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1、1/66Contents1.Introduction.21.1 Document Structure.21.2 KeyApplication Scenarios.32.Basic Principles of OTFS.52.1 Principles of OTFS Modulation Transmitter.62.2 Principles of OTFS Modulation Receiver.82.3Analysis of Input-Output Relationship in OTFS.103.Analysis of Delay Doppler Domain Channel Chara

2、cteristics.123.1 Characteristics of Delay Doppler Domain Channel.123.1.1 Deterministic Description of Channels.123.1.2 Coherent and Stationary Regions of Channels.143.2 Delay Doppler Domain Channel Characteristics in High-Speed Railway Scenario.153.2.1 Channel Spreading Function Measurement System B

3、ased on LTE-R.153.2.2 High-Speed Railway Channel Spreading Function Characterization Based on LTE-R.173.3 Performance Evaluation of OTFS in Measured Channels.194.OTFS Channel Estimation and Data Detection.214.1 Pilot Design for Low-PAPR OTFS Channel Estimation.214.2 Off-grid Channel Estimation for O

4、TFS.264.3 Low-Complexity OTFS Data Detection Scheme Based on Expectation Propagation.285.Extension Schemes of OTFS.315.1 Multi-Antenna OTFS Scheme.315.1.1 Pilot Design for MIMO-OTFS.315.1.2 Low-Complexity and Low-Overhead OTFS Transceiver Based on Multi-Antenna Array.365.2 MultipleAccess Technology

5、Scheme Empowered by OTFS.415.2.1 Orthogonal Time-Frequency Code Domain Multiple Access Scheme.415.2.2 OTFS-SCMA System Based on MemoryApproximate Message Passing(MAMP)Algorithm.455.3 OTFS-Empowered Integrated Sensing and Communication(OTFS-ISAC)Scheme.515.3.1Advantages of OTFS-ISAC Scheme.515.3.2 OT

6、FS-ISAC Waveform Design.526.Evolution Schemes for OTFS.556.1 New Delay Doppler Domain Multicarrier Modulation Scheme.556.2 Fusion Frame Structure Design of OTFS and OFDM.577.Summary and Outlook.62References.64Participant Units.662/661.IntroductionOrthogonal frequency division multiplexing(OFDM)is a

7、widely used modulationtechnique in wireless communication systems such as 4G,5G,and WiFi.OFDM based oncyclic prefixes can effectively deal with multipath fading and only requires low-complexityfrequency domain equalizers.With the development of wireless communications,high-speedmobile communication

8、scenarios in complex scattering environments are becomingincreasingly abundant,such as IoV,high-speed railways,and low-earth orbit satellitecommunications.These communication scenarios have already or will greatly change peopleslifestyles.However,OFDM under high-speed mobility will lose subcarrier o

9、rthogonality dueto the influence of Doppler spread,and its transmission reliability will deteriorate.Therefore,it is important to design new multicarrier modulation schemes for high-speed mobilescenarios in the next generation of mobile communication systems.In recent years,researchers have proposed

10、 the orthogonal time frequency space(OTFS)multicarrier modulation technology.Different from OFDM technology,OTFS performsresource mapping in the Delay Doppler(DD)domain,and based on the sparsity and stabilityof the DD domain channel,it can achieve higher data transmission reliability than OFDMunder

11、high-speed mobile conditions.To investigate the basic principles,research and application status,and futuredevelopment prospects of OTFS,and to provide technical references for industry andacademia,this white paper will introduce OTFS from the following six aspects:(1)Basicprinciples of OTFS;(2)Char

12、acteristics of DD domain channels;(3)Transmission waveformdesign of OTFS;(4)Receiver scheme design of OTFS;(5)Multi-antenna,multi-user,andintegrated sensing and communication schemes empowered by OTFS;(6)Evolution schemesfor OTFS.1.1 Document StructureChapter 1 is the introduction,which introduces t

13、he scope and structure of this whitepaper,and introduces the application scenarios of OTFS,pointing out the needs andchallenges brought by high-speed mobility in such scenarios,thus leading to the necessity ofOTFS technology research.3/66Chapter 2 describes the basic design principles of OTFS,includ

14、ing the introduction oftwo OTFS modulation implementation methods,SFFT and DZT,and a brief description ofthe transceiver scheme.Chapter 3 analyzes the channel characteristics of the Delay-Doppler domain,andanalyzes the sparsity,compactness,stability,and separability of the Delay-Doppler domainchanne

15、l for high-speed mobile scenarios such as high-speed railways.Chapter 4 introduces the design of the OTFS receiver,including the pilot design oflow-PAPR channel estimation,OTFS channel estimation under non-integer grids,andlow-complexity OTFS data detection scheme based on expectation propagation.Ch

16、apter 5 introduces OTFS-empowered multi-antenna,multi-user,and integratedsensing and communication schemes,including the system design of MIMO-OTFS,grant-free multiple access schemes for high-speed mobile scenarios such as satellites andhigh-speed railways for massive machine type communications,and

17、 performance analysis ofintegrated sensing and communication system design based on OTFS.Chapter 6 introduces the evolution schemes for OTFS,including the joint frame structuredesign of OFDM and OTFS that is forward compatible with OFDM,and a new type ofmulticarrier modulation scheme in the Delay-Do

18、ppler domain.Chapter 7 provides the conclusion and outlook.1.2 KeyApplication ScenariosHigh-speed railway scenario:For railways,continuously improving train speeds is acommon goal in global railway development.At present,the Beijing-Shanghai high-speedrailway has achieved a test speed of 470 kilomet

19、ers per hour,and the CR450,a 450 km/hhigh-speed train,will be completed in 2024.At the same time,the Central Japan RailwayCompany has achieved a test speed of 603 km/h for maglev trains in Yamanashi-ken,Japan.In addition,the pipeline flying car,which can reach a speed of over 1,000 km/h,is also unde

20、rdevelopment.Based on the high-speed development of railways,countries worldwide withdeveloped high-speed railway systems are focusing on the intelligence of high-speed railways.The intelligence development of high-speed railways requires advanced communication4/66systems and standards to provide su

21、pport,but the high-speed movement of trains inhigh-speed railway scenarios will pose a great challenge to the reliability of ground-to-trainand train-to-train communication.Low-earth orbit satellite scenario:Low-earth orbit(LEO)satellite communication is atechnology that uses satellites in low-earth

22、 orbit to achieve communication.Unlike traditionalhigh-earth orbit satellite communication,LEO satellite communication satellites are typicallylocated between hundreds of kilometers and two thousand kilometers from the ground.Compared with traditional geosynchronous orbit satellites,it has the advan

23、tages of low launchcost,low communication delay,low transmission loss,and seamless global coverage afternetworking,and has attracted the attention of many Internet,communication,and aerospacecompanies around the world.Air coverage scenario:With the progress of aviation communication,airplanes aretra

24、nsforming from the past isolated islands of information networks into key carriers forrealizing global interconnection.The emergence of in-flight Wi-Fi allows passengers toaccess the Internet on airplanes.However,the arrival of the 5G era has brought unprecedentedchallengestoair communicationthedema

25、ndfor massivereal-timeInternetdatatransmission.This challenge requires communication systems to be highly adaptive,andcapable of improving communication quality between airplanes and ground stations orsatellites in high-speed mobile environments,ensuring low-latency and high-reliabilitytransmission

26、of internet data.Internet of Vehicles:Based on the OTFS-ISAC mechanism,the following Internet ofVehicles functions or applications can be supported:Accurately sensing the surroundingdriving environment,including vehicles,obstacles,road conditions,etc.,to enhance drivingsafety and achieve intelligent

27、 driving;accurately sensing the positions and motion states ofboth receivers and transmitters,providing prior information for channel estimation,beamforming,etc.,to improve communication performance;distributed node collaborativesensing,expanding the range of node sensing,and enhancing the accuracy

28、and precision ofsensing.Underwater Acoustic Communication:The Smart Ocean project is a major projectrelated to the national strategy of building a maritime power,and with the advancement of the5/66maritime power and the construction of the Smart Ocean project,rapid development hasbeen achieved in va

29、rious fields such as modern fisheries,marine observation and monitoring,offshore oil and gas exploration and development,and marine transportation.Underwateracoustic communication is an important part of the marine communication network.Acousticwaves are currently the only effective long-distance in

30、formation transmission carrierunderwater.The under water acoustic(UWA)channel is a channel with fast time-varyingcharacteristics,large delay spread,serious Doppler effect,and limited available bandwidth.Incommon marine environments,multipath effects,Doppler effects,and environmental noiseexist durin

31、g the propagation of underwater acoustic signals,which makes it impossible for thereceiving end of the communication system to obtain correct channel information whendetecting signals.This brings great obstacles to the design of the communication system.Atthe same time,the phase fluctuations in the

32、channel make it very difficult for the receivingend to recover the carrier and perform coherent demodulation.The OFDM modulationtechnology widely used in UWA communication networks is easily affected by Dopplerspread,leading to severe degradation in system performance.How to achieve efficient datatr

33、ansmission in complex and variable mobile UWA communication scenarios is currently akey issue that needs to be addressed.2.Basic Principles of OTFSOTFS was proposed by R.Hadani et al.in 2017 2.1,and it was pointed out thatcompared with OFDM modulation,it could use the full diversity gain of the time

34、-frequencydomain to achieve better data transmission performance under high mobility 2.2.Accordingto the content of this chapter,it can be found that OTFS can be regarded as a precoded OFDMsystem,which has the potential to be compatible with OFDM systems.However,comparedwith the OFDM scheme that has

35、 been maturely applied in 5G NR,LTE,Wi-Fi,and otherprotocols,OTFS faces many new challenges,such as DD domain channel modeling,reliableDD domain channel estimation,low-complexity equalization,multi-antenna OTFS systemdesign,multi-user OTFS system design,OTFS-enabled communication-sensing systemdesig

36、n,etc.This section will briefly introduce the basic principles of OTFS modulation,withthe remaining content being elaborated in subsequent sections.This section mainly refers to6/66the literature 2.3.2.1 Principles of OTFS Modulation TransmitterFigure 2.1 Block Diagram of the ISFFT-based OTFS Transm

37、itterFigure 2.1 shows the block diagram of the ISFFT-based OTFS transmitter.Consider thesystem bandwidthM fand time durationNT,whereMis the number of subcarriers,fis the subcarrier spacing,Nis the number of slots,andTis the slot duration.1Let,0,1,DDXk lkNl0,1M represent the QAM modulated symbolmappe

38、d on the DD grid,OTFS modulation first uses the Inverse Symplectic Finite FourierTransform(ISFFT)to map the DD domain symbols,DDXk lto the TF grid to obtain,TFXn m:211001,nkmljNMNMTFDDklXn mXk l eNM(2-1)where0,1,0,1nNmM.The discrete resource grid relationship between theDD domain and the TF domain i

39、n the equation(2-1)is shown in Figure 2.2.1Note that unlike OFDM,which only considers multicarrier data for one symbol time,OTFS considersmulticarrier network packets with a period of.7/66Figure 2.2 Resource Grid Relationship between DD Domain and TF DomainFigure 2.3 IDZT-based OTFS TransmitterSubse

40、quently,the time-frequency domain signal,TFXn mis embedded with a CP andtransformed into the time domain signal s tthrough wireless channel transmission usingthe Heisenberg transformation as follows:11200,NMjm f t nTTFtxnms tXn m gtnT e(2-2)where()txg tis the transmit pulse shaping filter.Based on t

41、he above content,it can be foundthat the ISFFT-based OTFS system can be compatible with the OFDM system and thecorresponding time-frequency domain signal processing methods.Additionally,the OTFStransmitter can also be designed based on the Inverse Discrete Zak Transform(IDZT),andthe transmitter bloc

