsthat100moresymbols(50moresymbolsattherstandlaststeps)aredetectedotherthantheLsymbolsusedtoupdatetheCIRateachstep.These50marginsymbolsoneitherendserveasguardintervalsbecausetheerrorstendtohappenatthebeginningandendofeachblock.Thisispartlyduetonomutesymbolsbeingavailablewithinthepayloadsequence. 45

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Table2-4. Biterrorrate(BER)forL=200. UncodedBER(%)CodedBER(%)Tx1Tx2Tx3Tx4Tx1Tx2Tx3Tx4 MP30.456.8014.383.8346.7008.850OMP12.150.602.000.352.40000LSMP12.150.602.000.352.40000IAA4.630.100.3500000 InTable 2-4 weshowtheuncodedandcodedBERsobtainedviaMP,OMP,LSMPorIAAasthechannelestimationalgorithm.Fortheresultspresentedinthistable,thenumberofpayloadsymbolsusedforupdatingthechannelcoefcientsis200,i.e.,L=200.WeobservethatIAAprovidesthebestperformanceamongallfouralgorithms.TheaverageuncodedBERforIAAis1.27%,MPis13.86%,andOMPandLSMPis3.78%andthecodedaverageBERforIAAis0%,MPis13.89%,andOMPandLSMPis0.6%.Asexpected,thesequencewiththestrongest(weakest)channelcoefcientsisestimatedwiththehighest(lowest)accuracy;seeFigure 2-6 InTable 2-5 theuncodedandcodedBERsareshownforL=400.ThismeansthatthechannelwillbeupdatedlessfrequentlythaninthecasewhereL=200.WeobservethatnowIAA,OMPandLSMPshowalmostidenticalperformance.TheaverageuncodedBERforIAAis0.38%,MPis2.09%,andOMPandLSMPis0.37%andthecodedaverageBERforIAAis0%,MPis0.01%,andOMPandLSMPis0%.Aswementionedpreviously,whenLislargeorthesequenceusedforupdatingthechanneliswell-structured,theperformanceofMPtypeofalgorithmsapproachesthatofIAA.However,itmightnotbealwayspossibletoselectLlargeinpractice. ThechoiceofLdeterminestherateatwhichtheCIRwillbeupdatedinthedecision-directedmode.ItalsodeterminestheaccuracyoftheCIRs.Aspreviouslymentioned,thelargertheL,themoreaccuratethechannelestimateswillbeassumingthatthepreviouslydetectedsymbolsarecorrectandthechannelisstationary.On 46

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Table2-5. BERforL=400. UncodedBER(%)CodedBER(%)Tx1Tx2Tx3Tx4Tx1Tx2Tx3Tx4 MP6.980.231.050.130.05000OMP1.480000000LSMP1.480000000IAA1.500000000 theotherhand,forlargerL,thechannelwillbeupdatedlessfrequentlyandhencetheresultswillbeinaccurateforarapidlyvaryingchannel.Therefore,thechoiceofLhasadirecteffectontheperformancesofMP,OMP,LSMPandIAA.Moreover,Lalsodeterminesthecomputationalcomplexitiesofthesealgorithms.Forthecurrentsetofdata,weobservedthatthechannelisratherbenignandusingalargeLvalueresultsinbetterestimatesthanusingaloweroneasseeninTables 2-4 and 2-5 .However,forarapidlyvaryingchannelwhereLhastobeselectedsmall,IAAappearstobethebestcandidateforchannelestimationasitsperformanceisstillgoodwithsmallLwhereasMPtypeofalgorithmsshowrelativelyworseperformance.Notethatinourexperiments,neitherthetrainingsequencelengthPnorthegaplengthshavebeenoptimizedforthebestperformanceasnopriorinformationoftheexperimentalconditionswasavailable.Moreover,forthecurrentexperimentalconditions,a1/2rateconvolutionalcodeappearstobeontheconservativesidetoachievezerocodedBER. 47

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Figure2-1. Thestructureofasingledatapackage. 48

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Figure2-2. AnNMMIMOUACsystem.Theblocksinsidethedashedrectanglearethefocusofourattentioninthischapter. 49

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A B C D Figure2-3. ThemodulusofthesimulatedCIRsbetweenthefourtransmittersandthereceiverina41MISOsystem. 50

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A B Figure2-4. MSEoftheCIRestimatesfora41MISOsystemusingtheQPSKandCAtrainingsequenceswithP=128symbols.Eachpointisaveragedover100Monte-Carlotrials. 51

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A B C D Figure2-5. TheBERsofeachofthefourtransmittedpayloadsequencesfora412MIMOsystem.ThetrainingsequencesconsistofP=512symbolsandaredesignedbytheCAalgorithm.ThedetectionperformanceofCLEAN-BLASTandRELAX-BLASTarecomparedintermsofBERaveragedover100independentMonte-Carlotrialsforvaryinglevelsofthenoisevariance2. 52

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A B C D Figure2-6. ThemodulusofthefourRACE08CIRsestimatedbyIAAfortherstreceiverfromepoch\224. 53

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Figure2-7. Thechanneltrackingprocedure. 54

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CHAPTER3ONBAYESIANCHANNELESTIMATIONANDFASTFOURIERTRANSFORMBASEDSYMBOLDETECTIONINMIMOUAC Inthischapter,severalnewMIMOUACschemesaredevelopedtoimprovetheoverallefciencyandperformanceofUACsystems.WestilladdressthetwoimportantaspectsofcodedMIMOUACsystems:i)enhancedestimationoftheunderwaterCIRandii)efcientsymboldetectioninthepresenceofsevereinterference.Morespecically,weproposeaBayesianchannelestimationalgorithmthatprovidesgoodchannelestimationperformancealongwithreducedcomputationalcomplexitycomparedtoIAA.Moreover,inordertopursuereal-timeimplementation,weexploittheconjugategradientmethodanddiagonalizationpropertiesofthecirculantmatrixtosignicantlyspeedupsymboldetection.TheproposedMIMOUACtechniquesarethoroughlytestedusingin-waterexperimentalmeasurementsrecentlyacquiredbyWHOIduringthe2008SurfaceProcessesandAcousticCommunicationsExperiment(SPACE08). AsidefromthefactthatIAAisuserparameterfree,itwasshowninChapter 2 thatitoutperformsMPbasedalgorithms.Meanwhile,thecomputationalcomplexityrequiredbyIAAissomewhathigh.Inthischapter,anovel,userparameterfreemethodispresentedasanalternativetotheaforementionedmethodsforsparsechannelestimation.Thisisamaximumaposteriori(MAP)basedBayesianapproach,referredtoassparselearningviaiterativeminimization(SLIM),Asshownlater,thechannelestimationperformanceofSLIMissimilartothatofIAAbutataconsiderablylowercomputationalcost.Inaddition,SLIMgeneratesnotonlyCIRestimates,butalsothevariancethereofquantifyingthecondenceintheSLIMestimate.Bymakinguseoftheserst-andsecond-orderstatistics,aschemetoautomaticallydeterminethenumberofrelevantchanneltapsisalsopresented. Anotherimportantaspectofdigitalcommunicationsissymboldetectiongiventheestimatedchannelcoefcients.ItwasdemonstratedinChapter 2 thatRELAX-BLASTprovidesbetterperformancethanLCNandV-BLAST.AlthoughRELAX-BLASTdoes 55

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notneedthecomputationofasmanyltersasMIMOdecisionfeedbackequalizer(MIMO-DFE)[ 59 ],itisstillrelativelymorecomplexcomparedtoV-BLAST.ThisissueisaddressedhereinbytheefcientimplementationofRELAX-BLASTusingtheconjugategradient(CG)method[ 24 62 ].Moreover,thespeedoftheCGmethodissignicantlyimprovedbyusingafastFouriertransform(FFT)-basedmatrixdecompositiontechniquethatexploitsthecirculantpropertiesofthechannelmatrix[ 18 77 ]. Therestofthischapterisorganizedasfollows.Section 3.1 outlinesthesystemcongurationanddescribestheconsidereddatapackagestructure.Section 3.2 formulatestheCIRestimationproblemandpresentstheSLIMalgorithmforchannelestimationtogetherwithaschemeofautomaticallyselectingthechannellength.Next,anoverviewofthesymboldetectionproblemisprovidedandaCGbasedmethodtoimprovetheefciencyofRELAX-BLASTispresentedinSection 3.3 .Section 3.4 presentssimulationresults,aswellasin-waterexperimentalresultsusingthedatagatheredintheSPACE08experiment. 3.1SystemOutline ConsideranNMMIMOUACsystemequippedwithNtransmittransducersandMreceivehydrophones.Thedatastreamofeachtransmitterformsapackageandeachpackageconsistsofasequenceofpackets.Eachpacketcomprisesatrainingsequencefollowedbyapayloadsequence,asshowninFigure 3-1 .ItisworthpointingoutthatforthesakeofincreasingthedatarateandpreventingtheCIRestimatesfromoutdating,theguardintervalsbetweenthetrainingsequenceandpayloadsequence,asdesignedfortheRACE08experiment(Figure 2-1 ),arenotpresenthere.Thepayloadsequencecontainsthedatatobetransmittedandisgenerallyencodedbysomecodingscheme.Ratherthanencodingtheentirepayloadsequenceatonce,thesequenceisdividedintoseveralblocks,eachofwhichisencodedseparately.Thiscodingschemeimprovestheaccuracyofthepayloadsymbolestimatesandconsequentlyresultsinbetteroverallperformancebymitigatingerrorpropagation.Foreachpayloaddatablock,convolutional 56

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encodingandrandominterleavingareemployed.Also,separateencodersareusedforthedifferenttransmitters.Furthermore,Graycodedquadraturephase-shiftkeying(QPSK)[ 57 ]isusedtomapbitsintosymbols.ThefourconstellationpointsofQPSKsymbols,i.e.,fej(2n)]TJ /F9 7.97 Tf 6.58 0 Td[(1) 4g4n=1,lieontheunitcircleandhaveunitmodulus,apropertythatisdesirablefromanamplierefciencypointofview.Similarly,thetrainingsymbolsshouldalsohaveunitmodulus,whilenorestrictionisimposedontheirphasevalues. AsshowninFigure 3-2 ,themeasuredsignalsarerstpassedthroughanequalizer,whichconsistsoftwosteps:1)CIRestimation(intraining-ordecision-directedmode)and2)symboldetection.Byreversingthestepsinthesymbolgenerationprocess,thesymbolestimatesattheequalizeroutputarethendemapped,deinterleavedandnallydecodedusingaMax-Log-MAPapproach[ 58 ].Inaddition,theestimatedsourcebitsareusedtoenhancetheequalizerperformance;thisfeedbackmechanismisreferredtoasinterferencecancellation[ 84 ].Inwhatfollows,ourconsiderationisconnedtoonedatapacketoftheformgiveninFigure 3-1 (thesameanalysisisrepeatedforalldatapacketsofinterest).Itisassumedthatthesamplingandsynchronizationprocedureshavealreadybeenemployed,andthatthesampledcomplexbasebandsignalsareavailableatthereceiver. 3.2ChannelEstimation 3.2.1Training-DirectedMode Thetraining-directedchannelestimationproblemisalmostthesameasthatpresentedinSection 2.2.1.1 .Intheabsenceoftheguardintervalbetweenthetrainingsequenceandpayloadsequence(Figure 3-1 ),~Xnisconstructedas: ~Xn=266666664xn(1)0...0xn(2)xn(1)...0............xn(P)xn(P)]TJ /F4 11.955 Tf 11.96 0 Td[(1)...xn(P)]TJ /F3 11.955 Tf 11.95 0 Td[(R+1)377777775,n=1,...,N.(3) 57

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Bycomparing( 3 )with( 2 ),onecanseethat~Xnin( 3 )canbeobtainedbydiscardingthebottomR)]TJ /F4 11.955 Tf 12.74 0 Td[(1rowsfrom~Xnin( 2 ).Toconformwiththedimensionsof~Xnin( 3 ),Themeasurementvectoratthemthreceiverisgivenby: ym=[ym(1),...,ym(P)]T,m=1,...,M,(3) whichcontainsthePsynchronizedmeasuredsymbols(forinstance,fym(1)gmapstofxn(1)g)atthemthreceiver.Withthenewdenitionsforymand~Xn,( 2 )canstillbeused.Training-directedchannelestimationproblelm,onceagain,reducestoestimatingthechannelshmfromthemeasurementsymandknownX. 3.2.2ChannelEstimationAlgorithm Thechannelestimationproblemateachreceiver,ineithertraining-directedmode(Equation( 2 ))ordecision-directedmode(Section 2.2.1.2 orSection 3.2.4 ),hasthegenericformgivenby y=Xh+e.(3) Thereceiverindexmisomittedherefornotationalsimplicity.Wenotethatthechannelestimationateachreceivercanbedoneinparallel,andwealsoremarkthatthenumberofelementsiny,namelydy,mightvaryindifferentmodes.ein( 3 )isassumedtocontaincircularlysymmetricindependentandidenticallydistributed(i.i.d.)complex-valuedGaussianrandomvariableswithzeromeanandvariance,denotedaseCN(0,I)(ThepracticalvalidityofthisassumptionwillbeveriedbyanalyzingexperimentalambientnoiseinSection 3.4.2.2 ).Theproblemisthentoestimateh,givenyandX.InUACsystems,thechannelhisusuallysparse,i.e.,althoughitcontainsNRunknowns,manyofthesecanbeapproximatedaszero.WepresenttheSLIMalgorithmtosolvethissparsechannelestimationproblem.NotethatsincehcontainstheCIRofallNtransmitters,theSLIMalgorithmwillestimatethemsimultaneously. 58

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ConsiderthefollowinghierarchicalBayesianmodel: yjh,CN(Xh,I), (3) hjpCN(0,P), (3) where( 3 )followsdirectlyfromtheassumptioneCN(0,I).Byassumingindependentchanneltaps,thecovariancematrixPin( 3 )becomesdiagonalP=diag(p)withp=[p1,p2,...,pNR]T,wherepnisthevarianceofhn,thenthelementofh.Furthermore,byconsideringaatprioronbothandfpngNRn=1,thechannelvectorh,thecovariancematrixP(ormoreprecisely,itsdiagonalelementsp)andthenoisepowercanbeestimatedbasedonthemaximumaposteriori(MAP)criterion: maxh,p,p(h,p,jy)=maxh,p,p(yjh,)p(hjp).(3) Bycombining( 3 ),( 3 )and( 3 ),andbytakingthenegativelogarithmofthecostfunction,theoptimizationproblemformulatedin( 3 )becomes minh,p, dylog+ky)]TJ /F12 11.955 Tf 11.96 0 Td[(Xhk2 +NRXn=1logpn+NRXn=1jhnj2 pn!,(3) whichcanbesolvedusinganalternatingapproach(alsoknownasthecoordinatedescentmethod[ 85 ]):ateachiteration,oneoftheparametersh,pandisupdatedwhilekeepingtheothertwoxed.Inthisway,thesingledifcultoptimizationproblemisdividedinto3simplersubproblems.SLIMkeepsiteratinguntilapredenednumberofiterationsisreached.Undermildconditions,thecyclicoptimizationschemeguaranteesthattheSLIMalgorithmconverges,atleasttoalocalminimumof( 3 )[ 101 ]. The4stepsoftheSLIMalgorithmatthetthiterationareoutlinedbelow: 1. Givenh(t)]TJ /F9 7.97 Tf 6.58 0 Td[(1),theoptimalP(t)thatminimizesthecostfunctionin( 3 )isgivenby: p(t)n=h(t)]TJ /F9 7.97 Tf 6.59 0 Td[(1)n2n=1,...,NR.(3) 59

