Contents

1.Introduction....................................................................................................................................2

1.1DocumentStructure.........................................................................................................................2

1.2KeyApplicationScenarios..............................................................................................................3

2.BasicPrinciplesofOTFS................................................................................................................5

2.1PrinciplesofOTFSModulationTransmitter...................................................................................6

2.2PrinciplesofOTFSModulationReceiver.......................................................................................8

2.3AnalysisofInput-OutputRelationshipinOTFS...........................................................................10

3.AnalysisofDelayDopplerDomainChannelCharacteristics......................................................12

3.1CharacteristicsofDelayDopplerDomainChannel......................................................................12

3.1.1DeterministicDescriptionofChannels..................................................................................12

3.1.2CoherentandStationaryRegionsofChannels......................................................................14

3.2DelayDopplerDomainChannelCharacteristicsinHigh-SpeedRailwayScenario.....................15

3.2.1ChannelSpreadingFunctionMeasurementSystemBasedonLTE-R...................................15

3.2.2High-SpeedRailwayChannelSpreadingFunctionCharacterizationBasedonLTE-R........17

3.3PerformanceEvaluationofOTFSinMeasuredChannels............................................................19

4.OTFSChannelEstimationandDataDetection...........................................................................21

4.1PilotDesignforLow-PAPROTFSChannelEstimation...............................................................21

4.2Off-gridChannelEstimationforOTFS.........................................................................................26

4.3Low-ComplexityOTFSDataDetectionSchemeBasedonExpectationPropagation..................28

5.ExtensionSchemesofOTFS.........................................................................................................31

5.1Multi-AntennaOTFSScheme.......................................................................................................31

5.1.1PilotDesignforMIMO-OTFS...............................................................................................31

5.1.2Low-ComplexityandLow-OverheadOTFSTransceiverBasedonMulti-AntennaArray...36

5.2MultipleAccessTechnologySchemeEmpoweredbyOTFS.......................................................41

5.2.1OrthogonalTime-FrequencyCodeDomainMultipleAccessScheme..................................41

5.2.2OTFS-SCMASystemBasedonMemoryApproximateMessagePassing(MAMP)

Algorithm........................................................................................................................................45

5.3OTFS-EmpoweredIntegratedSensingandCommunication(OTFS-ISAC)Scheme..................51

5.3.1AdvantagesofOTFS-ISACScheme......................................................................................51

5.3.2OTFS-ISACWaveformDesign.............................................................................................52

6.EvolutionSchemesforOTFS.......................................................................................................55

6.1NewDelayDopplerDomainMulticarrierModulationScheme...................................................55

6.2FusionFrameStructureDesignofOTFSandOFDM..................................................................57

7.SummaryandOutlook.................................................................................................................62

References.........................................................................................................................................64

ParticipantUnits...............................................................................................................................66

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1.Introduction

Orthogonalfrequencydivisionmultiplexing(OFDM)isawidelyusedmodulation

techniqueinwirelesscommunicationsystemssuchas4G,5G,andWiFi.OFDMbasedon

cyclicprefixescaneffectivelydealwithmultipathfadingandonlyrequireslow-complexity

frequencydomainequalizers.Withthedevelopmentofwirelesscommunications,high-speed

mobilecommunicationscenariosincomplexscatteringenvironmentsarebecoming

increasinglyabundant,suchasIoV,high-speedrailways,andlow-earthorbitsatellite

communications.Thesecommunicationscenarioshavealreadyorwillgreatlychangepeople's

lifestyles.However,OFDMunderhigh-speedmobilitywilllosesubcarrierorthogonalitydue

totheinfluenceofDopplerspread,anditstransmissionreliabilitywilldeteriorate.Therefore,

itisimportanttodesignnewmulticarriermodulationschemesforhigh-speedmobile

scenariosinthenextgenerationofmobilecommunicationsystems.

Inrecentyears,researchershaveproposedtheorthogonaltimefrequencyspace(OTFS)

multicarriermodulationtechnology.DifferentfromOFDMtechnology,OTFSperforms

resourcemappingintheDelayDoppler(DD)domain,andbasedonthesparsityandstability

oftheDDdomainchannel,itcanachievehigherdatatransmissionreliabilitythanOFDM

underhigh-speedmobileconditions.