42、k diagram is shown in Figure 2.3.8/662.2 Principles of OTFS Modulation ReceiverFigure 2.4 OTFS Waveform Receiver Block DiagramFigure 2.4 shows the block diagram of the SFFT-based OTFS receiver(The blockdiagram of the OTFS receiver based on DZT is analogous to Figures 2.3 and 2.4 and istherefore not

43、elaborated here).The Delay-Doppler domain channel spreading function isrepresented as,hv,where andvrepresent the delay and Doppler,respectively.Thenthe received signal r tcan be represented as(ignoring noise for simplicity):2,jv tr thv s ted dv(2-3)Note that there are usually only a few reflectors i

44、n the channel,so,hvexhibitssparsity and can be represented as2:1,Piiiihvhvv(2-4)wherePis the number of propagation paths,ih,i,andivrepresent the path gain,delay,and Doppler shift of thei-th path,respectively,and()represents the Dirac delta function.The delay and Doppler taps of thei-th path are expr

45、essed as follows:iilM f,iivvikKvNT(2-5)Since the delay resolution1M fis usually small enough,ilcould be regarded as aninteger;the Doppler resolution1NTis usually limited,soivkis used to represent its integerpart and0.5,0.5ivK is used to represent its fractional part.At the receiver,thetime-frequency

46、 domain signal obtained through the Wigner transform is represented as:2Channel characterization under high-speed movement conditions will be introduced in detail in Chapter 3.9/66,TFt nT fm fYn mY t f(2-6)where0,1,0,1nNmM,2*,rxjf ttgrrxY t fAt fgtt r t edt(2-7),rxgrAt frepresents the time-frequency

47、 domain signal(cross-ambiguity function)obtained by matched filtering.Substituting Equations(2-1)to(2-3)into Equation(2-6)yieldsthe input-output relationship of OTFS in the time-frequency domain as follows:11,00,NMTFn mTFnmYn mHn mXn m(2-8)where,n mHn mrepresents the equivalent channel considering i

48、nter-subcarrierinterference and inter-symbol interference(ISI):,rxtxn mggHn mhv Ann Tmmfv 22jv mfn n Tjvn Teed dv(2-9)It can be found that,n mHn mis affected by the transmitting pulse,channelresponse,and receiving pulse.Finally,TFYn mis converted to the DD domain throughthe SFFT operation to obtain

49、the received signal,DDYk l:211001,nkmljNMNMDDTFklYk lYn m eNM(2-10)For ideal transmitting and receiving pulses,the following input-outputrelationship holds:11001,NMDDDDklYk lXk l hkk llNM(2-11)10/66where.,.his the sampled version of the impulse response function:,k kl lvNTM fhkk llhv(2-12)For,hvis t

50、he circular convolution of the channel response and thewindow function SFFT in the time-frequency domain:2,jvhvhvvved dv (2-13)11200,NMjvnTm fnmve(2-14)2.3Analysis of Input-Output Relationship in OTFSAccording to equation(2-11),it can be found that the received signal,DDYk lis alinear combination of

51、 all transmitted signals,DDXk l.Considering the sparsity of,hvin equation(2-4),equation(2-13)can be further expressed as:21,i iPjviiiihvh evv 21,i iPjviiiih eG v v F (2-15)where120,iMjmfimFe (2-16)120,iNjv v n TinG v ve(2-17)WhenllM f,iF will be further expressed as:11/66221201,1iiijl lljl llmMMimjl

52、 llMlleFeM fe (2-18)SinceiilM f,andilis usually an integer,then:,0,0,iMiMlllllFM f其他(2-19)where Mxrepresents the modulo operation on the integerM,that ismod,x M.Inaddition,ikkGvNTcan be expressed as:221,1vviivviijk kkKijk kkKNkkeGvNTe (2-20)It can be found that when0ivK,0ikkGvNT.This phenomenon intr

53、oducesinterferenceknownasDopplerInterference.Accordingtoequation(2-20),sin1,sinNkkGviNNTNcan be obtained.WheniivvkkkKN,sin1cossincos1sin11cossinsinNNNNNNNN(2-21)WhenNis large,1,ikkGvNNTwill decrease rapidly,indicating that Dopplerinterference mainly comes from adjacent DD domain resource grids.There

54、fore,we considerthat Doppler interference mainly comes from the neighboringiNgrid points.When,iNNk,iivi Mvi NkNkkkN,considering the derivation process above,DDYk lin equation(2-21)can be simplified as:12/6622211,viii iiiviijq KNPjvDDiDDvNMjk q KiqNNeYk lh eXkkqllNeN (2-22)Equation(2-22)indicates tha

55、t the received signal,DDYk lin the DD domain issignificantly affected by inter-symbol interference,and the equivalent channel in the DDdomain is difficult to be unitarily diagonalized.Therefore,compared to OFDM,OTFS willrequire higher equalization complexity.Additionally,according to the reference 2

56、.4,OTFSchannel estimation will introduce significant pilot overhead and result in a largerpeak-to-average power ratio(PAPR).On the other hand,compared to OFDM,OTFS usesfewer CPs(only one segment per frame),thereby improving spectral efficiency.Furthermore,OTFS has stronger resistance to Doppler freq

57、uency offset and multipath interference.Potential solutions to the challenges in OTFS channel estimation and equalization will beprovided in Chapter 4.3.Analysis of Delay Doppler Domain Channel Characteristics3.1 Characteristics of Delay Doppler Domain ChannelThe most significant feature that distin

58、guishes OTFS from traditional multicarriermodulation schemes such as OFDM is that it performs resource reuse,channel estimation,and data detection in the Delay Doppler domain.Therefore,the channel characteristics in theDelay Doppler domain play a crucial role in the research of OTFS schemes.This sec

59、tion willexplain the different representation forms,physical connections,and characteristics of theDelay Doppler domain channel.The main reference for this section is 3.1,and it onlyfocuses on the small-scale fading caused by multipath propagation of the channel,and doesnot consider large-scale fadi

60、ng characteristics such as shadow fading.3.1.1 Deterministic Description of ChannelsIn the Time-delay(TD)domain,wireless channels are typically characterized using13/66Channel Impulse Response(CIR).Denoting the CIR as,h t,consisting ofPtapswhere each tap is composed of several indivisible multipaths

61、,h tcan be expressed asfollows:1,Piiih th t(3-1)where ih tandirepresent the time-varying channel fading and delay of theitap,respectively,and1,2,iP,()represents the delta function.Under high-speedmobility conditions,ih tmay vary over time due to factors such as multipath fading,Doppler shift,etc.If

62、considering only the effect of Doppler shift,ih tcan be expressed as:2,ijvtiih the(3-2)whereihandivrepresent the fading and Doppler shift of the tap,respectively.Note thateach tap is composed of several indivisible multipaths,and in rich scattering environments,ihis typically modeled as complex Gaus

63、sian random variables with amplitude followingRayleigh distribution.In the Delay-Doppler(TD)domain,wireless channels can be characterized as Channelspreading functions(CSF).Denoting the CSF as,hv,and assuming that thetime-varying characteristics of the taps are solely caused by Doppler shift,the CSF

64、 can beexpressed in terms of CIR as follows:21,.Pjvtiiiihvh tedthvv(3-3)whereivrepresents the Doppler shift of the tap.In the Time frequency(TF)domain,wireless channels are characterized as ChannelTransfer Functions(CTF),h t f,assuming that the time-varying characteristics of the tapsare solely caus

65、ed by Doppler shift.The relationship between CTF and CIR is given by:14/662221,.iiPjv tjfjfiih t fh tedh ee(3-4)It can be seen that the CIR in the TD domain,the CSF in the DD domain,and the CTF inthe TF domain are mutually Fourier transform pairs.Particularly,if the number of tapsPisregarded as the

66、number of scatterers,and assuming that the systems delay and Dopplerresolutions are sufficiently small(network packet bandwidth and duration are sufficientlylarge),then under finite delay spread and Doppler spread,the CSF exhibits clear sparsity,separability,and compactness in the DD domain.3.1.2 Co

67、herent and Stationary Regions of ChannelsThe time-varying nature of the channel under high-speed mobility poses challenges foraccurate channel estimation.For CIR and CTF,the channel coherence time and coherencebandwidth are commonly used to approximately consider the channel as invariant.They canbe

68、approximated by the inverse of the channel Doppler spread and delay spread,respectively.For DD domain channel CSF,the channel smoothness time and smoothness bandwidth can beused to approximately consider the channel as statistically invariant,i.e.,satisfying theWide-sense stationary uncorrelated sca

69、ttering(WSSUS)assumption:*,E hv hvCvvv(3-5)where,Cvrepresents the channel scattering function,which denotes the average densityof the two-dimensional scattering function random process.According to reference 3.1,thechannels stationary time and stationary bandwidth are usually much larger than the ch

70、annelscoherence time and coherence bandwidth.Therefore,resource reuse based on CSFcharacteristics can potentially save the overhead of channel estimation under high-speedmobility conditions.However,it should be noted that the fadingihobserved for each tap at any givenmoment is a random variable rath

71、er than a deterministic constant,so it cannot be simplyassumed thatihis constant within the stationary time and bandwidth of the channel,as15/66stated in(3-5).Nevertheless,most current research still assumes the hypothesis that ihremains constant within the stationary time and bandwidth of the chann

72、el.To investigate thevalidity of this hypothesis,we conducted measurements and characterization of CSF inhigh-speed railway scenarios.3.2 Delay Doppler Domain Channel Characteristics in High-Speed RailwayScenarioAs a preliminary work,we characterized the channel spreading function of High-speedrailw

73、ay(HSR)channels based on channel measurements,and evaluated the performance ofOTFS in HSR 3.2.3.2.1 Channel Spreading Function Measurement System Based on LTE-RFirstly,we characterized the Channel spreading function(CSF)of the HSR channelbased on measured channel data from the LTE-R network on the B

74、eijing-Shenyang line.Thechannel measurement scenario is shown in Figure 3.1.Since it is challenging to transmitOTFS-modulated signals from HSR base stations,hvis difficult to obtain throughdirect measurement.According to the relationship between,hvwith CTF described in3.1,we first obtain the channel

75、 transfer function CTF and then transform it into the Channelspreading function CSF.In the measurement system,the carrier frequency iscf=465MHz,the subcarrier spacing isf=15 kHz,the OFDM symbol time length isT=66.7s,thenumber of subcarriers isM=300,and the number of OFDM symbolsNis determined bythe

76、measurement duration.The train moves at a speed of 371.1 km/h.As shown in Figure 3.1,the LTE-R base station continuously transmits LTE signals during the measurement.Twoomnidirectional antennas are connected to the Universal software radio peripheral(USRP)and placed outside the roof to collect downl

77、ink signals.Additionally,the USRP devices wereconnected to the Global Positioning System(GPS)to record the trains speed and position.Figure 3.2 shows the processing flow for obtaining the channel spreading function.Upon16/66receiving the signal,synchronization and channel estimation are performed fo

78、r 4 data streams,and 1 data stream is randomly selected to characterize the channel spreading function.Specifically,cell search and frame offset estimation are conducted based on the Primarysynchronization signal(PSS)and Secondary synchronization signal(SSS)for framesynchronization.Frequency synchro

79、nization is achieved based on the Cyclic Prefix(CP).Inchannel estimation,inter-subcarrier interference and inter-symbol interference(ISI)aretreated as noise.Finally,a two-dimensional Fourier transform is applied to the obtainedchannel transfer function(CTF)to derive the measured channel spreading fu