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Thisresultcanbefoundbytakingthepartialderivativeof( 3 )withrespecttopn(withallthetermsirrelevanttopndropped): @ @pn0B@logpn+h(t)]TJ /F9 7.97 Tf 6.59 0 Td[(1)n2 pn1CA=1 pn)]TJ /F17 11.955 Tf 13.15 26.18 Td[(h(t)]TJ /F9 7.97 Tf 6.58 0 Td[(1)n2 p2n.(3) Settingtheabovepartialderivativeto0yieldstheoptimalvaluep(t)nin( 3 ). Forbetternumericalstability,wesetp(t)n(orequivalentlyh(t)n)tozeroifp(t)n<10)]TJ /F9 7.97 Tf 6.58 0 Td[(15.NotethattheSLIMalgorithmachievessparsityduetothehierarchicalBayesianmodel,notthroughthiscompare-and-nullstep. 2. OnceP(t)isavailable,weproceedtoupdatetheCIRestimate.Equivalently,h(t)isobtainedbytakingthepartialderivativeof( 3 )withrespecttohandsettingtheresulttozero.BynoticingthatPNRn=1jhnj2 p(t)n=hH)]TJ /F12 11.955 Tf 5.48 -9.69 Td[(P(t))]TJ /F9 7.97 Tf 6.58 0 Td[(1handbysolving @ @h ky)]TJ /F12 11.955 Tf 11.96 0 Td[(Xhk2 (t)]TJ /F9 7.97 Tf 6.59 0 Td[(1)+hH)]TJ /F12 11.955 Tf 5.48 -9.68 Td[(P(t))]TJ /F9 7.97 Tf 6.59 0 Td[(1h!=XHX (t)]TJ /F9 7.97 Tf 6.58 0 Td[(1)+)]TJ /F12 11.955 Tf 5.48 -9.68 Td[(P(t))]TJ /F9 7.97 Tf 6.59 0 Td[(1h)]TJ /F12 11.955 Tf 16.35 8.09 Td[(XHy (t)]TJ /F9 7.97 Tf 6.59 0 Td[(1)=0,(3) weget: h(t)=hXHX+(t)]TJ /F9 7.97 Tf 6.58 0 Td[(1))]TJ /F12 11.955 Tf 5.48 -9.68 Td[(P(t))]TJ /F9 7.97 Tf 6.58 0 Td[(1i)]TJ /F9 7.97 Tf 6.59 0 Td[(1XHy.(3) WhileinvertingP(t),itszerodiagonalentriesareremoved,andtheassociatedcolumnsinXarediscarded. 3. Usingthemostrecentlyobtainedh(t)in( 3 ),wenallyestimatethenoisepowerbysolving: @ @ dylog+y)]TJ /F12 11.955 Tf 11.96 0 Td[(Xh(t)2 !=dy )]TJ /F17 11.955 Tf 13.15 19.01 Td[(y)]TJ /F12 11.955 Tf 11.96 0 Td[(Xh(t)2 2=0.(3) Thesolutionisgivenby: (t)=1 dyy)]TJ /F12 11.955 Tf 11.96 0 Td[(Xh(t)2.(3) 4. t=t+1.GobacktoStep1iftislessthanthepredenediterationnumber,orterminateotherwise. Intraining-directedmode,thechannelcharacteristicsareingeneralnotavailableapriori.Inourexamples,h(0)isinitializedusingthestandardmatchedlter,andthenoisepower(0)isinitializedwithasmallpositivenumber,forinstance,10)]TJ /F9 7.97 Tf 6.59 0 Td[(10.OurempiricalexperiencesuggeststhattheSLIMalgorithmdoesnotprovidesignicantperformance 60

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improvementsafterabout15iterations.Next,weproceedtocomparethecomputationalcomplexitybetweenSLIMandIAA.Aspresentedin[ 48 ],eachIAAiterationhasacomplexityonthescaleofO(d3y),wheredyisdenedafter( 3 ).Referringtothe3updatetasksinvolvedateachSLIMiteration,wecanseethatthebottleneckofSLIMstemsfromthematrixinversein( 3 ),whichhasacomplexityO(N3R3).Therefore,thecomplexityofSLIMissmallerthanthatofIAAwhenNR
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Theposteriordensityhgiveny,i.e.,p(hjy),canbeobtainedbyintegratingoutthevariablespandinp(hjy,p,): p(hjy)=ZZp(hjy,p,)p(p)p()dpdp(^hjy,P,). (3) Theapproximationabovefollowsbyassumingthatbothp(p)andp()canbemodeledasDiracfunctions[ 79 ],i.e.,p(p)=QNRn=1(pn)]TJ /F3 11.955 Tf 12.06 0 Td[(pn)andp()=()]TJ /F5 11.955 Tf 12.06 0 Td[().Consequently,wecanapproximatelyconsider hjyCN(,).(3) Sofar,thediscussionsandderivationsaredevelopedwiththereceiverindexmomitted.Thesubsequentderivations,however,requireincorporatingthereceiverindex.Forclarity,wehencerewrite( 3 )as hmjymCN(m,m),m=1,...,M,(3) toremindusthattheresultsarewithrespecttothemthreceiver.Undertheassumptionthatthechanneltapsareindependent,eachelementofhmgivenymcanindividuallybecharacterizedthroughacomplex-valuedGaussianstatistic.Using( 2 )andthedenitionofhmafter( 2 ),wehave hn,m(r)jymCN(n,m(r),2n,m(r)),(3) wheren=1,...,N,m=1,...,Mandr=1,...,R.Themeann,m(r)andthevariance2n,m(r)areappropriateentriesofmanddiagonalentryofm,respectively. Let n,m(r)=jn,m(r)j n,m(r)andn(r)=1 MMXm=1n,m(r).(3) Intuitively,thereal-valuedquantityn,m(r)in( 3 )quantiesourcondenceinkeepingtherthtapasaneffectivechanneltapforthenthtransmitter,whichismorelikelyto 62

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happenwhenthechannelmodulusislarge(i.e.,jn,m(r)jislarge)andwearecondentoftheestimate(i.e.,n,m(r)issmall).Theproposedchanneltapselectionschemeisthentousen(r)asfollows:forthenthtransmitter,westartbytestingthelast(i.e.,theRth)channeltap.Ifn(R)<3(i.e.,3timesthestandardderivation,notethatn,m(R)isanormalizedstatistic),weproceedtotestthe(R)]TJ /F4 11.955 Tf 12.39 0 Td[(1)stchanneltapandcontinueuntilwecomeacrossachanneltap,saythe~Rthntap,thatrendersn(~Rn)3forthersttime.Thisprocedureisthenrepeatedforn=1,...,N,i.e.,Ntimes,andinsuchawaythatweobtain~Rnforeachtransmitter.Finally,~Risdeterminedas~R=minf~RngNn=1(using~R=maxf~RngNn=1yieldssimilardetectionperformance).Theso-obtained~Risthenusedforsubsequentprocessing. 3.2.4Decision-DirectedMode Theproblemindecision-directedmodeisalmostidenticaltothatpresentedinSection 2.2.1.2 exceptthatRisnowreplacedby~R,theautomaticallydeterminedchannellength(Section 3.2.3 ).Thatis,~Xnisconstructedas: ~Xn=266666664^xn(ti)^xn(ti)]TJ /F4 11.955 Tf 11.96 0 Td[(1)...^xn(ti)]TJ /F4 11.955 Tf 13.32 2.66 Td[(~R+1)^xn(ti+1)^xn(ti)...^xn(ti)]TJ /F4 11.955 Tf 13.32 2.66 Td[(~R+2).........^xn(tf)^xn(tf)]TJ /F4 11.955 Tf 11.96 0 Td[(1)...^xn(tf)]TJ /F4 11.955 Tf 13.31 2.65 Td[(~R+1)377777775,n=1,...,N.(3) Whenconductingdecision-directedchanneltracking,forthesakeofcomputationalefciency,p(0)isinitializedwiththepreviouschannelestimates(witheachzeroreplacedbyasmallnumber,10)]TJ /F9 7.97 Tf 6.59 0 Td[(5),followedby3iterationsofSLIM.Thepurposeofreplacingeachzerowith10)]TJ /F9 7.97 Tf 6.59 0 Td[(5istoallowforactivationofapreviouslyassumedzerotap. 3.3SymbolDetection 3.3.1DetectionScheme ThegeneralideabehindRELAX-BLASTistodetectthestrongeststreamrstusinganyofthethreeaforementioneddetectionalgorithms(RELAX-BLAST,V-BLAST 63

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andLCNbecomeidenticalapproachesforthesingletransmittercase),andretrievethesourcebitscarriedinthestrongeststreamthroughdecoding;seeFigure 3-2 .TomakeuseofSIC,giventheestimatedsourcebits,werstfollowthestepsinthesymbolgenerationprocessshowninFigure 3-1 byassumingthatthestructureoftheencoderandinterleaverisperfectlyknownatthereceiverside:theestimatedsourcebitsarefedintotheconvolutionalencoder,followedbyarandominterleaverandQPSKmappingmodule.Thisway,anerror-freedecodingcanprovideaperfectrecoveryofthetransmittedQPSKsymbolsinthestrongeststream.Then,there-constructedQPSKsymbolsareconvolvedwiththeassociatedCIRestimatestoyieldtheinterferencestreamseenbytheremainingundetectedstreams.Theso-obtainedinterferencestreamwillbesubtractedoutfromthemeasurementstoaidthedetectionoftheremainingstreams(thisiswheretheinterferencecancellationmechanismshowninFigure 3-2 comesintoplay).Next,thesecondstrongeststream(whichnowbecomesthestrongestoneamongtheremainingN)]TJ /F4 11.955 Tf 12.1 0 Td[(1streamssincethecontributionsofthestrongeststreamhavebeenremoved)isestimated.Thetwodetectedstreamsareupdatedinaniterativemanneruntiltheestimatesdonotchangesignicantlyintwoconsecutiveiterations.Byiterativeupdate,wemeanthatoncetheestimatedsourcebitsofthesecondstrongeststreamareavailable,theircorrespondinginterferencestreamissubtractedoutfromtheoriginalmeasurementstore-determinethestrongeststream.Duetotheabsenceofthesecondstrongeststreamandhenceahighersignal-to-interference-plus-noiseratio(SINR),thisre-determinationstageyieldsabetterestimateofthestrongeststream.Thisiterativeupdateofthetwostrongeststreamsiscontinueduntilaprescribediterationnumberisreached(typically3iterationsareenough).Then,thetwodominantstreamsaresubtractedoutfromthemeasurementstoestimatethethirdstrongeststream.Therstthreestreamsarethenupdatediterativelybyupdatingonestreamatatime.Thesameprocedureisrepeateduntilallthetransmitteddatastreamsaredetectedand 64

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updated.ItistheiterativerenementstepofRELAX-BLASTthatprovidesperformanceimprovements,ascomparedto,forinstance,V-BLAST;see[ 48 ]. 3.3.2EfcientLMMSEFiltering Let sn=[^hTn,1,...,^hTn,M]T,n=1,...,N,(3) denotethesteeringvectorcorrespondingtoxn(t0)in( 2 ).TheWienerltercorrespondingtoxn(t0),denotedasfn,A,isthengivenby[ 48 91 ] fn,A=Q)]TJ /F9 7.97 Tf 6.59 0 Td[(1Asn,n=1,...,N,(3) wheresnandfn,A2CM~R1,and QA=NXj=1,j=2A^Hj^HHj+I(3) denotestheresiduesignalcovariancematrix.Itpossiblycontainssomeofthetransmitteddatastreams,whoseindicesarecollectedinthesetA,subtractedoutfromthemeasurements~y.Inouranalysis,thenoisepowerin( 3 )isdeterminedasthenoisepowerobtainedusingtheSLIMalgorithm,see( 3 ),averagedovertheMreceivers.Thesymbolestimate^xn(t0)isthenobtainedbymultiplyingfHn,Awiththecorrespondingresiduesignal(i.e.,themeasurementsignalwiththecontributionsfromthetransmittersinAremoved). Duetoitsiterativenature,RELAX-BLASTrequirescomputationofmultipleLMMSElters[ 48 ].Asanexample,inthepresenceof3transmittersandassumingthatthedetectionorderistransmitter1to3,wheretransmitters1and3encounterthestrongestandweakestchannels,respectively,RELAX-BLASTrequires6distinctlters:f1,f;g,f2,f1g,f1,f2g,f3,f1,2g,f1,f2,3gandf2,f1,3g.InthegeneralcasewithNtransmitters,N(N+1)=2LMMSEltersintotalareneeded.TheprocessbecomescomputationallyexpensiveduetotheM~RM~Rmatrixinversionrequiredinordertodetermineeachindividuallter.Fortunately,theconjugategradient(CG)[ 62 ]methodcanbeemployed 65

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inRELAX-BLASTtoeasethecomputationalburden.Thepseudo-codeforobtainingtheLMMSEltersfn,AusingtheCGmethodisgiveninTable 3-1 .Asobserved,thebottleneckintheCGimplementationisthematrix-vectormultiplicationQAd(i)requiredineachiteration.Weusethediagonalizationpropertyofcirculantmatricestoreplacethismatrix-vectorproductwithsimpleandefcientFFToperations.OurempiricalexperienceindicatesthattheCGmethod,ifnotusedinconjunctionwiththeFFTimplementation,doesnothaveanoticeableadvantageintermsofcomputationalcomplexityoverexploitingthewell-knownmatrixinversionlemma.Specically,theproblemofinterestistondafastwaytocomputeQAd(theCGiterationindexiisomittedfornotationalsimplicity),orequivalently, zn=^Hn^HHnd,n=1,...,N,n=2A,(3) see( 3 ).Beforeproceedingtodemonstratehowtoexploittheblockstructureofthechannelmatrix^Hninordertocomputeznefciently,itisinstructivetoreviewtheelegantdiagonalizationpropertiesofacirculantmatrix. Itiswell-knownthataKKcomplex-valuedcirculantmatrixCcanbeexpressedasC=FFH.Here,FistheKKFFTmatrixandholdstheKeigenvaluesofCalongitsdiagonal(e.g.,[ 71 ]).Furthermore,theseeigenvaluescanefcientlybecomputedbyapplyingFFTtotherstrowofC.LetCn,m2C(2~R)]TJ /F9 7.97 Tf 6.58 0 Td[(1)(2~R)]TJ /F9 7.97 Tf 6.59 0 Td[(1)denotethecirculantmatrixobtainedbyappendingtheappropriate(~R)]TJ /F4 11.955 Tf 12.12 0 Td[(1)(2~R)]TJ /F4 11.955 Tf 12.12 0 Td[(1)matrixtothebottomof^Hn,m.Thatis,Cn,mcanbeconstructedbycyclicallyshiftingthelastrowof^Hn,mtotherightforatotalof~R)]TJ /F4 11.955 Tf 12.15 0 Td[(1times.Then,basedontheaboveobservation,Cn,mcanbediagonalizedas Cn,m=Fn,mFH,(3) forn=1,...,Nandm=1,...,M.Throughthisconstruction,( 3 )canbecomputedusing~zn=CnCHn~d,whereCn2CM(2~R)]TJ /F9 7.97 Tf 6.59 0 Td[(1)(2~R)]TJ /F9 7.97 Tf 6.58 0 Td[(1)isobtainedsimilarlyto^Hnin( 3 ),asCn=[CTn,1...CTn,M]T,and~d2CM(2~R)]TJ /F9 7.97 Tf 6.59 0 Td[(1)1isconstructedbyrstdividingdintoM 66

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Table3-1. TheconjugategradientmethodforRELAX-BLAST. d(0)=r(0)=sn;~f(0)=0;i=0repeat(i)=jjr(i)jj2 d(i)HQAd(i)%determinethestepsize~f(i+1)=~f(i)+(i)d(i)%updatetheestimater(i+1)=r(i))]TJ /F5 11.955 Tf 11.95 0 Td[((i)QAd(i)%calculateanewresiduald(i+1)=r(i+1)+jjr(i+1)jj2 jjr(i)jj2d(i)%calculateanewsearchdirectioni=i+1untiljjr(i)jj jjsnjj
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onlyreducesthecomputationalcomplexityofRELAX-BLASTconsiderably,butalsomakesRELAX-BLASTamenabletoparallelimplementations. Therequirednumberofiterationsneededtoyieldthesolutionin( 3 )isequaltothenumberofdistinctiveeigenvaluesofQA.Moreoftenthannot,however,theCGiterationcanbeterminatedearlyforthesakeofcomputationalsavingsandpossiblyalsoforbetterequalizationperformance[ 25 ].ItwasempiricallyobservedinourexperimentsthatitsufcestoterminatetheCGiterationswhentheratiooftheEuclideannormoftheresiduevectortotheEuclideannormofthesteeringvectorsnbecomeslessthanapredenedthresholdtCG.TheselectionoftCGwillbeinvestigatedinthefollowingsection. 3.4NumericalandExperimentalResults 3.4.1Simulations 3.4.1.1Channelestimation WeconsidertheproblemofCIRestimationina41multi-inputsingle-output(MISO)systemwithtime-invariantchannels.ThemodulusofthesimulatedCIRscorrespondingtothefourtransmittersareshowninFigure 3-3 ,where~R=20delaytapsareconsidered.Thechannellengthisassumedtobeknownbythereceiverandtheautomaticdeterminationofchannellengthisthusnotinvolvedinthisexample.Fourtrainingsequencesaresynthesizedbythecyclicapproach(CA)[ 48 ],eachoflengthP=128.GiventheCIRsandtrainingsymbols,thereceivedmeasurementsareconstructedasin( 2 )withe1CN(0,I). Themean-squarederrors(MSEs)ofthechannelestimatesobtainedbyIAA,SLIMandLSareshowninFigure 3-4 ,whereeachpointistheaverageerrorover100Monte-Carlotrials.(Therefore,MSE=1 100P100i=1kh1)]TJ /F4 11.955 Tf 12.59 2.66 Td[(^h(i)1k2.ThecombinedCIRvectorh1oflength4~R=80hasbeendenedin( 2 )and^h(i)1representsitsestimateattheithMonte-Carlotrial.)ItisobservedthatSLIMyieldsslightlybetterMSEperformancethanIAA(Figure 3-4 ).Itisalsointerestingtonotethatinthisexample,itisonaverage 68

