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Rate And Reliability Oriented Underwater Acoustic Communications

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Title:
Rate And Reliability Oriented Underwater Acoustic Communications
Creator:
Qu, Fengzhong
Place of Publication:
[Gainesville, Fla.]
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (105 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Electrical and Computer Engineering
Committee Chair:
Yang, Liuqing
Committee Members:
Lin, Jenshan
Li, Tao
Chen, Shigang
Graduation Date:
8/8/2009

Subjects

Subjects / Keywords:
Estimators ( jstor )
Hydrophones ( jstor )
Matrices ( jstor )
Receivers ( jstor )
Seas ( jstor )
Signals ( jstor )
Simulations ( jstor )
Supernova remnants ( jstor )
Transducers ( jstor )
Underwater acoustics ( jstor )
Electrical and Computer Engineering -- Dissertations, Academic -- UF
bem, dostbc, dsss, ls, mimo, rate, rliability, uac
Genre:
Electronic Thesis or Dissertation
born-digital ( sobekcm )
Electrical and Computer Engineering thesis, Ph.D.

Notes

Abstract:
Underwater acoustic communication (UAC) channels inherently have very limited bandwidth and are doubly-selective in both delay-frequency and time-Doppler domains. The limited bandwidth and the double selectivity make high data rate and reliability difficult to achieve. In this dissertation, we will design three UAC schemes, one designed for a high data rate and the other two for high reliability. The rate-oriented discrete Fourier transform (DFT)-basis expansion model (BEM)-based coherent scheme provides a high transmitted data rate with satisfactory performance at the price of high receiver processing complexity and a large receiver array. In practice, some receivers such as small-size sensors or autonomous underwater vehicles (AUVs) do not have a large number of hydrophones and cannot afford such complexity. Therefore, we also develop and test two reliability-oriented systems, where resilience against the channel variation is facilitated by carefully designed transmitter processing while preserving receiver simplicity. The first reliability-oriented system is a differential orthogonal space-time block code (DOSTBC) scheme, which, like the high-rate scheme, is based on BEMs. By analyzing the tradeoff between the channel modeling accuracy and the bias/noise effect of two prevalent BEMs, we find that the DFT-BEM is more preferable for differential schemes, while for coherent schemes, the choice of BEMs depends on specific system parameters and scenario settings. Our analyses, simulations, and experiment results show that when comparing BEMs, the basis-dependent processing of the model fitting bias and noise that occurs in the transformation process between channel parameters and BEM coefficients has an equal impact on system error performance as the model approximation accuracy of the BEM itself. The second high-reliability system is called high reliability direct-sequence spread spectrum (HR-DSSS), and is operated with simple matched filter receiver. We will show the advantages of each of our schemes by comparing with existing alternatives. All three schemes are tested in recent sea trials. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2009.
Local:
Adviser: Yang, Liuqing.
Statement of Responsibility:
by Fengzhong Qu.

Record Information

Source Institution:
UFRGP
Rights Management:
Copyright Qu, Fengzhong. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
489203798 ( OCLC )
Classification:
LD1780 2009 ( lcc )

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ThisdissertationconsistsofmyresearchworkconductedsinceIjoinedtheSignalProcessing,CommunicationsandNetworking(SCaN)Groupin2005.IamgreatlyindebtedtoDr.LiuqingYang,myadvisor.Iwouldliketoexpressmyprofoundgratitudetoherforherinvaluablesupport,encouragementandsupervisionthroughoutmyentireresearch.Hertimelyfeedbackandvaluablesuggestionshavegreatlypromotedmyresearchprogress.Ideeplythankherforherinterestingdiscussions,excellentguidanceandvaluableadvicethroughoutmyPh.D.study.Shehasbeensupportingmyworkonaday-to-daybasisinsomanywaysthatitisdiculttoeverthankherproperly.Secondly,IwouldliketothankmyPh.D.supervisorycommitteemembers,Dr.ShigangChen,Dr.TaoLiandDr.JenshanLin,fortheirtimeandeortsinservingonmysupervisorcommittee.Lastbutnotleast,mythanksgotoallmembersofSCaNgroup:WoongCho,HuilinXu,RuiCao,DongliangDuan,WenshuZhang,SivaKumarBalaga,WeiZang,PanDeng,BoYu,andJulieCummings,forselesslysharingtheirideasandinspiringdiscussionswithme.Ihavebenetedimmenselyfromtheirfriendshipandsupport. 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 7 LISTOFFIGURES .................................... 8 ABSTRACT ........................................ 10 CHAPTER LISTOFSYMBOLS .................................... 12 1INTRODUCTION .................................. 13 1.1ProblemDescription .............................. 13 1.2PreviousWork ................................. 16 1.3ProposedRateandReliabilityOrientedSchemes ............... 18 1.4SummaryofContributions ........................... 21 2RATE-ORIENTEDCOHERENTSCHEMEFORUPLINK ........... 22 2.1SystemModel .................................. 23 2.2WLSEstimator ................................. 25 2.2.1MMSEorLS? .............................. 25 2.2.2WLSEstimatorDesign ......................... 26 2.2.3OptimumPilotPatternDesign ..................... 29 2.2.4Discussions ................................ 30 2.3SimulationResults ............................... 31 2.4ExperimentResults ............................... 34 2.5Summary .................................... 36 3RELIABILITY-ORIENTEDDOSTBCFORDOWNLINK ............ 38 3.1SystemModel .................................. 39 3.2Subblock-wiseDOSTBCDesign ........................ 42 3.2.1EquivalentTime-InvariantChannel .................. 42 3.2.2Subblock-wiseDOSTBC ........................ 46 3.2.3DiversityandComplexity ........................ 48 3.3SimulationResults ............................... 50 3.4ExperimentResults ............................... 51 3.5Summary .................................... 56 4INVESTIGATIONONBEMSINDIFFERENTSCHEMES ........... 59 4.1GeneralExpressionforBEM .......................... 60 4.2BEMProperties ................................. 61 5

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......................... 64 4.3.1CoherentSchemeforGeneralBEM .................. 65 4.3.2DFT-BEMvs.DPSS-BEM ....................... 66 4.3.3SimulatedComparisons ......................... 68 4.4BEMfortheDierentialScheme ....................... 70 4.4.1DierentialSchemeforGeneralBEM ................. 70 4.4.2DFT-BEMvs.DPSS-BEM ....................... 72 4.4.3SimulatedComparisons ......................... 73 4.5ExperimentResults ............................... 75 4.5.1CoherentScheme ............................ 75 4.5.2DierentialScheme ........................... 78 4.6Summary .................................... 79 5HR-DSSSFORDOWNLINK ............................ 80 5.1HR-DSSSScheme ................................ 80 5.1.1TransmittedSignals ........................... 80 5.1.2UACChannelPropagation ....................... 82 5.1.3ReceiverProcessing ........................... 83 5.1.4PerformanceAnalysis .......................... 85 5.2DiscussionsandComparisons ......................... 88 5.2.1HR-DSSSwithOtherSequences .................... 88 5.2.2OFDM .................................. 89 5.3Simulations ................................... 89 5.3.1Time-InvariantNon-FadingChannels ................. 90 5.3.2Time-VaryingFadingChannels ..................... 91 5.4ExperimentResults ............................... 92 5.4.1GLINT08SeaExperiment ....................... 92 5.4.2GOMEXSeaExperiment ........................ 93 5.5Summary .................................... 94 6CONCLUSIONSANDFUTUREWORK ...................... 96 6.1Conclusions ................................... 96 6.2FutureWork ................................... 97 LISTOFREFERENCES ................................. 99 BIOGRAPHICALSKETCH ................................ 105 6

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Table page 2-1Simulationparameters ................................ 30 2-2Coherentschemes'BERswith12hydrophones ................... 36 3-1Dierentialschemes'uncodedBERsata1000mdistanceinRACE08 ...... 50 3-2CorrelationbetweenBERsandwindspeedinRACE08 .............. 58 3-3CorrelationbetweenBERsandseasurfaceheightabovebottominRACE08 .. 58 4-1Coherentschemes'BERswith12hydrophones ................... 75 4-2Dierentialschemes'uncodedBERsata1000mdistanceinRACE08 ...... 77 5-1UncodedBERforHR-DSSSwithasinglehydrophoneinGLINT08 ....... 92 7

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Figure page 2-1Basebandequivalentsystemwiththewindowedleastsquares(WLS)estimator. 27 2-2Theoptimumtrainingpattern. ........................... 30 2-3OnesnapshotoftheWLSestimationresults. .................... 31 2-4MSEvs.SNRperformanceoftheWLSandtheMMSEchannelestimators. ... 32 2-5BERvs.SNRperformanceoftheWLSandtheMMSEchannelestimators. ... 33 2-6Thescatteringfunctionforadatapacketincalmperiods. ............ 34 2-7Thescatteringfunctionforadatapacketinroughperiods. ............ 35 2-8Coherentschemes'BERsacrossdierenthydrophonesinRACE08ata1000mdistance. ........................................ 37 3-1Baseband-sampled-equivalentsystemmodel .................... 49 3-2BERversusSNR.TI:time-invariantchannelswithfmax=0;TV:time-varyingchannelswithfmax=3:3Hz;QPSK:plainQPSKwithnocoding;LCF:codingin[ 36 ]withKG=3. ................................. 49 3-3DOSTBCQPSKuncodedBERinRACE08with2transducersand1hydrophoneata1000mdistance. ................................. 51 3-4DOSTBCQPSKuncodedBERinRACE08with2transducersand2hydrophonesata1000mdistance.Zero-errorisillustratedas105. ............... 52 3-5DOSTBCQPSKuncodedBERinRACE08with2transducersand12hydrophonesata1000mdistance.Zero-errorisillustratedas105. ............... 53 3-6DOSTBC8PSKuncodedBERinRACE08with2transducersand1hydrophoneata1000mdistance. ................................. 54 3-7DOSTBC8PSKuncodedBERinRACE08with2transducersand2hydrophonesata1000mdistance. ................................. 55 3-8DOSTBC8PSKuncodedBERinRACE08with2transducersand12hydrophonesata1000mdistance. ................................. 56 3-9ThewindspeedmeasuredinRACE08 ....................... 57 3-10TheseasurfaceheightabovebottommeasuredinRACE08 ............ 57 4-1BERvs.SNRperformanceoftheDFT-andtheDPSS-BEMbasedcoherentschemes. ........................................ 68 8

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... 74 4-3Coherentschemes'BERsacrossdierenthydrophonesinRACE08ata1000mdistance. ........................................ 75 4-4DOSTBCQPSKuncodedBERforblocksinRACE08with2transducersand2hydrophonesata1000mdistance.Zero-errorisillustratedas105. ....... 77 4-5DOSTBCQPSKuncodedBERforblocksinRACE08with2transducersand12hydrophonesata1000mdistance.Zero-errorisillustratedas105. ...... 78 5-1ThebasebandtransceiverdiagramfortheHR-DSSSscheme. ........... 85 5-2ThechannelestimationblockinFig. 5-1 ...................... 86 5-3ThejthdemodulationblockinFig. 5-1 ...................... 86 5-4OnesnapshotofthechannelsinGOMEX ..................... 88 5-5BERvs.SNRperformanceforthenonfadingchannels. ............. 90 5-6BERvs.SNRperformanceforthetime-varyingfadingchannelswithfmax=4:7Hz ......................................... 92 5-7ThescatteringfunctionintheGOMEXexperiment. ................ 94 9

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Underwateracousticcommunication(UAC)channelsinherentlyhaveverylimitedbandwidthandaredoubly-selectiveinbothdelay-frequencyandtime-Dopplerdomains.Thelimitedbandwidthandthedoubleselectivitymakehighdatarateandreliabilitydiculttoachieve. Inthisdissertation,wewilldesignthreeUACschemes,onedesignedforahighdatarateandtheothertwoforhighreliability.Therate-orienteddiscreteFouriertransform(DFT)-basisexpansionmodel(BEM)-basedcoherentschemeprovidesahightransmitteddataratewithsatisfactoryperformanceatthepriceofhighreceiverprocessingcomplexityandalargereceiverarray.Inpractice,somereceiverssuchassmall-sizesensorsorautonomousunderwatervehicles(AUVs)donothavealargenumberofhydrophonesandcannotaordsuchcomplexity.Therefore,wealsodevelopandtesttworeliability-orientedsystems,whereresilienceagainstthechannelvariationisfacilitatedbycarefullydesignedtransmitterprocessingwhilethereceiverispreservedsimple.Therstreliability-orientedsystemisadierentialorthogonalspace-timeblockcode(DOSTBC)scheme,which,likethehigh-ratescheme,isbasedonBEMs.Byanalyzingthetradeobetweenthechannelmodelingaccuracyandthebias/noiseeectoftwoprevalentBEMs,wendthattheDFT-BEMispreferablefordierentialschemes,whileforcoherentschemes,thechoiceofBEMsdependsonspecicsystemparametersandscenariosettings.Ouranalyses,simulations,andexperimentresultsshowthatwhencomparingBEMs, 10

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Boldfacelowercaseletters: VectorsBoldfaceuppercaseletters: Matrices[x]n: Thenthelementofvectorx[X]n;m: The(n;m)thelementofmatrixXEfg: ExpectationtrfXg: ThetraceofmatrixX: Convolution: KroneckerproductfgH: MatrixHermitianfgT: Matrixtranspositionfg: ConjugationIN: TheNNidentitymatrix0N: TheN1allzerovector0NM: TheNMall0matrix1N: TheN1allonevectorde: Ceilingbc: Floorkk2: ThesquaredFrobeniusnormDfhg: ThediagonalmatrixwiththeelementsofthevectorhsittingonthediagonalDfh1;:::;hNg: Theblock-diagonalmatrixwiththesubmatriceshnonthediagonalCN(;2): ThecomplexGaussiandistributionwithmeanandvariance2

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Inthischapter,wewillstartbypresentingthemainproblem,rate-andreliability-orientedunderwateracousticcommunications(UAC),discussedinthisdissertationandthepreviousworkregardingtotheproblem.Then,wewillgiveourapproachestoproblem-solvingandlistthecontributionsofthisdissertation. 19 ].Apossiblealternative,laserbeams,requireshighprecisionbeamalignment.Inaddition,theapplicationoflaserbeamsislimitedwhenthewaterclarityislow[ 51 ].Hence,acousticwavesbecomeanattractivemediumfortransmittingsignalsunderwater.Theydonotattenuateasrapidlyastheelectromagneticwavesandcanaccommodatekilometersoftransmissionrange. However,theacousticwavemediahasitsownsetofchallengesforunderwatercommunicationsystemdesigns: 1. UACchannelshaveverylimitedbandwidth,typicallytensofkHz,becauseofthelowcarrierfrequenciesofacousticwaves,whicharetypicallynomorethanahundredkHz.Thus,highbandwidtheciencyiskeyinachievinghighdatarateinUACchannels. 2. UACchannelsaredoubly-selectiveinbothdelay-frequencyandtime-Dopplerdomains,especiallyinshallowwater.Thischaracteristicposesthemostchallenging 13

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28 ].Therefore,thechannelsexhibitfrequencyselectivityfortypicalcommunicationbandwidths. Thelowpropagationspeedofacousticwavesunderwateralsoinducestimeselectivity.RecallthatDopplershiftfdisgivenby Cf;(1{1) wherevisthevehiclemovingvelocity,fisthemediumfrequencyandCisthemediumpropagationspeed.ComparedwithterrestrialRFcommunicationswithelectromagneticwavespropagatingat3108m/sinair,UACexperienceslowsoundpropagationspeedat1500m/sunderwater.Accordingto( 1{1 ),thesmalldenominatorofUACchannelswillgiverisetoDopplerspreadthatismuchmoresignicantthanterrestrialRFsystems.Additionally,inshallowwater,surfacewaveandbubbleswillalsointroduceDopplerevenwhenthetransceiversarenotmoving[ 15 41 ]. 3. ThereisnowidelyacceptedchannelmodelforUAC,despitemanypapersdevotedtothemodelingofUACchannelsbyincorporatingthechannelphysics(seee.g.,[ 1 4 8 11 { 13 17 61 66 67 ]).Thisismainlyduetothefactthatmodelingofthechannelisrelatedtomanyphysicalfactors,includingwaterdepth,soundspeed, 14