80、nction(CSF).Figure 3.1:High-speed Railway Channel Measurement System:(a)Schematic Diagram of theMeasurement System;(b)Viaduct;(c)Tunnel.The red circle and black arrow are used foremphasis,and the yellow lightning bolt represents the downlink signal.Figure 3.2 Measurement System for High-Speed Railwa

81、y Channel Spreading Function Basedon LTE17/663.2.2 High-Speed Railway Channel Spreading Function Characterization Basedon LTE-RBased on the channel measurement system described above,the number of channelmultipathsmN,the degrees of freedom of the channel spreading functionD,the squareroot of delay s

82、pread,and the square root of Doppler shift spreadvare shown in Table3.1 3.2.The measured channel spreading functions obtained in the high-speed railwayviaduct scenario are shown in Figure 3.3(a)and Figure 3.3(b).For comparison,Figure 3.3(c)and Figure 3.3(d)show the spreading functions generated by a

83、 Tapped Delay Line(TDL)model under the assumption of channel spreading function remains constant overNTperiod.This refers to the high-speed railway viaduct scenario channel TDL model proposedin 3.3.Table 3.1:Parameter Measurements of the Channel Spreading Function in Viaduct and TunnelScenarios18/66

84、Figure 3.3:Comparison of Channel Spreading Function in High-Speed Railway ViaductScenario and TDL-Based:(a)Normalized Power of CSF in Viaduct Scenario;(b)NormalizedPower Profile of CSF in Viaduct Scenario;(c)Normalized Power of CSF Based on TDLModel 3.3;(d)Normalized Amplitude of CSF Based on TDL Mo

85、del.The black circles inFigure 3(a)and Figure 3(b)indicate the positions of the effective multipaths.To show thesidelobes and mainlobes more clearly,Figure 3(b)only plots the effective multipaths withnormalized power greater than-55 dB.For more detailed descriptions of Figure 3.3,pleaserefer to 3.2.

86、As can be seen from Figure 3.3,the CSF measured in the high-speed railway scenario isnot as sparse and compact as the CSF function generated based on the TDL model.In fact,TDL is a simplified channel model.According to the reference 3.3,the modeling process ofTDL is as follows:First,the CIR is obtai

87、ned by performing the discrete Fourier transform onthe CTF;Second,the CIR is averaged over 20 wavelengths to mitigate the effects ofsmall-scale fading and obtain the Power delay profile(PDP);Subsequently,the peaks of thePDP are detected to obtain the delays of multipath,and the delays close toT,whic

88、h aregenerated by the discrete Fourier transform and lack clear physical significance,are ignored.Finally,the TDL model is established based on the detected multipaths.According to the above process,it can be observed that the TDL model ignoressmall-scale fading(including coherent and incoherent int

89、erference between indivisiblemultipaths,multipath fading,etc.)and the virtual taps generated by the discrete Fouriertransform.However,for OTFS that reuse data inNTtime duration,the impact ofsmall-scale fading(the variability of the random variableih)and the virtual taps generatedby the discrete Four

90、ier transform cannot be simply ignored.Based on the theoretical formulain reference 3.2(omitted here for brevity),the 12 sidelobes along the Doppler domain inFigure 3(a)and Figure 3(b)reflect the influence of inseparable multipaths.Based on the19/66measurement system in this paper,it can be determin

91、ed that the time-invariant duration of thechannel spreading function in the high-speed railway viaduct scenario is about12T 0.8 ms,which is greater than the CRS interval40.26T ms,much smaller than the systemnetwork packet length17NT ms and the widely used channel stationary time5.6ms.Therefore,when

92、designing an OTFS system,it cannot be simply assumed that ihremains constant within the stationary time and bandwidth of the channel.It should be notedthat this conclusion is based on channel measurements obtained from narrow-band LTEstandards,and such indirect CSF measurement methods may introduce

93、inevitable systemerrors.To more accurately characterize the channel characteristics of different scenarios,especially the temporal variations ofih,extensive CSF measurements and modeling workare still required.3.3 Performance Evaluation of OTFS in Measured ChannelsFigure 3.4:OTFS Modulation BER Perf

94、ormance under Different Equalization MethodsBased on the measured channel data,we evaluate the performance of MP detection andMMSE equalizer with perfect CSI under different channel conditions.The system bit errorrate(BER)under QPSK is shown in Figure 3.4.The parameter settings of the MP algorithmre

95、fer to 2.4.For comparison,the performance of MP detection in the EVA channelenvironment is shown,where the taps have integer delays and the channel spreading function20/66is assumed to be constant withinNT.First,according to the BER performance of OTFS and OFDM under MMSE equalization,it can be foun

96、d that OTFS and OFDM have similar performance in the low SNR region underdifferent data block sizes,but OTFS performs better in the high SNR region.This is becausethe single-tap equalization mode used by OFDM performs poorly when the channel is deeplyfaded,which is more obvious in the high SNR regio

97、n.In addition,comparing theperformance of OTFS under64MNand32MN,it can be found that OTFSperforms better when the data block is larger,that is,the delay and resolution are larger.Thisis because the fractional Doppler and virtual taps generated by the discrete Fourier transformwill cause inter-delay

98、and inter-Doppler interference,which leads to performance degradation.However,with the increase of channel resolution,the full diversity gain of OTFS dominatesthe equalization performance.However,the performance of MP detection under the measured channel is worse thanthat in 2.4.This is because the

99、MP detection algorithm relies on the sparsity of the channelspreading function.According to the characteristics of the measured channel spreadingfunction shown in Table 3.1,due to the influence of fractional delay,discrete Fouriertransform,and small-scale fading,the CSF in the band-limited system is

100、 no longer as sparseas the channel generated by the EVA model.In fact,the performance of MP detection ishighly dependent on the structure of the Tanner graph.The girth of the factor graph inreference 2.4 is 4,which will lead to performance degradation when the number of virtualtaps is large.At the s

101、ame time,in the band-limited system,the number of virtual taps willincrease when increases,which will increase the complexity of MP detection.Inaddition,the complexity of MMSE equalization is33()O M N,which will also produce alarge computational overhead for practical systems.Based on the performanc

102、e evaluation of OTFS in real high-speed railway scenarios,thefollowing challenges caused by the degradation of sparsity and compactness of CSF are listed.First,it is necessary to model the time-invariant interval of CSF under different scenarios,toset reasonable OTFS block size and frame structure a

103、ccordingly.Second,band-limited OTFSmodulation systems require low-complexity and high-reliability channel equalization schemes.21/66Under the influence of time-domain channel small-scale fading,fractional Doppler shift,andfractional delay,the real channel extension function is no longer sparse.There

104、fore,MP datadetection needs to be improved by designing Tanner graphs with longer girth.MMSEequalization needs to be improved by reducing complexity.Third,it is necessary to studylow-cost and high-precision channel estimation schemes.The embedded pilot-aided channelestimation scheme is sensitive to

105、CSFs that are not compact enough to be affected bysmall-scale fading.To ensure high channel estimation performance,the correlation betweenmultipaths can be used to estimate physical multipaths instead of sampling multipaths.4.OTFS Channel Estimation and Data Detection4.1 Pilot Design for Low-PAPR OT

106、FS Channel EstimationThis section focuses on the design of low-PAPR OTFS channel estimation schemes.Currently,the classic channel estimation scheme for OTFS is the embedded pilot-aidedscheme proposed in 2.4.When only data symbols are included,the PAPR of the OTFSmodulated time-domain waveform is sim

107、ilar to that of the OFDM system,which is caused bythe power fluctuation of the transmit samples caused by IDFT.However,if the single-pointpulse pilot design with power enhancement in 2.4 is adopted,the PAPR of the OTFStime-domain waveform will be significantly increased,which will bring difficulties

108、 tohardware design.Similar to the previous section,consider the time-delay Doppler domain resource grid ofMN.To carry out channel estimation,data,pilots and guard symbols will be mapped atthe same time.To ensure the detection performance of single-point pulse pilots,the pilottransmit power is genera

109、lly enhanced during system design,and the empirical value isgenerally tens of dB.The disadvantage of this pulse is that the total power of the row wherethe pulse is located is very large,while the total power of the row where the pilot guardsymbol is located is very small.Therefore,after OTFS modula

110、tion,the power distribution ofthe time-domain samples will be uneven.22/66Figure 4.1 Formation of OTFSTime-Domain WaveformFigure 4.2 Time-Domain Waveform ofPulse Pilot Fluctuates ViolentlyFor OTFS systems using pulse pilots,some pre/post-processing methods can be used toaverage the power of the high

111、-power part into the entire waveform to achieve the purpose ofreducing PAPR.For example,for OTFS implemented based on OFDM,we first use theISFFT transform to map the pilots and data in the Delay Doppler domain to theTime-frequency domain.Then,we scramble the symbols in the time domain using sequence

112、s,and the scrambled symbols are sent as samples of time-domain waveforms by applying IDFTto the symbols.The process and results are shown in Figures 4.3 and 4.4,respectively.Figure 4.3 Schematic Diagram ofTime-Frequency Domain Scrambling toReduce PilotFigure 4.4 The Effect of Scrambling toReduce PAP

113、RThe above methods can effectively reduce PAPR,but they increase the complexity of thesystem in two aspects.One is the computational complexity caused by the additionalscrambling and de-scrambling processing.The second is the additional complexity of23/66cross-domain transformation.This is because t

114、he scrambling and de-scrambling at thetransmitting and receiving ends both need to transform the signal to the time-frequencydomain for processing,so it is difficult to adopt the simplified OTFS implementation usingthe ZAK transform.Therefore,we can reduce the PAPR problem of OTFS time-domainwavefor

115、ms by designing pilots.The high PAPR of OTFS modulation with pulse pilots is caused by the uneven powerdistribution of each row in the delay dimension.We can replace the pilot pulses with pilotsequences with the same total power,and the power of each element in the pilot sequence isequal.The placeme

116、nt of the pilot sequence is spread along the delay dimension,whichensures that the total power of each row in the delay dimension is the same.Aftertransforming to the time domain signal,its PAPR is maintained at a low level.The diagram ofthis method is shown in Figure 4.Figure 4.5 Balancing the Tota

117、l Power of Each Row in the Delay Dimension Using SequencePilotsDue to the double convolution property of the Delay Doppler domain channel,thetransmitted sequence appears as a Doppler offset and a cyclic shift corresponding to thechannel delay at the receiver side in the Delay Doppler plane.Therefore

118、,from the perspectiveof sequence detection,we need to select sequences with high autocorrelation and low mutualcorrelation with their own cyclic shifts,such as M sequences.The sequence pilots in thissection cannot use traditional power detection for channel estimation.We can use the slidingcorrelati

119、on operation of the sequence to estimate the delay and Doppler of the signal.As24/66shown in Figure 4.6.Figure 4.6 Detection of Sequence Pilots in the Delay Doppler DomainFigure 4.6 shows the channel estimation process,which can be divided into two mainsteps:path identification and channel coefficie

120、nt estimation.Path Identification:By utilizing known pilot sequences and performing column-wisecyclic shifting correlation operations with the received Delay Doppler domain signals,peaksare determined using preset thresholds.The positions of these peaks indicate the delay andDoppler of the signals.E

121、ach delay and Doppler pair represents a path in a multipath channel.Channel Coefficient Estimation:Using the delay and Doppler information obtained inStep 1,we can determine the cyclic shifts of the pilot sequences and the offset values in theDoppler dimension.If there is only one received pilot seq

122、uence on a column in a certainDoppler dimension,we can use point-wise division to obtain the channel coefficients.Ifmultiple received pilot sequences are aliased in a Doppler dimension column,we canconstruct linear equations based on the deterministic superposition relationship derived fromthe known