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3.8timesfasterthanIAA(notethatthecomplexitiesofSLIMandIAA,asremarkedinSection 3.2.2 ,areO(N3~R3)andO(d3y),respectively,andinthisexample,N~R=80anddy=P+~R)]TJ /F4 11.955 Tf 12.2 0 Td[(1=147).LSgivestheworstperformance,mainlybecauseitinvolvesnomechanismtoaddresssparsityandisadata-independentapproach. 3.4.1.2Symboldetection ComparisonsbetweenV-BLASTandRELAX-BLAST,intermsofcodedBERperformance,isconsideredforasimulated412MIMOsystem.Themodulusofthe4simulatedCIRsatreceiver1areshowninFigure 3-3 ,andtheCIRsfortheother11receiverssharesimilarstructure.Thedetectionorderisdeterminedas1(strongest),2,4and3(weakest).WeassumethatchannelcharacteristicsareknowntothereceiveraspriorknowledgeandthatthenoiseisdistributedaccordingtoCN(0,I).Ineachtrial,eachtransmittersendsonepayloadblock(i.e.,250codedQPSKsymbols),which,perthediscussioninSection 3.1 ,isgeneratedbyfeeding250sourcebitsintoa1/2-rateconvolutionalencoderwithgeneratorpolynomials(10011)and(11011)followedbyarandominterleaverandQPSKmapping.CodedBERperformanceofV-BLASTandRELAX-BLASTareshowninFigure 3-5 .Eachpointisaveragedover26000Monte-Carloruns.TheSINRfortransmittern(n2f1,2,3,4ginthisexample)isdenedas SINR=P12m=1khn,mk2 P4j=1,j6=nP12m=1khj,mk2+.(3) Thebinarysourcebits,themappingindicesoftherandominterleaverandthenoisepatternsvaryindependentlyfromonetrialtoanother.OneobservesfromFigure 3-5 thatRELAX-BLASTsignicantlyoutperformsV-BLAST.Thisobservationisalsoconsistentwithourin-waterempiricalexperiences.Therefore,theSPACE08resultswediscussbelowareallobtainedusingRELAX-BLAST. 69

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3.4.2SPACE08In-WaterExperimentationResults 3.4.2.1Experimentalspecications TheSPACE08wasconductedbyWHOIattheAir-SeaInteractionTower,2milessouthtothecoastofMartha'sVineyard,MAatawaterdepthofabout15m.TheMIMOsystemwasequippedwith4transmittransducers.Theprimarytransmittransducerwaslocatedapproximately4mabovethebottomoftheoceanusingastationarytripod.Belowtheprimarytransducer,asourcearrayconsistingof3transducerswasdeployedverticallywithaspacingof0.5mbetweentheelements.Thetopelementofthesourcearraywas3mabovethebottomoftheocean.Threeseparatereceivercongurationswereemployed:1)a32hydrophonecrossarraymountedat60m,2)a24hydrophoneverticallinearraymountedat200m,and3)a12hydrophoneverticallinearraymountedat1km.Forthe60mcrossarray,ahorizontallegandaverticallegwereseamedtogetheratthecenter,andeachlegwasmountedwith16hydrophones.Thecenter-to-centerspacingbetweenindividualelementswas3.75cm,5cmand12cmforcongurations1-3,respectively.Thetophydrophoneforeachcongurationwasapproximately3.3mabovetheoceanoor.Thecarrierfrequencyandbandwidthusedintheexperimentswere13KHzand10KHz,respectively.ThesymbolrateemployedinSPACE08was7.8125Ksymbolspersecondateachtransmitter.Thepulseshapinglterwasasquaredraisedcosinelterwitharollofffactor0.25.Thebasebandsamplingratewas7.8125KHz,i.e.,asymbolratesamplingschemewasadopted. ThetransmitteddatapacketsusedCAtrainingsequencesoflength512followedbyQPSKpayloadsymbols.Notethatalthoughguardintervalswerenotpresentintheexperimentaldata(forthesakeofincreasingthedatarateandpreventingtheCIRestimatesfromoutdating),CAtrainingsequenceswerestillobservedtoprovidesatisfactoryperformanceaswillbeshownshortly.Thepayloadsequenceoflength8Kwasdividedinto32blocks,eachoflength250.Thegenerationofeach250-symbol 70

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blockfollowsthesameprocedureaselaboratedinSection 3.4.1.2 ).Theemploymentof4transducersandQPSKmodulationresultsinacodedpayloaddatarateof31.25Kbps. TheSPACE08dataencounteredrichchannelconditionsoverthecourseoftheexperiments,whichisevidentinFigure 3-6 ,wherethedynamicvariationsoftheaveragewaveheightisshown.Usingthewaveheightasareference,channelconditionshavebeenroughlydividedintotheuglycategoryonJuliandates300and301(indicatedwiththemarksinFigure 3-6 ),badcategoryondates294,295,296,299and302,andgoodcategoryontheremaining5dates.Thegooddaysarechosensuchthatthecorrespondingwaveheightisconsistentlylessthan1.25m,indicatedasthedash-dotlineinFigure 3-6 .Inthisway,ourexperimentaldataconsistsof9differentscenariosasthereare3receivercongurationsand3channelconditions.Figure 3-7 showstheevolutionofthenormalizedCIRbetweenagiventransmitterandreceiverpairovertimeforthese9scenarios.Intheseplots,asingletransducercontinuallytransmitsanm-sequence,whiletheothertransducersareinactive.Oneobservesthatthechanneltapsexperiencesignicantvariationsovertimeaswaveheightincreases. 3.4.2.2Ambientnoiseanalysis Theseaambientnoisewasmodeledasacircularlysymmetriccomplex-valuedzero-meanwhiteGaussianrandomprocess;see( 3 ).Toverifythepracticalvalidityofthisassumption,Figure 3-8 showsthespectralestimateof1kmmeasurementsacquiredonJuliandate300.Figure 3-8A isobtainedfrom10Ksamplesofin-waterambientnoise,whileFigure 3-8B isduringthedatatransmissionwherethefourtransmittersaretransmittingsignalsimultaneously.Recallingthatthebandwidth(orsymbolrate)employedinSPACE08in-waterexperimentwas7.8125KHz,thefrequencyrangeshowninFigure 3-8 isconnedto[)]TJ /F4 11.955 Tf 9.3 0 Td[(39003900]HzduetoNyquistsamplingtheory.TheatpowerspectrumshowninFigure 3-8A indicatesthatitisreasonabletoapproximatetheoceannoiseasawhiteGaussianprocess. 71

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3.4.2.3Channellengthselection Weprovideheretwoexperimentalexamplestoillustratehowthechannellengthestimatorperforms.AsmentionedinSection 3.2.3 ,apotentiallylargechanneltapnumberRshouldinitiallybechosen.ForSPACE08,weusedR=100.Considerapacketfromepoch\224withreceiverconguration1.Theresultingration(r)averagedoverthe32receiversareplottedsuperimposedinFigure 3-9A .Notethatonlythe50th)]TJ /F4 11.955 Tf 11.21 0 Td[(100thtapsareshownandthehorizontaldash-dotlinerepresentsthethresholdvalue3.Weobservethatthetapindicesatwhichthecurvesrstcrossthethresholdare74,73,71and70fortransmitters1-4,respectively.Therefore,~Risdeterminedastheminimalofthe4candidatevalues,i.e.,70inthisexample.Figure 3-9B showsn(r)byconsideringapacketfromepoch\224withreceiverconguration2.Thesameguidelinedetermines~Ras72. 3.4.2.4Stoppingcriterionfortheconjugategradientmethod RecallthattheCGiterationsareterminatedwhentheratiooftheEuclideannormoftheresidualtermtotheEuclideannormofthesteeringvectorbecomeslessthantCG,seeTable 3-1 .InthissectionwepresentguidelinesonhowtoselecttCG.Considertraining-directedchannelestimationwithchanneltapnumber~R=70undergoodchannelconditions(otherchannelconditionsleadtosimilarresults).TheaveragenumberofiterationsrequiredbytheCGmethodfordifferenttCGsettingsisplottedinFigure 3-10 .OneobservesthatfortCG>10)]TJ /F9 7.97 Tf 6.59 0 Td[(2,theaverageiterationnumberfor3receivercongurationsshowsgoodagreement.Itispreferabletokeeptheiterationnumberwithin10forthesakeofcomputationalefciency.Therefore,tCGisxedat0.05collectivelyforreceivercongurations1-3.ItwasempiricallyobservedinourexperimentsthatthisthresholdvalueyieldsexcellentBERperformance.Moreover,wealsonoticedthattheBERperformanceisnotsensitivetothechoiceoftCG. 72

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3.4.2.5Codedbiterrorrateperformance ThechanneltrackingapproachadoptedinthispaperisillustratedinFigure 3-11 .Inthisapproach,theCIRisrstestimatedintraining-directedmode.Subsequently,basedontheinitialCIRestimates,therstSpayloadsymbols(Sissetto250)areobtainedusingRELAX-BLAST.Next,thechannelsareupdatedindecision-directedmodeusingLsymbols(containingthepreviouslydetectedpayloadsymbols,andpossiblyaportionofthetrainingsequenceaswell),seeFigure 3-11 .RegardingthetrackinglengthL,itisadvantageoustosetdifferentLvaluesfordifferentreceiverlocations,andourempiricalexperiencesuggeststoxLat450,500,and700forreceivercongurations1-3,respectively.WiththeupdatedCIRs,thesubsequentSpayloadsymbolsaredetectedusingRELAX-BLAST.Thisprocesscontinuesuntilallpayloadsymbolsaredetected. Acomprehensivesummaryofthedetectionperformanceforreceiverconguration2(i.e.,the424MIMOsystemat200mdistance)isprovidedinTable 3-2 basedonouranalysisofall96packetsrecordedovertheentirecourseoftheSPACE08underallofthechannelconditionsexperienced.WedeemapayloaddatablocktobesuccessfullydetectedifitscodedBERaveragedoverthe4transmittersislessthan0.1.ByadoptingtheproposedMIMOUACtechniques,wehavesucceededintrackingtheentire32payloadblocksfor92outofthe96packets.AcodedBERof4.2710)]TJ /F9 7.97 Tf 6.59 0 Td[(5isachievedafteraveragingoverthe7.36105sourcebitsprocessed(recallthateachpacketcarries8000sourcebitsandwehave92suchpackets).Theresultingdatarateisapproximately31.25Kbps. Withtheremaining4packets(2onJuliandate300,and2on301),welosttrackofthechannelduringthepayloadsymboldetectionandchanneltrackingprocess.FromFigure 3-6 ,itisobservedthatthesetwodays(markedas)indeedexperiencedthemostseverechannelconditions.Nevertheless,itisstillencouragingthatwesucceededintrackingatleastthersttwodatablocksforthese4packets,thankstothegoodauto-andcross-correlationpropertiesoftheCAtrainingsequencesusedintheexperiment 73

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[ 48 ].ThecodedBERoftherst2datablocksaveragedoverthese4packetsis6.2510)]TJ /F9 7.97 Tf 6.59 0 Td[(4.Therefore,whenthechannelconditionsareverysevere,wecanconsidertheschemeshowninFigure 3-12 ,wheretheestimatedchannelisusedtoinitializechannelequalizationanddecodingfor2payloaddatablocksprecedingandfollowingthetrainingsequence.Inthisscheme,though,thetrainingsequencesplayamajorroleforchannelestimation.Duetothetrainingoverhead,thisschemeresultsinadatarateof20.7Kbps. Thereceivercongurations1and3encountermorechallengingchannelconditionsthanthereceiverconguration2.Toseethis,Table 3-3 detailsthecodedBERperformanceofreceiverconguration3.Itisobservedthatundergoodchannelconditions,theentire32datablocksforallthe48packetscanbesuccessfullydetectedwithanaveragecodedBERof3.8610)]TJ /F9 7.97 Tf 6.59 0 Td[(4.Underbadchannelconditions,amongthe30packetsprocessed,thereare10forwhichthechannelcannotbetracked.However,westillsucceedtrackingatleastthersttwodatablocksfor9outofthese10packets.Forthe18packetstransmittedunderuglychannelconditions,atleasttherst2blocksof10ofthesepacketsweresuccessfullydetected.Fortheremaining8packets,onlytherstblockhasbeensuccessfullydetectedfor5packets,andtheremaining3packetscouldnotbedetected.Table 3-4 showsthesameanalysisonperformancewithreceiverconguration1.Itcanbeobservedthatamongthe3receivercongurationsconsidered,thisparticularreceiverat60mgivestheworstoverallperformance. Itisworthpointingoutthatalthoughthesurface-interactivetapsatboth60mand200mrangesexperiencesignicantvariations(Figure 3-7 ),itisthedifferenceintheirpowerlevelsthataccountfortheremarkablecontrastintheresultingBERperformance.Thesurface-interactivetapsat200mdoesnotpossessmuchpower,butthoseat60maremuchmorepowerful.Underseverechannelconditions,thesetapsareextremelydifculttotrack,whichcanseverelydegradetheBERperformance.Themorepowerfulthesetapsare,themoreseveretheBERdegradation. 74

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Table3-2. 200mperformanceofusingsparselearningviaiterativeminimization(SLIM). NumberofAll32blockssuccessfulFirst2blockssuccessfulFirstblocksuccessfulDatesPackets%averageBER%averageBER%averageBER good481003.2610)]TJ /F9 7.97 Tf 6.59 0 Td[(6----bad301007.3010)]TJ /F9 7.97 Tf 6.59 0 Td[(6----ugly1877.82.5410)]TJ /F9 7.97 Tf 6.59 0 Td[(422.26.2510)]TJ /F9 7.97 Tf 6.59 0 Td[(4-Table3-3. 1kmperformanceofusingSLIM. NumberofAll32blockssuccessfulFirst2blockssuccessfulFirstblocksuccessfulDatesPackets%averageBER%averageBER%averageBER good481003.8610)]TJ /F9 7.97 Tf 6.59 0 Td[(4----bad3066.71.0410)]TJ /F9 7.97 Tf 6.59 0 Td[(3301.9310)]TJ /F9 7.97 Tf 6.59 0 Td[(2--ugly180-55.61.4810)]TJ /F9 7.97 Tf 6.59 0 Td[(227.86.4210)]TJ /F9 7.97 Tf 6.58 0 Td[(2 Table3-4. 60mperformanceofusingSLIM. NumberofAll32blockssuccessfulFirst2blockssuccessfulFirstblocksuccessfulDatesPackets%averageBER%averageBER%averageBER good4854.27.0210)]TJ /F9 7.97 Tf 6.59 0 Td[(431.36.2010)]TJ /F9 7.97 Tf 6.59 0 Td[(38.35.2010)]TJ /F9 7.97 Tf 6.58 0 Td[(2bad30601.6110)]TJ /F9 7.97 Tf 6.59 0 Td[(323.34.9310)]TJ /F9 7.97 Tf 6.59 0 Td[(36.73.0010)]TJ /F9 7.97 Tf 6.58 0 Td[(2ugly185.63.1310)]TJ /F9 7.97 Tf 6.59 0 Td[(427.84.8010)]TJ /F9 7.97 Tf 6.59 0 Td[(311.14.9010)]TJ /F9 7.97 Tf 6.58 0 Td[(2 75