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4. BecauseoftheUACchannel'stime-varyingcharacteristicandthelowpropagationspeedofacousticwaves,itisnotrealisticforthetransmittertohavechannelstateinformation(CSI).InRFcommunications,manydesignsassumeCSIatthetransmitter(seee.g.,[ 23 27 ]).However,systemdesignforUACcannotbebuiltonsimilarassumptions. Basedonalltheseconsiderations,wesetouttodevelophighqualityUACsystems.Inunderwaterapplications,fourtypesofsignalsareusuallytransmitted:control,telemetry,speechandvideosignals[ 51 ].Dierentsignalshavedierentrateandreliabilityrequirements.Controlcommandscanhavelowratetransmissionsduetotheirsmalldatasize,butrequirehighreliability.Comparedwithcontrolcommands,speechandvideosignalsrequirehigherdatarates,butreliabilityislesscrucialtothedesign.Additionally,dierentsignalsareusuallysenttodierentdestinations.AnexampleistheasymmetriclinkbetweensurfacevesselsandAUVs.LetusdenetheuplinkasthelinkfromsmallAUVstosurfacevesselsandthedownlinkastheotherdirection.ThedatafromAUVstothesurfacevesselsthroughtheuplinkaremostlikelytobespeech,imageorvideodata,whilethedatatothesmallAUVsthroughthedownlinkaretypicallycontrolcommands.Toaccountfortheasymmetryofthecommunicationsystem,onealsoneedstoconsiderthenumberofavailablehydrophonesandthesignalprocessingcapabilityatthereceivers.Itisreasonabletoassumethatforsurfacevessels,largehydrophonearraysandhighreceiverprocessingcapabilitiesareavailable.IfthereceiversaresmallAUVs,therewillbelowsignalprocessingcapabilityandonlyafewhydrophonesbecauseofthesizeandpowerlimitations.Datarateandreliabilityaretwocriticalguresofmeritincommunicationsystems,especiallyinUACchannelswithlimitedbandwidthanddoubleselectivity.Given 15

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1. Rate-orienteduplinksystem.Alargehydrophonearrayandhighsignalprocessingcapabilityatthereceiverareavailablewhilethereareonlyoneorafewtransducersandlimitedsignalprocessingcapabilityatthetransmitter. 2. Reliability-orienteddownlinksystem.Onlyafewhydrophonesareavailableatthereceiver.Carefultransmitterdesignisadoptedtoensurehighreliabilityandtoavoidhighcomputationalcomplexityatthereceiver. 26 ].Toovercomethechanneldoubleselectivity,inthe1980's,frequency-shift-keying(FSK)modulationwithnoncoherentenergydetectionwasadoptedforUAC[ 2 16 39 ].However,thelowbandwidtheciencyofnoncoherentenergydetectionschemesisinherentlyunsuitableforUAC'sextremelylimitedbandwidth. Inthepasttwodecades,signicantprogressonphasecoherentmodulationshasbeenmadeinUAC.Dierentcoherentmethodsareproposedintheliterature(seee.g.,[ 10 26 40 52 53 ]).Thesesystemstypicallyrelyonasequentialdatatransmission,wherethetime-varyingchanneliscontinuouslyestimatedandtrackedandtheinter-symbolinterference(ISI)issuppressedvialinearornon-linearequalizationincludingadaptivedecisionfeedbacktechniques.Notonlyisthecontinuoustrackingofthechannelcomputationallyexpensive;thetrackingerrorscanalsoinducesymboldetectionerrorswhichcanhaveacumulativeeectinadecision-feedbackequalizer(DFE).Asanalternativetosequentialdatatransmissions,block-basedtransmissionsareproposedin[ 33 35 ].However,thechannelDopplerspreadisalwaysaproblemforthoseschemes. 16

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33 ]isbasedonanoverly-simpliedassumptionthattheDopplerspreadisasimplecarrierfrequencyshift.IftheDopplerforallthechannelarrivalpathsarethesame,itcanbecompensatedbythepassbandresamplingatthereceiver(asopposedtobasebandresamplingin[ 35 ]).Thisassumption,however,isnotrealisticinUACenvironments(seee.g.[ 54 ]).InadditiontocontinuoustrackingmethodsandsimpliedDopplerassumptions,basisexpansionmodels(BEM)havelongbeenemployedtoestimatetime-varyingchannelsbyusingarelativelysmallnumberofBEMcoecientstocaptureaframeofchannelparameters,accordingtotheintrinsicdegreeoffreedomofthechannel(see,e.g.,[ 37 55 68 69 ]). Whenthesignalblocklengthisshorterthanthechannelcoherencetime,UACchannelscanbeapproximatedasquasi-static.Basedonthequasi-staticchannelmodel,[ 38 65 ]proposeseveraldirect-sequencespreadspectrum(DSSS)schemes,whichusesimplematchedlerreceivers.TheseschemestransmitasingleBPSKsymbolpersequenceblockduration,whichlimitsthedatarateto1bitpersequence.Inaddition,thedecision-directed(DD)anddierentialDSSSapproachesin[ 38 65 ]requirethechannelcoherencetimetobeatleasttwospreadingsequencelong,andarethuspronetochannelvariations. AlthoughasymmetriclinksoftenariseinUACscenarios,thisproblemhasneverbeenaddressedinexistingworks.Mostofthepreviousworksmentionedabovecanbeviewedasrate-orientedschemes,requiringalargereceiverhydrophonearrayandhighreceiversignalprocessingcapability.Recently,lowrateschemeshavebeenproposedin[ 31 32 59 ].Themulticarrierspreadspectrum(MCSS)schemein[ 59 ]requiresarecursiveleast-squares(RLS)equalizer,whichhashighcomputationalcomplexity.Theorthogonalfrequency-divisionmultiplexing(OFDM)schemebasedonaBEMisproposedin[ 31 32 ].Inthisscheme,boththechannelestimatorandtheequalizercontainmatrixinversionoperation,resultinginhighreceiverprocessingcomplexity.Therefore,thelow-rate 17

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31 32 59 65 ]donotmeetthesimplereceiverrequirementofthedownlink. Inthenextsection,wewillbrieyintroduceourrate-andreliability-orientedschemes. 18 ],whichinturnenablespilot-assistedcoherent[ 37 ]anddierential[ 6 ]schemesforsingle-inputsingle-output(SISO)systems.Here,weproposeourrate-orientedcoherentschemeforuplinkcommunicationsandreliability-orienteddierentialorthogonalspace-timecode(DOSTBC)fordownlinkcommunicationsinChapters 2 and 3 ,bothbasedonBEM. InChapter 2 ,wewillpresentasimplewindowingandde-windowingtechniqueatthereceivertoimprovetheaccuracyofthediscreteFouriertransform(DFT)BEM.Buildingonthis,wedevelopawindowedleast-squares(WLS)channelestimatorfortherate-orientedcoherentUACsystemsfortheuplink(seeourpublications[ 45 46 ]).Inaddition,wewillshowthatthewindowingandde-windowingtechniquewillalsoimprovetheminimummeansquareerror(MMSE)estimatorsin[ 37 ].Windowingtechniqueshavebeenproposedin[ 22 30 ]forchannelestimation,however,in[ 22 ]thewindowingoperationisperformedatthetransmitter,whichcouldaectthesignal-to-noiseratio(SNR)ofthesymbolsattheedgesofthewindowwithrelativelysmallcoecientsandwhichwouldinturnaectthebiterrorrate(BER)performance.Inourapproach,thewindowingandde-windowingprocedureisperformedonlyatthereceiverandonlyonthechannelestimationbranch.Although[ 30 ]usesawindowatthereceiver,itdoesnotincludeadetailedanalysisoranoptimumpilotpatterndesign.Ourapproachwillgiveathoroughanalysisaswellastheoptimumpilotpattern.Analysis,simulationsandseaexperimentresultswillbeprovidedtoverifytheperformanceimprovementsofoursimpleestimatorincomparisonwithexistingdesigns. 18

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InChapter 3 ,wewillpresentaDFT-BEM-basedDOSTBCschemethatisdesignedforreliability-orientedcommunications(seeourpublication[ 43 ]).Inthisscheme,eachinformationsymbolismappedintoKtransmissionslots,whereKisthedegreeoffreedomofonetime-varyingchanneltap.ThisgivesK-timetransmissionenergypersymbol.TheschemeusesOFDMtosolvethemultipathproblemandBEMtoensurerobustnessagainstDopplervariation.Moreimportantly,itutilizesmultipletransducerstoachievetransmitdiversitytocombatfading.Wewillshowthatthisschemethusachievesthree-dimensionaldiversityinspace,delayandDopplerdomains.Inaddition,theDOSTBCschemeweproposehasverylowcomplexitysignalprocessingatthereceiver,becausethereceiverdoesnotcontainachannelestimatororanequalizer;doesnotrequireanymatrixinversionoperationandthecomplexityincreaseslinearlywiththetransducernumber,notexponentially.WetestedourproposedschemeinaseaexperimentandfoundthattheBERata1000-meterdistancewasaround0:1%forallthe74packetscollectedover8days.DOSTBConplainOFDMwasalsotestedintheexperimentasthecontrolgroup.ItwasshownintheexperimentthatourproposedBEM-basedDOSTBChadconsistentlybetterperformance.Inaddition,thecorrelationsbetweentheBERsandenvironmentalparameterssuchaswindspeedandseasurfaceheightabovebottomwerecalculatedintheexperiment.OurproposedBEM-basedDOSTBCschemehadmuchsmallercorrelationsthantheplainOFDMsystem,showinghigherreliabilityagainstdierentseaconditions. BothofthecoherentanddierentialschemesinChapters 2 and 3 arebasedsolelyonDFT-BEM.Intheseschemes,adoptingotherBEMsmayrenderdierentperformance. 19

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4 ,wewillrstgeneralizeourpreviouslyproposedcoherentanddierentialschemestoaccommodatearbitraryBEMs,andtheninvestigatetheperformancedierenceofdierentBEMsinthecoherentanddierentialschemes(seeourpublication[ 44 ]).Usingthesegeneralizedschemes,weshowthatthemodelingaccuracyisnottheonlyfactordeterminingthesystemerrorperformance.Intermsofmodelingaccuracy,discreteprolatespheroidalsequence(DPSS-)BEMispreferabletoDFT-BEM,sincetheformerprovidesacloserapproximationtothechannel[ 68 ].However,ouranalyses,simulations,andexperimentalresultsshowthatitserrorperformanceisnotnecessarilybetterthanthatofthesimpleDFT-BEM,becausetheerrorperformanceisalsoaectedbythenatureofthemodelttingbiasandnoiseeects.OurresultssuggestthatBEMisapowerfulsolutionforcoherentanddierentialschemesinUAC,andthatthereisatradeobetweenthemodelingaccuracyandthenatureofmodelttingbias/noiseeectsfordierentBEMs.ThistradeosuggestsdierentBEMchoicesincoherentanddierentialapproaches. InadditiontotheBEM-basedDOSTBCforthedownlink,inChapter 5 wewillalsopresentahighreliability(HR-)DSSSschemethatonlyrequiresasimplematchedlterreceiver(seeourpublication[ 47 ]).Themultipathproblemissolvedbythegoodcirculantautocorrelationpropertyofthespreadingsequencesandbycyclicprexing(CP)beforeeachblock.Unlikeexistingschemes,ourHR-DSSStransmitsmultipledistinctsymbolsonmultiplesuperimposedspreadingsequencesduringeachblock.Amongthosesymbols,oneisusedasthepilotforchannelestimationandallotherscarrydata.Viathesuperimposedpilot,ourHR-DSSSrequiresonlyonesequence-longchannelcoherencetime,providingrobustnessagainstchannelvariation.Inaddition,ourHR-DSSSmarkedlyincreasesthedataratebytransmittingmultiplesymbolspersequencedurationandallowingforarbitrarymodulationsincludingQPSK,QAM,etc. 20

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1. Theuniqueasymmetriclinkconsiderations.Dierentlinktypesdeterminetherequireddatarateandreliabilitylevel,aswellastheavailableresourcesatthereceiver,includingthenumberofhydrophonesandthesignalprocessingcapability. 2. TheBEM-basedWLSchannelestimatorforhigh-ratecoherentsystems.OurWLSestimatoroutperformstheexistingleast-squares(LS)channelestimatorandthewindowingprocedurealsohelpstheexistingMMSEone.Theproposedschemeperformsthewindowingandde-windowingprocedureonlyatthereceiverandonlyonthepilots,aectingneitherthedatatransmissionpatternnorthedemodulator.Wealsodesigntheoptimumpilotpattern. 3. TheBEM-basedhigh-reliabilityDOSTBCwithlowcomplexitysignalprocessingatthereceiver.Itsolvesthedoubly-selectivechannelproblematthetransmitterandcollectsthree-dimensionaldiversityinspace,delayandDopplerdomainstoensurereliability.Inaddition,itrequiresonlyafewhydrophonesatthereceiver. 4. TheinvestigationoftheperformancedierencebetweendierentBEMsinbothcoherentanddierentialschemes.Thereisatradeobetweenthemodelingaccuracyandthenatureofmodelttingbias/noiseeectsfordierentBEMs.ThistradeosuggestsdierentBEMchoicesincoherentanddierentialapproaches. 5. TheHR-DSSSschemeforthedownlink.Wetransmitmultiplesymbolsduringonesequenceblock.Ourjudiciousdesigncanenhancereliablechannelestimationandsymboldemodulationinthepresenceofchannelvariation,aswellasenablehigherdatarate. 6. Thereliabilityevaluationinexperiments.WearethersttoevaluatethereliabilityofUACsystemsthroughthecorrelationsbetweentheBERsandenvironmentalparameters,includingwindspeedandseasurfaceheight. 21

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UACchannelsareinherentlydoubly-selectivewithlargefractionalbandwidthandunstablepropagationmedia.Forhigh-ratecoherentUACsystems,channelestimationisaninevitablestepfordemodulation.Asaresult,estimationofdoubly-selectivefadingchannelshasbeenextensivelystudiedinrecentyears(seee.g.,[ 5 22 37 69 ]). Inordertoestimatethedoubly-selectiveUACchannelsbyusinglimitednumberofpilots,oneimmediateideaistoreducethenumberofcoecientstobeestimated,sincethechannelcoecientsintimedomainaretypicallyhighlycorrelated.Basedonthisidea,dierentBEMshavebeenproposedinliterature.ThepolynomialBEMin[ 5 ]reachestherealchannelwhenthepolynomialorderapproachesinnity.TheKarhunen-LoevedecompositionBEMin[ 69 ]requireschannelstatistics.ThebasisoftheSlepiansequenceBEMin[ 68 ]varieswiththemaximumDoppler.ThoughtheDFTBEMin[ 37 ]avoidsthesedisadvantages,itsuersfromhighfrequencyleakageaswewillanalyzeindetaillater. Inthischapter,weproposeasimplewindowingandde-windowingtechniqueatthereceivertoimprovetheprecisionoftheDFTBEM,basedonwhichwedevelopaWLSchannelestimator.Inaddition,wewillshowthatthewindowingandde-windowingtechniquewillalsoimprovetheMMSEestimatorsin[ 37 ].Intheliterature,windowingtechniqueshavebeenproposedin[ 22 30 ]forchannelestimation.However,in[ 22 ]thewindowingoperationisperformedatthetransmitter,whichcouldaecttheSNRofthesymbolsattheedgesofthewindowwithrelativelysmallcoecientsandintheconsequentialBERperformance.Although[ 30 ]usesawindowatthereceiver,neitherdetailedanalysisnoroptimumpilotpatterndesignisgiven.Inourapproach,thewindowingandde-windowingprocedureisperformedonlyatthereceiverandonlyonthechannelestimationbranch.Andwealsodesigntheoptimumpilotpattern.Analysisandsimulationswillbeprovidedtoverifytheperformanceimprovementofoursimple 22

