Orthogonal time frequency space (OTFS) has emerged as the most sought-after modulation technique in a high mobility scenario. Sparse code multiple access (SCMA) is an attractive code-domain non-orthogonal multiple access (NOMA) technique. Recently a code-domain NOMA approach for OTFS, named OTFS-SCMA, is proposed. OTFS-SCMA is a promising framework that meets the demands of high mobility and massive connectivity. This paper presents a channel estimation technique based on the convolutional sparse coding (CSC) approach for OTFS-SCMA in the uplink. The channel estimation task is formulated as a CSC problem following a careful rearrangement of the OTFS input-output relation. We use an embedded pilot-aided sparse-pilot structure that enjoys the features of both OTFS and SCMA. The existing channel estimation techniques for OTFS in multi-user scenarios for uplink demand extremely high overhead for pilot and guard symbols, proportional to the number of users. The proposed method maintains a minimal overhead equivalent to a single user without compromising on the estimation error. The results show that the proposed channel estimation algorithm is very efficient in bit error rate (BER), normalized mean square error (NMSE), and spectral efficiency (SE).

We consider the problem of degradation in performance of multi-carrier multi-user massive MIMO systems when channel induced Doppler spread is high. Recently, Orthogonal Time Frequency Space (OTFS) modulation has been shown to be robust to channel induced Doppler spread. In OTFS based systems, information symbols are embedded in the delay-Doppler (DD) domain where they are jointly modulated to generate the time-domain transmit signal. Due to the multi-path delay and Doppler shifts, the DD domain information symbols need to be jointly demodulated at the receiver. For multi-carrier based communication (e.g., Orthogonal Frequency Division Multiplexing (OFDM)), massive MIMO systems have been shown to achieve high spectral and energy efficiency with low complexity multi-user precoding in the downlink. Extending the same to OTFS based downlink multi-user massive MIMO systems is challenging due to the requirement for joint demodulation of all information symbols at the user terminal (UT). In this paper, we solve this problem by proposing a novel OTFS based multi-user precoder at the base station (BS) and a corresponding low complexity detector (LCD) at the user terminals (UTs), which allows for separate demodulation of each DD domain information symbol at the UT. The complexity of the proposed precoder increases only linearly with increasing number BS antennas Q and the number of UTs. We show, through analysis, that as Q increases (with total transmitted power decreased linearly with Q), the proposed low complexity detector achieves a sum SE close to that achieved with optimal joint demodulation at each UT. Numerical simulations confirm our analysis and also show that the SE and error rate performance of the proposed OTFS based massive MIMO precoder and LCD detector is significantly more robust to channel induced Doppler spread when compared to OFDM based multi-user massive MIMO systems.

We consider the problem of uplink timing synchronization for Orthogonal Time Frequency Space (OTFS) modulation based systems where information is embedded in the delay-Doppler (DD) domain. For this, we propose a novel Random Access (RA) preamble waveform based on OTFS modulation. We also propose a method to estimate the round-trip propagation delay between a user terminal (UT) and the base station (BS) based on the received RA preambles in the DD domain. This estimate (known as the timing advance estimate) is fed back to the respective UTs so that they can advance their uplink timing in order that the signal from all UTs in a cell is received at the BS in a time-synchronized manner. Through analysis and simulations we study the impact of OTFS modulation parameters of the RA preamble on the probability of timing error, which gives valuable insights on how to choose these parameters. Exhaustive numerical simulations of high mobility scenarios suggests that the timing error probability (TEP) performance of the proposed OTFS based RA is much more robust to channel induced multi-path Doppler shift when compared to the RA method in Fourth Generation (4G) systems.

Orthogonal time frequency space (OTFS) modulation, which encodes information symbols in the delay-Doppler domain, offers a promising solution to the problem of high Doppler sensitivity of orthogonal frequency division multiplexing (OFDM) transmission. In this letter we study the diversity of OTFS assuming rectangular waveforms and a delay-Doppler channel with two paths. After introducing the concept of effective diversity (ED), which we argue to be more significant than "standard" diversity in the case of a large number of transmitted symbols, we examine the conditions under which OTFS achieves full ED for QAM symbols. We validate our analytical results through numerical simulations, which show that OTFS practically achieves full ED with sufficiently large signal constellations.