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Table3-5. 200mperformanceofusingleasesquares(LS). NumberofAll32blockssuccessfulFirst2blockssuccessfulFirstblocksuccessfulDatesPackets%averageBER%averageBER%averageBER good4897.92.5310)]TJ /F9 7.97 Tf 6.59 0 Td[(52.12.0010)]TJ /F9 7.97 Tf 6.59 0 Td[(3--bad301007.8110)]TJ /F9 7.97 Tf 6.59 0 Td[(5----ugly1822.2077.82.5710)]TJ /F9 7.97 Tf 6.59 0 Td[(3-Table3-6. 1kmperformanceofusingLS. NumberofAll32blockssuccessfulFirst2blockssuccessfulFirstblocksuccessfulDatesPackets%averageBER%averageBER%averageBER good4897.95.5710)]TJ /F9 7.97 Tf 6.59 0 Td[(42.15.0010)]TJ /F9 7.97 Tf 6.59 0 Td[(4--bad3056.72.5210)]TJ /F9 7.97 Tf 6.59 0 Td[(443.31.5810)]TJ /F9 7.97 Tf 6.59 0 Td[(2--ugly180-55.61.8710)]TJ /F9 7.97 Tf 6.59 0 Td[(222.23.3810)]TJ /F9 7.97 Tf 6.58 0 Td[(2 Table3-7. 60mperformanceofusingLS. NumberofAll32blockssuccessfulFirst2blockssuccessfulFirstblocksuccessfulDatesPackets%averageBER%averageBER%averageBER good486.31.2610)]TJ /F9 7.97 Tf 6.59 0 Td[(375.04.8610)]TJ /F9 7.97 Tf 6.59 0 Td[(314.65.3610)]TJ /F9 7.97 Tf 6.58 0 Td[(2bad3023.39.1510)]TJ /F9 7.97 Tf 6.59 0 Td[(453.37.8810)]TJ /F9 7.97 Tf 6.59 0 Td[(313.33.3010)]TJ /F9 7.97 Tf 6.58 0 Td[(2ugly185.61.1610)]TJ /F9 7.97 Tf 6.59 0 Td[(311.11.5010)]TJ /F9 7.97 Tf 6.59 0 Td[(316.73.1010)]TJ /F9 7.97 Tf 6.58 0 Td[(2 76

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Finally,weanalyzetheSPACE08in-waterexperimentaldatausingLSaschannelestimationalgorithmsinsteadofSLIM,andtheempiricalBERresultsaresummarizedinTables 3-5 3-7 .UnliketheSLIMalgorithm,LSdoesnotpossessthecapabilityofautomaticallydeterminingthechanneltapnumber,andtherefore,thetapnumberofeachpacketdeterminedbySLIMisusedhereforfaircomparison.ComparingtheLSresultswiththeSLIMresultssummarizedinTables 3-2 3-4 ,oneobservesthatSLIMoutperformsLSsignicantly,especiallyunderchallengingchannelconditions.Morespecically,at200mrangeunderuglychannelconditions,amongthe18packagesprocessed,SLIMsuccessfullydetectstheentirepayloadsequencefor14packages,comparedto4packagesbyLS.Moreover,at60mrangeundergoodandbadchannelconditions,SLIMdetectstheentirepayloadsequenceforsignicantlymorepackagesthanLS. 77

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Figure3-1. Eachpacketconsistsofatrainingsequencefollowedbyapayloadsequence.Eachpayloadsequenceisdividedintoblocksofequallengthandeachblockisencodedseparately. Figure3-2. AnNMMIMOUACsystemwithNtransmittransducersandMreceivetransducers. 78

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Figure3-3. ThemodulusofthesimulatedCIRsbetweenthefourtransmittersandthereceiver. Figure3-4. MSEsoftheCIRestimatesusingCAtrainingsequencesoflengthP=128symbols.Eachpointisaveragedover100Monte-Carlotrials. 79

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A B C D Figure3-5. ThecodedBERsofeachofthefourtransmittedpayloadsequencesfora412MIMOsystemassumingthereceiverhasperfectknowledgeontheCIRcharacteristics.ThedetectionperformancesofV-BLASTandRELAX-BLASTarecomparedintermsofcodedBERaveragedover26000Monte-Carlotrialsforvaryinglevelsofthenoisepower. 80

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Figure3-6. SPACE08meteorologicaldata.Theaveragewaveheight(m)isshownoverthecourseoftheexperiments.TwomarksdenoteJuliandates300and301,whichexperiencedtheuglychannelconditions.Awaveheightof1.25m,representedasthedash-dotline,dividestheremaining10Juliandatesintotwocategories,namelybadchannelconditionsonJuliandates294,295,296,299and302,andgoodchannelconditionsonJuliandates291,292,293,297and298. 81

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A B C D E F G H I Figure3-7. NormalizedCIRevolutionoverapproximatelya1minperiod.ThemodulusofthechanneltapisshownindB.CIRisestimatedusingm-sequences.A)-C)good,badanduglychannelconditionsat60m.B)-F)good,badanduglychannelconditionsat200m.G)-I)good,badanduglychannelconditionsat1km.A)D)G)measurementsrecodedonJuliandate292.B)E)H)measurementsrecordedonJuliandate294.C)F)I)measurementsrecordedonJuliandate300. 82

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A B Figure3-8. Spectralestimationofthereceivedmeasurementsat1kmdistanceonJuliandate300.(A)Theambientseanoise.(B)Thesimultaneouslytransmittedsignalontopoftheseanoise. 83

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A B Figure3-9. Theplotofn(r)versusthechanneltaps.Onlythelast51tapsareshownandthehorizontaldash-dotlinerepresentsthethresholdvalue3.A)consideringapacketfromepoch\224withreceiverconguration1,andB)consideringapacketfromepoch\224withreceiverconguration2. 84

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Figure3-10. TheimpactoftCGontheaveragenumberofiterationsrequiredbytheconjugategradientmethod. Figure3-11. Thechanneltrackingprocedureemployedinouranalysis. Figure3-12. Datapacketstructure. 85

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CHAPTER4MIMOUACOVERSPARSEANDFREQUENCYMODULATEDACOUSTICCHANNELS Sofar,wehavestudiedUACoverISIacousticchannelsbyignoringtheDopplereffects.Inthischapter,weincorporatetheDopplereffectsbydiscussingthecoherentMIMOUACoverdoublespreadingacousticchannels(i.e.,thechannelssubjecttobothISIandDopplereffects)coupledwithtime-varyingcharacteristics.Bothchannelestimationandsymboldetectionwillbediscussed,butwithmoreemphasisontheformer.AsmentionedinSection 1.1 ,apreferabletooltocharacterizeadoublespreadingchannelisthescatteringfunction(SF),whichessentiallydecouplestheacousticchannelintoabankofpathsthatexperiencedifferentdelaysandDopplerfrequencies[ 43 ].Duetolargedegreesoffreedom,obtainingSF,moreoftenthannot,isequivalenttosolvinganunderdeterminedproblem,wherethenumberofunknownsismuchlargerthanthatofequations[ 100 ](thisisparticularlytrueintheMIMOcontextsincetheSFsforallthetransmittransducersshouldbeestimatedsimultaneously).Sinceanunconstrainedunderdeterminedprobleminprincipleadmitsaninnitenumberofsolutions,sparsityrequirementsshouldbeimposedonthesolution[ 82 ].Bysparsity,wemeanthattheunderwaterchannelconsistsofonlyafewdominantdelayandDopplertaps,whilealltheremainingtapscanbeapproximatedaszero[ 47 100 ].Adetailedtreatmentofpopularalgorithmstosolvesuchsparsity-basedchannelestimationproblemispresentedin[ 100 ],alongwithathoroughcomparisonoftheirperformances. ThemajorconcerninSF-basedchannelestimation,aspreviouslyremarked,isthattheproblembecomesoverparameterized(i.e.,toomanydegreesoffreedom).Itispracticallymorebenecialtolookforachannelmodelwiththesmallestnumberofparameters,butonethatstillsufcientlyreectsthedeningcharacteristicsoftheacousticchannelofinterest.Tothisend,analternativemethodtoSF(butstillrelatedtoSF)isproposedin[ 65 ],wherethecontributionofDopplereffectscomesthroughonecommonfrequencyvalueforallthetransmitters.Thenumberofunknowns,asa 86

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consequence,issignicantlyreduced.Whilenofurtheraccountsareprovidedin[ 65 ]astoatwhatchannelconditionssuchsimplicationbecomesvalid,wewillshowviaexperimentalresultspresentedlateronthattheassumptionofacommonDopplerfrequencyisgenerallyvalidwhentheDopplereffectsareinducedbytherelativemotionsbetweenthetransmitterandreceiverarrays.In[ 65 ],thechannelestimationisperformedintwoseparatesteps.Thatis,theCIRsandtheunderlyingDopplerfrequencyareestimatedinaseparatemanner.ItisadvantageoustoestimateboththeCIRsandDopplerfrequencyjointly.ThismotivatestheintroductioninthischapterofanextensionoftheSLIMalgorithm(SLIM,asproposedinSection 3.2.2 ,wasdevelopedforISIchannels),referredtoasgeneralizationofSLIM(GoSLIM).ThefundamentalsofthesparseapproachisestablishedbasedonahierarchicalBayesianmodel,solvedthroughmaximizingtheaposterioriprobability(MAP).LikeSLIM,GoSLIMisalsouserparameterfree,makingiteasytouseinpractice. AnotherimportantaspectofUACissymboldetectiongiventheestimatesofCIRsandDopplerfrequencies.Theadversephaseshiftinducedbythechannelshouldrstbecompensatedforusingtheso-obtainedDopplerfrequencyestimate[ 65 ].SuchphasecompensationtaskeffectivelyconvertstheoriginaldoublespreadingchanneltoanISIchannel,whichallowsfortheemploymentofvarioustechniquesthateffectivelycombatISI,includingtheAlamoutidiversity[ 44 ]andBellLabsLayeredSpace-Time(BLAST)typeofschemes[ 47 ].TheAlamoutidiversityschemeispracticallyattractivesinceitfullyextractsthetransmitdiversity[ 84 ]andallowsforefcientsymboldetection[ 44 ].EarlyattemptsofemployingtheAlamoutidiversityschemeintheUACregimewerereportedin[ 53 86 ].Theschemeadoptedin[ 53 ]isadirectimplementationoftheoriginalAlamoutiideathatworkswellforat-fadingchannelsonly[ 2 ].In[ 86 ],theextendedAlamoutischemetoISIchannels[ 44 ]isusedtoimplementintermediatenodestorelaythesignalbetweensourceanddestination,anditseffectivenessisveriedusingsimulateddata.Inthepresentpaper,wewillshowviain-waterexperimentation 87

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resultsthat,aslongastheDopplereffectsaresufcientlycompensatedfor,theAlamoutidiversityschemeisapromisingcandidateinUACsystemsoperatingatamoderatedatarate.Topursueahighdatarate,RELAX-BLASTisalsoconsideredinourMIMOexperiment. Therestofthischapterisorganizedasfollows.Section 4.1 formulatesthechannelestimationprobleminbothtraining-directedanddecision-directedmodes.ThenweproposetheGoSLIMalgorithmforjointlyestimatingCIRsandDopplerfrequencies.Section 4.2 brieyoverviewsthesymboldetectionprocess.Section 4.3 presentsthesimulationresultsofGoSLIM,followedbytheexperimentalresultsobtainedfromanalyzingtheWHOI09andACOMM10experimentdata. 4.1ChannelEstimation Inthissection,westartwiththeproblemformulationofdoublespreadingchannelestimationinbothtraining-directedanddecision-directedmodes.Then,wepresenttheGoSLIMalgorithmforjointlyestimatingtheunderlyingCIRsandDopplerfrequencies.ConsideraMIMOUACsystemequippedwithNtransmittransducersandMreceivehydrophones.Inwhatfollows,unlessotherwisestated,itisassumedthatateachreceiverthechanneltapsforalltheNtransducersexperiencethesameDopplerfrequency,butdifferentreceivehydrophonesexperiencedifferentDopplershifts. 4.1.1Training-DirectedMode Asusual,theinitialtaskofthereceiveristoacquireknowledgeoftheunderlyingchannelbetweenalltransmitterandreceiverpairsusingthetrainingsequences.Byadoptingthecyclicprexschemein[ 84 ],thetrainingsequenceatthenthtransmitter(n=1,2,...,N)isgivenby xn=[xn(P)]TJ /F3 11.955 Tf 11.95 0 Td[(LCP+1),...,xn(P)| {z }LCPprexsymbols,xn(1),xn(2),...,xn(P)| {z }Pcoretrainingsymbols],(4) where[xn(1),...,xn(P)]isthecoretrainingsequenceandtheleadingLCPsymbolsformthecyclicprex.Ingeneral,wehaveP>LCPR)]TJ /F4 11.955 Tf 12.89 0 Td[(1,withRbeingthechannel 88

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tapnumber.Fromanamplierefciencypointofview,itispracticallydesirabletouseunimodulartrainingsequences,i.e.,jxn(p)j=1forn=1,...,Nandp=1,...,P. ForMIMOUACoverdoublespreadingchannels,themeasurementvectorscanbewrittenas[ 43 56 ] ym=mNXn=1~Xnhn,m+em,m=1,...,M,(4) whereymisdenedin( 3 )andhn,misgivenin( 2 ).In( 4 ),emrepresentsadditivenoise(thermalorhardwarerelatednoise,aswellastheambientseanoise)atthemthreceiver.Byemployingthecyclicprexscheme,~Xn2CPRin( 4 )isgivenby ~Xn=266666664xn(1)xn(P)...xn(P)]TJ /F3 11.955 Tf 11.95 0 Td[(R+2)xn(2)xn(1)...xn(P)]TJ /F3 11.955 Tf 11.95 0 Td[(R+3)............xn(P)xn(P)]TJ /F4 11.955 Tf 11.96 0 Td[(1)...xn(P)]TJ /F3 11.955 Tf 11.95 0 Td[(R+1)377777775,n=1,...,N.(4) Thecyclicprexschemeentrusts~Xnwithacyclicshiftproperty,i.e.,therthcolumnof~Xncanbederivedbycyclicallyrotatingtherstcolumnbyr)]TJ /F4 11.955 Tf 12.42 0 Td[(1symbolsforr=2,...,R.Itisworthpointingoutthatthestructureof~Xnshouldreectthecharacteristicsofthetrainingsequences,aswellashowwedesignthetransmittedsignal.Specically,forCAsequenceswithgoodaperiodiccorrelationpropertiescoupledwiththeguardintervalbetweenthetrainingandpayloadsequence,~Xnisgivenin( 2 ).Forthesamesequenceswithouttheguardinterval,~Xnbecomes( 3 ).Whenemployingtrainingsequenceswithgoodperiodiccorrelationpropertiescoupledwiththecyclicprexscheme,asconsideredherein,~Xnisconstructedaccordingto( 4 ).Althoughthesamematrix~Xnisusedinthreedifferentscenarios,thestructureof~Xnshouldbeclearfromthecontext.Theso-calledDopplershiftmatrixm2CPPin( 4 )isconstructedas: m=diag\0021,e)]TJ /F9 7.97 Tf 6.58 0 Td[(2jfmTs,...,e)]TJ /F9 7.97 Tf 6.59 0 Td[(2jfmTs(P)]TJ /F9 7.97 Tf 6.59 0 Td[(1),m=1,...,M,(4) whereTsrepresentsthesymbolperiod. 89

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TheISIandDopplershifteffectscanbeviewedseparatelyin( 4 ).Morespecically,thetermPNn=1~Xnhn,mindicatesthenetcontributionofNISIchannels,whiletheimpactoftheDopplereffectsonthemeasurementscomesthroughmonly,whichcorrespondstotheassumptionthatatthemthreceiver,alltheNRCIRtapsinvolved(recallthatwehaveNtransmittransducersandeachtransducercorrespondstoanR-tapchannel)experiencethesameDopplerfrequencyfm.Thepurposeofsettingtherstdiagonalelementofmto1(Equation( 4 ))istoeliminateambiguities.Inourexample,relativetofym(1)g,agenericmeasurement,sayym(p),experiencesaphaseshiftof)]TJ /F3 11.955 Tf 9.3 0 Td[(fmTs(p)]TJ /F4 11.955 Tf 11.95 0 Td[(1). Weexpress( 4 )inamorecompactform: ym=mXhm+em,(4) whereX=[~X1,...,~XN]andhm=[hT1,m,...,hTN,m]T.Thenthetraining-directedchannelestimationreducestoestimatinghmandfmfromthemeasurementvectorymandknownXform=1,...,M.Equation( 4 )implicitlyassumesthatthechannelsfhn,mgandthefrequenciesffmgremainconstantoverthelengthoffymg(i.e.,duringthedurationofthetrainingsequences)andthatthetransmittedsignalsarenotscaled(stretchedorcompressed)overthelengthoffymg.Notethat( 4 )includesanISIchannelestimationproblemasaspecialcasebysettingfm=0.Thesubjectofsynthesizingunimodulartrainingsequences,coupledwiththeemploymentofthecyclicprexscheme,tofacilitateISIchannelestimationisthoroughlytreatedin[ 46 ].TheshiftedPeCANwaveforms[ 26 ]areusedasthetrainingsequencesintheWHOI09andACOMM10in-waterexperimentations. 4.1.2Decision-DirectedMode Thedecision-directedchannelestimationproblemisonlyaslighttwistofitstraining-directedcounterpart.Fortheformer,weusethepreviouslyestimatedpayloadsymbols,insteadofthetrainingsymbols,toestimatethechannels.Accordingly,( 4 ) 90