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3 25 57 62 ]: wheremaxdenotesthemaximumdelayspread;thatis,h(t;)=0,if>max.Theequivalentdiscrete-timesystemsampledatsymboldurationTsis: wherex(n)andy(n)denotethenthtransmittedandreceivedsymbolrespectively,z(n)isthei.i.d.AWGNwiththedistributionCN(0;2z),h(n;l)isthediscrete-timebasebandequivalentchannelcoecient,andL:=bmax=Tscisthenumberofchanneltaps.Weadoptthewide-sensestationaryuncorrelatedscattering(WSSUS)assumptionsothatthechannelcoecientsfromdierentdelaytapsareindependent[ 26 ]. Duetothemaximummovingspeedlimit,thereisamaximumDopplerfrequencyfmax.Thediscrete-timeFouriertransform(DTFT)ofh(n;l)givenbyH(f;l)=1Xn=h(n;l)e2nfsatisesH(f;l)=0,forjfj>fmax.Inpractice,however,oneonlyhastheobservationofthechanneloveraniteblock.LetNbetheblocksize,h(l):=[h(1;l);:::;h(N;l)]TbetheN1truncatedchannelforthelthdelaytapandthe(NN)diagonalmatrixWwith[W]k;k=w(k)6=0bethewindowmultipliedtothechanneltruncation.Ifitisarectangularwindow,wehaveW=IN.Then,thetime-andDoppler-domainrelationshipofthechannelcanbeobtainedas: 23

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whereFKandFNKdenotetheKlow-frequencyandthe(NK)high-frequencyrowsoftheN-pointDFTmatrixFrespectively;~g(l):=[~g(1;l);:::;~g(N;l)]TdenotestheDFTofthewindowedchannelvectorWh(l);~gK(l)and~gNK(l)denotetheKlow-frequencyandthe(NK)high-frequencycomponentsof~g(l)respectively.WitharectangularwindowW=IN,K=2dfmaxNTse+1,whichissimplycalculatedbyfmaxdividedbytheDoppler-domainresolution(NTs)1(samplinginDopplerdomain)and~gNK(l)=0,Eq.( 2{3 )becomestheDFTBEMusedin[ 22 37 ],wherethehighfrequencycomponentsaresimplysettozero.However,wewillshownextthatthismodelisnotaccurate. LetustreatthechannelasrandomwitheachrealizationsatisfyingH(f;l)=0whenjfj>fmax.ItfollowsthattheautocorrelationfunctionofH(f;l)inDopplerdomain(f)satisesRl(f;)=0whenjfj>fmax.Actually,oneoftheclassicalmethodstogeneratetime-varyingfadingchannelsistopassawhiteGaussianrandomsignalthroughalterwithafrequencyresponseequaltothesquare-rootofthedesiredDopplerspectrum[ 48 ,Chapter5].Hence,wealsoassumethatRl(f;)=0when6=0. LetW(f)bethespectrumofthewindowfunction,weobtainthepowerspectrumdensity(PSD)ofthewindowedchannelas: ~Rl(f;0)=E[fH(f;l)W(f)g2]=Rl(f;0)jW(f)j2:(2{4) Then,samplingintheDopplerdomainattheintervalof(NTs)1,thePSDofthewindowedchannelbecomes~Rlk NTs;0;k=1;2;:::;N:ThiscorrespondstotheenergydistributionofthechannelinDopplerdomain. Noticethat,however,W(f)inEq.( 2{4 )isneverstrictlyband-limited.Morespecically,ifonesimplytruncatesthesignalor,equivalently,usesarectangularwindowasin[ 37 ],W(f)isafoldedsincfunction.Asaresult,thePSD~Rl(f;0)6=0when 24

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Infact,theaveragesignal-to-interferenceratio(SIR)canbedenedas: SIR:=Xk=2(K=2;NK=2)LXl=0~Rlk NTs;0 Xk2(K=2;NK=2)LXl=0~Rlk NTs;0:(2{5) Eq.( 2{5 )impliesthattheSIRcanbeimprovedbybetterconcentratingthechannelenergyonthelow-frequencycomponents.Clearly,thedirecttruncationin[ 37 ]isequivalenttoarectangularwindow,whosesidelobesdecayveryslowly,leadingtosignicantenergyleakageintothehigh-frequencyrange.TodesigntheoptimumwindowthatmaximizestheSIRinEq.( 2{5 ),channelstatisticsRl(f;0)isrequired.Here,weconsiderthesituationwherethechannelstatisticsarenotavailable,sincetheBEMbecomesunnecessaryotherwise,aswewillshowinthenextsection.Inthiscase,windowswithlowersidelobesareclearlydesirableaccordingtoEq.( 2{5 ).Ofcourse,windowswithlowersidelobesusuallyleadtoabroadermainlobe.ThisimpliesthatKshouldbeslightlylargerthan(2dfmaxNTse+1).Inthenextsection,wewillintroduceanimprovedLSestimatorbasedonthewindowingadvantagediscussedabove. 2.2.1MMSEorLS? 24 ,Chapter12]withanynumberofpilotobservationstointerpolateh(n;l),neithertime-DoppleranalysisnorBEMrequired.However,estimationofthechannelstatisticsisoftendicultbecausethestatisticsmaychangeovertime[ 49 ].Inparticular,forunderwateracousticchannels,thereisevennopropermodeltocharacterizethechannelsincethechannelappearstobeneitherRayleighnorRician 25

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66 ].Motivatedbythese,weproposeaWLSestimatorthatdoesnotrequireanychannelstatistics. where~Histhe(N+L)Nwindowedchannelmatrixwithentries[~H]n;m=w(n)h(n;n+Lm).Withthetime-DopplerrelationshipshowninEq.( 2{3 ),wehave ~H=NXk=1DHk~Gk=Xk=2(K=2;NK=2)DHk~Gk+Xk2(K=2;NK=2)DHk~Gk;(2{7) whereDkistheNNdiagonalmatrixwiththekthrowofF,and~GkisaToeplitzmatrixwiththerstcolumn[~g(k;0);:::;~g(k;L);0;:::;0]T.Here,thehigh-frequencyandlow-frequencycomponentsareseparated.Stackingthewindowedreceivedsymbolsfrom 26

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Basebandequivalentsystemwiththewindowedleastsquares(WLS)estimator. thepilots,weobtain whereubisthebthpilotsubblock,Dk;band~Gk;barethesubmatricesofDkand~Gkcorrespondingtoub.Thesubscriptpdenotespilot.SinceweneedtoLSttheK(L+1)low-frequencyDopplerdomaincoecients,thepilotsneedtobedesignedtomakeypaK(L+1)1vector;thatis,BXb=1(Nb+L)=K.DuetothecommuntativitylawofToeplitzmatrixandvectormultiplication,weget~Gk;bub=Ubg(k);whereUbisan(Nb+L)(L+1)ToeplitzmatrixwiththerstcolumnubpaddedbyLzerosandg(k)=[~g(k;0);:::;~g(k;L)]T:Eq.( 2{8 )canberewrittenas whereg=[gT(1);:::;gT(N)]T;andtheK(L+1)K(L+1)matrixisgivenby 27

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2{7 ),weobtain: whereKandgKconsistof(k)andg(k),withkK=2orkNK=2;NKandgNKconsistof(k)andg(k),withK=2
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2{15 ),wecanseethatourWLSestimatorperformsthewindowingandde-windowingprocedureonlyatthereceiverandonlyonthepilots,aectingneitherthedatatransmissionpatternnorthedemodulator.ThesystemwithourWLSchannelestimatorisillustratedinFig. 2-1 WiththisWLSestimatorready,anaturalquestionwillarise:whatistheoptimumpilotpattern? MSE=Efkh^hk2g=MSENK+MSEz;(2{16) where MSENK=En1HNKHK1KNKgNK2o(2{17) denotestheMSEresultedfromthehigh-frequencycomponentsintheDopplerdomainand MSEz=En1HK1KWpzp2o(2{18) denotestheMSEresultedfromAWGN. InEq.( 2{17 ),sincethewindowswithlowersidelobesarebell-shapedintimedomainsuppressingthesignalsateitheredgeofthetruncatedsignalblock,MSENKisactuallyaweightedsummationofindividualsquareerrors,withinversebell-shapedweightsinthetimedomain.Hence,theresultantweightedMSEatthecenterofthewindowedtruncationissmallerthantheedges.Thismotivatesustoonlyretaintheresultsatthecenter,andtouseaslidingwindowtocovertheentiretimedomain.Therefore,allthepilotsubblocksareofidenticalimportance.Thepilotsubblocksshouldthenbeidenticalandsoarethespacesbetweenthepilotsubblocks. Next,letusdeterminehowmanypilotseachpilotsubblockshouldhaveandhowtheyshouldbeplaced.Asweareretainingtheestimationresultsforthecentersymbolsofeach 29

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Theoptimumtrainingpattern. Table2-1. Simulationparameters 2dfmaxNTse+1=7 PilotEnergy=61 Channeldelayprole:s(l)=e0:1l DemodulationEqualizer:MMSE slidingblock,wherethewindowweightisapproximately1,withthetotalpilotenergyEK,weobtain: MSEzEnHK1Kzp2o=trEHK1KzpzHp(1K)HK=2ztr1K(1K)H2zNP=E:(2{19) Thelaststepisderivedwithasimilarprocedurein[ 58 ].Theequalityatthelaststepholdsifandonlyif1K(1K)Hisadiagonalmatrixwithidenticaldiagonalentries.Therefore,theoptimumpilotpatternistheonewithonly1nonzeropilotineachpilotsubblockandatotalKsuchpilotsinablock,asillustratedinFig. 2-2 .Itisworthnotingthatthisdesigncoincideswiththeonein[ 37 ]. 30

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OnesnapshotoftheWLSestimationresults. windowingtechniquehelpsimprovingtheLSestimator.Actually,ourwindowedBEMisexpectedtohelpimproveotherBEM-basedestimators,suchastheMMSEestimatorin[ 37 ],aswewillconrmbysimulationsnext. 2-1 Fig. 2-3 showsonerealizationofourWLSestimatorintheabsenceofAWGN.WLSestimatorswithaBlackmanwindowandwitharectangularwindowarecompared.OurWLSestimatortstherealchannelmuchbetterinthecenter.Inaddition,wealsoobservethatevenwitharectangularwindow,thechannelestimationerrorforthedata 31

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MSEvs.SNRperformanceoftheWLSandtheMMSEchannelestimators. timeslotsinthecenterisalsosmallerthantheedges.Thereasonisthatthechannelestimatesoftheentireblockareobtainedfromthoseofthepilotsusingaprocedurereminiscentofinterpolation,andthatthecenteroftheblockbenetsfromthepilotsonbothsides. Figs. 2-4 and 2-5 showtheMSEandBERperformanceofseveraldierentestimators.WeuseaslidingwindowforourWLSscheme,andonlytaketheestimationanddemodulationresultsbetweenthe2centerpilots.Noticethatamongthe4dierentwindows,Blackmanwindowgivesthebestperformance,andrectangulartheworst.ThisjustiesouranalysisinSection 2.2 .Ifthechannelstatisticsareavailable,theMMSEestimatorin[ 37 ]canbeadopted.Inadditiontothexedrectangularwindow(directtruncation)in[ 37 ],wealsotestedthisMMSEestimatorwithourslidingwindowapproach.FromFigs. 2-4 and 2-5 ,wehavethefollowingobservations: 32

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BERvs.SNRperformanceoftheWLSandtheMMSEchannelestimators. i) IntermsofchannelestimationMSE,theMMSEestimatorsoutperformtheLSonesatlowSNR,bytakingadvantageofthechannelstatistics.However,thisMSEadvantagedoesnotseemtodirectlycarryovertotheBERcomparisons.InFig. 2-5 ,weobservethattheBERperformanceof[ 37 ]isidenticalwiththeWLSestimatorsatlowSNR,despiteitsMSEadvantageshowninFig. 2-4 ii) Theschemein[ 37 ]resultsintheworstperformanceamongallMMSEestimators.Thisconrmstheadvantageofourslidingwindowapproach.Sincetheschemeswithslidingwindowonlytaketheresultsbetweenthe2centerpilots,theyrequireKtimescomputationastheoneswithxedwindows,butwithoutalteringthetransceiverarchitecture. iii) TheMMSEestimatorswithrectangularwindowsareworsethanappropriatelywindowedLSestimatorsathighSNR.Inparticular,theschemein[ 37 ]withaxedrectangularwindowisworsethanallWLSestimatorsevenatmediumSNR.This 33

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Thescatteringfunctionforadatapacketincalmperiods. conrmsthatoursimplewindowedapproachhelpsnotonlyLSestimators,butalsoMMSEones. 34

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Thescatteringfunctionforadatapacketinroughperiods. Thesamplerateatthetransmitterandreceiverfsisabout39kHz(107=256).Thecarrierfrequencyis14kHzandthesymbolrateisfs=57:8k/s.TheblocklengthisN=4200andeachblockcontainsK=7subblocks.Eachsubblockhas507QPSKsymbolsledby93zeros.Therst110non-zerosymbolsareusedaspilotsandtherestasdata.Thedataratecanbecalculatedas10:6kbps.DFEisusedforequalization.Forcomparison,wealsodecodethereceivedsignalswith2non-BEMmethods.Therstoneestimatesthechannelusingtherstsubblock,andthendecodestherestwithoutchannelstateinformationupdated[ 63 ].Thesecondoneestimatesthechannelusingtherstblockandusesthedecodedresultstoupdatethechannelstateinformation. Duringtheexperiment,mostofthechannelconditionsarestablebuttherearealsosomeroughperiods.Thescatteringfunctionestimatedbyamatchedlter[ 9 ]foracalm 35

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Coherentschemes'BERswith12hydrophones Squarewindow Blackmanwindow BER 0:71% 0:58% periodisshowninFig. 2-6 ,wherewecanhardlyobserveanyDoppler.ThescatteringfunctionforaroughperiodisshowninFig. 2-7 .Wepick3datapacketsduringtheroughperiodswhenthechannelschangeremarkably.Eachpacketcontains38025QPSKsymbols.Inthesepacketsthe2non-BEMschemeshavenearly50%BERsbecausethechannelschangeseverely.TheuncodedBERsatdierenthydrophonesforthedierentschemesareshowninFig. 2-8 .TheuncodedBERscombiningall12hydrophonesareshowninTable 2-2 .TheBEMbasedschemeworksverywell.TheBERsareattheorderof103,with12hydrophones.ItveriesthattheBEM-basedchannelestimatoriseectiveinUACforcoherentdetections.Fromthegureandthetable,weobservethattheBERwithaBlackmanwindowisalwaysbetter.ItsupportsthatourproposedWLSchannelestimatorimprovestheerrorperformanceofrate-orientedcoherentUACsystems,consistentwiththesimulationresultsshowninSection 2.3 Thisrate-orientedcoherentschemeisfortheuplinkrequiringlargenumberofhydrophones(12intheRACE08experiment)andareceiverwithchannelestimationcapability.Infact,thereceiversignalprocessingcomplexitycanbehighbecauseofthematrixinversionoperationandtheslidingwindowoperation.Inthenextchapter,wewill 36