Toinvestigatethebasicprinciples,researchandapplicationstatus,andfuture

developmentprospectsofOTFS,andtoprovidetechnicalreferencesforindustryand

academia,thiswhitepaperwillintroduceOTFSfromthefollowingsixaspects:(1)Basic

principlesofOTFS;(2)CharacteristicsofDDdomainchannels;(3)Transmissionwaveform

designofOTFS;(4)ReceiverschemedesignofOTFS;(5)Multi-antenna,multi-user,and

integratedsensingandcommunicationschemesempoweredbyOTFS;(6)Evolutionschemes

forOTFS.

1.1DocumentStructure

Chapter1istheintroduction,whichintroducesthescopeandstructureofthiswhite

paper,andintroducestheapplicationscenariosofOTFS,pointingouttheneedsand

challengesbroughtbyhigh-speedmobilityinsuchscenarios,thusleadingtothenecessityof

OTFStechnologyresearch.

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Chapter2describesthebasicdesignprinciplesofOTFS,includingtheintroductionof

twoOTFSmodulationimplementationmethods,SFFTandDZT,andabriefdescriptionof

thetransceiverscheme.

Chapter3analyzesthechannelcharacteristicsoftheDelay-Dopplerdomain,and

analyzesthesparsity,compactness,stability,andseparabilityoftheDelay-Dopplerdomain

channelforhigh-speedmobilescenariossuchashigh-speedrailways.

Chapter4introducesthedesignoftheOTFSreceiver,includingthepilotdesignof

low-PAPRchannelestimation,OTFSchannelestimationundernon-integergrids,and

low-complexityOTFSdatadetectionschemebasedonexpectationpropagation.

Chapter5introducesOTFS-empoweredmulti-antenna,multi-user,andintegrated

sensingandcommunicationschemes,includingthesystemdesignofMIMO-OTFS,

grant-freemultipleaccessschemesforhigh-speedmobilescenariossuchassatellitesand

high-speedrailwaysformassivemachinetypecommunications,andperformanceanalysisof

integratedsensingandcommunicationsystemdesignbasedonOTFS.

Chapter6introducestheevolutionschemesforOTFS,includingthejointframestructure

designofOFDMandOTFSthatisforwardcompatiblewithOFDM,andanewtypeof

multicarriermodulationschemeintheDelay-Dopplerdomain.

Chapter7providestheconclusionandoutlook.

1.2KeyApplicationScenarios

High-speedrailwayscenario:Forrailways,continuouslyimprovingtrainspeedsisa

commongoalinglobalrailwaydevelopment.Atpresent,theBeijing-Shanghaihigh-speed

railwayhasachievedatestspeedof470kilometersperhour,andtheCR450,a450km/h

high-speedtrain,willbecompletedin2024.Atthesametime,theCentralJapanRailway

Companyhasachievedatestspeedof603km/hformaglevtrainsinYamanashi-ken,Japan.

Inaddition,thepipelineflyingcar,whichcanreachaspeedofover1,000km/h,isalsounder

development.Basedonthehigh-speeddevelopmentofrailways,countriesworldwidewith

developedhigh-speedrailwaysystemsarefocusingontheintelligenceofhigh-speedrailways.

Theintelligencedevelopmentofhigh-speedrailwaysrequiresadvancedcommunication

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systemsandstandardstoprovidesupport,butthehigh-speedmovementoftrainsin

high-speedrailwayscenarioswillposeagreatchallengetothereliabilityofground-to-train

andtrain-to-traincommunication.

Low-earthorbitsatellitescenario:Low-earthorbit(LEO)satellitecommunicationisa

technologythatusessatellitesinlow-earthorbittoachievecommunication.Unliketraditional

high-earthorbitsatellitecommunication,LEOsatellitecommunicationsatellitesaretypically

locatedbetweenhundredsofkilometersandtwothousandkilometersfromtheground.

Comparedwithtraditionalgeosynchronousorbitsatellites,ithastheadvantagesoflowlaunch

cost,lowcommunicationdelay,lowtransmissionloss,andseamlessglobalcoverageafter

networking,andhasattractedtheattentionofmanyInternet,communication,andaerospace

companiesaroundtheworld.

