<%BANNER%>

Rate And Reliability Oriented Underwater Acoustic Communications

Permanent Link: http://ufdc.ufl.edu/UFE0024916/00001

Material Information

Title: Rate And Reliability Oriented Underwater Acoustic Communications
Physical Description: 1 online resource (105 p.)
Language: english
Creator: Qu, Fengzhong
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: bem, dostbc, dsss, ls, mimo, rate, rliability, uac
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: 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.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Fengzhong Qu.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Yang, Liuqing.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024916:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024916/00001

Material Information

Title: Rate And Reliability Oriented Underwater Acoustic Communications
Physical Description: 1 online resource (105 p.)
Language: english
Creator: Qu, Fengzhong
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: bem, dostbc, dsss, ls, mimo, rate, rliability, uac
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: 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.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Fengzhong Qu.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Yang, Liuqing.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024916:00001


This item has the following downloads:


Full Text

PAGE 1

1

PAGE 2

2

PAGE 3

3

PAGE 4

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

PAGE 5

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

PAGE 6

......................... 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

PAGE 7

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

PAGE 8

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

PAGE 9

... 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

PAGE 10

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

PAGE 11

11

PAGE 12

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

PAGE 13

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

PAGE 14

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

PAGE 15

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

PAGE 16

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

PAGE 17

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

PAGE 18

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

PAGE 19

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

PAGE 20

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

PAGE 21

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

PAGE 22

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

PAGE 23

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

PAGE 24

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

PAGE 25

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

PAGE 26

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

PAGE 27

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

PAGE 28

2{7 ),weobtain: whereKandgKconsistof(k)andg(k),withkK=2orkNK=2;NKandgNKconsistof(k)andg(k),withK=2
PAGE 29

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

PAGE 30

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

PAGE 31

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

PAGE 32

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

PAGE 33

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

PAGE 34

Thescatteringfunctionforadatapacketincalmperiods. conrmsthatoursimplewindowedapproachhelpsnotonlyLSestimators,butalsoMMSEones. 34

PAGE 35

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

PAGE 36

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

PAGE 37

Coherentschemes'BERsacrossdierenthydrophonesinRACE08ata1000mdistance. introduceareliability-orientedschemeforthedownlink,whichprovidesgoodperformanceevenwithasmallnumberofhydrophonesandrequireslowcomplexityofsignalprocessingatthereceiver. 37

PAGE 38

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

PAGE 39

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

PAGE 40

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

PAGE 41

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

PAGE 42

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

PAGE 43

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

PAGE 44

~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

PAGE 45

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

PAGE 46

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

PAGE 47

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

PAGE 48

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

PAGE 49

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

PAGE 50

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

PAGE 51

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

PAGE 52

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

PAGE 53

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

PAGE 54

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

PAGE 55

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

PAGE 56

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

PAGE 57

ThewindspeedmeasuredinRACE08 Figure3-10. TheseasurfaceheightabovebottommeasuredinRACE08 57

PAGE 58

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

PAGE 59

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

PAGE 60

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

PAGE 61

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

PAGE 62

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

PAGE 63

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

PAGE 64

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

PAGE 65

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

PAGE 66

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

PAGE 67

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

PAGE 68

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

PAGE 69

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

PAGE 70

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

PAGE 71

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

PAGE 72

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

PAGE 73

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

PAGE 74

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

PAGE 75

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

PAGE 76

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

PAGE 77

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

PAGE 78

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

PAGE 79

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

PAGE 80

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

PAGE 81

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

PAGE 82

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

PAGE 83

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

PAGE 84

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

PAGE 85

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

PAGE 86

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

PAGE 87

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

PAGE 88

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

PAGE 89

foraZCZsequencec.From( 5{16 ),weknowthatZCZsequencecanbeusedinsteadofm-sequenceinourproposedHR-DSSS.However,fortheZCZsequences,becausetheshiftregionisreducedfromMtobM=2candaccordinglyJZCZmax=jM 5.1.2 arealsousedinOFDMsystems,whichareextensivelyemployedformultipathquasi-staticchannels.Itcanalsobeadoptedtolow-ratehigh-reliabilitysystemsbytransmittingJ(
PAGE 90