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Coherentschemes'BERsacrossdierenthydrophonesinRACE08ata1000mdistance. introduceareliability-orientedschemeforthedownlink,whichprovidesgoodperformanceevenwithasmallnumberofhydrophonesandrequireslowcomplexityofsignalprocessingatthereceiver. 37

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Intheprecedingchapter,wehaveseenarate-orientedcoherentscheme,whichusesasingletransducer.Whenmultipletransducersareemployed,transmitspatialdiversitybecomesavailable.Ifappropriatelyenabledatthetransducersandeectivelycollectedatthehydrophones,thespatialdiversitygaincanconsiderablyreducetherequiredSNRtoachieveaprescribederrorperformance.ThisreducedSNRcanbetranslatedtoanincreasedcommunicationreliabilityifthesametransmitpowerisused.Forcoherentmultipleinputmultipleoutput(MIMO)schemes,catchingthevariationofthechannelsrequiresalargenumberofpilots,whichnotonlyconsiderablyreducethebandwidtheciencyofthesystembutalsointroducehighprocessingcomplexity.Forexample,inthe2-transducerMIMO-OFDMschemeproposedin[ 34 ],about1=3ofthesubcarriersareusedaspilots.Fortheschemeswithmoretransducers,evenmorepilotsareexpected.Inthischapter,wewilldevelopareliability-orienteddierentialschemeforthedownlink,wherethereisnoneedtoestimatethechannelatthereceiver. Dierentialschemesrequirethechannelstobeatfadingandtimeinvariant.FlatfadingchannelsleadtoISI-freereceivedsignals.Thetime-invariantchannelpropertymakestheprevioussymbolorsymbolblockqualiedtobethechannelreferenceofthenextonesincethechannelhasnotchanged.However,UACchannelsmeetneitherofthetworequirementsbecauseofthedoubleselectivity.OFDMhaslongbeenusedtoconvertthefrequency-selectivechannelstoatfadingonesinRFcommunications.ItwasextendedtotheUACregime[ 33 35 ].However,thechannelDopplerspreadisalwaysaproblemforthoseschemes.Ref.[ 33 ]isbasedonanoverly-simpliedassumptionthattheDopplerspreadisasimplecarrierfrequencyshift.IftheDopplerforallthechannelarrivalpathsarethesame,itcanbecompensatedbythepassbandresamplingatthereceiver([ 35 ]doesbasebandresampling).Thisassumption,however,isnotrealisticinUACenvironments(seee.g.[ 54 ]).PlainOFDMsolvesonlyhalfofthedoubleselectivity 38

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18 ],whichenablespilot-assistedcoherent[ 37 ]anddierential[ 6 ]schemesforSISOsystems.ThepossiblesolutiontodoubleselectivityistocombineOFDMforfrequencyselectivitywithBEMfortimeselectivity. Inthischapter,weimplementOFDMandadopttheBEMchannelmodelconsideringaMIMOsetup.Wewilldevelopasubblock-wiseDOSTBCschemeoverUACchannels.Thedierentialschemebypasseschannelestimation,savingthebandwidthoccupiedbypilotsandthecomputationalpowercostbychannelestimation.Wewillshowthatourproposedapproachhashighreliabilitybycollectingfulldiversitygainsinthreedimensions:space,delayandDoppler.Simulationswillbeprovidedtoverifythesegains.Wealsotestedourproposedschemeinaseaexperiment.TheBERat1000-meterdistancewithonly2hydrophonesisaround0:2%byaveragingallthe74packetscollectedover8days.DOSTBConplainOFDMisalsotestedintheexperimentasthecontrolgroup.ItisshownintheexperimentthatourproposedBEM-basedschemeisalwaysbetter.Inaddition,thecorrelationsbetweenthe2schemes'BERsandtheenvironmentalparameters,suchaswindspeedandseasurfaceheightabovebottom,arecalculatedintheexperiment.OurproposedschemehasmuchsmallercorrelationsthantheplainOFDMone,showinghighreliabilityagainstdierentseaconditions. Inthenextsection,wewillintroducethetransformationbetweenBEMandchannelcoecients.OurBEM-basedDOSTBCschemewillbeproposedinSection 3.2 .SimulationandexperimentresultswillbegiveninSection 3.3 and 3.4 .Finally,concludingremarkswillbegiveninSection 3.5 39

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LetusconsideraframeofNsymbolsfx(b)nt(n)gN1n=0fromthent-thtransducer,whereb:=bn=Ncistheframeindex.Thebasebandequivalentdiscrete-timechannelcanberepresentedusingDFT-BEMinthepreviouschapter(seealso[ 37 ])asfollows: where!:=2=N, denotesthechannellengthand capturesthetime-varyingcharacteristic.NoticethatthechannelvariationofeachpathindexedbyliscapturedbyKcoecientsfg(k)nr;nt(b;l)gKk=0thatremaininvariantwithineachframe,butareallowedtochangefromoneframetoanother.Asaresult,inanyframewithNsymbols,thechannelischaracterizedbyK(L+1)BEMcoecients.ThisimpliesK(L+1)Nand,accordingly,2fmaxmax<1[c.f.( 3{2 )and( 3{3 )].Thelatterconditionturnsouttobetheoneyieldinganunderspreadchannel[ 42 ,Chapter14]. Atthereceiver,then-thsampleinthek-threceivedframeatthenr-thhydrophone,y(k)nr;nt(n),canbeexpressedas: wherezk(n)isAWGNwithzeromeanandvarianceN0=2. Tofacilitateourtransmit/receiveprocessingdesignintheensuingsections,wewillnowdevelopsomemoreconvenientalternativerepresentationsofthechannelcoecients. 40

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3{1 )intoavectorinnerproductform,weobtain: with capturingthetimevariation,andgnr;nt(b;l):=[g(1)(b;l);:::;g(K)(b;l)]Tcapturingthetime-invariantcharacteristicsofthechannel. From( 3{5 ),wenoticetwothings.First,thebasisvectorgnr;nt(b;l)doesnotchangewithinaframe.ThisimpliesthattheN(L+1)channelcoecientsarecapturedbyK(L+1)BEMcoecients.Secondly,therowvectorwTnlinkingthechannelwiththeBEMcoecientsdoesnotdependontheframeindexk.Inaddition,thefollowinglemmacanbereadilyproved: UsingmatrixWnin( 3{7 ),thecollectionofchannelcoecientsh(b)nr;nt(n;l)=h(b)nr;nt(n;l);:::;h(b)nr;nt(n+(K1)B;l)T Eq.( 3{9 )explicitlyshowsthat,foranypathl,theNchannelcoecientscanberepresentedbytheKBEMcoecients. 41

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6 ],suchadierentialschemewasintroducedforaSISOsystem.Inthefollowingstepswewillrstintroducethetransformintoatime-invariantequivalentrepresentationasin[ 6 ],andthenconstructDOSTBCforaMIMOsetup. 6 ],eachframecontainsPsubblocksconsistingofMsymbols,andeverysubblockisrepeatedKtimes.Wewillgivethedetailslater.Atthetransmitter,acyclicprex(CP)oflengthLisaddedtoeveryMsymbols,andatthereceiver,theCPsegmentsareremoved.Therefore,thetransmittedframehasasizeofN=P(M+L)K.AfterremovingtheCPsegments,thematrix-vectorI/Orelationshipis whereyisthePMK1receivedvector,HisthePMKPMKblockdiagonalchannelmatrix,xisthePMK1transmittedvectorandzisthePMK1noisevector.The 42

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andupondeningMi:=iM+(i+1)Lforbrevity,thei-thMMmatrixentryHiisshownas 1 and( 3{9 ),weknowthatinordertogetthebasisg(l)weneedtohaveh(n;l),whichconsistsofthechannelcoecientswiththesamedelaylandeveryP(M+L)timeindex.Therefore,thenextstepisinterleavingtoconstructh(n;l)inthechannelmatrix.Denetheinterleavingmatrix whereeTmisthem-throwofmatrixIPM,andthenmultiplyTtothetransmittedvectorx:=T~x(beforeinsertingCP)andtothereceivedvector~y:=y(afterremovingCP).Sinceisaunitarymatrix,i.e.,T=IPMK,theI/Orelationshipcanberewrittenas ~y=~H~x+~z;(3{14) 43

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~H:=HT(3{15) istheequivalentchannelmatrix,and~zisstillAWGN.From( 3{13 )and( 3{15 ),weseethattheinterleavingoperationactuallyinterleaveseveryPMcolumnsandrowsofH.RecallthatHisthechannelmatrixafterremovingtheCPsegments,sothatactuallytheinterleavingoperationinterleaveschannelcoecientsseparatedbyP(M+L)symboldurations.Thatisexactlyhowweconstructh(n;l)inLemma 1 and( 3{9 ).Thus,~Hcanbewrittenas: ~H:=266666664~H(0)000~H(1)............00~H(P1)377777775;(3{16) where~H(p)isgivenin where~y(p)=[~y]pMK;:::;[~y](p+1)MK1T,~x(p)=[~x]pMK;:::;[~x](p+1)MK1Tand~z(p)=[~z]pMK;:::;[~z](p+1)MK1T. 44

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1 and( 3{9 )indicatethat,inordertoobtaing(l),weneedtomultiplyWHnbyh(n;l);thatis,tomultiply with~y(p).Noticethattheentriesin( 3{17 )areDfh(n;l)g,whichisdierentfromh(n;l)requiredin( 3{9 ).Therefore,inordertoconstructanequivalentchannelmatrixconsistingofg(l),thetransmittedsymbolshavetoberepeatedforKtimesineachsubblock,i.e., ~x(p)=u(p)1K;(3{20) whereu(p)istheM1datavector.Then,theI/Orelationshipbecomes y(p)=KGu(p)+z(p);(3{21) wherey(p):=H(p)~y(p)istheMK1vectoratthereceiver, istheMKMequivalentchannelmatrix,andz(p)isstillAWGNsinceH(p)(p)=KIMK.Noticethatin( 3{22 )wegetatime-invariantblockcircularchannelequivalentGthatisirrelevanttop.Then,thenextstepistodiagonalizeG.Asweknow,inversediscreteFouriertransform(IDFT)atthetransmitterandDFTatthereceivercanbe 45

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whereFMistheM-pointDFTmatrixand(p)isthep-thdierentiallyencodedsubblock.InSISOdierentialsystems,(p)isgivenby whereSd(p)isthep-thMMdiagonaldatamatrix.Thendene~FM:=[IKf1;:::;IKfM],wherefmisthem-thcolumnoftheM-pointDFTmatrix.WithDFTatthereceiver,weget Therefore,theI/Orelationshipbecomes where~D=K[D(VMg(1));:::;D(VMg(K))]TwithVMdenotingtherstL+1columnsofFM,g(k):=[g(k)(0);:::;g(k)(L)]TandisstillAWGN.Tillnow,wehaveatime-invariantblock-diagonalequivalentchannelmatrix~D.Therefore,weget ~DSd(p)=SD(p)~D;(3{27) whichmeansthatthechannelandthedataaremultiplicationexchangeablewhenSd(p)isreplacedbySD(p),whereSD(p)=IKSd(p).TheI/Orelationshipbecomes[ 6 ] 20 56 ]fortime-invariantchannelsintotheonefordoubly-selectivechannelswiththisequivalenttime-invariantblock-diagonal 46

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56 ]and[ 20 ],DOSTBCsystemsovertime-invariantat-fadingchannelsareproposedfortwo-transmit-antennaandgeneralcases,respectively.Theat-fadingchannelrequirementenablesthemultiplicationexchangelawforthechannelandthedata.Recallthatourequivalentchannelsarealsoinvariantfromsubblocktosubblockandthemultiplicationexchangelawisalsoapplicable( 3{27 ).Withoutlossofgenerality,wewillnextgiveanexamplewithNt=2andNr=1. Wegroup2consecutivesubblocksintoablockandindexitwithpb.Consequently,therearePb=P=2blocksineveryframe.Let [1(pb);2(pb)]=[Sd1(pb);Sd2(pb)]2641(pb1)2(pb1)2(pb1)1(pb1)375;(3{29) whereSd1(pb)andSd2(pb)aretwoMMdiagonalmatriceswithdiagonalentriesbeingtheinformationsymbolstobetransmittedinthepb-thblock,1(pb)and2(pb)areM1vectorsforthepb-thblock,and1(pb1)and2(pb1)areforthe(pb1)-thblock.Thenweencodethesubblocksas: wherethesubscriptsofdenotetheindicesofthetransducers.AfterthesameprocessintroducedintheprevioussubsectionfortheSISOsystemtogetanequivalenttime-invariantblock-diagonalchannelmatrix,weobtainthesubblocksatthereceiveras: 47

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3{31 )and( 3{32 )hassimilarformsasthosein[ 56 ].TheMLdecoderisgivenby ForthegeneralcasewhenNt>2,wejustneedtofollowthestepsin[ 20 ]besidesreplacingthesymbolsbysubblocks. Asweknow,DOSTBCdoesnothaveanyrequirementonthenumberofthehydrophones.OnlysimpleMRCisneededwhenmultiplehydrophoneisusedatthereceiver[ 56 ],[ 20 ].Thebaseband-sampled-equivalentsystemmodeldiagramwith2transducersandmultiplehydrophonesisshowninFig. 3-1 56 ],[ 20 ].In[ 6 ],ithasbeenprovedthattheSISOdierentialschemecollectsfulltime-varyingdiversity.OnesubblockcanbedividedintosmallgroupswithlengthKG.Whenthelinearcomplexeld(LCF)codein[ 36 ]isusedwithingroupsandKGL,fulldelaydiversityiscollected[ 6 ].Therefore,ourdierentialschemecancollectfullthree-dimensionaldiversity:space,delayandDoppler. However,asmentionedin[ 6 36 ],thedecodingcomplexityincreasesexponentiallyasthegrouplengthKincreases.AsindicatedbythemeasureddatainUACchannels,withsymbolratethousandssymbolspersecond,thechannelcanbeaslongastensofsymboldurations.Then,iffulldelaydiversityistobecollected,thedecodingcomplexitycanbeoverwhelming.Therefore,forpracticalconsiderations,smallerKcanbeusedtoprovide 48

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Baseband-sampled-equivalentsystemmodel Figure3-2. BERversusSNR.TI:time-invariantchannelswithfmax=0;TV:time-varyingchannelswithfmax=3:3Hz;QPSK:plainQPSKwithnocoding;LCF:codingin[ 36 ]withKG=3. theoptimumdiversity-complexitytradeo.Ontheotherhand,aswecanseein( 3{33 )and( 3{34 ),thedecodingcomplexityonlyincreaseslinearlyasthenumberoftransducersincreases.Also,sinceMRCisusedatthemultiplehydrophones,thedecodingcomplexityalsoincreaseslinearlywiththenumberofhydrophones.Thatis,thecomplexityofcollectingthespatialdiversityisconsiderablylowerthanthatfordelaydiversitycollection. 49

