WANG Dong, WANG Fanggang, LI Xiran, YUAN Pu, JIANG Dajie

Abstract： The application of the orthogonal time frequency space （OTFS） modulation in multiple-antenna systems is investigated. The diversity and/or the multiplexing gain can be achieved by deploying various multiple-antenna techniques， and thus the reliability and/or the spectral efficiency are improved correspondingly. We provide two classes of OTFSbased multiple-antenna approaches for both the open-loop and the closed-loop systems. Spe?cifically， in the open-loop system， a transmitting diversity approach， which resembles the space-time coding technique， is proposed by allocating the information symbols appropriate?ly in the delay-Doppler domain. In the closed-loop system， we adopt the Tomlinson-Harashi? ma precoding in our derived delay-Doppler equivalent transmission model. Numerical evalu?ations demonstrate the advantages of applying the multiple-antenna techniques to the OTFS. At last， several challenges and opportunities are presented.

Keywords： OTFS; space-time coding; Tomlinson-Harashima precoding

Citation （IEEE Format）： D. Wang， F. G. Wang， X. R. Li， et al.，“Orthogonal time frequency space modulation in multiple-antenna sys? tems， ”ZTE Communications， vol. 19， no. 4， pp. 71 –78， Dec. 2021. doi： 10. 12142/ZTECOM.202104008.

1 Introduction

Recently， the orthogonal time frequency space （OTFS） modulation has been proposed to deal with the severe inter-carrier interference problem caused by the Dop ? pler effect in the high-speed mobility scenario[ 1]. In the OTFS system， the modulation symbols are multiplexed in the delay-Doppler domain instead of the time-frequency do? main， which provides an alternative representation of a time- varyingchannelgeometrymodelingofthetransmission paths[2]. However， the two-dimensional convolution of the in? put-output relation in the OTFS system makes the equaliza? tion involved.The OTFS equalization schemes have been extensively studied[3 –5]. In Ref.[3]， a message-passing （MP） al? gorithm was developed for joint interference cancellation and symbol detection.In Ref.[4]， the authors proposed a crossdomain iterative detection algorithm to enhance the error per? formance of OTFS modulation.

By utilizing the mathematical least-square minimum residu? al algorithm， the authors in Ref. [5] proposed a low-complexity equalizer and a block-wise interference eliminator.

The aforementioned OTFS schemes focus on the single-in? put and single-output system. By exploiting the multiple an? tenna techniques， the reliability and/or the spectral efficiency can be improved in the OTFS multiple-antenna system. Simi? lar to the orthogonal frequency division multiplexing （OFDM） multiple-antenna system， the transmission schemes in the OT? FS multiple-antenna system can be categorized into two class ? es： open-loop and closed-loop. The main difference is that the channel state information （CSI） reported to the transmitter isrequired in the closed-loop system whereas it is not necessary for the open-loop system. In the literature of the open-loop OT? FS， the authors in Ref. [6] proposed a low-complexity linear equalizer by utilizing the block circulant property of the equiv ? alent channel. In Ref. [7]， the quasi-banded sparse structure of the equalization matrix was used to design a low-complexity linear equalization scheme in the delay-Doppler domain. How? ever， the transmission schemes in Refs. [6] and [7] only con? sider the equalization at the receiver without designing the transmitter， the spatial diversity of which is not fully exploit? ed. Then， several papers studied the spatial diversity schemes in OTFS multiple-antenna systems， which can be harnessed by the space-time coding scheme[8 – 10]. In Ref. [11]， a space- time coding scheme with cyclic delay diversity was presented. By assuming that the delay-Doppler channel is invariant in the two consecutive OTFS frames， a space-time code using the Alamouti code structure is proposed in the open-loop sys? tem[12]. However， the channel varies drastically in the two con ? secutive OTFS frames under the high-speed scenarios， which degrades the bit error ratio （BER） performance. In the closed- loop transmission， the feedback of the channel information is required， which further improves the throughput of the OTFS multiple-antenna system. The authors in Ref. [13] proposed a Tomlinson-Harashima precoding （THP） scheme in the delay- time domain. In Ref. [14]， an uplink-aided high mobility down? link channel estimation scheme for the massive multiple-input and multiple-output （MIMO） -OTFS systems was proposed. Theexpectation-maximization-basedvariationalBayesian framework was adopted to recover the uplink channel parame ? ters including the angle， the delay， the Doppler frequency， and the channel gain for each physical scattering path. Then， in Ref. [15]， the authors designed an effective path scheduling algorithm to map different users to the delay-Doppler domain grids without inter-user interference in the same OTFS block. The authors in Ref. [16] proposed a maximal ratio combining （MRC） precoding scheme in the multi-user massive MIMO- OTFS system. However， the previous work mainly focuses on the ideal pulse shaping for the transmission design whereas the problem of its application with the practical pulses， such as the rectangular pulse shaping， is not fully addressed.