123、 delay and Doppler information,and then use the least squares method to solve forthe channel coefficient of each path.The sequence pilot proposed in this section shows significant advantages in PAPRperformance.In the results shown,all PAPR samples of the proposed scheme are below 9 dB,and about 2%of

124、 the samples are between 5 dB and 9 dB.This result is even slightly lowerthan the OTFS time-domain waveform with only data symbols,which is used as the baseline.In contrast,in the time-domain waveform of traditional pulse-pilot OTFS,more than 2%of25/66the simulation samples have PAPR between 5 dB an

125、d 17 dB.Figure 4.7 PAPR Performance of theProposed MethodFigure 4.8 NMSE Performance ComparisonAdditionally,the extension of pilots to various symbols in the delay dimension in theproposed scheme results in a slight enhancement of channel estimation accuracy at high SNRs.As shown inFigure 4.8,in ter

126、ms of channel estimation accuracy measured by NMSE,theNMSE of the proposed method surpasses that of pulse pilots at SNRs above 6 dB andapproaches zero at SNRs above 15 dB.This trend is also reflected in the error rate curvesshown in Figure 4.9.Figure 4.9 Bit Error Rate Performance ComparisonWhen ana

127、lyzing the PAPR of OTFS waveforms,we cannot ignore the incremental PAPRproblem caused by the pilot design.For pulse pilots,some pre-processing or post-processingmethods need to be used for PAPR reduction.Additionally,sequence pilots can also be usedto reduce PAPR.26/664.2 Off-grid Channel Estimation

128、 for OTFSThis section focuses on proposing an off-grid channel estimation algorithm for OTFSwith rectangular waveforms in the presence of fractional delay and Doppler.Since thebandwidth and duration of an OTFS signal frame are always limited,the corresponding delayand Doppler resolution in the DD gr

129、id are also limited.Therefore,continuous-valued delayand Doppler shifts in the physical channel may not fall on integer grid points in the DDdomain.This phenomenon is called off-grid delay and Doppler.The presence of off-griddelay and Doppler leads to a reduction in the performance of channel estima

130、tion methods thatrely on the sparsity of the effective channel.To address this challenge,we first derive theclosed-form Delay Doppler domain input-output relationship considering off-grid factorsunder rectangular pulses.We find that the factors of delay and Doppler under rectangularwaveforms cannot

131、be directly decoupled,so the existing low-complexity channel estimationalgorithms for the dual fractional case fail.Finally,a high-precision channel estimationalgorithm GESBI 4.1 suitable for this scenario was proposed.Figure 4.10 Visualization of Grid Evolution ProcessThe idea of this algorithm is

132、to use Bayesian judgment based on the hierarchicalBayesian framework in the inner iteration to obtain the mean of the sparse vector to beestimated,as well as the fractional delay and fractional Doppler information.In the outeriteration,the dual fractional information and the known virtual DD domain

133、grid point are usedto perform grid evolution and update the delay and Doppler information of the27/66two-dimensional virtual grid point.After the outer iteration,the virtual DD domain grid pointexhibits a non-uniform distribution and becomes closer and closer to the delay and Doppler ofthe actual ch

134、annel.This non-uniform distribution reduces the approximation error in thefirst-order approximation process and improves the accuracy of channel estimation.Visualization of the grid evolution process is shown in Figure 4.10.Assuming there arefour paths in the channel,all exhibiting dual fractional d

135、istributions in the DD domain asshown in(a),after 2,5,and 10 iterations of grid evolution,the distributions of the virtualtwo-dimensional DD domain grid points correspond to(b),(c),and(d),respectively.It can beseen that the distribution of the two-dimensional virtual grid points is no longer uniform

136、 andtends to be closer to the actual positions of the DD domain in the channel.Figure 4.2.2compares the channel estimation accuracy of the OGSBI,ESBI,GESBI,and ESBI+GEalgorithms.It can be seen that the proposed GESBI algorithm has better accuracy than thecompared algorithms.Figure 4.11 Comparison of

137、 ChannelEstimationAccuracyFigure 4.12 Comparison of Doppler ShiftEstimationAccuracyFor OTFS systems,if the bandwidth is sufficient,the delay in the DD domain channelcan usually be considered as integers.In this case,channel estimation only needs to considerthe Doppler domain spread caused by fractio

138、nal Doppler shift.For DD domain channelestimation where both delay and Doppler are integers,a classic algorithm is the channelestimation algorithm based on Orthogonal Matching Pursuit(OMP)4.2.The core idea is tocontinuously find the sequence with the largest correlation with the known pilot sequence

139、from the received signal.When Doppler cannot be regarded as an integer,due to the off-gridphenomenon,the sequence with the largest correlation with the known sequence is no longer28/66aligned with the integer grid points.A natural extension is to use the Newtonized OMP(NOMP)method,which uses gradien

140、t descent and other algorithms to find the sequence withthe maximum correlation on continuous variables 4.3.However,this algorithm requires a lotof iterative calculations.To achieve low-cost and high-precision fractional Doppler shiftestimation,a channel estimation algorithm based on the least squar

141、es method is proposed4.4.This algorithm utilizes the characteristics of the Doppler domain channel off-grid andtransforms the problem of solving fractional Doppler into a linear fitting based on the leastsquares(LS).This algorithm only uses part of the pilot symbols in the Doppler domain andhas a lo

142、wer computational complexity.Figure 4.12 compares the performance of severalDoppler estimation algorithms.It can be seen that the NOMP algorithm can reach theCramr-Rao Lower Bound(CRLB),and the LS-based algorithm can gradually reach theperformance of the Maximum Likelihood(ML)estimation,which is onl

143、y 1 dB different fromthe CRLB.4.3 Low-Complexity OTFS Data Detection Scheme Based on ExpectationPropagationThis section introduces a low-complexity and high-precision OTFS symbol detectionscheme based on the Expectation Propagation algorithm of statistical inference.It utilizes thestructural charact

144、eristics of the time-domain equalization matrix to achieve an effectivetrade-off between computational complexity and symbol detection performance.For theperformance degradation of the traditional message passing(MP)algorithm under fractionalDoppler shift and continuous Doppler spread,we find that e

145、xpectation propagation(EP)canovercome this problem.A low-complexity EP detection is proposed below,which utilizes thequasi-band structure and the sparsity of the submatrix to reduce the complexity of invertinglarge-scale matrices 4.5.DD domain OTFS symbol detection algorithm based on expectation pro

146、pagation:assuming a real-valued OTFS systemyHxn(4-1)29/66In the equation,y,x,n,andHrepresent the real-valued Delay-Dopplerdomain received symbols,transmitted symbols,equivalent noise,and equivalentchannelmatrix,respectively.Theposteriorprobabilitydistributionofthetransmitted symbol vector is express

147、ed as follows:21221();,i ii iKxxKiqexy HxIN(4-2)In the equation,iand0iare real constants.After derivation,the posteriordistribution of the symbol follows a Gaussian distribution,with the mean vectorand thecovariance matrixexpressed as follows:12diag H H(4-3)2H y(4-4)In the equation,T12,K,T12,K,and D

148、D-domain equalizationmatrixDD are defined as follows:2DDdiagH H (4-5)Expectation propagation will recursively update the prior parameter pair,ii toupdate the transmitted symbol.In a single EP iteration,the covariance matrixisrecomputed based on the updated prior parameters.The block-cyclic structure

149、 and quasi-bandsparse structure of the matrixH Hcan be used to reduce the computational complexity ofthe covariance matrix.Since the elements of in EP detection are not the same,the matrixis no longer block cyclic,so it is necessary to explore the structure of the equalization matrixin other transfo

150、rm domains to reduce the complexity of EP detection.Low-complexity cross-domain expectation propagation symbol detection algorithm:Thereal-valued time-domain system model is as follows:30/66THrsn(4-7)In the equation,r,s,andnare the real-valued received symbols,transmitted symbols,and time-domain noi

151、se,respectively;22TMNMNHis the real-valued time-domainequivalent channel matrix.The posterior probability approximation of the time-domaintransmitted symbol vector is as follows:21222T1();,i ii iMNssiq ser H sIN(4-8)In the equation,iandiare real constants.()q ssatisfies the Gaussian distribution,wit

152、h the mean vectorT and the covariance matrixT as follows:112TTTTTdiagH H (4-9)2TTTTH r(4-10)The matrixT is sparse and block quasi-band,and it can be reconstructed as follows:TABBAD(4-11)In the equation,22TTTT,AH HBH HandDare the elements of thediagonal matrix.The original high-complexity equalizatio

153、n matrix inversion in the DDdomain is transformed into a time-domain block quasi-band and sparse matrix inversionproblem.Finally,theequalizermathematical expression isobtainedby usingthenon-Gaussian symbol set constraint in the DD domain and the sparse block quasi-bandtime-domain equalization matrix

154、 inversion.Figure 4.13 compares the performance of different detectors under 16-QAM.It can beseen that the proposed EP scheme outperforms MMSE,cross-domain,MP,AMP-EP,and31/66Rake detectors.In addition,the performance of the proposed low-complexity EP is almost thesame as that of the EP without appro

155、ximation.Compared with the Rake detector and the 103level cross-domain detection,the proposed scheme achieves 2 dB and 3 dB performancegains,respectively.Figure 4.14 compares the number of complex multiplications of differentdetection schemes under different frame sizes.Compared with AMP-EP,the prop

156、osed schemehas lower complexity in small frames and higher complexity in large frames.In addition,compared with MP,MMSE,and Delay Doppler domain EP,the proposed scheme reduces thecomplexity by nearly two,three,and four orders of magnitude,respectively.Although Rakedetection can achieve lower complex

157、ity,the proposed scheme has better error performance.The proposed scheme achieves an ideal trade-off between performance and complexity.Figure 4.13 Performance Comparison ofDifferent DetectorsFigure 4.14 Comparison of the Number ofComplex Multiplications of DifferentDetectors5.Extension Schemes of O

158、TFS5.1 Multi-Antenna OTFS Scheme5.1.1 Pilot Design for MIMO-OTFSThis section discusses low-cost pilot design schemes for MIMO-OTFS systems.Takingthe single-user MIMO-OTFS system as an example,lets assume that the number of antennasat the transmitter and receiver ends are respectivelyRNandTN.The syst

159、em model isshown in Figure 5.1:32/66Figure 5.1 MIMO-OTFS System ModelHere,(1,2,)TDD nTTnNXrepresents the symbols transmitted by the transmitantennaTnin the Delay-Doppler domain.The transmit symbols in the Delay-Dopplerdomain can be considered as aMNgrid with a quantization interval of1M fand1NTinthe

160、 time and Doppler dimensions,respectively.,(1,2,)RDD nRRnNYrepresents thesignal received by the receiving antennaRn,and,RTnnHrepresents the transmissionchannel between the antenna pairs.Specifically,the channel between each transmit-receiveantenna pair can be expressed as follows:1,R TR TnnR TR TR T

161、n nn nPppn nn npplkhvhvM fNT (5-1)whereR Tn nphrepresents the channel of theppath between the antenna pair,RTn n.Thecorresponding channel delay ismaxR TR Tn npn npllM fM fand the channel Doppler shift ismaxR Tn npkvNT.R Tn nplandR Tn npkrepresent the quantization indices of channel delay andDoppler,

162、respectively.maxlandmaxkrepresent the quantization indices corresponding tothe maximum delay and maximum Doppler shift value on the entire transmit channel,respectively.Based on the above system model,the input-output relationship of the systemcan be expressed as 5.1:33/66,11max2,exp2R TR TnnR TTRR