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Dierentialschemes'uncodedBERsata1000mdistanceinRACE08 UncodedBER Numberofhydrophones 1 2 12 QPSK BEM 0:78% 0:20% 0:12% PlainOFDM 6:30% 3:30% 1:91% 8PSK BEM 2:92% 1:15% 0:82% PlainOFDM 11:27% 7:26% 3:22% 21 ].WechooseNt=2andNr=1.Inthesimulation,weusemaximumDopplerspreadasfmax=3:3Hz,symboldurationasTs=104sandthenumberofDopplerraysas200.WechoosetheframelengthN=3000,therefore,K=3.Dierentpathsareassumedtobeindependent.Themultipathintensityproleisselectedas()=exp(0:1=Ts)andthenthetotalenergyisnormalizedto1.Inthesimulations,wechooseL=8andtheLCFgrouplengthKG=3,i.e.,partialdelaydiversitywillbecollected. TheBERversusSNRcurvesareplottedinFig. 3-2 .RecallthatthereisDFTandIDFTinourscheme.OurproposedDOSTBCisactuallyamulticarrierscheme.Here,weprovideDOSTBCschemeonplainOFDMwith120subcarriersforcomparison.InFig. 3-2 ,weseethatfortheplainOFDMschemeovertime-varyingchannels,thereisanerroroorbecauseoftheinter-carrierinterference(ICI)causedbythechannelvariation.OurproposedDOSTBCschemewithK=2hasaverygoodBERperformanceoverdoubly-selectivechannelswithtime-variation. Thediversityadvantageofourproposedschemecanalsobeobservedinthegure.WecanclearlyseethediversitydierencesamongtheBERcurves.Dopplerdiversitycanbeobservedbycomparingthetwocurvesfortime-varyingandtime-invariantchannels.Then,comparingthecurvegeneratedusingtheSISOschemein[ 6 ]totheoneusingourschemewithLCFcodingsizeKG=3andK=3overtime-varyingchannels,weobserveevidentspatialdiversityadvantageofourschemeovertheSISOscheme.Finally, 50

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DOSTBCQPSKuncodedBERinRACE08with2transducersand1hydrophoneata1000mdistance. comparingthetwocurvesusingQPSKandLCFcodingovertime-invariantchannels,weseethatthecodingin[ 36 ]providesdiversityadvantage.Therefore,Fig. 3-2 veriesthatourschemecollectsthree-dimensionaldiversity:space,delayandDoppler. 2.4 .Forcomparison,DOSTBConplainOFDMwasalsotestedintheexperimentasthecontrolgroup.Thewaterdepthwasfrom9toabout14m.The2transducersfortheDOSTBCschemeswereplaced3mand1:8mabovetheseabottomvertically,bothonastationarytripod.Axedreceivingarraywith12verticallyplacedhydrophoneswaslocatedata1000mdistance.Thespacebetweenadjacenthydrophoneswas0:12m. Thesamplerateatthetransmitterandreceiverfsisabout39kHz(107=256).Thecarrierfrequencyis10:5kHzandthesymbolrateisfs=84:9ksymbolspersecond. 51

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DOSTBCQPSKuncodedBERinRACE08with2transducersand2hydrophonesata1000mdistance.Zero-errorisillustratedas105. DOSTBConplainOFDMhas512subcarriersandtheCPlengthis100.FortheBEM-basedDOSTBC,theframelengthisN=2772,thesubblocklengthis189andtheCPlengthis42.QPSKand8PSKmodulationsareusedforbothschemes.The74datapacketswerecollectedover8days.Ineachpacket,withQPSKmodulation,thereare9072bitsfortheBEM-basedschemeand16384bitsfortheplainOFDMone.With8PSKmodulation,thereare13608and24576bitsforthe2schemesrespectively.Noerrorcontrolcodingisusedforanyschemes. UncodedaverageBERsusing1,2andallthe12hydrophonesaregiveninTable 3-1 .TheBERsusingasinglehydrophonearecalculatedbyaveragingtheBERsusingeachoneoutofthe12hydrophonesandtheBERsusing2hydrophonesareobtainedbytakingthereceivedsignalsfromthetopandthebottomhydrophones.MRCisusedforthemultiple-hydrophonecasesatthereceiver.InTable 3-1 ,ourproposedBEM-basedDOSTBCisalwaysbetterthantheDOSTBCschemeonplainOFDM 52

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DOSTBCQPSKuncodedBERinRACE08with2transducersand12hydrophonesata1000mdistance.Zero-errorisillustratedas105. withanymodulationandanyhydrophonenumber.WealsoobservethatwithQPSKmodulation,ourproposedBEM-basedDOSTBCreachesaverygooduncodedBERat103levelevenwhenonly2hydrophonesareused.TheBERisstilllowwithasinglehydrophone.Forthemostchallengingcase,8PSKwithasinglehydrophone,ourschemestillachievesanacceptableBER2:92%,buttheplainOFDMonehasaBERashighas11:27%. Thepacket-wiseBERsareplottedinFigs. 3-3 { 3-8 .Inthesegures,westillobservethatourproposedBEM-basedDOSTBCoutperformstheDOSTBCschemeonplainOFDMwithanymodulationandanyhydrophonenumber.EspeciallyinFigs. 3-4 and 3-5 ,itisclearthattheBERsfortheplainOFDMschemeuctuateseverely,sometimesmorethan10%,butthetwoBEM-basedDOSTBCschemesachievearound103BERsconsistently.ItconrmsthatourBEM-basedDOSTBCismorerobust. 53

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DOSTBC8PSKuncodedBERinRACE08with2transducersand1hydrophoneata1000mdistance. InordertoexploretherobustnessofourproposedBEM-basedDOSTBCmoredeeply,welookintotheenvironmentaldataintheexperiment.ThewindspeedandtheseasurfaceheightabovebottomatthemomentofeverydatapackettransmittedareplottedinFigs. 3-9 and 3-10 .Inthegures,weobservethatduringtheexperiment,thewindspeedvariesfrom0to22knotsandtheseasurfaceheightchangesbetween9:2mand10:5m.Thelargedynamicrangeoftheenvironmentaldatameansthattheexperimentwascarriedonundervariousseaconditions,calmandrough.LookingatFigs. 3-3 { 3-8 forBERsandFigs. 3-9 and 3-10 fortheenvironmentaldatatogether,weareabletotellthatthereisarelationshipbetweentheBERsandtheenvironmentaldata.Thehigherthewindspeedis,thelargertheBERisandthelowersurfaceheightis,thelargertheBERis.ThereasonisthathighwindspeedcausessurgingwaveandaccordinglylargeDopplerspread,andlowseasurfaceheightmeansshallowwaterwherethechannelisaectedseverelybythesurfacewave.TherelationshipbetweentheBERsandtheenvironmental 54

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DOSTBC8PSKuncodedBERinRACE08with2transducersand2hydrophonesata1000mdistance. datacanbeexplicitlyrepresentedbythecorrelation,givenby (Ns1)srsa;(3{35) whereNsisthenumberofthedatapacketstestedintheexperiment,riandaiaretheBERandtheenvironmentaldataforthei-thpacket,randaarethesamplemeansoftheBERsandtheenvironmentaldata,andsrandsaarethesamplestandarddeviationsoftheBERsandtheenvironmentaldata,giveby and 55

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DOSTBC8PSKuncodedBERinRACE08with2transducersand12hydrophonesata1000mdistance. Therangeforthecorrelationis2[1;1]. ThecorrelationsbetweentheBERsandtheenvironmentaldataaregiveninTables 3-2 and 3-3 .Inthetables,weobservethatexceptforthe8PSKwithasinglehydrophonecase,theabsolutevaluesofthecorrelationsbetweentheBEM-basedDOSTBCBERsandtheenvironmentaldataarealwaysmuchsmallerthantheonesbetweentheDOSTBCschemeonplainOFDMBERsandtheenvironmentaldata.Especiallyforthecaseswithmultiplehydrophones,ourproposedschemehasapproximatelyzerocorrelationswhiletheabsolutevaluesofthecorrelationsforthecontrolgroup,DOSTBConplainOFDM,arenearly0:5.ItmeansthatourBEM-basedDOSTBCisfurthertestiedtoberobust,aectedverylittlebytheseaconditions. 56

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ThewindspeedmeasuredinRACE08 Figure3-10. TheseasurfaceheightabovebottommeasuredinRACE08 57

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CorrelationbetweenBERsandwindspeedinRACE08 Correlationwithwindspeed Numberofhydrophones 1 2 12 QPSK BEM 0:1861 0:0829 0:0270 PlainOFDM 0:3412 0:3580 0:3295 8PSK BEM 0:1839 0:1788 0:1787 PlainOFDM 0:3367 0:3454 0:2986 Table3-3. CorrelationbetweenBERsandseasurfaceheightabovebottominRACE08 Correlationwithsurfaceheight Numberofhydrophones 1 2 12 QPSK BEM 0:0611 PlainOFDM 8PSK BEM PlainOFDM isensuredbyourcarefulschemedesigntakingintoaccountthedoubleselectivityandbycollectingfullthree-dimensionaldiversity:space,delayandDoppler.Ourproposedschemeistestiedbybothsimulationsandseaexperiment.Intheexperiment,ourschemeexhibitssuperberrorperformance,achieving2103uncodedBERata1000mdistancewithonly2hydrophones.ThereliabilityisfurthertestiedbythesmallcorrelationvaluesbetweentheBERsandtheenvironmentaldataintheexperiment.ThisindicatesthatourBEM-basedDOSTBCsurvivesvariousseaconditions,calmorrough. WehaveshowntwoDFT-BEM-basedcoherentanddierentialschemesforuplinkanddownlinkUACrespectively.Inthenextchapter,wewillshowthattheseschemescanbeslightlymodiedtoaccommodategeneralBEMs.Then,wewillinvestigatetheeectontheerrorperformanceofvariousBEMsincoherentanddierentialschemes. 58

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InChapters 2 and 3 ,wepresentedacoherentschemewithaWLSchannelestimatorforuplinkandaMIMOdierentialschemefordownlink,bothofwhicharesolelybasedonDFT-BEM.However,therearemanychoicesofBEMswithdierenttypesofbases.Forexample,DFT-BEMusesafewlow-frequencycolumnsoftheinverse(I)DFTmatrixasthebasis[ 37 ],relayingonthechanneltime-Dopplerrelationship;Karhunen-Loevedecomposition(KL-)BEMusestheeigenvectorscorrespondingtothelargesteigenvaluesofthecovariancematrixofthechannel[ 57 ,Chapter3],bycapturingthechanneleigenmodes;andDPSS-BEMusesthesetofeigenvectorscorrespondingtothelargesteigenvaluesoftheband-limitedrectangularpowerspectrumsignal[ 50 ],similartoKL-BEMbutwithoutrequiringthechannelcovariancematrix.Hence,inthischapter,wewillrstgeneralizeourpreviouslypresentedcoherentanddierentialschemestoaccommodatearbitraryBEMs.Usingthesegeneralizedschemes,wewillshowthatthemodelingaccuracyisnottheonlyfactordeterminingthesystemerrorperformance.Intermsofmodelingaccuracy,DPSS-BEMispreferabletoDFT-BEM,sincetheformerprovidesacloserapproximationtothechannel[ 68 ].However,ouranalyses,simulations,andexperimentalresultsshowthatitserrorperformanceisnotnecessarilybetterthanthatofthesimpleDFT-BEM,becausetheerrorperformanceisalsoaectedbythenatureofthemodelttingbiasandnoiseeect.OurresultssuggestthatBEMisapowerfulsolutionforcoherentanddierentialschemesinUAC,andthatthereisatradeobetweenthemodelingaccuracyandthenatureofmodelttingbias/noiseeectsfordierentBEMs.ThistradeosuggestsdierentBEMchoicesincoherentanddierentialapproaches. InSection 4.1 ,wewillintroducethegeneralexpressionforBEM.PropertiesofdierentBEMswillbediscussedinSection 4.2 .InSections 4.3 and 4.4 ,wewillderivethegeneralcoherentanddierentialschemestoaccommodatearbitraryBEMs.Modelingaccuracyandthemodelttingbias/noiseprocessingeectswillalsobeanalyzedinthese 59

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4.5 ,followedbysummarizingremarksinSection 4.6 wherefbk(n)gKk=1isasetoflinearlyindependent(typicallyorthogonal)sequencesusedasthebasis,g(k;l)saretheBEMcoecientsforthelthchanneltap,and(n;l)isthemodelttingbias.Thematrixformof( 4{1 )is: whereh(l)andg(l)aretheN1channelvectorandtheK1BEMcoecientvectorrespectively,BistheNKbasismatrixwithelements[B]n;k=bk(n)and(l)istheN1modelttingbiasvector.Thedistributionsofg(l)and(l)dependonboththechannelstatisticsandtheBEMselection.GiventhelackofwidelyacceptedUACchannelmodels,weassumethattheelementsing(l)and(l)arebothi.i.d.withnitemeansandvariances. In( 4{1 )and( 4{2 ),BEMshowstwonicefeatures:i)ThenumberofchannelcoecientsisgreatlyreducedtoK(L+1)N,thankstothelimiteddegreesoffreedominthechannelvariation;andii)TheBEMcoecientsremaintime-invariantwithineachblock.Theconsiderablyreducedcoecientnumberfacilitatescoherentdetectionbasedon 35 ]).Then,( 4{1 )canbeusedtodealwiththeresidualDoppler. 60

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DierentBEMsusedierentbasesBandaccordinglyinducedierentmodelttingbias(l).ThisdierenceisessentialinchoosingBEMsincoherentanddierentialschemes.Inthenextsection,wewillanalyzethepropertiesofdierentBEMs. 37 ]. AsweanalyzedinChapter 2 ,however,highfrequencycomponentsareintroducedbytruncatingthechannelintoanN-pointblockintimedomain.Therefore,theDFT-BEMrepresentationofthechannelisonlyanapproximationtotherealoneandsuersfromlargemodelttingbiasin( 4{2 ).ToapproximatetherealUACchannelmoreaccuratelybyremovingthesehighfrequencycomponents,weintroducedasimplewindowingandde-windowingprocedureinChapter 2 AnalternativewaytoimprovetheaccuracyoftheapproximationistousealternativeBEMs.ThebasisofKL-BEMconsistsoftheeigenvectorscorrespondingtothelargesteigenvaluesofthechannelcovariancematrix[ 57 ,Chapter3].InUAC,however,therelacksawidelyacceptedchannelmodel,andthechannelstatisticsmayalsochangeovertime 61

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66 ].AvoidingtheneedofthechannelcovariancematrixwhileimposingnodiscriminationonanyDopplerfrequency,DPSS-BEMregardsthepowerspectrumasbeingatwithinthefmaxlimits[ 50 ].Thecovariancematrixresultedfromsucharectangularpowerspectrumisthenusedtogeneratethebasis.OnemaythinkthatanMMSEestimatorbasedonthisatchannelDopplerspectrumcanbeappliedtoobtaintheN(L+1)channelparametersfromanynumberofpilots[ 24 ,Chapter4],eliminatinganyneedofinvokingBEM.However,itisnotthecasebecausetheMMSEestimatorrequiresaknownchanneldelayproleinadditiontothisDopplerspectrumcapturingtimedependence. Concentratingtheenergyonafewsequences,DPSS-BEMyieldsamorepreciseapproximationtotherealchannel,incomparisontoDFT-BEM[ 68 ].Thatis,Efk(l)k2gfortheDPSS-BEMissmallerthanthatfortheDFT-BEM.Ifthechannelstatisticsareavailable,KL-BEMprovidesthebestapproximationtothechannelsinceitutilizestheeigenvectorscorrespondingtothelargesteigenvaluesofthechannelcovariancematrix.Whenthechannelstatisticsareunknown,thenthebestonecandoistheKL-BEMthatdoesnotemphasizeanyfrequencywithinthemaximumDopplerlimits,whichgivesrisetoDPSS-BEM.NowthequestioniswhetherthiscomputationallymorecomplexDPSS-BEMgivesbettererrorperformancethanthesimpleDFT-BEMincoherentanddierentialschemes. Beforeansweringthisquestioninthefollowingsections,letusrstnotesomeBEMpropertiesforfuturereference. P1. TheBEMcoecientscanbecalculatedfromthechannelparameters.Withoutlossofgenerality,letN=KQ,whereQisapositiveinteger.ThentheBEMcoecientscanbeobtainedas: whereBnistheKKequally-spaceddecimatedbasismatrixwith[Bn]i;k=bk((i1)Q+n),hn(l)istheK1equally-spaceddecimatedchannelvectorwith[hn(l)]i=h((i1)Q+n;l)andn(l)isthecorrespondingK1modeltting 62