In this paper， we investigate the transmission schemes in the open-loop and closed-loop OTFS multiple-antenna sys? tems. We preclude the assumption that the channel states in the two consecutive frames are invariant. Both the ideal pulse shaping and the rectangular pulse shaping are studied. The main contributions of this paper are summarized as follows：

· We design a transmit diversity approach within one OTFS frame duration in the open-loop systems. The guards are care? fully allocated to avoid sub-frames interfering with each other and to ensure the two sub-frames can be regarded as passing the identical channel in the delay-Doppler domain.

· We then design a scheme with the rectangular pulse shap ? ing. In addition to the guards in the ideal pulse shaping， weplace the guards at the last lmax symbols along the delay domain in the rectangular pulse shaping. Then， the channel of each sub- frame in the equivalent transmission model is identical.

· We further indicate that the linear precoding in the time- frequency domain can be alternatively expressed in the delay- Doppler domain. By deriving the equivalent transmission mod ? el in the OTFS system， the THP-based schemes in the delay- Doppler domain under the zero-forcing （ZF） and minimum mean square error （MMSE） criterion are designed.

2 Open-Loop System

In the open-loop system， the channel information is not re? quired at the transmitter， which is suitable for the transmis? sion in the high-speed scenarios. In contrast to the two-frame block fading assumption[12]， we introduce the transmit diversi? ty approach within one OTFS frame duration by appropriately allocating information symbols， guards， and pilots with the ide? al pulse shaping and rectangular pulse shaping.

2.1 Spatial Diversity Approach

In this paper， we consider the wide-sense non-stationary channel with the Jakesformula， different from the wide- sense stationary channel. The amplitude and the phase shift of each path are different in the two consecutive frames， which causes the delay-Doppler channel changes. The traditional space-time coding is applied on two-time slots by assuming the invariant channel， which is not practical in the non-station? ary channel. Then， how to design a transmit diversity within one frame duration is a challenge in the OTFS system. Consid? ering a scenario that the transmitter is equipped with two an ? tennas and the receiver is equipped with a single antenna， we propose a spatial diversity scheme within one frame by allocat? ing information symbols， guards， and pilots. The positions of information symbols and guards are the same for each transmit antenna， which is shown in Fig. 1. Information symbols， guards， and pilots are appropriately allocated in one OTFS frame. In addition to the guards allocated in the ideal pulse shaping， we place the guards at the last lmax symbols along the delay domain in the rectangular pulse shaping. Then， the channel of each sub-frame in the equivalent transmission mod ? el is identical.

Firstly， we divide the resource units of a frame into two sub- frames along the Doppler domain. Symbols in the first sub- frameandthesecondsub-frameareexpressedas x [ l，k 1 ] ，k 1 ∈ { 0， 1，...，- 1}andx [ l，k2 ] ，k2 ∈ {，+ 1，...，N - 1}， respectively. Then， the received signal of each sub-frame can be obtained as：

where y [ l，k 1 ] and y [ l，k2 ] represent the received signal of the first and the second sub-frame， respectively; hpdenotes the channel response of the p-th path; lpand kpare the delay and Doppler indices of the p-th path. For the first sub-frame sig? nal， since k 1 ∈ { 0， 1，...，- 1} ， and kp∈ { -kmax，...，0， 1，...，kmax}， we can obtain [ k - kp ] N∈ [ 0，- 1 + kmax] ∪ [ N - kmax，N - 1]. From Eq. （1）， we can see that the received signal of the first sub-frame is interfered by symbols of the second sub- frame when [ k - kp ] N>- 1. In order to avoid the interfer? ence with the first sub-frame， the guards are placed at the in? terference symbols in the second sub-frame， i. e.， x [ l，k ] = 0，l = { 0， 1，...，M - 1} ，k ∈1，where1 = { [，- 1 + kmax] ∪ [ N - kmax，N - 1] }. Moreover， interference symbols in the first frame are similar to the above analysis. Overall， the al? location of the information symbols can be obtained asx [ l，k ] ，l = { 0， 1，...，M - 1} ，k ∈1 ∪2 ，where2 ={ [ 0，kmax - 1] ∪ [- kmax，- 1] }. Therefore， two sub-frames are not interfered with each other， and the equivalent channel of each sub-frame is identical. Furthermore， by considering the channel estimation in the delay-Doppler domain， pilots and guards should be carefully placed to protect the pilots from interference with other information symbols at the receiv ? er. In order to utilize guard patterns introduced in this section， we allocate the pilots and the guards to the last 3lmax + 2 sym? bol positions along the delay domain. The allocation of the pi? lots and the corresponding guards for the i-th antenna is given by：