Aircoveragescenario:Withtheprogressofaviationcommunication,airplanesare

transformingfromthepast"isolatedislands"ofinformationnetworksintokeycarriersfor

realizingglobalinterconnection.Theemergenceofin-flightWi-Fiallowspassengersto

accesstheInternetonairplanes.However,thearrivalofthe5Gerahasbroughtunprecedented

challengestoaircommunication—thedemandformassivereal-timeInternetdata

transmission.Thischallengerequirescommunicationsystemstobehighlyadaptive,and

capableofimprovingcommunicationqualitybetweenairplanesandgroundstationsor

satellitesinhigh-speedmobileenvironments,ensuringlow-latencyandhigh-reliability

transmissionofinternetdata.

InternetofVehicles:BasedontheOTFS-ISACmechanism,thefollowingInternetof

Vehiclesfunctionsorapplicationscanbesupported:Accuratelysensingthesurrounding

drivingenvironment,includingvehicles,obstacles,roadconditions,etc.,toenhancedriving

safetyandachieveintelligentdriving;accuratelysensingthepositionsandmotionstatesof

bothreceiversandtransmitters,providingpriorinformationforchannelestimation,

beamforming,etc.,toimprovecommunicationperformance;distributednodecollaborative

sensing,expandingtherangeofnodesensing,andenhancingtheaccuracyandprecisionof

sensing.

UnderwaterAcousticCommunication:The"SmartOcean"projectisamajorproject

relatedtothenationalstrategyofbuildingamaritimepower,andwiththeadvancementofthe

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maritimepowerandtheconstructionofthe"SmartOcean"project,rapiddevelopmenthas

beenachievedinvariousfieldssuchasmodernfisheries,marineobservationandmonitoring,

offshoreoilandgasexplorationanddevelopment,andmarinetransportation.Underwater

acousticcommunicationisanimportantpartofthemarinecommunicationnetwork.Acoustic

wavesarecurrentlytheonlyeffectivelong-distanceinformationtransmissioncarrier

underwater.Theunderwateracoustic(UWA)channelisachannelwithfasttime-varying

characteristics,largedelayspread,seriousDopplereffect,andlimitedavailablebandwidth.In

commonmarineenvironments,multipatheffects,Dopplereffects,andenvironmentalnoise

existduringthepropagationofunderwateracousticsignals,whichmakesitimpossibleforthe

receivingendofthecommunicationsystemtoobtaincorrectchannelinformationwhen

detectingsignals.Thisbringsgreatobstaclestothedesignofthecommunicationsystem.At

thesametime,thephasefluctuationsinthechannelmakeitverydifficultforthereceiving

endtorecoverthecarrierandperformcoherentdemodulation.TheOFDMmodulation

technologywidelyusedinUWAcommunicationnetworksiseasilyaffectedbyDoppler

spread,leadingtoseveredegradationinsystemperformance.Howtoachieveefficientdata

transmissionincomplexandvariablemobileUWAcommunicationscenariosiscurrentlya

keyissuethatneedstobeaddressed.

2.BasicPrinciplesofOTFS

OTFSwasproposedbyR.Hadanietal.in2017[2.1],anditwaspointedoutthat

comparedwithOFDMmodulation,itcouldusethefulldiversitygainofthetime-frequency

domaintoachievebetterdatatransmissionperformanceunderhighmobility[2.2].According

tothecontentofthischapter,itcanbefoundthatOTFScanberegardedasaprecodedOFDM

system,whichhasthepotentialtobecompatiblewithOFDMsystems.However,compared

withtheOFDMschemethathasbeenmaturelyappliedin5GNR,LTE,Wi-Fi,andother

protocols,OTFSfacesmanynewchallenges,suchasDDdomainchannelmodeling,reliable

DDdomainchannelestimation,low-complexityequalization,multi-antennaOTFSsystem

design,multi-userOTFSsystemdesign,OTFS-enabledcommunication-sensingsystem

design,etc.ThissectionwillbrieflyintroducethebasicprinciplesofOTFSmodulation,with

theremainingcontentbeingelaboratedinsubsequentsections.Thissectionmainlyrefersto

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theliterature[2.3].

2.1PrinciplesofOTFSModulationTransmitter

Figure2.1BlockDiagramoftheISFFT-basedOTFSTransmitter

Figure2.1showstheblockdiagramoftheISFFT-basedOTFStransmitter.Considerthe

systembandwidthMfandtimedurationNT,whereMisthenumberofsubcarriers,

fisthesubcarrierspacing,Nisthenumberofslots,andTistheslotduration.1Let

{XDD[k,l],k0,,N1,l0,,M1}representtheQAMmodulatedsymbol

mappedontheDDgrid,OTFSmodulationfirstusestheInverseSymplecticFiniteFourier

Transform(ISFFT)tomaptheDDdomainsymbolsXDD[k,l]totheTFgridtoobtain

XTF[n,m]:

nkml

j2

1N1M1NM

XTF[n,m]XDD[k,l]e

NMk0l0

(2-1)

wheren0,,N1,m0,,M1.Thediscreteresourcegridrelationshipbetweenthe

DDdomainandtheTFdomainintheequation(2-1)isshowninFigure2.2.