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

PAGE 91

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

PAGE 92

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

PAGE 93

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

PAGE 94

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

PAGE 95

95

PAGE 96

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

PAGE 97

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

PAGE 98

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

PAGE 99

[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

PAGE 100

A.Falahati,B.Woodward,andS.C.Bateman,\Underwateracousticchannelmodelsfor4800b/sQPSKsignals,"IEEEJournalofOceanicEngineering,vol.16,no.1,pp.12{20,January1991. [14] P.Z.Fan,N.Suehiro,N.Kuroyanagi,andX.M.Deng,\Classofbinarysequenceswithzerocorrelationzone,"IEEEElectronicsLetters,vol.35,no.10,pp.777{779,May1999. [15] D.M.Farmer,G.B.Deane,andS.Vagle,\Theinuenceofbubbleandcloudsonacousticpropagationinthesurfzone,"IEEEJournalofOceanicEngineering,vol.26,no.1,pp.113{124,January2001. [16] A.J.Garrood,\ApplicationsoftheMFSKacousticcommunicationssystems,"inProc.ofMTS/IEEEOceansConf.,Boston,MA,USA,September16,1981,pp.67{71. [17] X.GengandA.Zielinski,\Aneigenpathunderwateracousticcommunicationchannelmodel,"inProc.ofMTS/IEEEOceansConf.,vol.3,SanDiego,CA,December9-12,1995. [18] G.B.GiannakisandC.Tepedelenlioglu,\BasisExpansionModelsanddiversitytechniquesforblindidenticationandequalizationoftime-varyingchannels,"Proc.oftheIEEE,vol.86,no.10,pp.1969{1986,October1998. [19] J.E.J.Hill,ElectromagneticRadiationinSeaWater.NavalUnderwaterOrdnanceStationNewportRI,August,1960. [20] H.JafarkhaniandV.Tarokh,\Multipletransmitantennadierentialdetectionfromgeneralizedorthogonaldesigns,"IEEETrans.onInformationTheory,vol.47,no.6,pp.2626{2631,September2001. [21] W.C.Jakes,Microwavemobilecommunication.NewYork:Wiley,1974. [22] P.Jarvensivu,M.Matinmikko,andA.Mammela,\SignaldesignforLSandMMSEchannelestimators,"inProc.ofthe13thIEEEInternationalSymposiumonPersonal,IndoorandMobileRadioCommunications,vol.2,LisboaPortugal,September15-18,2002,pp.956{960. [23] Y.Jiang,J.Li,andW.W.Hager,\MIMOtransceiverdesignusinggeometricmeandecomposition,"inProc.oftheInformationTheoryWorkshop,SanAntonio,TX,Oct.24-292004,pp.193{197. [24] S.M.Kay,FundamentalsofStatisticalSignalProcessing,VolumeI:EstimationTheory.Prentice-Hall,1993. [25] R.S.Kennedy,FadingDispersiveCommunicationChannels.JohnWiley&Sons,1969. 100

PAGE 101

D.B.KilfoyleandA.B.Baggeroer,\Thestateoftheartinunderwateracoustictelemetry,"IEEEJournalofOceanicEngineering,vol.25,no.1,pp.4{27,January2000. [27] I.H.KimandD.J.Love,\Onthecapacityanddesignoflimitedfeedbackmultiusermimouplinks,"IEEETrans.onInformationTheory,vol.54,no.10,pp.4712{4724,October2008. [28] C.Kuchpil,A.Xavier,J.daSilva,andM.Jimenez,\Autonomouscontrolsystemforoshoreoilexploitationusingdigitalacousticcommunication,"inProc.ofMTS/IEEEOceansConf.,vol.2,Halifax,NovaScotia,October6-9,1997. [29] F.C.M.Lau,\Achievable-SIR-basedpredictiveclosed-looppowercontrolinaCDMAmobilesystem,"IEEETrans.onVehicularTech.,vol.51,no.4,pp.720{728,July2002. [30] G.Leus,\Ontheestimationofrapidlytime-varyingchannels,"inEuro.SignalProcess.Conf.(EUSIPCO),Vienna,Austria,September6-10,2004,pp.2227{2230. [31] G.LeusandP.vanWalree,\MultibandOFDMforcovertacousticcommunications,"IEEEJournalonSelectedAreasinCommunications,vol.26,no.9,pp.1662{1673,December2008. [32] G.Leus,P.Walree,J.Boschma,C.Fanciullacci,H.Gerritsen,andP.Tusoni,\CovertunderwatercommunicationswithmultibandOFDM,"inProc.ofMTS/IEEEOceansConf.,Quebec,Canada,September15-18,2008. [33] B.Li,S.Zhou,M.Stojanovic,andL.Freitag,\Pilot-tonebasedZP-OFDMdemodulationforanunderwateracousticchannel,"inProc.ofMTS/IEEEOceansConf.,Boston,MA,USA,September18-21,2006,pp.1{5. [34] B.Li,S.Zhou,M.Stojanovic,L.Freitag,J.Huang,andP.Willet,\MIMO-OFDMoveranunderwateracousticchannel,"inProc.ofMTS/IEEEOceansConf.,Vancouver,Canada,September29-October4,2007,pp.1{6. [35] B.Li,S.Zhou,M.Stojanovic,L.Freitag,andP.Willet,\Non-uniformDopplercompensationforzero-paddedOFDMoverfast-varyingunderwateracousticchannels,"inProc.ofMTS/IEEEOceansConf.,Aberdeen,Scotland,June18-21,2007,pp.1{6. [36] Z.LiuandG.B.Giannakis,\BlockdierentiallyencodedOFDMwithmaximummultipathdiversity,"IEEETrans.onWirelessCommunications,vol.2,no.3,pp.420{423,May2003. [37] X.Ma,G.B.Giannakis,andS.Ohno,\Optimaltrainingforblocktransmissionsoverdoublyselectivewirelessfadingchannels,"IEEETrans.onSignalProcessing,vol.51,no.5,pp.1351{1366,May2003. 101