where k0 =- 1 and i∈ { 1， 2 }.

Next， we introduce the transmit pattern. By deploying the Alamouti code structure， the transmit vectors at the first anten ? naandthesecondantennaareobtainedas1 = [ x 1（T） ，2（T）]T ∈NMand2 = [ x 2（T） ，1（T）]T ∈NM， where1 = Px 1 *，2 = -Px2 *， and P is the permutation matrix. Then， the re? ceived signal can be obtained as

where y 1 and y2 are received signals at the first and the sec ? ond sub-frame， respectively; H1 and H2 are the equivalent channels for the first and second sub-frame， respectively. From the block circulant property of H1 and H2， an alternative representation of Eqs. （3） and （4） are expressed as

where h 1 ∈MN/2 and h2 ∈MN/2 denote the first column of H1 and H2; X1 and X2 are the equivalent code words for the trans ? mit vectors x 1 and x2， respectively. By applying the maximal ratio combining receiver， the received signal of the two frames can be split apart as1 =x 1 +1and2 =e x2 +2， where= H1 H H1 + H2H2 H. Therefore， x 1 and x2 are not in? terfered with each other， then the maximal likelihood （ML） de? tector or MMSE detector can be applied to decode x 1 and x2， respectively. However， the computational complexity of the de ? tectors is high since the non-linear iterations is involved in the ML receiver and the inverse operation of a high-dimensional matrix is applied in the MMSE receiver. By exploiting the ma? trix transformation and matrix decomposition， the computation? al complexity of the detector can be reduced to O （l2maxMN3）， which is lower than the conventional MMSE receiver O （M3N3）.

2.2 Modified Approach with Rectangular Pulse Shaping

In this section， the transmission scheme in the rectangular pulse shaping is considered. We introduce the allocation of in? formation symbols with the rectangular pulse shaping and de ? sign the corresponding transmitting and receiving structure.

The allocation of the information symbols is based on the in ? put-output relation with rectangular pulse shaping， which is given by

where

Eq. （7） is the phase shift caused by the rectangular pulse shaping. The two sub-frames do not interfere with each other by allocating the guards introduced in Section 2.1. However， the equivalent channel of each sub-frame is different due tothe phase shift. From Eq. （7）， we can see that the phase shift of x [ l，k ] is related to l，k when l

where2 = P 2;1 and2 are received signals of the first subframe and the second sub-frame， respectively;1 and2 are equivalent channels for % 11 and %21， respectively. Then， the MMSE receiver or the MP receiver can be adopted to decode % 11 and %21. In summary， the transmitting and receiving pro? cess with rectangular pulse shaping is shown in Fig. 2. More? over， the proposed diversity scheme in this section can be ex? tended to the multiple-antenna scenarios by employing the structure similar toJafarkhani code， which is a quasi-orthogo? nal space-time block coding introduced in Ref. [19].

3 Closed-Loop System

In the closed-loop system， the transmitter dynamically var? ies the precoding matrix based on the CSI report such as the precoding matrix index， the rank indicator， and the channel quality indicator. However， the precoding problem in the closed-loop OTFS multiple-antenna system is not fully ad? dressed. In this section， we observe the equivalence of the lin? ear precoding between the delay-Doppler and the time-fre? quencydomain.Then，delay-DopplerTHP（DD-THP） schemes are introduced under the ZF or the MMSE criterion.Finally， we provide an overview of other closed-loop transmis? sion schemes in the OTFS multiple-antenna systems.