163、TTn nn nNPppDD nn npnpjkmlYm nhN Ml(5-2),TR TR TRDD nn nn nDD nppMNXmlnk(5-3)where,RDD nYm nand,TDD nXm nrepresent the elements in themrow andncolumn of the transmit matrix,TDD nXand the receive matrix,RDD nY,respectively.SymbolQrepresents the modulo operation ofQ.According to the input-output relat

164、ionship in the DD domain,for each symbol in theDelay Doppler domain,after channel transmission,there will be offset spreading in thelatency and Doppler domains.When the pilot signal is used for channel estimation,similarly,due to the influence of multipath and object motion,the transmitted pilot sym

165、bols will beoffset and spread at the receiving end.The offset is related to the maximum delay andDoppler of the channel,which will cause inter-symbol interference(ISI)and further affect thechannel estimation performance.To solve this problem,we can consider reserving a guard interval in the pilot de

166、sign toprevent interference between symbols.However,introducing a guard interval will reduce theamount of data transmitted,thereby reducing the transmission rate.In the multi-antennascenario,to measure the independent channels between multiple antennas,more pilot symbolsand guard intervals need to b

167、e placed.At this time,the impact on the transmission rate is moreobvious.Therefore,how to improve the transmission efficiency under the condition ofminimizing interference is one of the problems that need to be solved in the OTFS pilotdesign.One possible solution is to accurately design the pilot gu

168、ard interval according to themaximum delay and maximum Doppler value of the channel.Taking Figure 5.2 as anexample,assuming that the transmitted symbol in the Delay-Doppler domain is,aftertransmission,the received signal will be offset by at mostmaxlgrids in the positive directionof the delay axis a

169、t the receiving end,and at most maxkgrids in the Doppler axis.The offsetarea is shown by the red box in the figure.In order to avoid ISI,theoretically,for any pilot34/66symbol,it is necessary to reserve a protection interval of 2maxkin the Doppler dimensionand a protection interval of maxlin the del

170、ay dimension.Figure 5.2 Schematic Diagram of the Input-Output Relationship of the Signal in theDelay-Doppler DomainFigure 5.3 shows the pilot placement in a 44 MIMO-OTFS system.When there isenough space in the delay dimension to place all the pilots of multiple antennas(max1TTlNNM),the pilots can be

171、 placed along the delay dimension with aninterval ofmaxl.When there is not enough space in the delay dimension to place all the pilotsof multiple antennas(max1TTlNNM),partial pilot symbols can be first placedalong the delay dimension with an interval ofmaxl,then leave a protection interval ofmax2kin

172、 the Doppler dimension,and continue to place the remaining pilot symbols along the delaydimension.35/66Figure 5.3 Schematic Diagram of Pilot Pattern in a 44 MIMO-OTFS System inDelay-Doppler domains.As mentioned above,by accurately setting the protection interval and the commonprotection interval,the

173、 effect of saving pilot overhead as much as possible can be achieved.Itneeds to be noted that accurate setting of the protection interval requires the knowledge of themaximum delay and maximum Doppler offset parameters of the channel.Taking the Doppleroffset parameter as an example,assuming that the

174、 quantized index of the known maximumDoppler offset of the channel ismax2k,and the quantized index value of the actualmaximum Doppler of the channel ismax1,2,3realk,the BER performance of the system datadetection is shown in Figure 5.4.When the known maximum Doppler value of the channel isgreater th

175、an the actual maximum Doppler value,its BER performance is the same as thatwhen the maximum Doppler value of the channel is accurately obtained,but the protectioninterval left at this time is also larger,and the transmission rate is lower;When the knownmaximum Doppler value of the channel is smaller

176、 than the actual maximum Doppler value,itwill cause mutual interference between the symbols in the DD domain,which will affect thechannel estimation and data detection performance.36/66Figure 5.4 System BER Performance(maxrealk)under DifferentActual Channel MaximumDoppler Offset Parameters(max2k)In

177、addition to the pilot pattern design,the pilot design for OTFS-based systems canconsider pilot sequence design to reduce signal interference and system PAPR.In addition,low-complexity optimization channel estimation algorithms can be considered to improve thechannel estimation performance of the sys

178、tem.For MIMO-OTFS systems,it is also necessaryto further consider the pilot design scheme in the multi-user-equipment scenario.5.1.2Low-ComplexityandLow-OverheadOTFSTransceiverBasedonMulti-AntennaArrayThis section introduces a low-complexity and low-overhead OTFS transceiver designscheme based on a

179、large-scale antenna array,which can achieve a 20-fold reduction incomputational complexity compared to the EP algorithm with approximately 25%overheadof the classical pilot patterns 5.2.System model based on multi-antenna array:Consider a high-speed mobile downlinktransmission system,where the base

180、station sends signals to the mobile user equipment.Alarge-scale uniform linear antenna array is configured in the direction of movement of thereceiver.A total of MN symbols,including pilot symbols,guard symbols,and informationsymbols,are multiplexed in the two-dimensional grids in the DD domain.With

181、out loss ofgenerality,we assume that the transmit power is normalized,and the time-domain signal s tis transmitted after the Inverse Symplectic Finite Fourier Transform and Heisenberg37/66Transform.We assume that the multipath channel from the base station to theireceivingantenna can be represented

182、as:,112cos,00,pdip qpQPjf tip qEpqh tei I(5-4)whereEis the total number of receiving antennas,the maximum Doppler shiftdfisdefined asdvf,vis the user equipments movement speed,is the carrierwavelength.The phase of the receiving antenna is represented as12,iEii I(5-5)where0.5makes each receiving beam

183、 of the uniform array have only one main lobe.The received signal can be expressed as follows:,112cos,00pdip qQPjf tip qpipqr tes tz t(5-6)where iz tis the circularly symmetric complex Gaussian noise on theireceivingantenna,and at a time point,it obeys the distribution20,CN.Since the Doppler shift i

184、sidentified by the DOA of each path,the beamforming at the receiving end is to obtain thereceived signal from the direction of interest while reducing the signal from other directions.This is achieved by spatial matched filtering beamforming.The steering vector of theuniform antenna array is represe

185、nted as cos,ijiEei I(5-7)where,T011,E .To scan all possible DOAs of multipaths,we preset the matching angle to be able to match all possible directions.Since the DD domainchannel is sparse,only a small portion of the branches can receive the desired signal.Weassume that there areBbranches that can r

186、eceive the desired signal.TheseBbranchesare obtained by selecting the amplitude of the received signal of all branches through athreshold.In addition,assuming that all angles of interest are in the setBbBbI,38/66define a one-to-one mapping function,bp q,whereBbIis in this function,andthe subscript,p

187、 qis mapped to the subscriptbof the identified path.Therefore,thereceived signal from directionbcan be expressed as follows:,102cos,1coscos2cos,0,11dp qip qbdp qEbibiijf tp qpbEjjf tp qpip qbr tr tEes tztees tE(5-8)where,Bp qb bI,the equivalent noise on pathbis represented as follows:101,.EbibiBiztz

188、 tbEI(5-9)For large-scale antenna arrays,interference from other directions can be ignored.Based onthis,the received signal on the pathbcan be approximated as follows:2,bjv tbbbbBr tes tztbI(5-10)For simplicity,we define,bp q,bp,bp q,and vbis the Doppler shift onthe pathb.In addition,we can represen

189、t the channel on thebidentified path using theDirac function as a signal containing only a single delay and a single Doppler shift as follows:,.bbbbBhvvvb I(5-11)Low-complexity detection algorithm:The low-complexity detection algorithm operates in theDD domain.The time-domain received signal br ton

190、pathbis first converted to thetime-frequency domain,bym n,and the received symbols are converted to theDelay-Doppler domain by the Symplectic Fourier transform.39/66112001,nkmlMNjNMbbmnyl kym n eMN(5-12)whereBbI,MlI,Nk I.The input-output relationship of the received signal onpathbin the time-frequen

191、cy domain is:11222001120221,1,.bbbbbbbbbbbbMlMjm mfvjvmfM fjnTvbbmMMjm mfvTM fbmM ljvmfTjnTvBMNym ns m neeeMs m neMeebmn III(5-13)The input-output relationship corresponding to the Delay-Doppler domain under therectangular waveform is deduced and expressed as follows:222,1,1,0,bbbNbbl l kjMNbbbbMNk

192、kbl l kjjNbMNbbbMNexllkkll Myl kNeexllkkllN(5-14)whereBbI,MlI,Nk I,bblMf,andbbkNTv.Based on the input-outputrelationship in the DD domain,the low-complexity data detection scheme consists of twoparts:compensation for delay,Doppler,and phase,and maximum ratio combining.First,thecompensation is perfor

193、med as follows:222,0,1bbbMbl llkjMNbbbbMNklkbjjM NNbbbbMNeyllkkll My l kNeeyllkkllN(5-15)whereBbI,MlI,Nk I.Then the estimation is performed as follows:10120,BbbbMNBbbyl kx l klkII(5-16)40/66In Figure 5.5,the BER of the proposed receiver and MP under channel estimationconditions at a speed of 500 km/

194、h is evaluated.In addition,the performance of the proposedscheme under two other pilot patterns is also evaluated.It can be seen that the proposedscheme outperforms the conventional OTFS MP detection under channel estimation error.Inaddition,the performance of the naive pilot pattern is worse than t

195、hat of the other two pilotpatterns,since the interference is caused by the non-orthogonality of the beamformer.Theproposed receiver achieves better error performance with lower pilot overhead,at the cost of alarge-scale antenna array.Figure 5.6 compares the BER of the proposed receiver and MP with a

196、nd without channelestimation.The number of receiving antennas for the proposed receiver is set to 128.It can beseen that the proposed receiver achieves better error performance than the conventional OTFSMP detection with estimated channel or even perfect channel knowledge.The deployment oflarge-scal

197、e antenna arrays provides such high spatial resolution that the two-dimensionalconvolution between the data symbols and the channel can be decoupled in each identifiedpath.Compared to MP,the proposed receiver leverages array gain to achieve superior errorperformance without relying on the Gaussian a

198、pproximation of interference.In addition,theperformance of the proposed receiver is almost the same at three speeds,demonstrating therobustness of OTFS.Figure 5.5 Performance Comparison of theProposed Receiver with Existing Schemesunder Different Pilot PatternsFigure 5.6 Performance Comparison ofDif

199、ferent Detection and Channel EstimationSchemes at Three Speeds41/665.2 MultipleAccess Technology Scheme Empowered by OTFS5.2.1 Orthogonal Time-Frequency Code Domain MultipleAccess SchemeWith the emergence of high-mobility massive IoT,multi-access scheme design based onOTFS modulation is a potential

200、research direction.To realize reliable access for massive userequipments,researchers have proposed non-orthogonal multiple access(NOMA)schemes,such as power domain NOMA and code domain sparse code multiple access(SCMA).In theNOMA scheme,non-orthogonal multi-user-equipment active state and data detec

201、tion schemebased on iteration are usually considered,which will not only increase the complexity of thereceiver but also easily cause error propagation.In addition,researchers have proposedgrant-free random access(Grant-free)schemes,which reduce the interaction between devicesand base stations compa

202、red to grant-based random access,thereby reducing access costs.This section introduces a low-complexity grant-free MA scheme based on orthogonaltime-frequency code space modulation,namely orthogonal time frequency code spacemultiple access(OTFCSMA).Specifically,the orthogonal code domain resource is

203、introduced into the OTFS modulation,and the user equipment identification and datadetection complexity of the grant-free system is reduced based on orthogonal sequencedetection.Secondly,due to the limited DD domain resolution and the influence of small-scalefading,the compactness of the channel spre