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canstillbeused,whereymand~Xnaredenedin( 2 )and( 2 ),respectively.Toconformwiththematrixdimensions,theDopplershiftmatrixmnowisLbyL(thetrackinglengthLisdenedafter( 2 )),constructedasm=diag\0021,e)]TJ /F9 7.97 Tf 6.59 0 Td[(2jfmTs,...,e)]TJ /F9 7.97 Tf 6.59 0 Td[(2jfmTs(L)]TJ /F9 7.97 Tf 6.58 0 Td[(1)form=1,...,M.Similarlytothetraining-directedmode,thechannelestimationprobleminthedecision-directedmodeaimstoestimatehmandfmfromthemeasurementvectorymandknownXformedfromthedecision-directedf~XngNn=1in( 2 ),form=1,...,M,see( 4 ). 4.1.3ChannelEstimationAlgorithm Similarlyto( 3 ),thechannelestimationalgorithmateachreceiver,ineithertraining-ordecision-directedmode,hasthegenericformgivenby(Equation( 4 )) y=Xh+e.(4) Wecanseethatontopof( 3 ),( 4 )incorporatestheDopplershiftmatrix,whichbringsonemoreestimatetarget,namelytheDopplerfrequencyf.Furthermore,byconsideringaatprioronf,andfpngNRn=1,thechannelvectorh,Dopplerfrequencyf,thecovariancematrixP(ormoreprecisely,itsdiagonalelementsp)andthenoisepowercanbeestimatedbasedontheMAPcriterion: maxh,p,,fp(h,p,,fjy)=maxh,p,,fp(yjh,,f)p(hjp).(4) Bycombining( 3 ),( 3 )and( 4 ),andbytakingthenegativelogarithmofthecostfunction,theoptimizationproblemformulatedin( 4 )becomes minh,p,,f dylog+ky)]TJ /F12 11.955 Tf 11.96 0 Td[(Xhk2 +NRXn=1logpn+NRXn=1jhnj2 pn!,(4) which,inthesamespiritofSLIM,canbesolvedusinganalternatingapproach. The5stepsoftheGoSLIMalgorithmatthetthiterationareoutlinedbelow: 1. Givenh(t)]TJ /F9 7.97 Tf 6.58 0 Td[(1),theoptimalP(t)thatminimizesthecostfunctionin( 4 )isgivenby: p(t)n=h(t)]TJ /F9 7.97 Tf 6.59 0 Td[(1)n2,n=1,...,NR.(4) 91

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Forbetternumericalstability,wesetp(t)n(orequivalentlyh(t)n)tozeroifp(t)n<10)]TJ /F9 7.97 Tf 6.58 0 Td[(15.(NotethattheGoSLIMalgorithmachievessparsityduetothehierarchicalBayesianmodel,notthroughthiscompare-and-nullstep.) 2. OnceP(t)isavailable,weproceedtoupdatetheCIRvectoras: h(t)=(t)]TJ /F9 7.97 Tf 6.59 0 Td[(1)XH(t)]TJ /F9 7.97 Tf 6.58 0 Td[(1)X+(t)]TJ /F9 7.97 Tf 6.59 0 Td[(1))]TJ /F12 11.955 Tf 5.48 -9.68 Td[(P(t))]TJ /F9 7.97 Tf 6.59 0 Td[(1)]TJ /F9 7.97 Tf 6.58 0 Td[(1(t)]TJ /F9 7.97 Tf 6.58 0 Td[(1)XHy=hXHX+(t)]TJ /F9 7.97 Tf 6.59 0 Td[(1))]TJ /F12 11.955 Tf 5.48 -9.68 Td[(P(t))]TJ /F9 7.97 Tf 6.59 0 Td[(1i)]TJ /F9 7.97 Tf 6.59 0 Td[(1(t)]TJ /F9 7.97 Tf 6.59 0 Td[(1)XHy. (4) Thesecondequalityfollowsfromthefactthat(t)]TJ /F9 7.97 Tf 6.59 0 Td[(1)isunitary.WhileinvertingP(t),itszerodiagonalentriesareremoved,andtheassociatedcolumnsinXarediscarded. 3. Next,usingthemostrecentlyobtainedh(t)in( 4 ),weestimatetheDopplerfrequencyf.Foreaseofexposition,wedenotez(t)(i)=y(i)~x(t)(i),wherey(i)and~x(t)(i)represent,respectively,theithelementofthemeasurementvectoryand~x(t)with~x(t)=Xh(t),i=1,...,dy.Itiseasytoverifythat y)]TJ /F12 11.955 Tf 11.95 0 Td[(Xh(t)2=y)]TJ /F12 11.955 Tf 11.96 0 Td[(~x(t)2=const)]TJ /F4 11.955 Tf 11.95 0 Td[(2Re dyXi=1z(t)(i)e)]TJ /F9 7.97 Tf 6.59 0 Td[(2jfTs(i)]TJ /F9 7.97 Tf 6.58 0 Td[(1)!. (4) Sincetheconstanttermin( 4 )isnotafunctionoff,minimizingthecostfunctionin( 4 )isequivalenttosolving f(t)=argmaxfRe dyXi=1z(t)ie)]TJ /F9 7.97 Tf 6.59 0 Td[(2jfTs(i)]TJ /F9 7.97 Tf 6.59 0 Td[(1)!.(4) Notethatthesummationtermwithintheparenthesisaboveisnothingbutthediscrete-timeFouriertransform(DTFT)ofthesequencefzigdyi=1evaluatedatfrequencyf.Therefore,f(t)isobtainedasthelocationofthedominantpeakoftherealpartoftheDTFT.Inpractice,toensuretheaccuracyoftheestimate,fzigdyi=1shouldbezero-paddedandthentransformedbyusingthefastFouriertransform(FFT).Wezero-padthesequencetoalengthof220inourexamples. 4. Usingtheh(t)and(t)mostrecentlyobtainedvia( 4 )and( 4 ),respectively,wenallyestimatethenoisepoweras: (t)=1 dyy)]TJ /F12 11.955 Tf 11.95 0 Td[((t)Xh(t)2.(4) 5. Sett=t+1.GobacktoStep1iftislessthanapredenediterationnumber,orterminateotherwise. 92

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Inthetraining-directedmode,thechannelcharacteristicsareingeneralnotavailableapriori.Inourexamples,h(0)isinitializedusingthestandardmatchedlter,f(0)isinitializedas0andthenoisepower(0)isinitializedwithasmallpositivenumber,forinstance,10)]TJ /F9 7.97 Tf 6.58 0 Td[(10.OurempiricalexperiencesuggeststhattheGoSLIMalgorithmdoesnotprovidesignicantperformanceimprovementsafter20iterationsorless. 4.2SymbolDetection Inthissection,wefocusondeterminingthepayloadsymbolsgiventheGoSLIMestimatesofCIRsandDopplerfrequencies.Thesymboldetectiontaskisachievedviatwosteps:phasecompensationfollowedbyISIequalization.Werstpresenttheproblemformulation,andthen,describethephasecompensationscheme.Finally,theAlamoutidiversityschemeisbrieyreviewed. 4.2.1ProblemFormulation TreatingthetransmittedsymbolsastheunknownsandtheCIRsandDopplerfrequenciesasknownin( 4 ),themeasurementvectorcanbeexpressedas[ 43 56 ]: ym=^mNXn=1^Hn,m_xn+em,m=1,...,M,(4) wheretheestimatedCIRmatrix^Hn,m2CR(2R)]TJ /F9 7.97 Tf 6.59 0 Td[(1)isgivenin( 2 )while_xnandymaredenedin( 2 ).Perthediscussionsfollowing( 4 ),oncetheestimateofDopplerfrequency^fmisavailable,theestimatedDopplershiftmatrix^min( 4 )isconstructedas: ^m=diaghe)]TJ /F9 7.97 Tf 6.59 0 Td[(2j^fmTs(t0)]TJ /F9 7.97 Tf 6.59 0 Td[(1),...,e)]TJ /F9 7.97 Tf 6.59 0 Td[(2j^fmTs(t0+R)]TJ /F9 7.97 Tf 6.59 0 Td[(2)i.(4) Whendetectingsymbols,theestimatesf^hn,mgandf^fmgareassumedxedsincethepreviouschannelupdateandwetreatf^Hn,mgandf^mgin( 4 )asknown. 4.2.2PhaseCompensation Thistaskissimplyachievedbymultiplying^Hmtobothsidesof( 4 ),yielding ~ym=NXn=1^Hn,m_xn+~em,m=1,...,M,(4) 93

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where~ym=^Hmymand~em=^Hmem.GivenemCN(0,I),~emstillhasthedistributionofCN(0,I)since^Hmisunitary.PhasecompensationeffectivelyconvertstheoriginaldoublespreadingchanneltoanISIchannel.In( 4 ),giventhephase-compensatedmeasurementvectorsf~ymgandtheestimatedCIRmatricesf^Hn,mg,thetaskofdetectingthepayloadsymbolscontainedinf_xngisawell-denedISIequalizationproblem,anditcanbetackledbyemploying,forexample,theRELAX-BLASTalgorithm. 4.2.3AlamoutiDiversityScheme AsanalternativetothespatialmultiplexingschemeincludingRELAX-BLAST,wecanalsousethespace-timecodingschemesuchastheAlamoutidiversitytechniquetofacilitatethesymboldetectiontaskforreducedbiterrorrate(BER).TheAlamoutidiversityschemeispracticallyattractivesinceitfullyexploitsthetransmitdiversityandgenerallyallowsforveryefcientequalization[ 2 44 ].Forcompleteness,theAlamoutidiversityschemeisbrieyreviewedinthissection. Weaimtotransmit2LpayloadsymbolsusingasystemequippedwithN=2transmittersandM=1receiveroverISIchannels.The2Lsymbolsaredividedintotwosegments,sayaandb,eachoflengthL.Perthesuggestionspresentedin[ 44 ],thestructureofthetwotransmittedsequencesisshowninFigure 4-1 .Eachtransmittersendsthesignalintwoseparatebursts.InFigure 4-1 ,forexample,thersttransmittersendsaand)]TJ /F12 11.955 Tf 9.3 0 Td[(byduringtherstandsecondbursts,respectively.bydenotesaconjugatedtime-reversedversionofb(e.g.,ifb=[b(1),...,b(L)]T,thenby=[b(L),...,b(1)]T).Thesecondtransmittertransmitsbandayduringtherstandsecondbursts,respectively.Betweenthetwoburstsliesagap.Typically,thegaplengthislargerthanthechanneltapnumberRtoensurethattheinterferencefromtherstburstdoesnotextendtothesecondburst. 94

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DeneHn,1andHyn,12C(R+L)]TJ /F9 7.97 Tf 6.59 0 Td[(1)L,respectively,as: Hn,1=266666666664^hn,1(1)0......^hn,1(R)^hn,1(1)......0^hn,1(R)377777777775andHyn,1=266666666664^hn,1(R)0......^hn,1(1)^hn,1(R)......0^hn,1(1)377777777775,n=1,2.(4) OncetheCIRestimatesf^hn,1g2n=1andthephasecompensatedmeasurementvector~y1areavailable,~y1,l,aportionof~y1correspondingtotherstburst(Figure 4-1 ),canbeexpressedas: ~y1,l=H1,1a+H2,1b+~e1,l.(4) Similarly,~y1,r,aportionof~y1correspondingtothesecondburst,isgivenby: ~y1,r=H1,1)]TJ /F2 11.955 Tf 5.48 -9.68 Td[()]TJ /F12 11.955 Tf 9.3 0 Td[(by+H2,1ay+~e1,r.(4) Notethat( 4 )and( 4 )implicitlyassumethattheassumedISIchannelremainsconstantoveroneblocktime;seeFigure 4-1 Combining~y1,land~yy1,rfollows 264~y1,l~yy1,r375=264H1,1H2,1Hy2,1)]TJ /F4 11.955 Tf 10.91 2.66 Td[(Hy1,1375264ab375+264~e1,l~ey1,r375=H264ab375+264~e1,l~ey1,r375.(4) ItiseasytoverifythatthematrixproductHHH2C2L2Lpossessesablockdiagonalstructure:theentriesofthetwoLLmatricesontheoff-diagonalpositionareallzero,whereastheentriesofthetwoLLmatricesonthediagonalpositionaregenerallynonzero.ThissuggeststhatbymakinguseoftheAlamoutidiversityscheme,matchedlter(bymultiplyingHHonbothsidesof( 4 ))decomposestheoriginaldetectionproblemofdimension2Lintotwosubproblems,eachofdimensionL(i.e.,thedetection 95

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ofaandbisperformedseperately)[ 44 ].Notethatforeachsubproblem,bothofthepayloadsequencesaandbstillsufferfromISI,makingequalizationnecessary[ 44 ]. Ideally,ifthecolumnsinHin( 4 )arepairwiseorthogonal(i.e.,HHHbecomesdiagonal),thenthematchedltercoulddecoupletheoriginaldetectionproblemintoabankof2Lindependentscalarproblems.Moreover,undertheGaussiannoiseassumption,theso-obtainedmatchedlterresultisequivalenttothemaximumlikelihoodresult.Ithasbeendemonstratedin[ 1 ]thatsuchpairwiseorthogonalitypropertycanbeachievedinthefrequencydomain.Toseethis,itissuggestivetorstreviewthediagonalizationpropertyofacirculantmatrix.Itiswell-knownthataKKcomplex-valuedcirculantmatrixCcanbediagonalizedasC=FHF[ 71 ].Here,FistheKKFFTmatrixand)]TJ /F1 11.955 Tf 10.26 0 Td[(holdstheKeigenvaluesofConitsdiagonal[ 71 ].Furthermore,theseeigenvaluescanbeefcientlycomputedbyapplyingFFTtotherstcolumnofC.NotethatbothfHi,1g2i=1andfHyi,1g2i=1in( 4 )possesstheToeplitzstructure,whichcanbeexpandedtocirculantmatricesbyappendingtheappropriate(R+L)]TJ /F4 11.955 Tf 12.61 0 Td[(1)(R)]TJ /F4 11.955 Tf 12.61 0 Td[(1)matrixtotherighthandsideoftherespectivematrix.Thatis,Ci,1(Cyi,1)canbeconstructedbycyclicallyshiftingthelastcolumnofHi,1(Hyi,1)forR)]TJ /F4 11.955 Tf 12.14 0 Td[(1timestothebottomfori=1,2.Then,( 4 )canberewrittenas 264~y1,l~yy1,r375=264C1,1C2,1Cy2,1)]TJ /F4 11.955 Tf 10.36 2.66 Td[(Cy1,1375264ab375+264~e1,l~ey1,r375 (4) =264FH)]TJ /F9 7.97 Tf 6.94 -1.79 Td[(1FFH)]TJ /F9 7.97 Tf 6.94 -1.79 Td[(2FFH)]TJ /F9 7.97 Tf 6.94 -1.8 Td[(3F)]TJ /F12 11.955 Tf 9.29 0 Td[(FH)]TJ /F9 7.97 Tf 6.94 -1.8 Td[(4F375264ab375+264~e1,l~ey1,r375. (4) In( 4 ),a(b)isobtainedbypaddingR)]TJ /F4 11.955 Tf 11.85 0 Td[(1zerosattheendofa(b),and( 4 )followsdirectlyfromthediagonalizationpropertyofthecirculantmatrices. Equation( 4 )canberewrittenas: 264F~y1,lF~yy1,r375=264)]TJ /F9 7.97 Tf 6.94 -1.8 Td[(1)]TJ /F9 7.97 Tf 6.94 -1.8 Td[(2)]TJ /F9 7.97 Tf 6.94 -1.79 Td[(3)]TJ /F4 11.955 Tf 9.63 2.66 Td[()]TJ /F9 7.97 Tf 6.94 -1.79 Td[(4375264FaFb375+264F~e1,lF~ey1,r375.(4) 96