3.1 Linear Precoding in Delay-Doppler Domain

In this section， the linear precoding in the time-frequency and the equivalent representation in the delay-Doppler do? main are provided. We recall that in the MIMO-OFDM sys? tem， the linear codebook is selected to map symbols in the time-frequency domain to the transmit antennas. In contrast， symbols in the OTFS system are multiplexed in the delay-Dop? pler domain， then the precoding can be deployed in the delay- Doppler domain or the time-frequency domain. We observe that the precoding in the time-frequency domain can be alter? natively represented in the delay-Doppler domain， which is shown as an example in the following. Considering a scenario that the transmitter is equipped with Nt antennas and the re? ceiver is equipped with Nrantennas， we denote WTF = diag{ W1， W2，...， WMN} as the codebook in the time-frequency domain， where Wi ， i = 1， 2，...，MN is the codebook on each subcarrier. Then， the equivalent precoding in the delay-Dop? pler domain WDD is given by

where FNand FMare the discrete Fourier transform matrices with N-point and M-point， respectively; The operator ? de? notes the Kronecker product. By the equivalent representation in Eq. （9）， the precoding process can be carried out in the de ? lay-Doppler domain instead of the time-frequency domain since the channel estimation in the delay-Doppler domain is more stable than that in the time-frequency domain， especially in high-speed scenarios.

3.2 DD-THP Approach

THP is a well-known non-linear precoding scheme， which can also be adopted in the closed-loop OTFS multiple-antenna system. In this subsection， we introduce the DD-THP schemes in the delay-Doppler domain.

In the OTFS multiple-antenna system， the vector form of in? put-output relationship in the delay-Doppler domain is ex? pressed as

where H is the equivalent channel matrix in the delay-Doppler domain; x ∈NtMNis the vector form of the transmit symbols in the delay-Doppler domain; y ∈NrMNis the received sym ? bol in the delay-Doppler domain; v ∈NrMNis the vector form of the zero mean circularly symmetric complex Gaussian noise at the receiver.

The equivalent channel matrix H is fed back to the transmit? ter for the precoding. A block diagram of applying THP in the OTFS multiple-antenna system is shown in Fig. 3. For the ZF-DD-THP approach， the conjugate transpose of the equivalent channel matrix HH is decomposed into a unitary matrix and an upper triangular matrix， i.e.， HH = QR. Then， the forward and feedback filters are given by F = QG， B = RH G， respectively， where G = diag{ rrr } and r 1，r2，...，rNrMNare the di? agonal elements of RH. In addition， β is introduced to normal? ize the power of transmitted signals. The received signal is giv? en by

Alternatively， the MMSE criterion can also be employed in the THP approach， which is called MMSE-DD-THP. We define

Similarly，e is decomposed into a unitary matrix and an up ? per triangular matrix， i.e.，e= QR. We can obtain F = QG and B = RH G. Moreover， there are several approaches to fur? ther improvement of the MMSE-DD-THP. In Ref. [16]， the au? thors rearranged the precoding order of symbols by consider? ing the channel conditions. Furthermore， the linear Wiener transmit filter was adopted to obtain the optimizations after or? dering the symbols[17]. In Ref. [18]， a block-wise fashion and the Tx-Rx matrices were jointly optimized to minimize the MSE. However， it is noted that the computation complexity of DD-THP schemes is high due to the non-linear processing， which may limit the implementation of the DD-THP schemes in practice.

3.3 Other Precoding Approaches

The linear precoding is a widely used precoding technique in the cellular system. The advantage of the linear precoding over the THP is that the former has low computational com ? plexity. The linear precoding is studied in the MIMO-OTFS system[14 – 16]. By exploiting the reciprocity of the uplink channel and downlink channel， the authors in Ref. [ 14] proposed an uplink-aided transmission scheme in the MIMO-OTFS sys? tem.Sincetherearefewscatterersbetweenthetransmitter and the user， and the angular spread of transmitted signals is small in the high-speed scenarios where the received signals occupy only a small part of the channel in the whole angle do ? main. The channel of the MIMO-OTFS system in the angle do? main is sparse. By exploiting the reciprocity of wireless chan ? nels，theangle-delay-Dopplerchannelisestimatedthrough the uplink channel estimation[15]. Then， based on the estimat? ed angular direction of each user， each beamforming vector is formedtoavoidmulti-userinterferenceinthedownlink.In Ref.[ 16]， an MRC precoder was proposed in the multi-user massiveMIMO-OTFSsystem.Thetransmitterprecodesthe symbols by multiplying the Hermitian of the equivalent chan ? nels. Although the computational complexity of the precoding is low in Ref. [ 16]， the interference among users is not com ? pletely eliminated， which degrades the BER performance.