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45 46 ],weprovedthattheoptimumpilotsforDFT-BEMshouldbeequally-placed.ForDPSS-BEM,therelacksaproofoftheoptimalityforsuchaplacement,but[ 68 ]showsthattheequally-spacedpilotplacementworksverywell.Inaddition,theBEM-baseddierentialschemerequiresequally-spaceddecimatedchannelparameterstotransformthetime-varyingchannelsintotime-invariantBEMcoecients[ 43 ]. P2. ForDFT-BEM,Bnisascaledunitarymatrix;thatis,B1n=N=KBHnasshownin[ 43 ,Lemma1].However,DPSS-BEMdoesnothavesuchaniceproperty.ItdegradestheperformanceofDPSS-BEMbasedsystemsbyaectingbothmodelttingbiasandnoise,aswewillanalyzenext. ToseehowBnwillaectthesystemperformance,westartwiththefollowinglemma. Proof. 63

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becausetheelementsofxarei.i.d.Itthenfollowsthat KK1Xi=0jij2=a=Ekxk2:(4{8) Since withtheconstraintPK1i=0jij2=K,weobtain KK1Xi=01i2a=Ekxk2:(4{10) Theequalityholdsifandonlyifjij2=jjj2;8i;j.Notethatjij2=jjj2;8i;j,togetherwithPK1i=0jij2=K,isanecessaryandsucientconditionforAtobeaunitarymatrix.Inotherwords,theequalityin( 4{10 )holdsifandonlyifAisaunitarymatrix. InordertocomparetheeectsofmultiplyingB1ninthecasesofDFT-BEMandDPSS-BEM,wenormalizeBnsothatitseigenvaluessatisfyPK1i=0jij2=K.Withsuchanormalization,dierentBEMswillhavethesameEfkBng(l)k2gdespitetheirdierentBnmatrices.ThisfollowsdirectlyfromLemma 2 ;thatis,EfkBng(l)k2g=Efkg(l)k2gregardlessofBnsolongasitsatisestheeigenvalueconstraint. EquippedwiththeseBEMproperties,wearenowreadytoanalyzetheeectsofdierentBEMsontheperformanceofcoherentanddierentialschemesinthenextsections. 2 .Inthis 64

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2 awindowedLSchannelestimatortoimprovethesystemperformancebyreducingthehighfrequencycomponentsofthechannelDFTandaccordinglytheDFT-BEMmodelttingbiasusingasimplewindowingandde-windowingprocedureatthereceiver.IntheensuingderivationsforgeneralBEM,wewilluseagenericwindow.Theresultswithoutthewindowingandde-windowingprocedurecanbereadilyobtainedbysettingthewindowcoecientsasallones. InChapter 2 ,anoptimumpilotpatternwasestablishedforDFT-BEM,whereeveryequally-spacedpilotsymbolhasLleadingandtrailingzerosasdepictedinFig. 2-2 .ThispilotpatternhasalsobeenshowntoworkwellforDPSS-BEM[ 68 ].Letthepilotsbealloneswithoutlossofgenerality.TheLleadingzerosenabletheseparationofthereceivedpilotfromthedata,andtheLtrailingzerosfacilitatetheseparationofeverytapofthechannelresponse.Sincethechannelresponsesfromdierentchanneltapscanbeseparated,wewillomitthetapindexlintherestofthissubsectionfornotationalsimplicity.ForasegmentofthereceivedsymbolsinthetimedomainwithlengthNcontainingKpilots,thereceivedpilotvectorforacertainchanneltapcanbewrittenas whereyKistheK1receivedvector,hKistheK1channelvectoratthetimeslotsoccupiedbypilotsandzKistheAWGN.Choosingawindowwithnozeroelement,we 65

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4{2 )and( 4{11 )as: whereWKistheKKdiagonalwindowingmatrixforthepilotsconstructedbyextractingthepilot-correspondingcolumnsandrowsfromtheNNdiagonalwindowmatrixW,BKcontainsthepilot-correspondingrowsofB,~gistheBEMcoecientvectorand~Kisthepilot-correspondingelementsofthemodelttingbias~.Notethatboth~gand~arenowrelatedtothewindowedchannelresponseWKhKinsteadofhK.LetusLSttheestimateof~gas ^g=B1KWKyK;(4{13) andthenrecoverthechannelestimateas: ^h=W1B^g=W1BB1KWKyK:(4{14) ThisequationgivesawindowedLSchannelestimatorbasedongeneralBEM.Inthenextsubsection,wewillanalyzetheMSEinordertocomparetheperformanceusingdierentBEMs. 4{14 )canbeobtainedas: MSE=Enkh^hk2o=EnW1~BB1K(~K+WKzK)2o=EnW1~BB1K~K2o| {z }MSE+EnW1~BB1KWKzK2o| {z }MSEz;(4{15) whereMSEdenotestheMSEfromthemodelttingbiasandMSEztheMSEfromnoise.From( 4{15 ),weobtainthefollowingresults: 66

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Whenthechannelsarestrictlybandlimited,windowingdoesnothelpDPSS-BEM.AddingawindowcanalsoberegardedaschangingtheweightsoftheBEMbasis.SinceDPSSbestapproximatesthebandlimitedchannelparametersequencewhenitsstatisticsarenotavailable[ 68 ],suchaweightchangecanonlydegradetheapproximation. R1b. WhenthechannelsequencehasalargerDopplerthantheassumedmaximumfmax,windowinghelpsbothDFT-andDPSS-BEMs.Sincebotharedesignedtorepresentbandlimitedsequences,alltheout-of-bandenergybecomesmodelttingbiaswhenthechannelsarenotbandlimited.Addingawindowwithlowsidelobesreducestheout-of-bandenergyandconsequentlythemodelttingbiasforbothBEMs. R1c. Regardlessofthewindowshape,themodelttingbiasfortheDPSS-BEMisalwaysampliedandcoloredwhenpre-multipliedbyB1K,whilethatfortheDFT-BEMdoesnotchange.ThiscomesdirectlyfromPropertyP2andLemma 2 R1d. Witharectangularwindow,thenoisefortheDPSS-BEMisampliedandcoloredbypre-multiplyingwithB1K,whilethatfortheDFT-BEMisnot.ItcanbeprovedbyPropertyP2andLemma 2 Fromtheresultsabove,welearntthatalthoughDPSShasasmallermodelttingbias,itsuersfromampliedandcoloredmodelttingbiasandnoise.Therefore,thereisatradeobetweenthemodelingaccuracyandthebias/noiseamplifying/coloringeect.Thistradeoisalsoinuencedbytheselectionofthewindowingfunction,thesignal-to-noiseratio(SNR)andtherealUACchannels.Butevenwithouthavingthesespecicparameters,onecanexpectthat:i)Witharectangularwindow,theDPSS-BEMisbetterthantheDFT-BEMsincetheDFT-BEMsuersfromdominantlargemodelttingbias;ii)TheDPSS-BEMisnotnecessarilybetterthantheDFT-BEMwithalow-sidelobewindow.Thereasonistwofold:Ontheonehand,thewindowmayreducethemodelttingbiasoftheDFT-BEMtoacomparableleveltotheDPSS-BEM.Ontheother 67

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BERvs.SNRperformanceoftheDFT-andtheDPSS-BEMbasedcoherentschemes. hand,theDFT-BEMhasbettermodelttingbias/noiseprocessingproperty.Inthenextsubsectionwewillshowthesimulatedresultstosupportouranalysis. 40 ]andaccordinglyL=60.Themultipathintensityproleisexp(0:1l).TheaveragechannelgainisnormalizedtoEnPLl=0jh(n;l)j2o=1.WechoosetheblocklengthasN=1800andthepilotnumberasK=9.ThepilotenergyisnormalizedtoL+1=61.Dataareinsertedbetweenevery2pilotspaddedbyLleadingandtrailingzeros.QPSKmodulationisusedandthedatasymbolenergyisnormalizedto1.AnMMSEequalizerisusedfor 68

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4-1 showstheBERversusSNRcurvesusingDFT-andDPSS-BEMswithasingletransducerandasinglehydrophone. Werstconsiderarectangularwindow.AsshowninFig. 4-1 ,theDPSS-BEMoutperformstheDFT-BEM.Thisisduetothesmallermodelttingbiasoftheformerasweexpect.WhenaBlackmanwindowisemployed,weseefromFig. 4-1 thattheBlackmanwindowdoesnothelptheDPSS-BEMbasedscheme.AsindicatedinResultR1a,thisisbecausethechannelgeneratedbyJakes'modelisstrictlybandlimited. AmongallfourcurvesinFig. 4-1 ,theDFT-BEMbasedonewithaBlackmanwindowshowsthebestperformance.OnereasonisthattheBlackmanwindowaddedtoDFT-BEMreducesthemodelttingbiastoacomparableleveltoDPSS-BEM,andthatthebiasandnoiseoftheDPSS-BEMschemeareampliedandcolored.Thisagreesverywellwithouranalysis.However,theremaybeanadditionalreasonforsuchacomparisonresult.ThesimulatedchannelisgeneratedusingJakes'model,whichisdesignedforterrestrialRFcommunicationsandhasa\bowl-shaped"powerspectrum[ 48 ,Chapter5].Hence,thereisamismatchbetweenthesimulatedbowl-shapedchannelpowerspectrumandtherectangularoneassumedbyDPSS.ThisspectrummismatchdegradestheperformanceoftheDPSS-BEMbasedschemes.TheUACchannelsdierverymuchfromtheterrestrialRFchannels,anditispossiblethattheDPSSBEMwouldprovideaclosermatchinrealUACscenarios. CombiningtheanalysisresultsR1andthesimulations,thefollowingconclusionscanbedrawnforthecoherentscheme: C1a. Whenarectangularwindowisemployed,theDPSS-BEMoutperformstheDFT-BEM. C1b. ForDPSS-BEM,windowinginducesperformancedegradationwhenthechannelisstrictlybandlimited. C1c. Withalow-sidelobewindow,thetradeobetweenDFT-andDPSS-BEMsislikelytobesettingdependent. 69

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4.5.1 tofurtherverifytheaboveconclusions.Inthenextsection,wewillexplorethedierentialschemewithvariousBEMs. 4.4.1DierentialSchemeforGeneralBEM 3 ,aDOSTBCschemeisderivedspecicallybasedontheDFT-BEMandthemodelttingbiasisneglectedintheanalysistherein.Here,wewillderivethegeneraldierentialschemewhichcanadoptanyBEMinthepresenceofmodelttingbias.Wewillalsoanalyzetheperformancebytakingintoaccountboththemodelttingbiasandthenoise.FocusingontheimpactsofdierentBEMs,herewewillconsiderthespecialcasewithasingletransducerwithoutlossofgenerality. Inordertoimplementthedierentialscheme,thedoubly-selectiveUACchannelhastobetransformedtoadiagonaltime-invariantequivalent.Time-invariantchannelacrosssubblocksmakestheprecedingsubblockareferenceforthecurrentone,andthediagonalpropertyenablestheorderexchangebetweenthechannelandthedatathatisessentialfordierentialdemodulation.Letusrsttransformthetime-varyingchannelparametersintothetime-invariantequivalentrepresentedbytheBEMcoecientswithinablock.Time-InvariantEquivalentChannel 3{10 )to( 3{18 ),consideringthemodelttingbiasin( 3{18 ),weobtaintheI/Orelationship ~y(p)=((p)G+(p))u(p)+~z(p);(4{16) whereGistheMKMequivalentblockcirculantchannelmatrixwiththerstcolumn [gT(0);:::;gT(L);0T(ML1)K1]T;(4{17) 70

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istheMKMmodelttingbiasmatrix.NotethatG,(p)and(p)hereareforgeneralBEM.Then,bymultiplyingtheinverseof(p),weobtainthetimeinvariantI/Orelationshipas y(p)=Gu(p)+1(p)((p)u(p)+~z(p));(4{20) wherey(p):=1(p)~y(p)istheMK1vectoratthereceiver.ChannelBlock-Diagonalization 60 ].Weobtaintheblock-diagonalmatrix ~G=~FMGFHM;(4{21) whereFMistheM-pointDFTmatrixand~FM:=[IKf1;:::;IKfM]withfmthemthcolumnofFM.Hence,thetransmittedvectoris andthethereceivedoneis 71

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where isthemodelttingbiasandnoisevector.DierentialEncoding 4{24 ),wearereadytoaddthedierentialencoding,as whereSdistheMMdiagonalmatrixwiththediagonalentriesbeingtheinformationsymbolstobetransmittedinthepthsub-block.Substituting( 4{26 )into( 4{24 ),weobtain Theblock-diagonalpropertyof~Genablestheinterchange~GSd(p)=SD(p)~GwithSD(p):=IKSd(p),andthereby( 4{27 )becomes Sofar,wenishedderivingthedierentialschemeforarbitraryBEM.With( 4{28 )explicitlycontainingthemodelttingbiasterms,wearereadytocomparedierentBEMs. 4{28 ),weobtainthefollowingresultsforthedierentialscheme: 72

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Therearetwomodelttingbias/noisetermsin( 4{28 ),oneisdata-dependentandtheotherisdata-independent.Thesemodelttingbiastermscannotbecanceledbyeachothersincethedatarandomizesthebias. R2b. Inthetwomodelttingbias/noisetermsin( 4{28 ),boththemodelttingbiasandthenoisefortheDPSS-BEMareampliedandcoloredin( 4{25 ),whilethosefortheDFT-BEMarenot.Thereasonisthatin( 4{18 ),thesubmatricesof(p)sittingonthediagonalaresimplyBn.Hence,Lemma 2 directlyleadstothisresult. Althoughthereisalsoatradeobetweenthemodelingaccuracyandthebias/noiseamplifying/coloringeectbychoosingDPSS-orDFT-BEMasinthecoherentdetection,comparisonsbetween( 4{28 )and( 4{15 )implythatthedierentialschemesuersmorefromtheampliedandcoloredmodelttingbias/noisethanthecoherentcasewhenDPSS-BEMisused.Thereasonsareasfollows.Forthedierentialscheme,thetwomodelttingbias/noisetermsin( 4{28 )arebothampliedandcolored.Forthecoherentdetection,thesituationisverydierent.First,theMSEfromthemodelttingbias(MSEin( 4{15 ))isgivenbythedierenceoftheoriginalbias~andtheampliedoneBB1K~.Inotherwords,oneofthetwobiastermsisnotampliedinthecoherencecase;whereasbothtermsareampliedinthedierentialcase.Secondly,forthecoherencecase,theMSEfromthenoise(MSEzin( 4{15 ))isnotnecessarilyampliedunlessthewindowisrectangular.Thisisbecausewithanyotherwindow,theelementsinthenoisetermWKzKhavedierentdistributionsandLemma 2 doesnotapply.Inthedierentialcase,however,thenoiseisalwayscoloredandamplied.Asaresult,weexpectthedierentialschemetobemorefavorabletoDFT-BEM. 73

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BERvs.SNRfortheDFT-andtheDPSS-BEMbasedDOSTBCschemes. Fig. 4-2 showstheBERresultsfortheDFT-andDPSS-BEMbasedDOSTBCschemeswith2transducersand1hydrophone.TheDPSS-BEMbasedschemeisconsistentlyworsethantheDFT-BEMbasedoneatallSNR.ItisconsistentwithourprecedinganalysisthattheDPSS-BEMbasedschemesuersfromperformancedegradationinducedbytheampliedandcoloredmodelttingbiasandnoise. Accordingtotheanalysisandsimulationresultsinthissection,wedrawthefollowingconclusionforthedierentialscheme: C2. TheDFT-BEMbaseddierentialschemeoutperformstheDPSS-BEMbasedone. Thiswillbefurtherveriedbyseaexperimentresultsintheensuingsection. 74