Orthogonal time frequency space (OTFS) modulation was proposed to tackle the destructive Doppler effects in wireless communications, with potential applications to many other areas. In this paper, we investigate its application to radar systems, and propose a novel efficient OTFS-based matched filter algorithm for target range and velocity estimation. The proposed algorithm not only exhibits the inherent advantages due to multi-carrier modulation of the existing orthogonal frequency division multiplexing (OFDM-) based radar algorithms but also provides additional benefits to improve radar capability. Similar to OFDM, OTFS spreads the transmitted signal in the entire time--frequency resources to exploit the full diversity gains for radar processing. However, OTFS requires less cyclic prefix, and hence, shorter transmission duration than OFDM, allowing longer range radar and/or faster target tracking rate. Additionally, unlike OFDM, OTFS is inter-carrier interference-free, enabling larger Doppler frequency estimation. We demonstrate the performance of the proposed algorithm using numerical results under different system settings.

Orthogonal time frequency space (OTFS) transmits information symbols in the delay Doppler domain rather than in the time frequency domain (as with OFDM). In its original version, OTFS uses transmit and receive shaping waveforms which are biorthogonal with respect to translations by integer multiples of basic time and frequency intervals. In this paper we examine the performance of OTFS using general waveforms. Based on a discrete model of the modulation/demodulation procedure, we compute error probability, and we discuss the amount of diversity that can be achieved on fading channels.

Orthogonal time frequency space (OTFS) modulation was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) in delay-Doppler channels. In order to detect OTFS modulated data, the channel impulse response needs to be known at the receiver. In this paper, we propose embedded pilot-aided channel estimation schemes for OTFS. In each OTFS frame, we arrange pilot, guard, and data symbols in the delay-Doppler plane to suitably avoid interference between pilot and data symbols at the receiver. We develop such symbol arrangements for OTFS over multipath channels with integer and fractional Doppler shifts, respectively. At the receiver, channel estimation is performed based on a threshold method and the estimated channel information is used for data detection via a message passing algorithm. Thanks to our specific embedded symbol arrangements, both channel estimation and data detection are performed within the same OTFS frame with minimum overhead. We compare through simulations the error performance of OTFS using the proposed channel estimation and OTFS with ideally known channel information and observe only a marginal performance loss. We also demonstrate that the proposed channel estimation in OTFS significantly outperforms OFDM with known channel information. Finally, we present extensions of the proposed schemes to multiple-input multiple-output (MIMO) and multi-user uplink/downlink.

In this paper, we model $M\times N$ orthogonal time frequency space modulation (OTFS) over a $P$-path doubly dispersive channel with delays less than $\tau _{\max }$ and Doppler shifts in the range $(\nu _{\min },\nu _{\max })$. We first derive in a simple matrix form the input–output relation in the delay-Doppler domain for practical (e.g., rectangular) pulse-shaping waveforms, next generalize it to arbitrary waveforms. This relation extends the original OTFS input–output approach, which assumes ideal pulse-shaping waveforms that are bi-orthogonal in both time and frequency. We show that the OTFS input–output relation has a simple sparse structure that enables one to use low-complexity detection algorithms. Different from previous work, only a single cyclic prefix is added at the end of the OTFS frame, significantly reducing the overhead, without incurring any penalty from the loss of bi-orthogonality of the pulse-shaping waveforms. Finally, we compare the OTFS performance with different pulse-shaping waveforms, and show that the reduction of out-of-band power may introduce nonuniform channel gains for the transmitted symbols, thus impairing the overall error performance.

Orthogonal time frequency space (OTFS) modulation is known to achieve excellent error performance in delay-Doppler channels. However, its performance over static multipath channels has never been fully investigated. In this letter, we show that, in static multipath channels, the system structure of OTFS is equivalent to the asymmetric orthogonal frequency division multiplexing (A-OFDM), a scheme proposed by Zhang et al., bridging between cyclic prefix single carrier (CPSC) and traditional OFDM. We derive a condition on the parameters of OTFS to guarantee that all the transmitted symbols experience uniform channel gains, as in CPSC. Finally, we apply a low-complexity message passing detection to OTFS/A-OFDM and show a significant performance improvement over ZF and MMSE detection originally proposed for A-OFDM.

The recently proposed orthogonal time frequency space (OTFS) modulation technique was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) in Doppler channels. In this paper, we derive the explicit input-output relation describing OTFS modulation and demodulation (mod/demod) for delay-Doppler channels. We analyze the interferences and develop a novel low-complexity yet efficient message passing (MP) algorithm for joint interference cancellation (IC) and symbol detection. The proposed MP algorithm can effectively compensate for a wide range of channel Doppler spreads.