4 Simulation Results

Inthissection， weevaluatetheBERperformanceof the transmissionschemesintheopen-loopandtheclosed-loop MIMO-OTFS systems. The rectangular pulse shaping and the MMSE detector are employed in the simulation. The default setupof thesimulationislistedinTable1.Weadoptthe tapped-delay-line-A（TDL-A）channelmodel.TheDoppler shift corresponding to the i-th tap is generated by Jakesfor? mula.

We evaluate the BER performance of our proposed open- loop scheme and the existing works in Fig. 4. We set the num? ber of the receive antennas as one， and the number of the car? riers is M = 32. In Fig. 4， the proposed diversity transmission scheme outperforms the Naive Tx Div. and the scheme in Ref. [ 12] at the speed of 500 km/h. The fundamental reason can be summarized into the two aspects： 1） the diversity gain and the coding gain can be obtained by using the proposed code word structure. That is the reason why the diversity scheme outper? forms the Naive Tx Div. scheme; 2） The proposed scheme is achievedwithinoneframedurationbyprecludingthetwo- frame block fading assumption. However， the scheme in Ref. [ 12] is implemented over the duration of the two consecutive frameswherethechannelstatevariesrapidlyinthehigh- speed scenario， which leads to the poor BER performance. Incomparison， the BER performance of the scheme in Ref. [ 12] becomes slightly better than the proposed scheme when the ve ? locity reduces to120 km/h. This is because：1） the channel varies slowly at the speed of 120 km/h， which can be approxi? mately regarded as the same; 2） the equivalent code word in Ref. [ 12] can achieve much coding gain since the orthogonality of the code word. In addition， the larger Doppler diversity can be achieved at the speed of 500 km/h over 120 km/h， which re? sults in the better BER performance than that of 120 km/h.

In Fig. 5， we compare the BER performance of the ZF-DD- THP， the MMSE-DD-THP and the MMSE-THP with an order? ing matrix. The number of the receive antennas is 2， and thenumber of the carriers is set as M = 16. Benchmarks are shown as follows： 1） MMSE： each antenna transmits different symbols and uses MMSE equalization in the OTFS system; 2） ZF-THP： thetransmissionschemebasedonZF-DD-THP;3）MMSE- THP：thetransmissionschemebasedonMMSE-DD-THP; 4） Improved MMSE-THP： the transmission scheme based on the MMSE-THPconsideringthechannelcondition.Wecansee that compared with the ZF-DD-THP， the MMSE-DD-THP has a performance gain of about 4 – 5 dB at the same BER level. By considering the ordering matrix to encode the symbols in an op ? timized precoding order， the improved MMSE-THP can further improve the performance of MMSE-DD-THP.

5 Challenges and Opportunities

OTFSconfrontsmanychallengeswhencombinedwiththe multiple-antenna system in the high-speed scenarios. In this sec ? tion， we introduce challenges and opportunities in the open-loop and the closed-loop MIMO-OTFS transmission system.

5.1 Feedback in Closed-Loop Transmission

TheequivalentchannelwiththedimensionofNr MN × Nt MN in the delay-Doppler domain is required to feed back to the transmitter in the DD-THP OTFS system， which causes a high-feedbackoverhead.Sincethefasttime-varyingofthe high-speedscenarios，thefeedbackofchannelinformation may not match the current channel state， which results in the precodermismatchtothecurrentchannelstate. Therefore， how to reduce the feedback overhead and improve the real- time property of the precoder to match the current channel is inevitable in the closed-loop transmission systems. By observ? ingthelawof channelchanges，onepossiblesolutionisto adoptareliablechannelpredictionmethodbytheprevious channel estimation. Another approach is to design a codebook set to match the delay-Doppler channel， which issimilar to the feedback pattern to OFDM closed-loop networks. In this way， the receiver selects a codebook to match the estimated channel and feeds back to the transmitter by a specific indica? tor. Then， each feedback become less.

5.2 Low-Complexity Precoding and Receiving Approaches

Due to the two-dimensional convolution in the delay-Dop? pler domain， the size of the precoding and the equalization ma? trices are large which results in the high computational com ? plexity. Moreover， the linear receiver such as the MMSE re ? ceiver also leads to a high complexity due to the inverse opera? tionof a high-dimensional matrix. Therefore， how to reduce the complexity of the precoding and equalization schemes is a big challenge in the OTFS multiple-antenna system. The study of the variational Bayes can be utilized to be the detector in the OTFS multiple-antenna systems.