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Coherentschemes'BERswith12hydrophones BER Squarewindow Blackmanwindow DPSS-BEM 0:36% 0:24% DFT-BEM 0:71% 0:58% Figure4-3. Coherentschemes'BERsacrossdierenthydrophonesinRACE08ata1000mdistance. 4.5.1CoherentScheme 2.4 .Forcomparison,wealsodecodethereceivedsignalswith2non-BEMmethods.Therstoneestimatesthechannelusingtherstsub-block,andthendecodesalltheremainingsub-blockswithoutupdatingthechannelstateinformation.Thesecondoneestimatesthechannelusingtherstsub-blockandusesthedecodedresultstoupdatethechannelstateinformation. 75

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2.4 ,duringtheexperiment,mostofthechannelconditionsarestablebuttherearealsosomeroughperiods.Thescatteringfunctionestimatedbyamatchedlter[ 9 ]foracalmperiodisshowninFig. 2-6 ,wherewecanhardlyobserveanyDopplerandthescatteringfunctionforaroughperiodisshowninFig. 2-7 ,whichillustrateslargedelayandDopplerspreads.Wepick3datapacketsduringtheroughperiodswhenthechannelschangeremarkably.Eachpacketcontains38025QPSKsymbols. Inthe3packets,the2non-BEMschemeshavenearly50%BERsbecausethechannelschangeseverely.TheuncodedBERsoftheBEMbasedschemescombiningall12hydrophonesareshowninTable 4-1 .Fromthetable,weobservethattheschemesbasedonbothBEMsworkverywellatBERs,theorderof103,with12hydrophones.ItprovesthatBEMsarepowerfultoolsinUACforcoherentdetections. TocomparethetwoBEMs,rst,wecheckbothwitharectangularwindow.TheuncodedBERsversushydrophoneindexforthedierentBEMbasedschemesareshowninFig. 4-3 .BothTable 4-1 andFig. 4-3 showthattheDPSS-BEMoutperformstheDFT-BEM.TheseverifyconclusionC1ainSection 4.3.3 Next,weexaminethewindowingeectonBEMs.FromFig. 4-3 andTable 4-1 ,weobservethattheBlackmanwindowimprovesbothDFT-andDPSS-BEM.Thisisdierentfromthesimulationresults.RecallthatthesimulatedchannelsaregeneratedusingJakes'model,andthusstrictlybandlimited.However,therealUACchannelsarelikelynotstrictlybandlimitedsincetheyexperiencetransientcausticsduetotheeectsofsurfacewavefocusing[ 41 ]andbubbles[ 15 ].Here,theBlackmanwindowreducestheout-of-bandenergyforbothDFT-andDPSS-BEMsandimprovestheperformanceofboth.Therefore,thisseeminglycontradictoryexperimentresultveriesConclusionC1btogetherwiththesimulations. Finally,unlikethesimulationresultswheretheDFT-BEMoutperformstheDPSS-BEMwhentheBlackmanwindowisused,theDPSS-BEMbasedcoherentschemeoutperformstheDFT-BEMbasedone.AsweanalyzedSection 4.3.3 ,itispossiblethat 76

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Dierentialschemes'uncodedBERsata1000mdistanceinRACE08 UncodedBER Numberofhydrophones 1 2 12 DFT-BEM 0:78% 0:20% 0:12% DPSS-BEM 0:79% 0:22% 0:13% PlainOFDM 6:30% 3:30% 1:91% Figure4-4. DOSTBCQPSKuncodedBERforblocksinRACE08with2transducersand2hydrophonesata1000mdistance.Zero-errorisillustratedas105. theDPSSassumedrectangularspectrumyieldsabettermatchtotheUACchannelsthanthesimulatedRFones,resultinginabetterperformancethanDFT-BEMevenwhenbothout-of-bandinterferencesaretakencareofbytheBlackmanwindow.ThisdierencebetweenthesimulationandexperimentresultssupportsConclusionC1c,implyingthewindowedcaseismoresettingdependent. 77

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DOSTBCQPSKuncodedBERforblocksinRACE08with2transducersand12hydrophonesata1000mdistance.Zero-errorisillustratedas105. 3.4 .UncodedaverageBERsusing1,2andallthe12hydrophonesaregiveninTable 4-2 .Thepacket-wiseBERsareplottedinFigs. 4-4 4-5 with2and12hydrophones,respectively.TheBERswithasinglehydrophonearecalculatedbyaveragingtheBERsusingeachoneoutofthe12hydrophonesandtheBERsusing2hydrophonesareobtainedbytakingthereceivedsignalsfromthetopandthebottomhydrophones.Maximumratiocombining(MRC)isusedforthemultiple-hydrophonecasesatthereceiver.InTable 4-2 andFigs. 4-4 and 4-5 ,ourproposedBEM-basedDOSTBCsarealwaysbetterthantheplainOFDMoneregardlessofthenumberofhydrophones.Wealsoobservethatthe2BEM-basedDOSTBCsbothreachaverylowuncodedBERat103levelevenwithonly2hydrophones.Withasinglehydrophone,theBEM-basedBERsarestillbelow1%,whiletheBERfortheplainOFDM 78

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4-2 ,wealsoobservethattheDFT-BEMbasedDOSTBChaslowerBERsthantheDPSS-BEMbasedone.ThisagreeswithouranalysisandisconsistentwiththesimulationsaswellasConclusionC2inSection 4.4.3 WehaveexploredtheBEM-basedschemesforuplinkanddownlinkcommunicationsanddiscussedtheeectofvariousBEMsintheseschemes.Inthenextsection,anon-BEMDSSSschemewithhighreliabilitywillbeintroducedfordownlink. 79

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TheschemeswepresentedintheprecedingchaptersarebasedonBEM,whichmodelstheUACchannelbycapturingthetime-variation.Whenthesignalblocklengthisshorterthanthechannelcoherencetime,UACchannelscanbeapproximatedasquasi-static.Basedonthequasi-staticchannelmodel,severalDSSSschemesareproposedin[ 38 65 ]usingsimplematchedlerreceivers.TheseschemestransmitasingleBPSKsymbolpersequenceblockduration,whichlimitsthedatarateto1bitpersequence.Inaddition,theDDanddierentialDSSSapproachesin[ 38 65 ]requirethechannelcoherencetimetobeatleasttwospreadingsequencelong,andarethuspronetochannelvariations. Inthischapter,wewillpresentcoherentHR-DSSSschemethatalsorequiressimplematchedlteratthereceivertocollectfullmultipathdiversity.Unlikeexistingschemes,however,ourHR-DSSStransmitsmultipledistinctsymbolsonmultiplesuperimposedspreadingsequencesduringeachblock.Amongthosesymbols,oneisusedasthepilotforchannelestimationandotherscarrydata.Viathesuperimposedpilot,ourHR-DSSSrequiresonlyonesequence-longchannelcoherencetime,providingrobustnessagainstchannelvariation.Inaddition,ourHR-DSSSalsomarkedlyincreasesthedatarate,bytransmittingmultiplesymbolspersequenceduration,andbyallowingforarbitrarymodulationsincludingQPSK,QAM,etc.Wewillalsoprovethat,inourHR-DSSS,inter-block-interference(IBI)isentirelyeliminated,theself-interferenceduetomultipathandtheco-channelinterferencefromsimultaneouslytransmittedmultiplesymbolsarecontrollableandnegligiblebyourjudiciousdesign. 5.1.1TransmittedSignals 80

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65 ],suchaDSSSsystemwasintroducedtounderwatercommunications,wherethespreadingcodeisthemaximumlengthsequence(m-sequence). Herewealsoemploythem-sequenceasthespreadingcodeasin[ 65 ].However,insteadoftransmittingonesymbolperblockasin( 5{1 ),ourHR-DSSSschemesimultaneouslymodulatesmultiplesymbolsoncircularlyshiftedversionsofanm-sequenceduringeachblock.Denethecircularshiftmatrixas: whichintroducesacircularshiftby1uponpre-multiplyinganM1vector.Accordingly,vectorTjcisthecircularlyshiftedm-sequencebyjchips.Notethatanm-sequenceanditscircularlyshiftedversionhasthefollowingautocorrelationproperty: Hence,inaat-fadingchannel,distinctsymbolsridingoncandTmcwillinducenegligibleinterferencesamongthemselves,aslongasthecircularshiftm1.However,UACchannelsarewellknowntohaveextensivemultipath.LetmaxdenotethemaximumdelayspreadandTcthechipduration.Themultipathessentiallyspreadsover(L+1)chips,where Inordertoseparatethedelayedmultipathcomponentsofneighboringsymbols,thecircularshiftbetweenthem-sequencesconveyingadjacentsymbolsshouldbeatleast(L+1)chips.Hence,thetransmittedsignalblockinourHR-DSSSisgivenby: 81

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L+1:(5{6) ItisalsoworthmentioningthatJmaxisthemaximumnumberofsymbolsthatcanbesimultaneouslytransmittedwhenthedistributionandstrengthoftheactual(andpossiblysparse)channeltapsarenotavailableatthetransmitter.Iftheseinformationisalsoavailable,thenitispossibletoincreaseJmaxbysmartlyschedulingthesignals.Inaddition,inaverylowratesystem,onecanalsochoosetotransmitJ(2JJmax)symbolstofurtherreducetheinter-symbolinterference.Notethatinthisdesign,theonlyinformationaboutthechannelneededatthetransmitteristhechanneldelayspreadoranupperboundonit. 64 ].ForatypicalUACDSSSsystemwith10kchipspersecondusingaspreadingsequenceconsistingofabout1000chips,thesequenceblockdurationisabout100ms.Hence,itisreasonabletoassumethatthechannelremainstime-invariantwithinasequenceblockandisallowedtochangeacrossblocks. Forblock-wisetransmissionsovermultipathchannels,theith(M1)receivedblockr(i)containsnotonlythesignalsfromtheithtransmittedblock,butalsotheIBIfromthepreviousblock.TheI/Orelationshipinvectorformcanbewrittenas: wherethesecondtermHIBI(i)x(i1)istheIBI,the(MM)channelmatricesaregivenby[H(i)]m;n=h(i;mn)and[H(i)IBI]m;n=h(i;M+mn),form;n=1;:::;M,andz(i)isAWGN. 82

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5{7 ),atleasttworemediesareavailable(seee.g.,[ 60 ]).OneinsertsaCPwithlengthLtoeachblockatthetransmitter,andremovestheCPatthereceiver.TheequivalentchannelafterCPinsertionandremovalbecomesacirculantmatrix.TheothersimplypadsLtrailingzerostoeachblockatthetransmitter,givingrisetoanToeplitzchannelmatrix. Sincewearegoingtoseparatethedelayedmultipathcomponentsofsymbolsbytakingadvantageofthecircularautocorrelationpropertyofm-sequencesin( 5{3 ),aswillbedetailedlater,thecirculantchannelmatrixispreferable.Therefore,weadopttheCPapproach.AftertheCPinsertionandremovalonablock-by-blockbasis,theequivalentI/Oisgivenby wheretheequivalentcirculantchannelmatrixwiththerstcolumn[h(i;0);:::;h(i;L);01(ML1)]T.Usingthecircularshiftmatrixin( 5{2 ),itcanbere-expressedas ~H(i)=LXl=0h(i;l)Tl:(5{9) Withthisblock-wiseequivalentI/O,theblockindexiwillbedroppedintherestofthischapterfornotationalbrevity. 5{5 )and( 5{9 )into( 5{8 ),weobtainthereceivedblockas: In( 5{10 ),foreachsymbols(j),theI/Orelationshipistransformedfromonewhereasinglesequenceexperiencesacirculantmultipathchanneltoonewhere(L+1)superimposedcircularlyshiftedsequences,eachbeingmultipliedbyasinglechanneltap.ForallJsymbols,weobtainJ(L+1)superimposeddierentcircularlyshifted 83

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5{3 ). Multiplyingyby(Tj(L+1)+lc)T,whichisacircularlyshiftedsequenceservingasamatchedlter,weobtain where(j;l)=[Tj(L+1)+lc]Tzisthenoiseand istheinterferenceintroducedbythesidelobeofthecircularautocorrelationofm-sequences.Notethatthistermcontainsboththeself-interferenceduetomultipath,andtheco-channelinterferencefrommultiplesymbolstransmittedsimultaneously.Wewillshowlaterthatthisinterferenceisbounded,andpracticallynegligible.In( 5{11 ),weobservethatallthedelayedmultipathcomponentsofallsymbolsareseparated.Weuseonesymbol(say,s(0))asthepilottoformachannelestimateas ^h(l)=v(0;l) Thischannelestimatecanbethenusedtodemodulatethe(J1)datasymbolsasfollows: ^s(j)=LXl=0^h(l)v(j;l) Inthederivationsabove,thepilotanddatasymbolsrideonthesequencesinthesameblock;thatis,thepilotandthedatasymbolsexperienceexactlythesamechannel,eveninthepresenceofchannelvariation.Thisensuresthereliabilityagainstmoderatechannelvariation,aslongasitisnotsevereenoughtoruinthematchedlteroutputin( 5{11 ).ItisalsoworthmentioningthatourHR-DSSSdoescoherentdetectionwithout 84

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ThebasebandtransceiverdiagramfortheHR-DSSSscheme. anyphaseambiguity,whichenablesarbitrarymodulations(weadoptQPSKintheseaexperiments),notlimitedtoBPSK.Fig. 5-1 showsthebasebandtransceiverdiagram.Atthetransmitter,multiplesymbolsaremodulatedondierentcircularlyshiftedversionsofanm-sequence,andthereceiveronlyconsistsofthechannelestimationanddemodulationmodules,whichareillustratedinFig. 5-2 and 5-3 ,whereonlysimplematchedlterisrequired. 5{11 )quantitatively.Letusassumephasemodulationwithjs(j)j=1andindependenttapsofthechannelwithzeromean.Thefollowingresultholds: 85

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ThechannelestimationblockinFig. 5-1 Figure5-3. ThejthdemodulationblockinFig. 5-1 5{11 )foranysymbolislowerboundedbythem-sequencelengthM.WhenJequalsJmaxin( 5{6 ),thislowerboundisverytight. Proof. 5{11 ),therstterm,thelthdelayedmultipathcomponentofthejthsymbol,isthesignalandthesecondtermvI(j;l)istheinterference.Accumulatingthesignalandtheinterferenceenergyfromall(L+1)tapsasthenumeratorandthedenominatorasin[ 29 ], 86

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SIR(j)=E(LXl=0M2jh(l)s(j)j2) From( 5{6 ),weknowJmax(L+1)MandtherebyobtainthetightlowerboundofSIRasM. Theinterferencestatedhereincludestheself-channelinterferencefromthejthsymbolitself(j0=j),andtheco-channelinterferencefromothersymbolsridingonothersequences(j06=j).InUAC,thechannelshavelongdelayspread,typicallyfrom5totensofmilliseconds.Fig. 5-4 showsonesnapshotofthechannelsintheGulfofMexicoExperiment(GOMEX),wherethethechanneldelayspreadismorethan20ms.WithTc=0:2ms,weobtainthenumberofthedelaytapsasL=100from( 5{4 ).TheblockshouldbemuchlongerthanLfortheCPtobesucientlybandwidthecient[ 60 ],suchasM=511,1023orevenlarger.Therefore,theSIRin( 5{15 )issucientlyhighandtheinterferencein( 5{11 )becomesnegligible.Inaddition,theSIRcanbefurtherimprovedbyreducingJ,asshownin( 5{15 ). 87