PAGE 102

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

PAGE 103

||,\LowcomplexityOFDMdetectorforunderwateracousticchannels,"inProc.ofMTS/IEEEOceansConf.,Boston,MA,USA,September18-21,2006. [53] M.Stojanovic,J.A.Catipovic,andJ.G.Proakis,\Phase-coherentdigitalcommunicationsforunderwateracousticchannels,"IEEEJournalofOceanicEn-gineering,vol.19,no.1,pp.100{111,January1994. [54] M.Stojanovic,\Ontherelationshipbetweencapacityanddistanceinanunderwateracousticcommunicationchannel,"inACMWuWNet'06:Proc.ofthe1stACMinternationalworkshoponUnderwaternetworks,LosAngeles,CA,September25,2006,pp.41{47. [55] Z.Tang,R.C.Cannizzaro,G.Leus,andP.Banelli,\Pilot-assistedtime-varyingchannelsestimationforOFDMsystems,"IEEETrans.onSignalProcessing,vol.55,no.5,pp.2226{2238,May2007. [56] V.TarokhandH.Jafarkhani,\Adierentialdetectionschemefortransmitdiversity,"IEEEJournalonSelectedAreasinCommunications,vol.18,no.7,pp.1169{1174,July2000. [57] H.L.V.Trees,Detection,Estimation,andModulationTheory.Wiley-Interscience,NewYork,September2001. [58] T.L.Tung,K.Yang,andR.E.Hudson,\Channelestimationandadaptivepowerallocationforperformanceandcapacityimprovementofmultiple-antennaOFDMsystems,"inProc.ofthe3rdIEEESignalProcess.WorkshopSignalProcess.Adv.WirelessCommun.,Taoyuan,Taiwan,September20{23,2001,pp.82{85. [59] P.vanWalree,E.Sangfelt,andG.Leus,\Multicarrierspreadspectrumforcovertacousticcommunications,"inProc.ofMTS/IEEEOceansConf.,Quebec,Canada,September15-18,2008. [60] Z.WangandG.B.Giannakis,\Wirelessmulticarriercommunications,"IEEESignalProcessingMagazine,vol.17,no.3,pp.29{48,May2000. [61] Q.WenandJ.A.Ritcey,\Spatialdiversityequalizationappliedtounderwatercommunications,"IEEEJournalofOceanicEngineering,vol.19,no.2,pp.227{241,April1994. [62] E.C.Westereld,R.H.prager,andJ.L.Stewart,\Processinggainsagainstreverberation(clutter)usingmatchedlters,"IRETrans.onInformationTheory,vol.6,no.3,pp.342{348,June1960. [63] T.C.Yang,\Correlation-baseddecision-feedbackequalizerforunderwateracousticcommunications,"IEEEJournalofOceanicEngineering,vol.30,no.4,pp.865{880,October2005. 103

PAGE 104

||,\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

PAGE 105

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