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NotethatmultiplyingFontheleftsideofavectorisanFFToperation.Therefore,( 4 )ineffectconvertsourviewpointtothefrequencydomain.Weexpress( 4 )inamorecompactform: Y=D+E.(4) Inthepresentpaper,thisistheonlytimethatweuseboldfaceuppercaselettersY,DandEtorepresent,respectively,thefrequencyrepresentationsofthemeasurementvector,theestimatetargetsandnoiseterms.Further,ECN(0,I)followsfromthefactthatbothFFTandconjugatetime-reversionoperationpreservethestatisticalpropertyofthenoiseterms~e1,land~e1,r.Thekeyadvantageofthefrequencyviewpointisthatnowthecolumnsof)]TJ /F1 11.955 Tf 10.26 0 Td[(arepairwiseorthogonal(i.e.,)]TJ /F6 7.97 Tf 6.94 6.84 Td[(H)]TJ /F1 11.955 Tf 10.26 0 Td[(isdiagonal),incontrastto( 4 )whereHHHexhibitsablockdiagonalstructure.Therefore,inourexample,thematchedlterisemployedtoobtain^D.Once^Disavailable,theestimateofaandbcanbeobtainedviainverseFFT(IFFT).Finally,theestimateofa(b)in( 4 )canbeobtainedfromtheestimateofa(b)bystraightforwardre-indexing:theestimateofa(b)canbeobtainedfromtherstLelementsoftheestimateofa(b). 4.3NumericalandExperimentalResults 4.3.1SimulationofChannelEstimationPerformance WecomparethechannelestimationperformanceusingGoSLIMandamethodthatestimatesDopplerfrequenciesandCIRsseparately.Thelatterscheme,referredtoastwo-stepmethod,isimplementedasfollows.First,theDopplerfrequenciesareestimatedbysolvingtheoptimizationproblem: ^f=argmax~f~XHy2,(4) where~ismodeledsimilarlyto( 4 )as: ~=diagh1,e)]TJ /F9 7.97 Tf 6.59 0 Td[(2j~fTs,...,e)]TJ /F9 7.97 Tf 6.59 0 Td[(2j~fTs(P)]TJ /F9 7.97 Tf 6.59 0 Td[(1)i,(4) 97

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with~fbeingtheassumedDopplerfrequency.Once^fisavailable,wecompensatefortheDopplereffectsonthereceivedmeasurements,andthenestimatetheCIRsviathelinearminimummean-squarederror(LMMSE)ltering: ^h=)]TJ /F12 11.955 Tf 5.48 -9.68 Td[(XHX+I)]TJ /F9 7.97 Tf 6.59 0 Td[(1XH~y,(4) where~y=^HyrepresentsthemeasurementvectorafterDopplercompensationand^stillfollows( 4 )butwith~freplacedby^f. ConsideraUACsystemequippedwithN=2transmittersandM=1receiver.ThemodulusofthesimulatedsparseCIRscorrespondingtothetwotransmittersareshowninFigure 4-2 withR=20taps.Inoursimulation,wesettheDopplerfrequencyandthesymbolperiodasf=1HzandTs=0.125ms,respectively,andassumethatboththesimulatedCIRsandfareconstant.Twodifferenttypesoftrainingsequencesarecompared:oneistheshiftedPeCANsequence,whichcouldbeusedinthetraining-directedchannelestimation,andtheotheristherandomQPSKsequencetoresemblethedecision-directedchannelestimationscenario.BothsequenceshavealengthofP=dy=256symbols.ThePeCANsequencesareusedwithLCP=R)]TJ /F4 11.955 Tf 12.18 0 Td[(1=19cyclicprexsymbols,whileforQPSKsequences,thepreceding19symbolsarerandomlygeneratedQPSKsymbols.GiventheCIRtruths,trainingsequences,fandTs,thereceivedmeasurementsareconstructedasin( 4 )witheCN(0,I).NotethatfortheMMSECIRestimatorin( 4 ),thetruenoisevarianceisgivenasaprioriknowledge(inpractice,however,needstobeestimated). WhentheshiftedPeCANsequencesareemployed,themean-squarederrors(MSEs)oftheCIRestimatesandtheDopplerfrequencyestimatesobtainedbyGoSLIMandthetwo-stepmethodversusthenoisepowerareshowninFigures 4-3A and 4-3C ,respectively,andthoseforQPSKsequencesareshowninFigures 4-3B and 4-3D ,respectively.Eachpointhereisaveragedover100Monte-Carlotrials.Thenoisepatternvariesindependentlyforeachtrial.BycomparingFigures 4-3C with 4-3D ,oneobserves 98

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thattheDopplerfrequencyestimator( 4 )isquitesensitivetothecharacteristicsofthetrainingsequencesused.Inparticular,theMSEofthefrequencyestimateforQPSKsequencesismuchworsethanthatfortheshiftedPeCANsequences.Toverifythisobservation,weconsideradatamodelintheabsenceofnoise(i.e.,thenoisetermeisdroppedin( 4 )): y=Xh.(4) Werstconstruct~asin( 4 ),andthenleftmultiply~XHtobothsidesof( 4 ): ~XHy=XH~HXh.(4) WhentheshiftedPeCANsequencesareemployed,XHXessentiallyequalsdyI[ 26 ],and~=isthesolutionto( 4 ),leadingtoaperfectfrequencyestimate,i.e.,^f=f.Westarttheproofbyplugging( 4 )intothecostfunctionin( 4 ),whichgives: (~X)Hy2=XH~HXh2=XHXh2, where ,~H=diag\0021,e)]TJ /F9 7.97 Tf 6.59 0 Td[(2jfTs,...,e)]TJ /F9 7.97 Tf 6.58 0 Td[(2jfTs(dy)]TJ /F9 7.97 Tf 6.58 0 Td[(1),(4)withf,f)]TJ /F4 11.955 Tf 10.93 2.66 Td[(~f.Itiseasytoseethatisunitary.Fornotationalsimplicity,wehenceforthdroptheconstantdyandrewriteXHX=INRNR,i.e.,Xbecomessemi-unitary.(ThiscanbeachievedbyscalingeachelementinXby1 p dy.)Weappendtheappropriatedy(dy)]TJ /F3 11.955 Tf 11.96 0 Td[(NR)matrixtotheright-handsideofX2CdyNRandconstructaunitarymatrixhX~Xi2Cdydy.Then: hX~XiHHhX~XihX~XiHhX~Xi=Idydy.(4) Theleft-handsideofEquation( 4 )canbepartitionedasfollows: 264A11A12A21A22375=Idydy, 99

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whereA112CNRNR,A122CNR(dy)]TJ /F6 7.97 Tf 6.59 0 Td[(NR),A212C(dy)]TJ /F6 7.97 Tf 6.59 0 Td[(NR)NRandA222C(dy)]TJ /F6 7.97 Tf 6.58 0 Td[(NR)(dy)]TJ /F6 7.97 Tf 6.59 0 Td[(NR).ConningourfocustothesubmatrixA11,weget: A11=XHHXXHX+XHH~X~XHX=INRNR. Thus hHA11h=hHXHHXXHXh+hHXHH~X~XHXh=hHh. SinceXHH~X~XHXispositivesemi-denite,wehave hHXHH~X~XHXh0. Asaconsequence, hHXHHXXHXhhHh, whichisequivalentto XHXh2khk2. Theupperboundisachievedfor=I,i.e.,f=0(Equation( 4 )).Consequently,^f=fisthesolutionto( 4 ). Asaconsequence,onecanexpectthatasdecreases,theMSEcurveinFigure 4-3C willdecreaseandbecomezeroasgoestozero.Incontrast,whenapplyingtheQPSKsequences(i.e.,XHX6=dyI),~=isnolongerthesolutionto( 4 ),whichresultsinabiasedfrequencyestimate.ThisisinlinewiththeobservationthattheMSEcurveinFigure 4-3D islimitedtoacertainlevel.SuchbiasedDopplerfrequencyestimateswillfurtherdegradethesubsequentMMSE-basedCIRestimate,asobservedbycomparingFigures 4-3A and 4-3B GoSLIM,ontheotherhand,isrobustagainstthetypesofthesequencesused,whichisadesiredpropertyforachannelestimationalgorithm.WecanseefromFigure 4-3C thattheMSEofthefrequencyestimategivenbyGoSLIMisslightlybetterthanthatobtainedusing( 4 )duetoitsjointestimationmechanism.GoSLIMgivesconsistently 100

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betterCIRestimatethanitsMMSEcounterpart(Figures 4-3A and 4-3B )evenifthelatterhasthenoisepowerknownapriori.ThisismainlybecauseGoSLIMaddressessparsitywhileMMSEdoesnot.Insum,thetwo-stepmethodisinferiorthanGoSLIM,especiallywhenthetrainingsequencesdonotpossessgoodcorrelationproperties.Duetothisreason,wewilluseGoSLIMtoanalyzetheexperimentaldatainthefollowing. 4.3.2WHOI09In-WaterExperimentationResults 4.3.2.1Experimentspecics TheWHOI09in-waterexperimentwasconductedinDecember2009.The4transmittransducers,withsourcespacingupto1m,weresuspendedfromavesselheavingina14mmid-depthwatercolumn.Twoseparate4-hydrophonearraysweredeployedapproximately2kmand1kmawayfromthesourcearrayandtheyarereferredto,respectively,astheRB1andRB2receivingarrays.BothoftheRB1andRB2receivingarrayshad0.21mspacingbetweenadjacenthydrophones,andtheyweremountedonanchoredbuoysinamid-watercolumnduringthecourseofdatacollection.Formoredetailsabouttheexperiment,wereferthereadersto[ 89 ].TheDopplereffectsweremainlyduetotherelativemotionbetweenthetransmittersandreceivers.Thecarrierfrequency,thesamplingfrequencyandthesymbolrateemployedintheWHOI09experimentwere30kHz,200kHzand8kHz,respectively.TheAlamoutischemeswerethoroughlytestedintheWHOI09experiment.Inparticular,weexploredthedualitybetweentheUACsystemsequippedwith1transmitterand2receivers(1Tx)]TJ /F1 11.955 Tf 9.3 0 Td[(2Rx)and2transmittersand1receiver(2Tx)]TJ /F1 11.955 Tf 9.3 0 Td[(1Rx),bothattainingacoded(uncoded)datarateof3.5kbps(7kbps).Wealsoshowatthecostofincreasedcomputationalcomplexityatthereceiverside,2pairsofAlamouticodescouldalsobetransmittedsimultaneouslytodoublethedatarateusingareceiverarraywithmultipleelements.InWHOI09,thetransmittedsignalwasrecordedbybothRB1andRB2andeachofthedatapackageswedesignwastransmitted3times.Consequently,atotalof6epochswereavailableforourprocessing.Inwhatfollows,anepochisnamed,forexample,-RB1,which 101

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referstothemeasurementsacquiredbyRB1inresponsetothesignaltransmittedattime. Toexaminethechannelconditions,GoSLIMisemployedtoestimatetheunderlyingCIRsandDopplerfrequenciesbymakinguseoftheshiftedPeCANtrainingsequencesperiodicallyallocatedoverthetransmittedsequence.Figure 4-4 showstheCIRevolutionsbetweentheactivetransmitterandthe2ndreceivehydrophoneforeachepoch.Inaddition,Figure 4-5 plotstheevolutionsoftheDopplerfrequenciesforeachhydrophone.Onecanseethatthepositionoftheprincipalarrivalandthesurface-interactivepathsshowninFigure 4-4 areslowlyshiftingleftwardswithtimeduetotemporalcompression:overthe9speriodoftransmission(duringwhichatotalof71.1ksymbolsweretransmitted),thesignaliscompressedby4symbolsatmost(withFigure 4-4 (a)beingtheworstcase).Asaconsequence,theeffectsoftimestretchingareverylimitedandcanbeneglectedduringeachblockof0.14s. 4.3.2.2PerformanceoftheAlamouticodingscheme Toinvestigatetheperformanceofthe2Tx)]TJ /F1 11.955 Tf 9.29 0 Td[(1RxAlamoutischeme,thestructureofthetransmittedsequencesisshowninFigure 4-6 .Twosynchronizedtransmitterswereactivated,andeachtransmittersentfourdatapacketsinsuccession.Eachdatapacketcanbefurtherdividedinto16blocksfollowedbyagapoflength500.Thepresenceofthegapensurestheeliminationofinter-packetinterferences.TheconstructionofeachblockpairacrossthetwoactivetransmittersisquitesimilartothatinFigure 4-1 ,exceptthatthegapbetweenthetwopayloadsegmentsinFigure 4-1 isnowreplacedbyatrainingsequenceformedbyashiftedPeCANsequencewithP=512symbolsandLCP=99cyclicprexsymbols.Inourdesign,eachpayloadsegment(e.g.,aorbinFigure 4-6 )containsL=250QPSKsymbolsandhasundergonechannelcoding.Takingsegmentaforexample,itisgenerated,asshowninFigure 4-6 ,byfeeding250sourcebitsintoa1=2rateconvolutionalencoderwithgeneratorpolynomials(10011)and(11011)followedbyarandominterleaverandQPSKmodulationusingGraycode 102

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mapping.Segmentb,aswellasthesegmentsinotherblocks,issimilarlygeneratedbutwithdifferentsourcebitsandadifferentrandominterleaver.Notethatinner-blockinterferencescausedbythetrainingsequencescanbeeasilyremovedbysubtractingtheircontributionsoutfromthemeasurementsafterthechannelestimationhasbeendone,whileinter-blockinterferencescausedbypayloadsequencescanbemitigatedbyallocatingguardintervalsbetweenadjacentblocks,assuggestedin[ 44 ].TheAlamoutistructureshowninFigure 4-6 leadstoanuncoded(coded)datarateofapproximately7kbps(3.5kbps). Sinceeachpayloadblockcontainsitsowntrainingsequence(Figure 4-6 ),symboldetectioncanbeperformedonablock-by-blockbasis:werstconducttraining-directedchannelestimation,andthendetectthe500QPSKpayloadsymbolswithintheblockofcurrentinterestperthediscussionsinSection 4.2.3 .Asaconsequence,decision-directedchannelestimationisnotneeded.Inouranalysis,thechanneltapnumberisxedatR=30forallepochs.TheempiricalBERresultsatdifferentreceivehydrophones,byaveragingover192kuncodedbitsand96kcodedbits(recallthatthetransmittedsequenceshowninFigure 4-6 carries32kQPSKpayloadsymbols,i.e.,64kuncodedbitsor32kcodedbits,andwehave3epochsforeachreceivingarray),aresummarizedinTable 4-1 .OneobservesfromTable 4-1 thatthe2ndhydrophoneoftheRB1arrayyieldssignicantlyhigherBERsthanothers.ThiscanbeexplainedbylookingatFigure 4-4 ,whichshowsthecomparisonoftheestimatedCIRsforthe2ndhydrophoneoftheRB1andRB2arrays.Notethatthechannelamplitudeatthe2ndhydrophoneofRB1islowerthanthatofRB2byalmostanorderofmagnitude.Itisworthpointingoutthatwhenanalyzingthe2Tx)]TJ /F1 11.955 Tf 9.3 0 Td[(1TxAlamoutischeme,wecouldalsoextendtheGoSLIMalgorithmtoalloweachtransmittertohaveitsownDopplerfrequency,insteadofacommononeasassumedbyGoSLIM.Thisextension,however,didnotresultinvisibleperformanceimprovementovertheoriginalGoSLIM,anditsuffersfromahighercomputationalcomplexitycomparedtothelatter. 103