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OnesnapshotofthechannelsinGOMEX 5.2.1HR-DSSSwithOtherSequences 5{3 )thatensuresahighSIR.Thenaturalquestioniswhetheritispossibletodobetterbyemployinganysequencewithperfectlyzerosidelobetocompletelyeliminatetheinterference? Binaryzerocorrelationzone(ZCZ)sequencesproposedin[ 14 ]haveperfectlyzerosidelobewithinacertainshiftzonethatisahalfofthesequencelengthM.SincethecircularautocorrelationhasaperiodM,withoutlossofgenerality,consideringm2

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foraZCZsequencec.From( 5{16 ),weknowthatZCZsequencecanbeusedinsteadofm-sequenceinourproposedHR-DSSS.However,fortheZCZsequences,becausetheshiftregionisreducedfromMtobM=2candaccordinglyJZCZmax=jM 5.1.2 arealsousedinOFDMsystems,whichareextensivelyemployedformultipathquasi-staticchannels.Itcanalsobeadoptedtolow-ratehigh-reliabilitysystemsbytransmittingJ(
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BERvs.SNRperformanceforthenonfadingchannels. faircomparison,wechoosesimilarlengthsofallsequences:M=1023forthem-sequence,M=1024fortheZCZsequence,andM=1025subcarriersforOFDM.Asaresult,thedatarateinall4schemesare(symbols/sequenceduration):4forHR-DSSS(m-sequence),1forHR-DSSS(ZCZ),4forlow-rateOFDM,and1forDD-DSSS.Next,wewillpresentthesimulationresultsinnon-fadingandfadingchannelsseparately. 5-5 ,theyprovideidenticalperformance.RecallthatboththeOFDMandHR-DSSS(ZCZ)schemesarestrictlyinterferencefree.Thiscomparisonconrmsthattheself-andco-channelinterferenceisindeednegligibleinourHR-DSSS(m-sequence)schemeasindicatedbyProposition1. 90

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65 ,SectionII-D].Fig. 5-5 showsthatallthreegivesimilarperformance,withHR-DSSS(ZCZ)beingslightlybetter.ThisisbecauseHR-DSSS(ZCZ)isstrictlyinterferencefree,whileHR-DSSS(m-sequence)suersfromself-andco-channelinterferenceandDD-DSSSsuersfromself-andinter-symbolinterference.Clearly,bothinterferencesarenegligible. Inthepreviouscomparison,allthreeschemesusethesamemodulationbuthaveverydierentdatarates.WithBPSKmodulation,theHR-DSSS(m-sequence)gives4bits/sequenceduration,whereastheothertwoonlygive1bit/sequenceduration.Toequatetheirrates,wesimulateHR-DSSS(ZCZ)andDD-DSSSagainwith16QAM,leadingto4bits/sequence.TheBERcurvesarealsoplottedinFig. 5-5 .WeobservethatbothsignicantlyunderperformtheHR-DSSS(m-sequence)atthesamerate(BPSK)ordoublerate(QPSK). 21 ]withamaximumDoppleroffmax=4:7Hz.HereweuseQPSKforallfourschemes.Hence,HR-DSSS(m-sequence)andOFDMprovide4timesthedatarateofHR-DSSS(ZCZ)andDD-DSSS.TheBERperformanceisshowninFig. 5-6 .Weobservethat:i)theOFDMschemeexhibitssignicantperformancedegradationduetotheDoppler-inducedinter-carrierinterference;ii)theDD-DSSSschemehasnearly50%errorratebecausethechannelchangesfromonesymboltoanother,renderingthedecision-directedordierential 91

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BERvs.SNRperformanceforthetime-varyingfadingchannelswithfmax=4:7Hz Table5-1. UncodedBERforHR-DSSSwithasinglehydrophoneinGLINT08 Date Range Mov.speed Demodpackets Allbits Err.bits Failedpackets July25 5001500m Anchored 7 13440 0 0 July26 12031667m 00:9knots 16 30720 7 0 July27 3002000m 0:40:6knots 15 28800 226 2 July28 5001000m Anchored 4 7680 0 0 July29 5001000m Anchored 7 13440 0 0 operationsineective;andiii)ourHR-DSSSwithbothm-sequenceandZCZprovidesthebestperformance,andremainsrobustagainstchannelvariation. 5.4.1GLINT08SeaExperiment 92

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During5daysoftheexperiment,wecollectedatotalof51packets,withvarioussettingsincludingdierentrangesandstationmovingspeeds.Eachpacketcontains480databitscollectedbythe4verticallyplacedhydrophonesintheexperiment.Thus,eachpacketprovides4804=1920bitsforperformanceevaluation.Table 5-1 showstheuncodedBERswithonly1hydrophone,byasimplematchedlerwithoutresortingtoanyDopplerestimationorcompensation.Fromthetable,weobservethatin49outofall51packets,ourHR-DSSSschemeachievesnearly0uncodedBER.Thereare2packetsthatcannotbedemodulatedduetotheverylowSNR.Combiningalltheavailable4hydrophones,weget0errorforall49packets.TheoutstandingperformanceintheexperimentconrmsthatourproposedHR-DSSSschemewithm-sequenceisreliable,wheneverthestationisxedormoving. 93

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ThescatteringfunctionintheGOMEXexperiment. ofwhichcontains540databits.From8hydrophonesintheexperiment,atotalof540158=64800uncodedbitsareavailableforanalysiswithasinglehydrophone. Thedelay-DopplerscatteringfunctionofonepacketintheexperimentisshowninFig. 5-7 ,whereweobservesignicantDoppler.WedonotadoptanycomplicatedDopplerestimationandcompensationtechniques,butsimplecarrierfrequencyoset(CFO)estimationbyanOFDMpreamble.Thereareonly2erroneousbitsoutofall64800.ItconrmsthatourproposedHR-DSSSschemeisreliable. 94

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95

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TherearemanychoicesofBEMswithvarioustypesofbases.AfterpresentingtwoDFT-BEM-basedcoherentanddierentialschemesforasymmetricUAClinks,wegeneralizedthemforarbitraryBEMs.WeinvestigateddierentBEMsintermsofmodelingaccuracy,modelttingbiasandnoiseeectsincoherentanddierential 96

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InadditiontoBEM-basedschemes,wealsodevelopedaDSSSsolution(HR-DSSS)fordownlinkswithhighreliabilityrequirements.HR-DSSSrequiresonlyasimplematchedlterreceiverand,unlikeexistingDSSSapproaches,transmitsmultiplesymbolssimultaneouslymodulatedonshiftedversionsofanm-sequenceduringeachblock.Weshowedthatourjudiciousdesigncanenhancereliablechannelestimationandsymboldemodulationinthepresenceofchannelvariation,aswellasenablehigherdataratewithnegligible(self-andco-channel)interference.SimulationsandexperimentresultsconrmedthatourHR-DSSSschemeprovideshigh-qualityperformanceevenwithasinglehydrophone.SinceourHR-DSSSisacoherentscheme,collectingfullamplitudeandphaseinformation,arbitrarymodulationscanbeusedwithoutanychip-levelequalization. 1. HighratecoherentMIMOschemesforuplink.Multiple-inputmultiple-output(MIMO)techniqueshavelongbeenproventoimprovethechannelcapacityinterrestrialRFcommunications.Byusingmultiplexing-orientedspace-timecodes 97

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Althoughmultiplexing-orientedSTCscanprovidehighbandwidtheciencyinterrestrialcommunications,adaptingthemtoUACiscomplicatedbytwomajorobstacles:1)UACchannelsareinherentlydoubly-selectiveinbothfrequencyandtimedomains;and2)multiplexing-orientedSTCscanonlybedecodedcoherently. AsshowninChapter 2 ,forsingle-transducercoherentUACschemes,wedevelopedaWLSchannelestimator,whichcanbeextendedtotheMIMOcase. 2. Multiuserdownlink.ManyapplicationsrequiremultipleAUVs.DSSSisacodedivisionmultipleaccess(CDMA)technique,inherentlyapplicabletomultiusersituations.InChapter 5 ,wedevelopedanHR-DSSSschemeforasingleuser.Inordertoextendittomultiuser,additionalworkonthesequenceswithgoodcirculantautocorrelationandcrosscorrelationisrequired. 3. RelayUACtoincreasethetransmissiondistanceandtoenhancethereliability.Sofar,wefocusondirect-linktransmissions.Ifrelaynodesareavailable,properlydesignedrelaycommunicationswillbeveryhelpfulforthetransmissionrangeandthereliability.Somepreliminaryresultsareincludedinourpublication[ 7 ]. 98

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[1] S.ApplebyandJ.Davies,\Time,frequency,andangulardispersionmodelingintheunderwatercommunicationschannel,"inProc.ofMTS/IEEEOceansConf.,vol.2,Nice,France,September28-October1,1998. [2] A.Baggeroer,D.E.Koelsch,K.vonderHeydt,andJ.Catipovic,\DATS-adigitalacoustictelemetrysystemforunderwatercommunications,"inProc.ofMTS/IEEEOceansConf.,Boston,MA,USA,September16,1981,pp.55{60. [3] P.A.Bello,\Characterizationofrandomlytime-variantlinearchannels,"IEEETrans.Commun.Syst.,vol.11,pp.360{393,December1963. [4] C.Bjerrum-NieseandR.Lutzen,\Stochasticsimulationofacousticcommunicationinturbulentshallowwater,"IEEEJournalofOceanicEngineering,vol.25,no.4,pp.523{532,October2000. [5] D.BorahandB.T.Hart,\Frequency-selectivefadingchannelestimationwithapolynomialtime-varyingchannelmodel,"IEEETrans.onCommunications,vol.47,no.6,pp.862{873,June1999. [6] A.Cano,X.Ma,andG.B.Giannakis,\Block-dierentialmodulationoverdoublyselectivewirelessfadingchannels,"IEEETrans.onCommunications,vol.53,no.12,pp.2157{2166,December2005. [7] R.Cao,F.Qu,andL.Yang,\AsynchronousOFDMrelaycommunicationforunderwateracousticnetwork,"inProc.ofIntl.Conf.onAcoustics,Speech,andSignalProcessing,Dalas,TX,March15-19,2010(inpreparation). [8] M.C.Domingo,\Overviewofchannelmodelsforunderwaterwirelesscommunicationnetworks,"PhysicalCommunication,vol.1,no.3,pp.163{182,September2008. [9] T.H.Eggen,\UnderwateracousticcommunicationoverDopplerspreadchannels,"Ph.D.dissertation,MassachussettsInstituteofTechnoloty,1997. [10] T.H.Eggen,A.B.Baggeroer,andJ.C.Preisig,\CommunicationoverDopplerspreadchannels.partI:Channelandreceiverpresentation,"IEEEJournalofOceanicEngineering,vol.25,no.1,pp.62{71,January2000. [11] A.Essenbbar,G.Loubet,andF.Vial,\Underwateracousticchannelsimulationsforcommunication,"inProc.ofMTS/IEEEOceansConf.,vol.3,Brest,France,September13-16,1994. [12] A.EssenbbarandE.Vercelloni,\Underwateracousticchannelsimulationsforcommunication,"inProc.ofMTS/IEEEOceansConf.,vol.2,SanDiego,CA,December9-12,1995. 99

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S.Mason,S.Zhou,P.Gendron,andW.B.Yang,\Acomparativestudyofdierentialandnoncoherentdirectsequencespreadspectrumoverunderwateracousticchannelswithmultiuserinterference,"inProc.ofMTS/IEEEOceansConf.,Quebec,Canada,September15-18,2008. [39] S.D.Morgera,\Multipleterminalacousticcommunicationssystemdesign,"IEEEJournalofOceanicEngineering,vol.5,no.3,pp.199{204,July1980. [40] J.C.Preisig,\Performanceanalysisofadaptiveequalizationforcoherentacousticcommunicationsinthetime-varyingoceanenvironment,"JournaloftheAcousticalSocietyofAmerica,vol.118,no.1,pp.263{278,July2005. [41] J.C.PreisigandG.B.Deane,\Surfacewavefocusingandacousticcommunicationsinthesurfzone,"JournaloftheAcousticalSocietyofAmerica,vol.116,no.4,pp.2067{2080,October2004. [42] J.Proakis,DigitalCommunications,4thed.McGraw-Hill,NewYork,February2001. [43] F.QuandL.Yang,\Orthogonalspace-timeblock-dierentialmodulationoverunderwateracousticchannels,"inProc.ofMTS/IEEEOceansConf.,Vancouver,Canada,September29-October4,2007. [44] ||,\Basisexpansionmodelforunderwateracousticchannels?"inProc.ofMTS/IEEEOceansConf.,Quebec,Canada,September15-182008,pp.1{7. [45] ||,\Ontheestimationofdoubly-selectivefadingchannels,"inProc.ofConferenceonInfo.SciencesandSystems.,ThePrincetonUniv.,Princeton,March19-21,2008,pp.17{24. [46] ||,\Ontheestimationofdoubly-selectivefadingchannels,"IEEETrans.onWirelessCommunications,2008(accepted). [47] F.Qu,L.Yang,andT.C.Yang,\Highreliabilitydirect-sequencespreadspectrumforunderwateracousticcommunications,"inProc.ofMTS/IEEEOceansConf.,Biloxi,MS,October26-292009,pp.1{6. [48] T.S.Rappaport,WirelessCommunications.PrenticeHall,January2002. [49] D.Schafhuber,G.Matz,andF.Hlawatsch,\Kalmantrackingoftime-varyingchannelsinwirelessMIMO-OFDMsystems,"inProc.ofthe37thAsilomarConf.Sig-nals,Systems,Computers,PacicGrove,CA,November9-12,2003,pp.1261{1265. [50] D.Slepian,\Prolatespheroidalwavefunctions,Fourieranalysis,anduncertainty{V:Thediscretecase,"BellSynst.Tech.J.,vol.57,no.5,pp.1371{1430,May-June1978. [51] M.Stojanovic,\Underwateracousticcommunication,"WileyEncyclopediaofElectri-calandElectronicsEngineering,December1999. 102

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||,\Measurementsoftemporalcoherenceofsoundtransmissionsthroughshallowwater,"JournaloftheAcousticalSocietyofAmerica,vol.12,no.5,pp.2595{2614,November2006. [65] T.C.YangandW.Yang,\Performanceanalysisofdirect-sequencespread-spectrumunderwateracousticcommunicationswithlowsignal-to-noise-ratioinputsignals,"JournaloftheAcousticalSocietyofAmerica,vol.123,no.2,pp.842{855,February2008. [66] W.B.YangandT.C.Yang,\Characterizationandmodelingofunderwateracousticcommunicationschannelsforfrequency-shift-keyingsignals,"inProc.ofMTS/IEEEOceansConf.,Boston,MA,USA,September18{21,2006,pp.1{6. [67] Y.YoonandA.Zielinski,\Simulationoftheequalizerforshallowwateracousticcommunication,"inProc.ofMTS/IEEEOceansConf.,vol.2,SanDiego,CA,December9-12,1995. [68] T.ZemanandC.F.Mecklebrauker,\Time-variantchannelestimationusingdiscreteprolatespheroidalsequences,"IEEETrans.onSignalProcessing,vol.53,no.9,pp.3597{3607,September2005. [69] Q.T.Zhang,X.Y.Zhao,Y.X.Zeng,andS.H.Song,\EcientestimationoffastOFDMchannel,"inProc.ofIntl.Conf.onCommunications,Istanbul,Turkey,September11-15,2006,pp.4601{4605. 104

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FengzhongQuwasborninWenzhou,China.HeearnedhisBSandMSdegreesin2002and2005,bothinInformationScienceandElectronicsEngineeringfromZhejiangUniversity,Hangzhou,China.SinceAugust2005,hehasbeenaPhDstudentinelectricalandcomputerengineeringatUniversityofFlorida,Gainesville,Florida.Hisresearchinterestsincludewirelesscommunicationsoverdoubly-selectivechannels,underwateracousticcommunicationsandwirelesssensornetworks. 105