1NotethatunlikeOFDM,whichonlyconsidersmulticarrierdataforonesymboltime,OTFSconsiders

multicarriernetworkpacketswithaperiodof.

?

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Figure2.2ResourceGridRelationshipbetweenDDDomainandTFDomain

Figure2.3IDZT-basedOTFSTransmitter

Subsequently,thetime-frequencydomainsignalXTF[n,m]isembeddedwithaCPand

transformedintothetimedomainsignalstthroughwirelesschanneltransmissionusing

theHeisenbergtransformationasfollows:

N1M1j2mftnT

stX[n,m]gtnTe

n0m0TFtx

(2-2)

wheregtx(t)isthetransmitpulseshapingfilter.Basedontheabovecontent,itcanbefound

thattheISFFT-basedOTFSsystemcanbecompatiblewiththeOFDMsystemandthe

correspondingtime-frequencydomainsignalprocessingmethods.Additionally,theOTFS

transmittercanalsobedesignedbasedontheInverseDiscreteZakTransform(IDZT),and

thetransmitterblockdiagramisshowninFigure2.3.

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2.2PrinciplesofOTFSModulationReceiver

Figure2.4OTFSWaveformReceiverBlockDiagram

Figure2.4showstheblockdiagramoftheSFFT-basedOTFSreceiver(Theblock

diagramoftheOTFSreceiverbasedonDZTisanalogoustoFigures2.3and2.4andis

thereforenotelaboratedhere).TheDelay-Dopplerdomainchannelspreadingfunctionis

representedash,v,whereandvrepresentthedelayandDoppler,respectively.Then

?

thereceivedsignalrtcanberepresentedas(ignoringnoiseforsimplicity):

j2vt

rth,vsteddv

(2-3)

Notethatthereareusuallyonlyafewreflectorsinthechannel,soh,vexhibits

sparsityandcanberepresentedas2:

P

h,vhvv

i1iii

(2-4)

wherePisthenumberofpropagationpaths,hi,i,andvirepresentthepathgain,delay,

andDopplershiftofthei-thpath,respectively,and()representstheDiracdeltafunction.

ThedelayandDopplertapsofthei-thpathareexpressedasfollows:

lkvKv

i,vii

iMfiNT

(2-5)

Sincethedelayresolution1isusuallysmallenough,lcouldberegardedasan

Mfi

integer;theDopplerresolution1isusuallylimited,sokisusedtorepresentitsinteger

NTvi

partandK0.5,0.5isusedtorepresentitsfractionalpart.Atthereceiver,the

vi

time-frequencydomainsignalobtainedthroughtheWignertransformisrepresentedas:

2Channelcharacterizationunderhigh-speedmovementconditionswillbeintroducedindetailinChapter3.

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Yn,mYt,f

TFtnT,fmf

(2-6)

wheren0,,N1,m0,,M1,

j2ftt

Yt,fAt,fg*ttrtedt

grx,rrx

(2-7)

At,frepresentsthetime-frequencydomainsignal(cross-ambiguityfunction)

grx,r

obtainedbymatchedfiltering.SubstitutingEquations(2-1)to(2-3)intoEquation(2-6)yields

theinput-outputrelationshipofOTFSinthetime-frequencydomainasfollows:

N1M1

Yn,mHn,mXn,m

TFn0m0n,mTF

(2-8)

whereHn,mn,mrepresentstheequivalentchannelconsideringinter-subcarrier

interferenceandinter-symbolinterference(ISI):

Hn,mh,vAnnT,mmfv

n,mgrx,gtx,

j2vmfnnT

eej2vnTddv

(2-9)

ItcanbefoundthatHn,mn,misaffectedbythetransmittingpulse,channel

response,andreceivingpulse.Finally,YTFn,misconvertedtotheDDdomainthrough

theSFFToperationtoobtainthereceivedsignalYDDk,l:

nkml

j2

1N1M1NM

YDDk,lYTFn,me

NMk0l0

(2-10)