204、ading function will be further deterioratedcompared to the TDL model.To this end,OTFCSMA designs user equipment grant-freeaccess codes for multiple user equipment under weakly compact channels to improve the userequipment capacity and access reliability under weakly compact channels.5.2.1.1 Multi-Us

205、er-Equipment Codebook Design underWeakly Compact ChannelsIn OTFS modulation,the received signal can be regarded as a two-dimensional cyclicconvolution(ignoring noise)of the input signal and the equivalent channel.When thecompactness of the channel spreading function deteriorates,the data of multiple

206、-userequipment will be dispersed to more DD domain grids,and the inter-user equipmentinterference will become more significant.The number of user equipment that the system can42/66orthogonally access the data will be further reduced.To cope with this challenge in thegrant-free access mode,the follow

207、ing introduces an orthogonal spreading sequence-based,orthogonal spreading combination codebook suitable for multi-user-equipment transmission,as shown in Figure 5.7.Figure 5.7 Design of Orthogonal Spreading Combination for 3 User Equipments under 9Spreading SequencesThe numbers in Figure 5.7 repres

208、ent the serial number of DFT sequences,and thespreading factor is9q.If multiple-user equipment extends data along the latency domain,the length of the user equipment codebook isN,and the number of symbols mapped byeach user on each time delay axis isbandbqM.It can be found that the orthogonalspreadi

209、ng combination of each user equipment in the user equipment codebook is unique,andthe receiver can obtain the user equipment activation state information in the received signalby simple coherent detection according to the codebook.In addition,the orthogonal spreadingcombination is divided into pilot

210、 and data segments,which are used for channel estimationand data detection,respectively.It can be found that each user equipment in Figure 5.7 usestwo pilot segments.To ensure reliable channel estimation,it is necessary to ensure that thepilot segments of each user equipment can still guarantee orth

211、ogonal detection after beingaffected by the two-dimensional cyclic shift.Therefore,the maximum number of grant-freeuser equipments supported by the system is affected by the channel compactness.Toquantitatively characterize the compactness of the channel along the Doppler and latencydomains,the maxi

212、mum spreading of the significant taps of the channel along the time delayand Doppler domains are recorded asdelayRandDopplerR,1,2,delayRM,1,2,DopplerRN,respectively.Under different channel compactness conditions,the43/66system user equipment capacity can be quantitatively calculated,as shown in the

213、reference5.3.Figure 5.8 User Equipment Capacity of OTFCSMAunder Different Channel CompactnessConditions,100MN,10qFigure 5.8 compares the user equipment capacity of the OTFCSMA scheme and theorthogonal OTFS multi-access scheme based on the embedded pilot(EPA-OTFSMA)underdifferent channel compactness

214、conditions.The white squares represent the channelcompactness where the user equipment capacity of OTFS-MA is greater than that of theOTFCSMA scheme.It can be found that the user equipment capacity of OTFCSMA is greaterthan that of EPA-OTFSMA in most channel compactness conditions.This is becauseOTF

215、CSMAmakes additional use of the orthogonal code domain resource space to provide thesystem with freedom in managing inter-user-equipment interference.In particular,theadvantage of OTFCSMA in user equipment capacity is more obvious under the condition ofthe weakly compact channel spreading function.S

216、ince OTFCSMA adopts the design principle of orthogonal transmission when designinggrant-free user equipment transmission codebooks,this will limit the user equipment capacityof the system.To further expand the user equipment capacity,finite field redundant codes canbe used to sacrifice the user equi

217、pment transmission rate to improve the capacity.Specifically,each orthogonal spreading combination shown in Figure 5.7 can be converted into an elementof a finite field,and then the data redundancy fragment can be generated by using theredundant code generation matrix to further expand the system us

218、er equipment capacity.44/66Through this kind of idea,the power growth of user equipment capacity can be realized.Thespecific scheme is shown in the reference 5.3.5.2.1.2 PerformanceAnalysis of OTFCSMAFigure 5.9 BER Performance of OTFCSMAunder QPSK ModulationFigure 5.9 shows the BER performance of OT

219、FCSMA under QPSK modulation in ahigh-speed railway scenario.The simulation parameters are configured as12M,100N,10q,3delayRand5DopplerR.The performance of EPA-OTFSMA andOFDMA are shown as benchmarks.All schemes use MMSE equalizer,and the dotted linerepresents the BER of the scheme under ideal channe

220、l estimation.First,under this weakly compact channel condition,the user equipment capacity of theEPA-OTFSMA system is 2,while the user equipment capacity of the OTFCSMA is 6,whichis 3 times the user equipment capacity of the EPA-OTFCSMA system.This is one of theadvantages of introducing orthogonal c

221、ode domain resources into the OTFS scheme.Secondly,as shown by the dotted line in the figure,under the assumption of ideal channelestimation,OTFCSMA requires a smaller SNR to achieve the same BER as EPA-OTFSMA.The advantage of OTFCSMA in terms of SNR comes from the spreading gain of theorthogonal se

222、quence.When the spreading factor10q,its spreading gain is about 10 dB.Inaddition,under the assumption of ideal channel estimation,it can be found that theperformance of the OTFS-based scheme in the low SNR region is similar to that of OFDM,where deep fading dominates the BER performance of the two s

223、chemes.However,in the high45/66SNR region,the BER of EPA-OTFSMA and OTFCSMA are both better than OFDM.This isbecause OFDMs single-tap equalizer is more likely to cause transmission failures affected bydeep fading under high mobility.Finally,the BER of OTFCSMA is lower than that ofEPA-OTFCSMA in the

224、high SNR region.This is because OTFCSMA uses two-stage channelestimation,and the influence of noise during this period will cause estimation errors topropagate.AtpSNR=35 dB,the performance gain brought by the orthogonal spreadingsequence is reflected in OTFCSMA,which is about 10 dB higher than EPA-O

225、TFCSMA,which is the same as the ideal channel condition.It can be found that the OTFCSMA schemebased on orthogonal time-frequency code domain can not only bring greater system userequipment capacity under weakly compact channel conditions but also further improve thereliability of system transmissio

226、n based on the spreading gain of orthogonal spreadingsequence.5.2.2 OTFS-SCMA System Based on Memory Approximate Message Passing(MAMP)AlgorithmThis section introduces a low-complexity and efficient Memory Approximate MessagePassing(MAMP)detection algorithm designed for MIMO-OTFS SCMA systems.Thealgo

227、rithm reduces the receiver complexity by introducing a memory-matching filter andexploiting the sparsity of the OTFS channel matrix.The proposed MAMP detection algorithmonly requires a complexity that grows linearly with the system dimension and can achieve thesame performance as the Orthogonal/Vect

228、or Approximate Message Passing(OAMP/VAMP)detector.By adopting a vector damping scheme with closed-form expression,the proposedMAMP detection algorithm is more robust than the traditional GMP and EP detectors and hassignificant performance advantages.5.2.2.1 MIMO-OTFS SCMASystem ModelWe consider an u

229、plink MIMO-OTFS SCMA system,whereJindependent mobileuser equipments transmit signals to the base station simultaneously.The end-to-endinput-output relationship of thejuser equipment to theureceive antenna at the base46/66station in the Delay Doppler domain can be expressed as 5.411,010,P()(,),ujujPL

230、Nujuj ircsjuj iuj iuj ijMuj iNpiqYkhpTtkp q kXpkkq(5-17)whereP()rccan be equivalent to the raised cosine roll-off filter,1,1,0,uj iuj iuj iuj iuj iuj iuj iuj iuj il p kqplMNk l p q kl p kqk q klpN ,2,(,),uj iuj ikpjMNuj iuj ip ke,2,21,1uj iuj ijquj ijqNeqe ,2,.uj iNk kqjNuj ik q ke(5-18)The above fo

231、rmula can be further expressed as,ujujjyH x,where1,MNjujx y,MN MNujHis a sparse matrix.Therefore,the system input-output model of theMIMO-OTFS SCMAwe consider can be expressed as:,yHx(5-19)where12,MNJDUMNTTTTKUHHHHand112,TTTTUMNU.Forconvenience,we defineUMNMandMNJDKN.5.2.2.2 MemoryApproximate Messag

232、e Passing(MAMP)DetectorTo solve the detection problem with factor graphs,each factor nodeyis connected tomultiple variable nodes,1,2,/,ccMNJ Kx.We assume that the information updatedand passed between factor nodes and variable nodes follows a Gaussian distribution.Theimplementation of the Memory App

233、roximate Message Passing detection algorithm issummarized as follows(for a more detailed introduction,please refer to 5.5).The detailed47/66description of thetiteration is as follows:1)From factor nodeyto variable node,1,2,/,ccMNJ Kx:At factor nodey,wecan use the minimum mean square error criterion

234、to obtain the posterior estimate ofx:1()()(),ttHHttzHIHHyH(5-20)where2,/tt t.1()MNJDtKand,t trepresent the mean vector and variancepassed from the variable node at the(1)t iteration,respectively.We define()(1)()()tHtttttrIIHHryH,wheretis a relaxation parameter usedto ensure that the spectral radius

235、of matrixHttIIHHis less than 1.In addition,the optimized weight parametertcan be used to accelerate the convergence of theMemoryApproximateMessagePassing.WedefineHBIHH,soHtttBIIHH.Let1t,and(1)(0)r0,we can approximate to get(5-21)We defineHttAH B Hand,1,ttt iijj iitit,according to theorthogonality cr

236、iterion of 5.6,we can generate the estimated mean vector()()(),11tttit iitcrzafter orthogonal processing,where,11ttt iic,1trttaNAand,0,1,.,t tt it it iaitcait.Wefurtherexpresstheestimatedmeanvectoras1()()()()1/2,MNJDTTTTttttKMNJ Krrrr,where()1tDcr.After obtaining thecorresponding estimated variance,

237、t tand the optimal solution*1,the estimated mean()tcrand variance*,t ttare finally passed to the variable node,1,2,/,ccMNJ Kx.,()()()()(),11,t itttttHtHt iitt it it iiiFQzH rH ByA 48/662)From variable node,1,2,/,ccMNJ Kxto factor nodey:At each variable node,we can express the posterior estimated pro

238、bability as:()22()*,()()exp,tjctcjDcjt ttPPrxx(5-22)wherejjA,cKjMN.jAis the set containing the non-zero elements ofjA,andjis theDdimensional codeword injA.DcjPxrepresents the prior probability.Theposteriorprobabilityismappedto()(),1,2,ttccCN giiiD,where()(),jjttccjjgiPixA22()()().jjtttccjjciPigixAAc

239、cording to the Gaussian information merging criterion,the estimated mean and varianceare respectively expressed as:111*1,1,ttt tt(5-23)()()(1)1,1*,.tttcccttt ttgirii(5-24)Finally1(1)(1)(1)(1)12/,MNJDTTTTttttKMNJ K.3)Termination criteria of the algorithm:The MAMP detector will terminate when itconver

240、ges or reaches the maximum number of iterationsT.Finally,the transmitted symbolsare discriminated and the demapping of SCMA is applied to recover the transmitted bits ofeach user equipment.5.2.2.3 ComplexityAnalysisTable 5.1 compares the complexity of the proposed Memory Approximate MessagePassing(M

241、AMP)detector with Gaussian Message Passing(GMP),Expectation Propagation49/66(EP),and Orthogonal/Vector Approximate Message Passing(OAMP/VAMP).As can be seen,the proposed MAMP detector achieves comparable complexity to GMP and EP and has lowercomplexity than OAMP/VAMP.Table 5.1 Complexity Comparison

242、of Different DetectorsDetectorComplexityMemoryApproximateMessage Passing(MAMP)(23)(31)MNJDQUMN SSKBHOTExpectation Propagation(EP)2(6)MNJDQUMNS DS DQKHHOTGaussian Message Passing(GMP)(32)UMNS DQSHHOTOrthogonal/VectorApproximate MessagePassing(OAMP/VAMP)322(6)MNJDMNJDMNJDQUMNS DS DQSTKKK HHHO5.2.2.4 E