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Table4-1. BERperformanceofGoSLIMcoupledwithAlamoutidiversityschemefor2Tx-1Rxsystems. RB1RB2uncodedBERcodedBERuncodedBERcodedBER Rx12.710)]TJ /F9 7.97 Tf 6.59 0 Td[(401.910)]TJ /F9 7.97 Tf 6.59 0 Td[(40Rx21.810)]TJ /F9 7.97 Tf 6.59 0 Td[(22.110)]TJ /F9 7.97 Tf 6.59 0 Td[(31.310)]TJ /F9 7.97 Tf 6.59 0 Td[(40Rx31.610)]TJ /F9 7.97 Tf 6.59 0 Td[(406.210)]TJ /F9 7.97 Tf 6.59 0 Td[(50Rx43.210)]TJ /F9 7.97 Tf 6.59 0 Td[(401.110)]TJ /F9 7.97 Tf 6.59 0 Td[(40 Table4-2. BERperformanceofusingGoSLIMfor1Tx-2Rxsystems. RB1RB2indicesoftheRxsuncodedBERcodedBERuncodedBERcodedBER f1,2g3.010)]TJ /F9 7.97 Tf 6.58 0 Td[(32.310)]TJ /F9 7.97 Tf 6.58 0 Td[(300f1,3g5.210)]TJ /F9 7.97 Tf 6.58 0 Td[(6000f1,4g5.210)]TJ /F9 7.97 Tf 6.58 0 Td[(6000f2,3g2.710)]TJ /F9 7.97 Tf 6.58 0 Td[(38.910)]TJ /F9 7.97 Tf 6.58 0 Td[(41.610)]TJ /F9 7.97 Tf 6.58 0 Td[(50f2,4g6.610)]TJ /F9 7.97 Tf 6.58 0 Td[(33.510)]TJ /F9 7.97 Tf 6.58 0 Td[(32.110)]TJ /F9 7.97 Tf 6.58 0 Td[(50f3,4g4.010)]TJ /F9 7.97 Tf 6.58 0 Td[(41.010)]TJ /F9 7.97 Tf 6.58 0 Td[(55.210)]TJ /F9 7.97 Tf 6.58 0 Td[(60 Inadditiontotheconventional2Tx)]TJ /F1 11.955 Tf 9.3 0 Td[(1RxAlamouticodingtechnique,wealsotriedthe1Tx)]TJ /F1 11.955 Tf 9.3 0 Td[(2RxschemebyactivatingonlyTx1inFigure 4-6 .(Thissingle-inputsequenceisusedtoobtainFigures 4-4 and 4-5 .)Notethatthedatarateofthe1Tx)]TJ /F1 11.955 Tf 9.3 0 Td[(2Rxsystemisthesameasthatofits2Tx)]TJ /F1 11.955 Tf 9.3 0 Td[(1Rxcounterpart.TheuncodedandcodedBERresultsobtainedbyGoSLIMwiththe1Tx)]TJ /F1 11.955 Tf 9.29 0 Td[(2RxsystemcongurationaresummarizedinTable 4-2 .Onceagain,theBERresults,bothuncodedandcoded,becomepoorwheneverthesecondhydrophoneoftheRB1arrayisused.Onceagain,MFyieldsmuchhigherBERthanGoSLIM.ComparingTables 4-1 with 4-2 ,oneobservesthattheBERresultsofthe2Tx)]TJ /F1 11.955 Tf 9.3 0 Td[(1Rxsystemisworsethanthatofthe1Tx)]TJ /F1 11.955 Tf 9.3 0 Td[(2RxcounterpartwhenusingGoSLIM.Thiscouldbeduetothefactthattheformersystemhasmoreunknownparameters(perreceiver). 104

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Table4-3. BERperformanceofusingGoSLIMwithLMMSEfortransmitting2pairsofAlamouticodes. RB1RB2uncodedBERcodedBERuncodedBERcodedBER the1stpair2.010)]TJ /F9 7.97 Tf 6.58 0 Td[(401.010)]TJ /F9 7.97 Tf 6.59 0 Td[(40the2ndpair1.510)]TJ /F9 7.97 Tf 6.58 0 Td[(402.310)]TJ /F9 7.97 Tf 6.59 0 Td[(30 4.3.2.3Performanceoftransmitting2pairsofAlamouticodes Aspreviouslyremarked,2Tx)]TJ /F1 11.955 Tf 9.3 0 Td[(1Rxand1Tx)]TJ /F1 11.955 Tf 9.29 0 Td[(2Rxsystemcongurationsresultinthesamedatarate(i.e.,7kbpsuncodeddatarateand3.5kbpscoded).Thisdataratecouldbedoubledifwetransmit2pairsofAlamoutisequencesbyactivatingallofthe4transmitters:withTx1andTx2formingonepair,andTx3andTx4forminganother.TheconstructionofeachpairstillfollowsFigure 4-6 witheachpacketconsistingof8blocks.Asaconsequence,ineachepoch,the1sttransmitterpaircarries16kQPSKpayloadsymbols,whilethe2ndpaircarriesanother16ksymbols.Notethatthepricewepayforthisdoubleddatarateistheincreasedreceptioncomplexity.Forthe2-pairAlamouticongurations,theorthogonalityproperty(Section 4.2.3 )stillholdswithineachtransmitterpairinthefrequencydomain,whichisensuredbythestructureofthetransmittedsignals(Figure 4-1 ).Theorthogonalityproperty,however,nolongerholdsacrossthetwotransmitterpairs.Consequently,thedetectionproblemathandcannotbedecoupledintoabankofscalerproblemsusingthematchedlter.Todealwiththisproblem,theLMMSEbasedRELAX-BLASTschemeisemployedforsymboldetection.Totakeadvantageofthespacialdiversity,weusethemeasurementsfromthe1st,3rdand4threceivehydrophonesforsymboldetection(the2ndhydrophonesareavoidedpurposelyduetothedefectiveperformanceofthe2ndhydrophoneofRB1,asremarkedpreviously).TheresultingBERresults,obtainedbyaveragingover96kuncodedbitsand48kcodedbits,aresummarizedinTable 4-3 105

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4.3.3ACOMM10In-WaterExperimentationResults 4.3.3.1Experimentspecics TheACOMM10experimenttookplaceinJuly2010intheMid-AtlanticBightonthecontinentalshelfoffthecoastofNewJerseyinanareawithwaterdepthof78m.Thetransmitterarrayconsistedof12transducerswith0.8mspacingbetweenadjacentelements.Inourdesign,only4transducerswereactivated,i.e.,N=4.Thereceivingarraywascomposedof8hydrophones,i.e.,M=8.Thespacingbetweentheadjacenthydrophoneswas2.06mexcepttherstelement,whichwasspaced4mabovethesecondelement.Boththetransmitarrayandthereceivingarrayweremountedonanchoredbuoysandweredeployedapproximately3kmawayfromeachother.Thecarrierfrequency,thesamplingfrequencyandthesymbolrateemployedintheACOMM10experimentwere20kHz,80kHzand4kHz,respectively. TheBLASTdatapackageof20sindurationwastransmittedmultipletimesintheACOMM10experimentandwasrecordedbythereceivingarray.Atotalof89epochswereavailableandtheyarereferredtoasMIMO01MIMO89,respectively.Figures 4-7 and 4-8 show,respectively,theevolutionsofCIRandDopplerfrequenciesestimatedbyGoSLIM.Toobtainthesegures,wetreatthe4simultaneouslytransmittedsequencesasperfectlyknownatthereceiversideandweuseatrackinglengthofL=450. 4.3.3.2PerformanceoftheMIMOBLASTscheme Figure 4-9 showsthesourceinformationcontainedinthetransmittedpackage.Eachpackageconsistsof7packets.Therst4packetsconvey4grayscaleGatormascotsandthelast3packetscombinedformacoloredmascot.TheRGBcomponentsofthecoloredimagearetransmittedinthe5th,6thand7thpackets,respectively.Guardintervalsbetweenadjacentpacketsareusedtopreventinter-packetinterference.Eachpixelofthegrayscaleimageisrepresentedby5bits,correspondingto32differentintensities(e.g.,purewhiteandpuredarkpixelsarerepresentedby11111and00000, 106

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respectively).The64-pixelby100-pixelgrayscalemascotimage,asaconsequence,isrepresentedbyatotalof32ksourcebits.(Accordingly,acoloredmascotimageisrepresentedby96kbits.)Thecontrastofthegrayscaleimage,aswellasthehueofthecoloredimage,hasbeencarefullyadjustedsothattheimagecarriesapproximatelyequalnumbersof1'sand0's. WehereinelaboratehowtogenerateapacketfromthegrayscaleGatormascotimage(thepacketgenerationforeachoftheRGBcomponentsofthecoloredimagefollowsthesameprocedure).Specically,the32ksourcebitsarerstinterleavedsothatthebitsfeedingintotheconvolutionalencodermodulehaveanequalchanceofbeing0or1;seeFigure 4-10 .Theso-obtained32kinterleavedsourcebitsarethendividedinto32groups,eachcontains1kbits.Theithgroup(i=1,...,32)willbeusedtoconstructtheithpayloadsymbolblockacrossthe4transmittedsequences.Toseethis,Figure 4-10 illustratesascenariowithi=1(themethodologycanbemappedtothecaseswithi=2,...,32inastraightforwardmanner).Werstfeedthe1kbitscontainedinthe1stgroupintoa1=2rateconvolutionalencoderwithgeneratorpolynomials(10011)and(11011).The2kencodedbitsarethenpassedtoanotherrandominterleaver,followedbyQPSKmodulationusingGraycodemapping.Theresulting1kQPSKpayloadsymbolsarenallydemultiplexedintothe4payloadblocks(eachcontains250QPSKsymbols)acrossthe4transmittersinaround-robinfashion(thisiswheretheDemultiplexermoduleinFigure 4-10 comesintoplay).Morespecically,inourdesign,thesymbolswithindexfn+4ag249a=0formthepayloadblockatthenthtransmitter(n2f1,2,3,4g).TheshiftedPeCANtrainingsequenceswithlengthP=512,inconjunctionwithLCP=99cyclicprexsymbols,formthetrainingsection,whichislocatedbetweenthe16thand17thpayloadblocks.ThisMIMOUACdesignleadstoanetcodeddatarateof15kbps. BytransmittingN=4sequencessimultaneouslyandincorporatingthemeasurementsacquiredfromallofftheM=8receiverelementsforanalysis,weestablisheda48 107

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MIMOUACsystem.UnliketheAlamoutisequencesadoptedintheWHOI09experimentwherethetraining-directedchannelestimationcanbeconductedperiodically,onlyonetrainingsequenceisusedfortheBLASTdatainACOMM10(Figure 4-10 ).Therefore,thedecision-directedchannelestimationbecomesindispensablewhenanalyzingtheACOMM10data.Thechanneltapnumberandthetrackinglengtharexed,respectively,atR=55andL=450forallofthe89epochs.Thechanneltrackingstartswithtraining-directedchannelestimationusingGoSLIM.Thenweperformphasecompensationseparatelyateachreceivinghydrophoneasdonein( 4 )beforeproceedingtoemployRELAX-BLASTtodetecttherst250payloadsymbolscontainedinthe17thpayloadblockforeachtransmittedsequence.Next,thechannelsareupdatedinthedecision-directedmodeusing450symbols(containingthepreviouslydetectedpayloadsymbols,aswellasaportionofthetrainingsequenceaswell).WiththeupdatedCIRsandDopplerfrequencies,afterphasecompensation,thesubsequent250payloadsymbolscontainedinthe18thblockaredetectedusingRELAX-BLAST.Thisprocesscontinuesuntilallofthe16payloadblockstotheright-handsideofthetrainingsequencesaredetected.Thissametrackingschemecanbeappliedinareversemannertothedetectionofthe16payloadblocksaheadofthetrainingsequences. WedeemapackettobesuccessfullydetectedifitscodedBERislessthan0.1.Byadoptingtheaforementionedreceptionscheme,wehavesucceededintrackingtheentire32payloadblocksfor594outofthe623packets(recallthatwehave89epochsandeachconsistsof7packets).AcodedBERof5.110)]TJ /F9 7.97 Tf 6.59 0 Td[(3isachievedafteraveragingoverthe1.9107sourcebitsprocessed.Amongthe594successfulpackets,weselectedsomepacketstodemonstratetheimpactofcodedBERonthequalityoftherecoveredmascotimages.Figures 4-11A and 4-11D arefromepochMIMO08,correspondingtoBERsof0and5.010)]TJ /F9 7.97 Tf 6.59 0 Td[(5,respectively.TheseremarkableBERresultstranslateintoalmostperfectimagerecovery.Figures 4-11B and 4-11E arefromepochMIMO03,correspondingtoBERsof2.910)]TJ /F9 7.97 Tf 6.59 0 Td[(3and5.010)]TJ /F9 7.97 Tf 6.59 0 Td[(3,respectively.One 108

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observesthatthemascotdetailsarestillwellpreserveddespiteofthepresenceofthesparsenoisydotsduetothemoderateamountofbiterrors.Figures 4-11C and 4-11F arefromepochMIMO27,correspondingtoBERsof6.810)]TJ /F9 7.97 Tf 6.58 0 Td[(3and3.210)]TJ /F9 7.97 Tf 6.58 0 Td[(2,respectively.TheseBERresultsleadtofurtherdegradedreconstructedimages. Forcomparisonpurposes,weproceedtoassessthedetectionperformanceofSLIM[ 46 ],i.e.,withanISIchannelmodelinsteadofadoublespreadingchannelmodel,byanalyzingthedatapacketthatleadstoperfectrecoveryinFigure 4-11A usingGoSLIM.Thesamereceptionschemeisrepeated(exceptthatthephasecompensationstageisnolongerneededsinceSLIMassumesf=0)andtherecoveredmascotimageusingSLIMisshowninFigure 4-12 .Theimagebecomeshardtoidentifysincemoredetectionerrorsoccur(nalcodedBERis2.210)]TJ /F9 7.97 Tf 6.59 0 Td[(1).Thissuggeststhatinourexamples,itbecomesindispensabletotaketheDopplereffectsintoconsiderationforachievingreliableUAC. Finally,weremarkthatonepacketofgrayscalemascotimagewasalsotransmittedintheWHOI09experimentusingN=4transducersandM=4hydrophonesatacodeddatarateof30kbps.TheempiricalcodedBERsare1.710)]TJ /F9 7.97 Tf 6.59 0 Td[(3,1.310)]TJ /F9 7.97 Tf 6.59 0 Td[(3and4.710)]TJ /F9 7.97 Tf 6.59 0 Td[(4overtheentire32ksourcebitsforepochs-RB2,-RB2and-RB2,respectively.ThemeasurementsobtainedusingtheRB1array,however,cannotbeusedtoreconstructreasonablemascotsduetotheproblemsufferedbythesecondhydrophoneofRB1. 109

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Figure4-1. Alamoutidiversityschemeofasystemwith2transmittersand1receiver. A B Figure4-2. ThemodulusofthesimulatedCIRsbetweenthetwotransmittersandthereceiver. 110

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A B C D Figure4-3. A)MSEsofCIRestimatesforPeCANsequences.B)MSEsofCIRestimatesforQPSKsequences.C)MSEsofDopplerfrequencyestimatesforPeCANsequences.D)MSEsofDopplerfrequencyestimatesforQPSKsequences.Bothsequenceshavealengthof256symbols.Eachpointisaveragedover100Monte-Carlotrials. 111

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A B C D E F Figure4-4. EvolutionsoftheCIRsbetweentheactivetransmittertothesecondreceiveroftheRB1andRB2arraysforall6epochs. A B C D E F Figure4-5. EvolutionsoftheestimatedDopplerfrequenciesateachreceiverforall6epochs. 112

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Figure4-6. Thestructureofourtransmittedsymbolsforthe2Tx)]TJ /F1 11.955 Tf 9.3 0 Td[(1RxAlamoutischemeusedintheWHOI09experiment. A B C D Figure4-7. CIRevolutionsbetweenthefouractivetransmittersandonehydrophoneforEpochMIMO28. 113

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A B Figure4-8. EvolutionsoftheestimatedDopplerfrequenciesateachreceiverforEpochMIMO28. 114

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Figure4-9. EachpackagetransmittedintheACOMM10experimentcontains4grayscaleGatormascotimagesand1coloredimage.ThecoloredimageisdecomposedintoRGBcomponents. 115

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Figure4-10. Thestructureofthetransmittedsymbolsforthe48MIMOBLASTschemeusedinACOMM10. 116

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A B C D E F Figure4-11. A)GrayscalemascotrecoveredfromepochMIMO08.B)GrayscalemascotrecoveredfromepochMIMO03.C)GrayscalemascotrecoveredfromepochMIMO27.D)ColoredmascotrecoveredfromepochMIMO08.E)ColoredmascotrecoveredfromepochMIMO03.F)ColoredmascotrecoveredfromepochMIMO27. Figure4-12. GrayscalemascotrecoveredfromepochMIMO08usingSLIM. 117