5.3 Channel Estimation in MIMO-OTFS

The channel estimation with the fractional Doppler and thefractional delay is a more practical problem in the future re ? search. Furthermore， in the aspect of the Doppler spectrum， most of the existing works focus on the channel estimation of thediscrete-Doppler-spread（alsoknownaslimit-Doppler- spread） scenarios[20]. However， when the propagation environ? mentinvolvesmanyscatteringobjects，theDopplershiftof transmit paths are infinite and the Doppler spectrum is contin ? uous， which is treated as the continuous-Doppler-spread chan? nel. How to reduce the overhead of the channel estimation in the meantime improve the accuracy in these practical channel models is a big challenge. In Ref. [21]， a low-dimensional sub? space is constructed to characterize the variation of the equiva? lentchannelresponsesinthecontinuous-Doppler-spread channel， which is modeled by a sum of the projection coeffi ? cients and the basis functions.

6 Conclusions

Inthispaper，weintroduceboththeopen-loopandthe closed-loop multi-antenna approaches for the OTFS with the ideal and the rectangular pulse shaping. In the open-loop de? sign， the main contribution is that the transmit diversity ap ? proachesresemblingspace-timecodingareprovided， which takethepracticalissuesintoaccount，i. e.，therectangular pulse shaping and the rapidly time-varying channel. For the closed-loopdesign，wesuggesttoadopttheTomlinson-Ha ? rashima precoding in the delay-Doppler domain since we have developedtherelationbetweentheprecodingmatrixinthe time-frequency domain and that in the delay-Doppler domain. The reason why we recommend precoding in the delay-Dop? pler domain is that the channel in the delay-Doppler domain varies moreslowly withina frameincontrast to that in the time-frequency domain. In the end， we discuss challenges and opportunities of the OTFS multiple-antenna system， which can be further investigated in future.

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Biographies

WANG Dong received the B.Eng. degree from the School of Electronic and In ? formation Engineering， Hebei University， China in 2016. He is currently pursu? ing the Ph. D. degree with the State Key Laboratory of Rail Traffic Control and Safety，Beijing JiaotongUniversity，China.Hiscurrentresearchinterestsin? clude multiway relaying communications and MIMO communications.

WANG Fanggang （wangfg@bjtu. edu. cn） received the B. Eng. and Ph. D. de grees from the School of Information and Communication Engineering ， Beijing University of Posts and Telecommunications， China in 2005 and 2010， respectively. He was a Post-Doctoral Fellow with the Institute of Network Coding， The Chinese University of Hong Kong， China from 2010 to 2012. He was a visiting scholar with the Massachusetts Institute of Technology， USA from 2015 to 2016 and the Singapore University of Technology and Design， Singapore in 2014. He is currently a professor with the State Key Laboratory of Rail Traffic Control and Safety， School of Electronic and Information Engineering， Beijing Jiaotong University， China. His research interests are in wireless communications， signal processing， and information theory. He served as an editor for the IEEE Com munications Letters and a technical program committee member for several conferences.

LI Xiran received the B. Eng degree from the school of Information and Communication Engineering， Beijing Jiaotong University， China in 2021. She is cur rently pursuing the M. A. degree with the State Key Laboratory of Rail Traffic Control and Safety， Beijing Jiaotong University. Her current research interests include MIMO communications and orthogonal time frequency space.

YUAN Pu received the B. Eng. degree from Tianjin University， China in 2007 and the M.S. and Ph.D. degrees from Nanyang Technological University， Singa pore in 2010 and 2015， respectively. He is currently with vivo Mobile Communication Co.， Ltd.， China. From 2016 to 2019， he was a research engineer with the2012Laboratories，HuaweiTechnologiesCompany，Ltd.，China.Hisre searchinterestsincludesignalprocessingincommunicationandinformation theory.

JIANG Dajie received the B.S. degree in communication engineering and M.S. degree in digital signal processing from Beijing University of Posts and Tele ? communications， China in 2005 and 2008， respectively. From 2008 to 2017， he was a research engineer for 4G and 5G wireless research & standardization with China Mobile Research Institute. He is currently with vivo Mobile Communica? tion Co.， Ltd.， China. His research interests include potential technologies for 6G including RIS and joint communication and sensing.