243、xperimental SimulationIn this section,we test the performance of the MAMP detection algorithm(representedas Memory AMP in the figures)in a MIMO-OTFS SCMA system.First,we investigate theconvergence of the MAMP receiver performance and the impact of the vector damping lengthon it.Figure 5.10 shows the

244、 BER performance of the MAMP algorithm with different vectordamping lengths as the number of iterations increases.It can be seen that the BER decreasesmonotonically with the number of iterations and converges within a certain number ofiterations.We also note that there is no significant improvement

245、in performance when thevector damping length3L.In our following simulations,we will use a damping length of3L and a number of iterations of6Tfor simplicity.50/66Figure 5.10 ConvergenceAnalysis ofMemoryApproximate Message Passing(MAMP)with Different Vector DampingLengthsFigure 5.11 Impact of Number o

246、f BaseStationAntennas and EigenvalueApproximation on BER PerformanceFigure 5.11 further tests the impact of eigenvalue approximation on the performance ofthe MAMP receiver with different numbers of antennas.It is clear that the MAMP detectorwith the approximate eigenvalue upper bound can achieve sim

247、ilar performance to that withthe accurate eigenvalue.This strongly validates the effectiveness of using this eigenvalueapproximation method in the MAMP detector.We also note that as the number of base stationantennas increases,the system BER performance improves due to the additional spatialdiversit

248、y.Figure 5.12 BER Performance of MemoryApproximate Message Passing(MAMP)under Different User Speeds and SystemSettingsFigure 5.13 BER Performance Comparisonof Different DetectorAlgorithmsFigure 5.12 shows the BER performance of the memory approximate message passing51/66detector at different user sp

249、eeds under different system settings ofMandN.Withincreasing user speed,the BER performance first improves slightly and then saturates afterexceeding 300 km/h,especially at high SNR.This is because OTFS modulation can resolvemore different Doppler domain paths at higher speeds,and therefore the perfo

250、rmance will beimproved.We also observe that the BER performance decreases with decreasingMandN,especially at higher SNR.This is due to the loss of diversity caused by the reducedresolution of the OTFS Delay-Doppler grid.Figure 5.13 compares the BER performance of the MIMO-OTFS SCMA system underdiffe

251、rent detection algorithms.To highlight the excellent performance of the proposedMemoryApproximate Message Passing(MAMP)algorithm,we also provide the performanceof the traditional Gaussian Message Passing(GMP),Expectation Propagation(EP),andOrthogonal/Vector Approximate Message Passing(OAMP/VAMP)algo

252、rithms as benchmarksin Figure 5.13.The results show that the performance of the traditional Gaussian MessagePassing(GMP)and Expectation Propagation(EP)detectors is very sensitive to the dampingparameter.Unfortunately,there is no effective damping solution for Gaussian MessagePassing(GMP)and Expectat

253、ion Propagation(EP)detectors at present.However,ourproposed MAMP algorithm has a closed-form damping solution,and even with alow-complexity matched filter,it can achieve similar performance to the OAMP/VAMPalgorithm,and outperform the Gaussian Message Passing(GMP)and ExpectationPropagation(EP)detect

254、ors.These analyses show that our proposed MAMP detector can bringpractical implementation advantages in terms of low complexity and good performance.5.3 OTFS-Empowered Integrated Sensing and Communication(OTFS-ISAC)Scheme5.3.1Advantages of OTFS-ISAC SchemeIn scenarios of high-speed mobility in the I

255、nternet of Vehicles,along with the distributedcoexistence of various radar and communication standards,time-frequency selective fadingposes serious inter-symbol interference(ISI)and high pilot overhead challenges forOFDM-based integrated sensing and communication mechanisms.Compared with the52/66exi

256、sting OFDM-based ISAC system,in terms of communication,OTFS-ISAC uses a unitarytransformation to expand user data symbols to all time-frequency domains,achieve fulldiversity of time-frequency domain channels,and improve transmission reliability.In addition,the signal is modulated and demodulated in

257、the DD domain,which can cope with thefrequency and time selective channels caused by high-speed mobility,and alleviate theinter-subcarrier interference caused by Doppler shift.In terms of sensing,the channelspreading function in the DD domain can reflect the specific scattering environment and haspo

258、tential sparsity and compactness.The delay and Doppler shift can reflect the distance andspeed of objects in the physical world,enabling OTFS to directly estimate the targets speedand distance in the DD domain,which facilitates the processing of radar signals.The accuracyof OFDM radar speed estimati

259、on decreases linearly with increasing vehicle speed,while thespeed estimation accuracy of OTFS is almost unaffected by the vehicles moving speed.Therefore,in high-speed mobile scenarios such as the Internet of Vehicles,OTFS radarmechanisms can achieve accurate distance and speed detection,and their

260、speed detectionaccuracy is significantly better than that of OFDM radar mechanisms.5.3.2 OTFS-ISAC Waveform DesignIn high-speed mobile scenarios,the orthogonality between subcarriers of traditionalOFDM waveforms is destroyed due to frequency selective fading channels,which seriouslyaffects the commu

261、nication performance in high-speed mobile scenarios.OTFS modulationwaveforms can effectively solve this problem,making OTFS a waveform suitable forintegrated sensing and communication in high-speed scenarios.The OTFS waveformmodulates symbol information onto the DD domain,where the parameters of del

262、ay andDoppler frequency offset are directly associated with the distance and speed of objectscapable of reflecting signals in the physical world.This makes the OTFS waveform highlysuitable for implementing ISAC.The input-output relationship in the DD domain of OTFS is11DDDDDDDD00,NMklYk lXk l Hk l k

263、 lZk l (5-26)whereDDYis the symbol matrix in the DD domain,DD,Zk lrepresents the equivalentnoise in the DD domain,andDD,Hk l k l represents the discrete channel in the DDdomain after sampling,that is53/662DD1,i iPjiiiiHk l k lhk l k l k l e (5-27)whereikandilrepresent the Doppler and delay indices o

264、f theipath,respectively(usually distinguished between integer and fractional order scenarios based on whetherikandilare integers or fractions),and,iik l k l k l is the sampling function.A.Downlink Communication Scenario Using Base Station Self-Transmitting andSelf-Receiving Sensing and ReceptionInsp

265、ired by pulse compression in radar signal processing,a parameter estimationalgorithm based on two-dimensional correlation operation is designed.This algorithm can beregarded as a special kind of pulse compression performed in both Delay and Dopplerdomains simultaneously.Firstly,the base station tran

266、smits the OTFS-modulated signal and receives the reflectedecho from the sensing target.When the Doppler and delay indicesikandilof theipathare both integers,the input-output relationship of the DD domain can be simplified to:DDDDDD1,PiiiiiNMiYk lhXkkllk l k lZk l(5-28)where Nrepresents the modulo op

267、eration ofN,iik l k lis the phase offset whenusing the rectangular pulse shaping filter,22,1,0,1iiMiiiiMNl lkjMNiiil lkk Mk kMjMNiellMk l k lell(5-29)Let the matrix after two-dimensional correlation beV,then the correlation coefficientsunder different delay and Doppler indices are11*DDDD00,NMNMnmV k

268、 lYn m Xnkm l(5-30)54/66Figure 5.14(a)DD domain receiving matrixDDY(b)two-dimensional correlation matrixVWe use an example to intuitively illustrate the effectiveness of the proposed algorithm.Inthis example,we assume that there are four targets(4P)in the sensing scenario,and thesymbols transmitted

269、in the DD domain symbol matrix are randomly generated and normalizedQPSK symbols.Assuming that the number of continuous-time slots and the number ofsubcarriers of each OTFS frame are both 32(32,32MN),and the delay and Dopplerindices of the four targets are 14.29,7,3.37,11.12 and 11.72,2,5.06,22.65 r

270、espectively.The DD domain receiving signal matrixDDYin this case is shown in Figure 5.14-(a),andthe correlation matrixVafter two-dimensional correlation(pulse compression)is shown inFigure 5.14-(b).As can be seen from Figure 5.14,since the data symbols overlap with eachother after passing through th

271、e time-varying channel,the matrixDDYbecomes very dense.After the two-dimensional correlation,the resulting correlation matrix is no longer dense.From this,4 targets can be distinguished,namely the 4 peaks in the correlation matrix.Bytaking the delay and Doppler indices corresponding to the 4 peak va

272、lues,the delay andDoppler frequency offset of the corresponding target can be obtained.The base station can utilize the results obtained from two-dimensional correlation toestimate the channel.Simultaneously,it can predict the channel state for the next frame ofdata transmission based on the estimat

273、ed channel information and embed the predictionresults into the next frame of data.In this way,the user equipment can demodulate the dataaccording to the channel prediction result from the base station,thereby improvingcommunication efficiency.B.Uplink Communication Scenario Using User-Equipment-Tra

274、nsmitting,BaseStation-Receiving Sensing ModeThe data signal sent by the user equipment to the base station is not known to the basestation.In the uplink communication scenario where the user equipment transmits and the55/66base station receives,it is impossible to perform target sensing by the two-d

275、imensionalcorrelation of the receiving matrix and transmitting matrix.Therefore,it is necessary todesign a new transmission scheme for the uplink communication scenario where the userequipment transmits and the base station receives.Figure 5.15(a)DD domain transmitting matrixDDX(b)DD domain receivin

276、g matrixDDYAs shown in Figure 5.15,landkrepresent the maximum propagation delay andDoppler frequency offset,respectively.By setting a pilot on the matrixDDXsent in the DDdomain(with a coordinate,plk),and adding guard intervals(elements represented bycircles in the figure,with a value of 0),channel e

277、stimation and target sensing can beperformed in the DD domain.According to the DD domain input-output relationship derived in the previous section,inthe DD domain receiving matrixDDY,when the matrix elementDD,Yk lis located in theguard interval(i.e.,ppkkk kkand,ppllll),andDD,0Yk l,it canbe considere

278、d that there exists a propagation path,and the delay index of the propagation pathispll,and the Doppler frequency offset index ispk k.By identifying all non-zeromatrix elements within the guard interval,the base station can obtain the delay and Dopplerfrequency offset of the sensing target,and calcu

279、late the corresponding distance and velocityof the target for OTFS.6.Evolution Schemes for OTFS6.1 New Delay Doppler Domain Multicarrier Modulation SchemeSince the proposal of OTFS technology in 2017,more and more researchers have56/66realized the need for additional consideration of Doppler domain

280、information and the designof multicarrier modulation systems for future high-speed mobile communication scenarios.Meanwhile,researchers have also realized that the OTFS scheme has design drawbacks,andOTFS technology is also evolving gradually.The following summarizes the progress in theevolution of

281、OTFS waveform design and OTFS schemes under wideband channels forreaders reference.From the perspective of engineering implementation,waveform design plays a crucialrole.One design approach in OTFS is to use N rectangular waveforms(or other waveforms)for multicarrier modulation after the signal in t

282、he Delay Doppler domain is converted to thetime-frequency domain.However,this approach is challenging to implement in engineering.Firstly,the frequency-domain extension of rectangular waveforms is infinite,making itimpossible to assume that the received signal is a narrow-band transmission signalsup

283、erimposed with noise,but rather a superposition of low-pass filtered transmission signaland noise.Since low-pass filtering will cause large distortion in the OTFS scheme,this willaffect the transmission performance of the OTFS scheme.Secondly,the N time-domainsymbols are discontinuous,which increase