Foridealtransmittingandreceivingpulses,thefollowinginput-output

relationshipholds:

1N1M1

YDDk,lXDDk,lhkk,ll

NMk0l0

(2-11)

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whereh.,.isthesampledversionoftheimpulseresponsefunction:

hkk,llhv,kkll

v,

NTMf

(2-12)

Forhv,isthecircularconvolutionofthechannelresponseandthe

windowfunctionSFFTinthetime-frequencydomain:

j2v

hv,h,vvv,eddv

(2-13)

N1M1j2vnTmf

v,e

n0m0

(2-14)

2.3AnalysisofInput-OutputRelationshipinOTFS

Accordingtoequation(2-11),itcanbefoundthatthereceivedsignalYDDk,lisa

linearcombinationofalltransmittedsignalsXDDk,l.Consideringthesparsityof

h,vinequation(2-4),equation(2-13)canbefurtherexpressedas:

P

h,vhej2viivv,

i1iii

P

j2vii

hieGv,viF,i

i1

(2-15)

where

M1j2mf

F,ei

im0

(2-16)

N1j2vvnT

Gv,vei

in0

(2-17)

ll

When,F,willbefurtherexpressedas:

Mfi

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2j2lll

jlllmi

llM1ie1

M

F,im0e2

Mfjlll

eMi1

(2-18)

l

i

Since,andlisusuallyaninteger,then:

iMfi

M,lll0

lliM

F,i

Mf0,其他

(2-19)

wherexMrepresentsthemodulooperationontheintegerM,thatismodx,M.In

kk

addition,G,vicanbeexpressedas:

NT

j2kkkvKv

kkeii1

G,vi2

NTjkkkvKv

eNii1

(2-20)

kk

ItcanbefoundthatwhenKv0,G,vi0.Thisphenomenonintroduces

iNT

interferenceknownasDopplerInterference.Accordingtoequation(2-20),

1kksinN

G,vicanbeobtained.WhenkkkK,

NNTNsinNvivi

sinNsinN1cossincosN1N11

cos

NsinNsinNN

(2-21)

1kk

WhenNislarge,G,viwilldecreaserapidly,indicatingthatDoppler

NNT

interferencemainlycomesfromadjacentDDdomainresourcegrids.Therefore,weconsider

thatDopplerinterferencemainlycomesfromtheneighboringNigridpoints.When

kN]k[kkN]

NiN,[k,viiMviiN,consideringthederivationprocessabove,

YDDk,linequation(2-21)canbesimplifiedas:

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PNij2qKv

ei1

j2vii

YDDk,lhieXDDkkvq,ll

2iNiM

i1qNjkqKv

iNeNiN

(2-22)

Equation(2-22)indicatesthatthereceivedsignalYDDk,lintheDDdomainis

significantlyaffectedbyinter-symbolinterference,andtheequivalentchannelintheDD

domainisdifficulttobeunitarilydiagonalized.Therefore,comparedtoOFDM,OTFSwill

requirehigherequalizationcomplexity.Additionally,accordingtothereference[2.4],OTFS

channelestimationwillintroducesignificantpilotoverheadandresultinalarger

peak-to-averagepowerratio(PAPR).Ontheotherhand,comparedtoOFDM,OTFSuses

fewerCPs(onlyonesegmentperframe),therebyimprovingspectralefficiency.Furthermore,

OTFShasstrongerresistancetoDopplerfrequencyoffsetandmultipathinterference.

PotentialsolutionstothechallengesinOTFSchannelestimationandequalizationwillbe

providedinChapter4.

3.AnalysisofDelayDopplerDomainChannelCharacteristics

3.1CharacteristicsofDelayDopplerDomainChannel

ThemostsignificantfeaturethatdistinguishesOTFSfromtraditionalmulticarrier

modulationschemessuchasOFDMisthatitperformsresourcereuse,channelestimation,

anddatadetectionintheDelayDopplerdomain.Therefore,thechannelcharacteristicsinthe

DelayDopplerdomainplayacrucialroleintheresearchofOTFSschemes.Thissectionwill

explainthedifferentrepresentationforms,physicalconnections,andcharacteristicsofthe

DelayDopplerdomainchannel.Themainreferenceforthissectionis[3.1],anditonly

focusesonthesmall-scalefadingcausedbymultipathpropagationofthechannel,anddoes

notconsiderlarge-scal