The transceiver separations required for synthesizing full rank MIMO matrices in line of sight (LoS) geometries scale as the square root of the product of carrier wavelength and range. The wavelengths at millimeter (mm) wave carrier frequencies are small therefore enable LoS spatial multiplexing with practical node form factors at ranges of 10–100 m, depending on the carrier frequency. However, such LoS MIMO links become frequency selective even with small geometric mismatches. Exact channel inversion in an N x N MIMO system requires fractionally spaced equalization, which is practically infeasible when operating at the very high data rates (multiple Gbps) that we are interested in. In this paper, we investigate spatial oversampling (more receive antennas than transmitted data streams) with symbol rate sampling, introducing designed delay diversity across different receive antennas, as a means for removing error floors when linearly separating the spatially multiplexed streams. We study the tradeoff between the number of additional receive antennas and the complexity of temporal equalization, and argue that an attractive example architecture, compatible with form factor constraints, is one in which the number of receive antennas is double the number of transmitted data streams.

Orthogonal time frequency space (OTFS) modulation was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) over delay-Doppler channels. The channel impulse response is needed at the receiver to perform OTFS detection. In this work, we analyze OTFS-based channel estimation using a pilot symbol embedded in the data frame: the pilot symbol with a number of guard zero-symbols is suitably located on the delay-Doppler grid containing the information symbols. Different symbol arrangements are proposed depending on whether the channel has integer or fractional Doppler paths relative to an integer grid. The channel information is first estimated from a group of received symbols using a simple threshold method. The estimated information is then used for data detection within the same frame, via a message passing (MP) algorithm. Numerical results compare the error performance of the proposed schemes and the OTFS scheme with ideal channel estimation under similar spectral and energy efficiency. Moreover, our results show that OTFS with non-ideal channel estimation can still outperform OFDM with ideal channel estimation.

We elaborate on the recently proposed orthogonal time frequency space (OTFS) modulation technique, which provides significant advantages over orthogonal frequency division multiplexing (OFDM) in Doppler channels. We first derive the input--output relation describing OTFS modulation and demodulation (mod/demod) for delay--Doppler channels with arbitrary number of paths, with given delay and Doppler values. We then propose a low-complexity message passing (MP) detection algorithm, which is suitable for large-scale OTFS taking advantage of the inherent channel sparsity. Since the fractional Doppler paths (i.e., not exactly aligned with the Doppler taps) produce the inter Doppler interference (IDI), we adapt the MP detection algorithm to compensate for the effect of IDI in order to further improve performance. Simulations results illustrate the superior performance gains of OTFS over OFDM under various channel conditions.

We consider millimeter wave multiuser uplink system with low resolution phase shifters, where users transmit simultaneously to base station. Transmit and receive beamforming through large antenna arrays is used to compensate severe path loss of millimeter waves. We first propose a joint precoder and detector design based on the low-complexity local search algorithm that iteratively finds the preferred transmit and receive beamforming vectors, which maximizes the sum-rate of the multiuser uplink system. Although the joint design achieves similar sum-rate to a fully digital system, the computation complexity to determine good beamforming vectors is high. To reduce complexity, we then propose nonjoint designs of precoder and detector. For the precoder design, the transmit beamforming vectors are chosen to maximize either the signal to noise ratio or the signal to interference plus noise ratio of each user. For the detector design, the receiver beamforming vectors are selected using either an approximate ML detector or a successive cancellation detector. Through simulations, we show that our designs with low resolution phase shifters outperform the traditional methods using steering vectors as beamforming vectors with high resolution phase shifters.

In this letter, we consider analog beamforming using low resolution phase shifters for millimeter waves communications. We propose a hierarchical codebook design, where the beamforming vectors in the codebook are grouped into multiple levels and the preferred beamforming vector at each level is constructed to approximate an amplitude beamforming gain mask by using a low complexity local search algorithm. We show, by simulations, that the proposed codebook using low resolution phase shifters outperforms the existing schemes using high resolution phase shifters.

In this letter, we consider a multiple-input multiple-output (MIMO) source-relay-destination network, where the relay is a full-duplex MIMO transceiver (FD-MIMO) and uses spatial modulation (SM). We propose a transmission protocol for this system, where the source beamforms to the relay antennas that are not used for transmission, while the remaining antennas in the relay forward the previously decoded information using SM to the destination. We derive the analytical expressions for the bit error rate of the FD-MIMO relaying system. We show from the analytical results and simulations that our proposed FD-MIMO system outperforms the one that uses V-BLAST at relay. This performance advantage is due to the availability of more antennas at the relay dedicated to reception and the use of a lower order quadratic-amplitude modulation in SM, when compared with V-BLAST.