284、s the out-of-band leakage into the transmissionchannel,further degrading the performance of the OTFS scheme.To address this challenge,researchers have proposed the Orthogonal Delay Doppler Multiplexing(ODDM)scheme 6.1and the Zak-OTFS scheme 6.2.It is worth noting that the ODDM scheme proposesorthogo

285、nal waveforms for Orthogonal delay Doppler multiplexing signals,considering bothDoppler and delay resolution.This waveform is not a single impulse,but a pulse traincomposed of multiple root-raised cosine waveforms.Therefore,the signal can be directlyconverted from the Delay Doppler domain to the tim

286、e domain for transmission aftermulticarrier modulation.Thus,ODDM provides orthogonal transmit/receive waveformssuitable for Delay Doppler domain multiplexing systems from the perspective of multicarriermodulation systems.The Zak-OTFS scheme also adopts a similar approach,but rigorousproof for bi-ort

287、hogonal waveforms has not yet been provided.In addition,OTFS modulationis a scheme for time-varying narrow-band channels in ground RF communications.On theother hand,under water acoustic(UWA)and ultra-wideband(UWB)communication systemsface wideband time-varying channels.Unlike narrow-band channels,w

288、here time contraction57/66or expansion due to the Doppler effect can be approximated by frequency shift,the Dopplereffect in wideband channels causes a frequency-dependent non-uniform shift across the entiresignal bandwidth.When the product of data frame duration and bandwidth is sufficientlylarge,t

289、he phase difference caused by the difference in Doppler shift on both sides of thefrequency band cannot be ignored.Additionally,the variation in channel delay caused byobject movement is also manifested during the data frame duration.Reference 6.3 considersa similar scenario,models the channel in th

290、e Delay Doppler domain,and proposes acorresponding channel estimation algorithm.Similarly,researchers have proposed amodulation scheme similar to the OTFSOrthogonal Delay Scale Space(ODSS)modulationschemefor handling wideband time-varying channels 6.4.In this process,researchersintroduced the concep

291、t of convolutions in the delay scale space,parallel to the distortedconvolution used in time-frequency space.The preprocessing 2D transformation from theFourier-Mellin domain to the delay scale space in ODSS plays a role similar to the InverseSymplectic Finite Fourier Transform(ISFFT)in OTFS.Compare

292、d to OTFS and OrthogonalFrequency Division Multiplexing(OFDM),ODSS improves the BER performance inwideband time-varying channels.6.2 Fusion Frame Structure Design of OTFS and OFDMIn the design of future integrated sensing and communication systems,both the compatibilitywith existing protocols and th

293、e performance constraints of sensing itself need to be considered.This paper proposes a new underlay sensing pilot signal design for ISAC in a communicationsystem based on OFDM.Traditional parallel ISAC systems can be divided into two categories:data-driven sensing and pilot-driven sensing.The latte

294、r exhibits better anti-interferenceperformance in multi-user equipment systems,and common pilot signals can achieve multi-stationsensing.A pilot-driven ISAC system consists of two main parts:sensing signals and data signals,which are typically multiplexed using Frequency Division Multiplexing(FDM)or

295、 Time DivisionMultiplexing(TDM)in traditional ISAC systems.In this section,we propose a new ISAC systemsimilar to Code Division Multiplexing,in which the sensing pilot signal and data share the sametime-frequency resources but are modulated and detected in different domains.This approach58/66offers

296、several advantages:Scalability:Overlapping sensing pilot signals can span multiple OFDM time slots andsubcarriers without affecting the parameter settings or resource allocation of the communicationsystem.It can accommodate various sensing requirements,and the complexity of sensingdetection is linea

297、rly related to the pilot dimension.Flexibility:The covered two-dimensional pilot can be sparse in the Delay Doppler domain toachieve specific goals such as energy efficiency or interference avoidance.In addition,it supportsmulti-antenna ports and allows the two-dimensional pilot to be multi-layered,

298、with each layercorresponding to an antenna for estimating the Direction of Arrival(AoA)/Direction of Departure(AoD).Quasi-orthogonality:The covered sensing pilot can be generated from a set of sequences tomaintain low cross-correlation with the data signal.It can be regarded as a code divisionmultip

299、lexing technique,where the power of the sensing and communication signals is projectedinto different subspaces through different codewords,thus avoiding mutual interference.Separability:Interference from the sensing pilot signal on the data can be mitigated byauxiliary information.First,the known ti

300、me-frequency domain sensing pilot can be used as part ofthereferencesignal(RS)forchannelestimation,thusmaintainingtheSignal-to-Interference-plus-Noise Ratio(SINR)of the RS.Second,after obtaining the ChannelState Information(CSI),the communication receiver can easily eliminate the interference of the

301、sensing pilot.The two-dimensional pilot signal proposed in this chapter draws on the idea of OTFS,wherethe generation and detection of its symbols are both performed in the Delay Doppler domain.Interms of transmission,it is converted to the time-frequency plane and multiplexed with OFDMdata symbols

302、before being sent.The sensing signals are covered under the OFDM data,allowingfor the sharing of time-frequency resources.In this framework,sensing detection is achievedthrough simple two-dimensional correlation,taking advantage of the favorable autocorrelationproperties of the sensing pilot.In the

303、communication part,the sensing pilot,as a known signal,canbe used for channel estimation and equalization to ensure optimal symbol detection performance.The covered sensing pilot exhibits good scalability by accommodating different delay and Dopplerresolution requirements without violating the OFDM

304、framework structure.Experimental results59/66demonstrate the effective sensing performance of the proposed pilot signal,with only a portion ofthe power shared from the OFDM data,while maintaining satisfactory symbol detection incommunication.The two-dimensional pilot can be constructed from two one-

305、dimensionalsequences with good autocorrelation and cross-correlation properties.Without loss of generality,we assume that12,Qa aaaandT12,pb bbbare two known sequences withgood autocorrelation properties,then we have:TT1,011tr.,0qqqqqQQQa aa a(6-1)TT1,011tr.,0pppppPppbbbb=(6-2)T1212,QpaaabbbCab=ba=bb

306、baaa(6-3),q pqpCab(6-4)whereT()represents transpose,()irepresents vector cyclic shift ofibits,()i jdenotesmatrix cyclic shift ofibits in the row direction andjbits in the column direction.represents Kronecker Product operation,and1q,1q.The design philosophy of the two-dimensional pilot signal follow

307、s the idea that the couplingeffect of the channel on the transmitted pilot signal occurs through a distorted convolutionmechanism in the Delay Doppler domain.Specifically,after being coupled by the channel,thereceived pilot signal exhibits periodic shifts in both the Doppler and delay dimensions,as

308、well asphase shifts caused by the baseband processing of the transmitted pulse.In addition,traditionalpilot designs in the Delay Doppler domain can lead to PAPR problems.To address this issue,wepropose a two-dimensional pilot design that disperses the pilot power across the entire DelayDoppler plane

309、,thereby reducing the amplitude variation of the time-domain samples.As shown inFigure 6.1.60/66Figure 6.1 Non-Orthogonal Superimposition of Sensing Pilot and User Equipment DataIn the structure shown in Figure 6.1,for the detection of the sensing pilot,we design anefficient detection algorithm base

310、d on cyclic shift correlation,which utilizes the two-dimensionalconvolution property of the equivalent channel in the Delay Doppler domain.The received signalis transformed to the Delay Doppler domain,and then hypothesis testing is performed with eachcyclic shift version of the local two-dimensional

311、 pilot.Finally,the delay and Dopplercorresponding to the sensing channel are obtained,and the distance and speed of the sensing targetare inferred accordingly.At the same time,based on the aforementioned pilot design and detection method,thecorresponding sensing Signal-to-Interference-plus-Noise Rat

312、io(SINR)can be calculated asfollows:01100010,LLiiiiillMNhZhh(6-5)where0i,0i,and0irepresent the inner product of the received Delay Doppler domainpilot with the cyclic shift versions of the local pilot,the inner product with the OFDM data,andthe inner product with the noise,respectively.The sensing S

313、INRZhere actually represents adistortion metric of the sensing signal.Experimental results show that due to the excellentperformance of the designed two-dimensional sensing pilot,its performance is not significantlyaffected by noise and interference,and it will not increase significantly with the si

314、ze of the sensingpilot.Therefore,theoretically speaking,the accuracy of sensing can be improved by simplyincreasing the size of the pilot,i.e.,increasingMandN.In the structure shown in Figure 6.2.1,for the detection of OFDM data symbols,we stillfollow the traditional processing flow of the OFDM syst

315、em that is,using the Demodulation61/66Reference Signal(DMRS)embedded in the OFDM symbol for channel estimation.At the sametime,we regard the corresponding sensing pilot as part of the equivalent DMRS,that is,theequivalent DMRS used for channel estimation is the sum of DMRS and co-located sensing pil

316、ot.Therefore,if the communication receiver has prior knowledge of the sensing pilot,the influence ofthe sensing pilot on the communication system can be reduced to a minimum while maintainingthe channel estimation accuracy of OFDM.Numerical results show that the proposed scheme,which introduces sens

317、ing pilot andnon-orthogonal multiplexing with communication data,does not affect the demodulationperformance of data when interference cancellation is employed at the receiver.This is reflected inthe channel estimation and symbol detection performance,which is basically unchanged,as shownin Figure 6

318、.2 and Figure 6.3.In Figure 6.2,we evaluate the channel estimation errorperformance in three cases:OFDM without sensing pilots,OFDM with sensing pilots usingequivalent DMRS,and OFDM with underlying sensing pilots using original DMRS.It can beseen that the first two scenarios have similar performance

319、s,both of which are better than the lastone.In Figure 6.3,we compare the symbol detection performance between pure OFDM andOFDM with the sensing pilot,and the results are basically consistent in terms of BER,whichdemonstrates the effectiveness of the proposed channel estimation and interference canc

320、ellationscheme.Figure 6.2 Performance of EquivalentDMRS and OFDM EstimationFigure 6.3 OFDM DemodulationPerformance is MinimallyAffectedDue to the good autocorrelation and cross-correlation properties of the designedtwo-dimensional sensing pilot,its sensing and detection performance is also minimally

321、 affected bythe OFDM data.As its frame structure and parameter set are decoupled from the OFDM62/66communication system,the sensing pilot can be flexibly scaled to adapt to different sensingprecision requirements,as shown in Figure 6.4.Considering the Doppler detection errorperformance,we observe a

322、significant decrease in estimation error asNincreases from 64 to512.This is consistent with our analysis of the sensing SINR,which shows that increasing the sizeof the pilot can suppress the distortion of the sensing detection.In addition,comparison resultsshow that linear interpolation based on pea

323、k power effectively improves Doppler estimationaccuracy in the Delay Doppler domain.Figure 6.4 Impact of Different Sensing Pilot Sizes on SensingAccuracy7.Summary and OutlookBased on the basic principle of OTFS,user equipments map data symbols to the DelayDoppler domain instead of the traditional Ti

324、me-Frequency domain.This allows userequipment data symbols to be spread over all time-frequency domains using unitarytransforms such as the Symplectic Finite Fourier Transform,achieving full diversity oftime-frequency domain channels and improving transmission reliability.The channel spreading funct

325、ion in the DD domain can reflect the specific scatteringenvironment.Channel taps with different delays and Dopplers can correspond to differentmobile scatterers.Compared with the channel impulse response in the time latency domainand the channel transfer function in the time-frequency domain,the cha

326、nnel spreadingfunction in the DD domain has potential compactness,sparsity,and stability in high-speedmobile scenarios,which can reduce the signaling overhead of physical layer adaptiveschemes.Delay and Doppler shifts can reflect the distance and speed of objects in the physical63/66world,making OTF

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