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CHAPTER5FUTUREWORK InChapters 2 3 ,and 4 ,WehavestudiedvariouscriticalproblemsthatariseinpracticalMIMOUAC,suchasthesynthesisoftheeffectivetrainingsequencesatthetransmitter,thedevelopmentofthechannelestimationandsymboldetectionschemesatthereceiverside,etc.TheeffectivenessoftheproposedMIMOUACtechniquesisveriedusingbothnumericalexamplesandseveralin-waterexperiments.Thelong-termgoalofaUACprojectistoimplementsophisticatedsignalprocessingalgorithmsandcodingtechniquesinasmall-area,low-powerdevicethatcanbeequippedonawatercrafttoachievehighspeedandreliableUACinreal-time.Inthischapter,ourfocusisshiftedfromresearchideadevelopmenttoconcretesystemimplementationbycriticizingtheexistingMIMOUACschemesfromanapplicationpointofview.Moreover,wealsoprovideavisionforthefutureofUACbydiscussingthepossibilitiesandchallengesofemployingmultiusertechniquesintheunderwaterenvironments. 5.1MIMOUAC:AnApplicationPointofView 5.1.1DataRate Thespeedofadigitalwirelessserviceintermsofdatarateisnormallyoneofthemostimportantspecicationsacustomerwouldbeconcernedabout.ThehighestdataratewehadachievedduringtheparticipationintheMIMOUACprojectwas62.5Kbps,whichwasobtainedbyanalyzingthe200mmeasurementsacquiredongoodchannelconditionsduringthecourseoftheSPACE08in-waterexperiment.ThisdatarateallowsthesystemtotransmittwograyscaleGatormascots(Figure 4-10 )back-to-backinapproximatelyonesecond.Insharpcontrast,thecurrentWLANstandardoffersamaximumcollectivedatarateattensofMbps(Table 1-1 ),fastenoughtodownloada5-minutevideoinonesecond.AlthoughthepastthreedecadeshaveseenatremendousincreaseinthedatarateofdigitalUACsystemsresultingfrommajortechnicalbreakthroughsincludingtheemploymentofphasecoherent 118

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communicationschemesandaMIMOsystemtelemetry,todate,UACspeedisstillnotabletocompetewiththatachievedviawirelessradiocommunicationsmainlyduetotheuniquechallengesimposedbytheunderwaterenvironments(Section 1.1 ).ThedatarateinMIMOUAChastobefurtherincreasedbeforetheproposedMIMOUACschemescantransitionfromthecurrentresearchstagetopracticalmilitaryorcommercialapplicationsandmakeanimpactoneverydaylife. Ataxedsymbolrate,dataratecanbeincreasedbytradingoffcommunicationreliabilityintermsofBER.Forexample,wecanleteachsymbolconveymoreinformationviasophisticatedmodulationschemes[ 55 ].BesidestheQPSKmodulationschemeemployedthroughoutthepresentdissertationinwhichonesymbolcarriestwobits,wecanconsidermappingthreebitstoonesymbolthrough8-PSKmodulation,orevenmappingfourbitsthrough16-QAM(quadratureamplitudemodulation).8-PSKand16-QAMconstellationsareshowninFigures 5-1 and 5-2 ,respectively.Ataxedaveragetransmitpower,asasymbolcarriesmorebits,theconstellationpointsbecomemoreclustered(Figures 5-1 and 5-2 ),andtheresultingperformanceofsymboldetectionismorevulnerabletoambientnoiseand/orinterferences.Moreover,unlikethePSKmodulationscheme,whereonlythephaseofthetransmittedsymbolcontainsinformation,forQAM,theinformationbitsareencodedinboththeamplitudeandphaseofthesymbol;seeFigure 5-2 .Consequently,QAMmodulatedsignalsdonothaveconstantenvelop,whichisanundesiredfeaturefromanamplierefciencypointofview.Anotherpreferablemeanstoincreasethedatarateistoadoptanencoderwithahigherrateviapuncturing,ortocompletelyskipthechannelcodingstage(i.e.,directlytransmittinguncodedinformation)atthecostofreducederrorcorrectionability,ornoneatall[ 55 ].Inaddition,wecanalsoequipmoretransmitterstosendsignalssimultaneouslyovertheacousticchannel.Theresultingdetectionperformanceforaparticulartransmitterisexpecttodegradeowingtotheincreasedlevel 119

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ofinterferences.Ontopofthat,boththesystemcostandthereceivercomplexitywillincreaseaccordingly. 5.1.2Real-TimeImplementation Differentapplicationshavedifferentdelayconstraints.Serviceslikeemailorpagingingeneralcantolerateaconsiderableamountofdelay,whereasforotherapplications,suchaslivebroadcastorvoiceservices,real-timeconstraintneedstobeenforced.(Invoicesystems,adelaylargerthan0.1scouldbenoticedbytheenduser.)Asaconsequence,whethertoaddressthereal-timerequirementornotdependsonthespecicapplicationathand. FortypicalUACapplications,suchastacticalcommunicationsbetweensubmarinesinthebattleeldorbetweenUUVsengagedinacomplexanddangeroustask(oilspillcontrol,forinstance),eachwatercraftisrequiredtointerpretanorderandrespondpromptlybeforethebestchancedashesaway.Therefore,real-timereceptionindeedisacriticalfactoronwhichtheoverallUACsystemperformancedepends. Basedonthecurrentstateofhardware,itisfeasibletodevelopanembeddedsystemtoachievereliableUACreceptioninreal-time.Forinstance,DFE,coupledwithLMSorRLSalgorithmforupdatingtheltercoefcientsinvolved,isapreferablereceiverstructuretorealizereal-time.TheAlamoutidiversityschemepresentedinSection 4.2.3 isalsoamenabletoreal-timeimplementationonahardwareplatform.Bothsystems,however,donotfallintotheMIMOUACcategoryandthecorrespondingdatarateisingeneralmuchlowerthancouldbeachievedbyMIMOUACsystems. However,manytechnicalchallengesremaininimplementingtheproposedMIMOUACschemesonahardwareplatformtorealizehigh-speed(withrespecttothedatarateachievedbyDFEandAlamoutidiversityscheme),reliableUACinreal-time.Thebottleneckcomesfromboththelimitationofthehardwareandthemechanismofthealgorithm.Itiswellknownthatthefrequencyofacentralprocessingunit,thememorycapacity,andthewidthofthedatabusareamongthekeyfactors 120

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thatdeterminetheoverallspeedoftheresultingembeddedsystem.Advancesinhardwaretechniquesmakethedigitalhardwaresmoreaffordable,havefasterspeedandenhancedperformance,andwillcontinuetoheraldnovelandimprovedsignalprocessingapproachesinMIMOUACapplications. Inanalgorithmdevelopmentperspective,itispreferabletosimplifyanalgorithmasmuchaspossiblebeforetransplantingittoahardwareplatform.TheefcientcalculationoftheLMMSEltercoefcientselaboratedinSection 3.3.2 isagoodexampleinthisrespect.Specically,theCGmethodisemployedtosolvealinearsysteminaniterativemanner,whichavoidsinvertingamatrixwithlargedimensions.Moreover,thecomputationsinvolvedineachCGiterationaresignicantlyexpeditedbymakinguseofFFTandIFFToperations.Thisway,theoriginalcomputationallyexpensiveproblemisdecomposedintomultiplebasicoperationsthatcanbeeasilyhandledbynormalhardwares.Inaddition,ahardwareprocessingunit,suchasdigitalsignalprocessor(DSP)oreld-programmablegatearray(FPGA),isnormallydesigned,orcanbecongured,tohavemultiplesetsofthesamefunctionalunit.Theseparallelunitscanoperatesimultaneouslywithoutinterferingwitheachother.Therefore,aDSP-orFPGA-friendlyalgorithmisonethatexploitsparallelcomputations.AlthoughhighcomputationsofIAAmakesitunattractiveforhardwareimplementation,itsparallelupdatingprocedureelaboratedinSection 2.2.3 canstillbeappreciated. 5.2MultiuserUACSystems ThefocusofthisdissertationisonMIMOUACfromoneusertotheother.Adeningcharacteristicofsuchacommunicationschemeisthatthereisonlyoneactiveuserinvolvedandthetransmittedsignaloccupiesalltheresourcesthechannelprovides,includingtimeandbandwidth.Theexplosivegrowthofthecellularsystemsfeaturingmultiusertechniques(wheremultipleuserssharetheavailableresources)drivesustobrieystudythepossibilitiesandchallengesofimplementingasimilarmultiusersystemintheunderwaterenvironments. 121

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Multiusersystemsinvolvetwotypesofchannels:adownlinkchanneloverwhichonetransmitter(abasedstation)sendsinformationtomanyreceivers(endusers),andanuplinkchanneloverwhichmanytransmitters(endusers)sendinformationtoonereceiver(abasedstation)[ 21 ].Themostcommonmethodstodividetheavailableresourcesarealongthefrequency,time,andcodeaxes.Theresultingmultipleaccesstechniquesarerespectivelyreferredtoasfrequency-divisionmultipleaccess(FDMA),time-divisionmultipleaccess(TDMA),andcode-divisionmultipleaccess(CDMA),whichwewillstudyinsequel. 5.2.1Frequency-DivisionMultipleAccess InFDMAsystems,asshowninFigure 5-3 ,theavailablebandwidthisdividedintomultiplechannels,andeachuserisassignedadifferentchannel.Toensuretheabsenceofcross-channelinterferences,channelsdonotoverlapwitheachother.ThetransmissioninFDMAsystemsiscontinuousovertime,andafrequencymodulationmoduleisneededtotunethesignaltoaspeciedcarrierfrequencyassociatedwiththechannel. IftheFDMAschemetakesplaceinrealisticunderwateracousticenvironment,thenadditionalchallengesarepresent.AswepreviouslyremarkedinSection 1.1 ,theavailablebandwidthofferedbytheacousticchannelsisratherscarce:40KHzatmostcomparedto20MHzforWLAN.ThisessentiallylimitsthenumberofusersanunderwaterFDMAsystemcanaccommodate.Moreover,thechannel-inducedDopplereffectswillshiftthesignalbandwidthduringprorogation[ 55 ].Toseethis,supposeawatercraftisapproachingastationarybasestationatavelocityofvm/s,anditissendingasinusoidsignal.DuetotheDopplereffects,thetransmittedsinusoidatfrequencyfwillbeconvertedtoasinusoidoffrequencyof1+v cfatthereceiverside,inwhichcrepresentstheunderwatersoundspeed.Thefrequencyincrementvf ciscommonlyreferredtoasDopplershift.Inasimilarmanner,ifthewatercraftismovingawayfromthebasestation,thefrequencyatthereceiverbecomes1)]TJ /F3 11.955 Tf 13.15 8.08 Td[(v cfwitha 122

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Dopplershift)]TJ /F3 11.955 Tf 10.49 8.09 Td[(vf c.Tomitigatesuchfrequencyshiftandtheimperfectpulseshapinglter,aguardbandshouldbeallocatedbetweenadjacentchannels. 5.2.2Time-DivisionMultipleAccess TDMA,asthenamesuggests,segmentsthecontinuoustimeaxisintonon-overlappingtimeslicesofequallength;seeFigure 5-4 .Thetimeslicesareassignedtoeachuserinequalportionsandincircularorder(thisschedulingschemeisalsoreferredtoasaround-robinschedulingincomputernetworkcommunity).InTDMAsystemsalluserssharetheavailablefrequencybandwidth,andthetransmissionisnotcontinuousovertime.Theround-robinschedulingschemeguaranteesthatatanytimethereisatmostoneusertransmittingasignal,whicheliminatesthecross-userinterferences. TwocriticalproblemsneedtobeaddressedbeforeaTDMAsystemcanbesuccessfullyimplementedintheunderwaterenvironments.Therstproblemishowtoachievesynchronizationamongalltheusers.Asjustmentioned,thesuppressionofthecross-userinterferencesinTDMAsystemsiscompletelyrealizedviatiming:eachuserneedstoknowtheexacttimetoswitchthetransmissiononandoff.Forradiocommunications,synchronizationcanbesimplyachievedwiththehelpofaglobalpositioningsystem(GPS)signal.However,aGPSsignalexperiencestroublepenetratingthroughthewatermedium,whichleadsustodevelopingotherfeasiblemeanstoachievesynchronizationintheunderwaterenvironments.ThesecondproblemisthepresenceofsevereISIduetothelongCIR(Section 1.1 ).Inidealat-fadingchannelswithoutISI,rightafterthetransmissionofthecurrentuserisswitchedoff,thenextuserinlinecanstarttransmittingimmediately:notimeiswastedduringthetransition.However,inrealisticfrequencyselectivechannelswiththepresenceoftheISI,toensuretheabsenceofcross-userinterferences,thenextusermustpostponeitstransmissionuntilthesignalsentbythecurrentusercompletelydiesout.Inotherwords,guardintervalsarenecessarybetweenadjacenttimeslices,andthelengthoftheguardintervalsshouldbelongerthanthechanneldelayspread(typicallyintensofms).Since 123

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nosignalistransmittedduringguardintervals,aconsiderableamountoftimewillbewasted,especiallywhenthelengthoftheguardintervalbecomesasignicantfractionofthelengthofeachtimeslice. 5.2.3Code-DivisionMultipleAccess InCDMAsystemsdifferentusersemploydifferentspreadingsequencestomodulatetheinformationsignalbeforetransmission,andthemodulatedsignalssharethesametimeandbandwidthresourcesavailable;seeFigure 5-5 .Thelevelofthecross-userinterferenceinCDMAsystemsismainlydeterminedbythecorrelationpropertiesofthespreadingsequencesandthecharacteristicsoftheunderlyingchannel[ 21 ].Forexample,inanidealat-fadingdownlinkchannelwithperfectsynchronization,theHadamardsequences,whichareorthogonaltoeachother,couldbetheoptimalspreadingsequencesintermsofeliminatingallpossibleinterferences[ 60 ].However,inafrequencyselectivedownlinkchannel,Hadamardsequencesarenolongertheoptimalchoice.Instead,spreadingwaveformswithgoodauto-andcross-correlationsovercertainlagsarepreferred.Thesetypesofsequencesareusuallyreferredtoaszero-correlationzonesequencesandtherelevantliteratureisextensive[ 17 78 80 ]. Intheuplinkscenario,ontheotherhand,itisnaturaltoalloweachusertotransmitsignalstothebasestationatanyconvenienttime,andtherefore,therequirementofsynchronizationamonguserscannot,andshouldnot,beenforced.Therelaxationofthesynchronizationrequirementamountstosynthesizingspreadingsequenceswithgoodauto-andcross-correlationpropertiesovertheentirelags,suchastheGoldsequencesandKasamisequences[ 84 ]. WhenCDMAisimplementedintherealisticunderwaterenvironments,thetime-varyingnatureoftheacousticchannelpreferstheemploymentofshortspreadingsequencessinceotherwisetheblockfadingassumptioncanbeeasilyviolated[ 45 ].Onetopofthat,thepresenceofDopplereffectsalsoinducestemporalscaling(stretchingorcompression)tothetransmittedsignals.Dopplerinducedscalingeffectscan 124

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easilydestroytheorthogonalitypropertiesofthespreadingsequences.Toaddressthisproblem,itisdesirabletotransmitDoppler-sensitiveprobingsequenceswithgoodambiguityfunctions(ideally,thumbtack-likeauto-ambiguityfunctionsandzerocross-ambiguityfunctions).Duetotheextremedifcultyoftheproblem,itisstillanopenquestionastohowtosynthesizesuchdesiredspreadingsequenceseffectivelyandefciently[ 35 ]. 125

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Figure5-1. 8-PSKconstellation. Figure5-2. 16-QAMconstellation. 126

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Figure5-3. Frequency-divisionmultipleaccess(FMDA).Copyrightimagecourtesyof[ 21 ]. Figure5-4. Time-divisionmultipleaccess(TDMA).Copyrightimagecourtesyof[ 21 ]. 127

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Figure5-5. Code-divisionmultipleaccess(CDMA).Copyrightimagecourtesyof[ 21 ]. 128

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BIOGRAPHICALSKETCH JunLingreceivedBachelorofScienceandMasterofSciencedegreesinelectricalengineeringfromZhejiangUniversity,Hangzhou,China,in2004and2006,respectively.HegraduatedwithaDoctorofPhilosophyfromtheElectricalandComputerEngineeringDepartmentattheUniversityofFloridainthesummerof2011.Hisresearchinterestsincludesignalprocessinganditsapplicationtomulti-inputmulti-outputunderwateracousticcommunications.HewilljointheMathworksupongraduation. 137