Generalized Spatial modulation (GSM) uses n(t) antenna elements but fewer radio frequency chains (n(rf)) at the transmitter. Spatial modulation and spatial multiplexing are special cases of GSM with n(rf) = 1 and n(rf) = n(t), respectively. In GSM, apart from conveying information bits through n(rf) modulation symbols, information bits are also conveyed through the indices of the active n(rf) transmit antennas. In this paper, we derive analytical bounds on the code-word and bit error probabilities of maximum likelihood detection in GSM. The bounds are shown to be tight at medium to high signal-to-noise ratios (SNR). We also present a low-complexity detection algorithm based on reactive tabu search (RTS) for GSM in large-scale MIMO systems. Simulation results show that the proposed algorithm performs well and scales well in complexity.

Spatial modulation (SM) is attractive for multi-antenna wireless communications. SM uses multiple transmit antenna elements but only one transmit radio frequency (RF) chain. In SM, in addition to the information bits conveyed through conventional modulation symbols (e.g., QAM), the index of the active transmit antenna also conveys information bits. In this paper, we establish that SM has significant signal-to-noise (SNR) advantage over conventional modulation in large-scale multiuser (multiple-input multiple-output) MIMO systems. Our new contribution in this paper addresses the key issue of large-dimension signal processing at the base station (BS) receiver (e.g., signal detection) in large-scale multiuser SM-MIMO systems, where each user is equipped with multiple transmit antennas (e.g., 2 or 4 antennas) but only one transmit RF chain, and the BS is equipped with tens to hundreds of (e.g., 128) receive antennas. Specifically, we propose two novel algorithms for detection of large-scale SM-MIMO signals at the BS; one is based on message passing and the other is based on local search. The proposed algorithms achieve very good performance and scale well. For the same spectral efficiency, multiuser SM-MIMO outperforms conventional multiuser MIMO (recently being referred to as massive MIMO) by several dBs. The SNR advantage of SM-MIMO over massive MIMO can be attributed to: (i) because of the spatial index bits, SM-MIMO can use a lower-order QAM alphabet compared to that in massive MIMO to achieve the same spectral efficiency, and (ii) for the same spectral efficiency and QAM size, massive MIMO will need more spatial streams per user which leads to increased spatial interference.

In this paper, we propose algorithms for signal detection in large-scale multiuser {\em spatial modulation multiple-input multiple-output (SM-MIMO)} systems. In large-scale SM-MIMO, each user is equipped with multiple transmit antennas (e.g., 2 or 4 antennas) but only one transmit RF chain, and the base station (BS) is equipped with tens to hundreds of (e.g., 128) receive antennas. In SM-MIMO, in a given channel use, each user activates any one of its multiple transmit antennas and the index of the activated antenna conveys information bits in addition to the information bits conveyed through conventional modulation symbols (e.g., QAM). We propose two different algorithms for detection of large-scale SM-MIMO signals at the BS; one is based on {\em message passing} and the other is based on {\em local search}. The proposed algorithms are shown to achieve very good performance and scale well. Also, for the same spectral efficiency, multiuser SM-MIMO outperforms conventional multiuser MIMO (recently being referred to as massive MIMO) by several dBs; for e.g., with 16 users, 128 antennas at the BS and 4 bpcu per user, SM-MIMO with 4 transmit antennas per user and 4-QAM outperforms massive MIMO with 1 transmit antenna per user and 16-QAM by about 4 to 5 dB at 10-3 uncoded BER. This SNR advantage essentially comes about because the spatial index bits allow SM-MIMO to achieve a given spectral efficiency using a lower order modulation alphabet than in conventional multiuser MIMO.

In this paper, we propose algorithms for signal detection in large-scale multiuser {\em spatial modulation multiple-input multiple-output (SM-MIMO)} systems. In large-scale SM-MIMO, each user is equipped with multiple transmit antennas (e.g., 2 or 4 antennas) but only one transmit RF chain, and the base station (BS) is equipped with tens to hundreds of (e.g., 128) receive antennas. In SM-MIMO, in a given channel use, each user activates any one of its multiple transmit antennas and the index of the activated antenna conveys information bits in addition to the information bits conveyed through conventional modulation symbols (e.g., QAM). We propose two different algorithms for detection of large-scale SM-MIMO signals at the BS; one is based on {\em message passing} and the other is based on {\em local search}. The proposed algorithms are shown to achieve very good performance and scale well. Also, for the same spectral efficiency, multiuser SM-MIMO outperforms conventional multiuser MIMO (recently being referred to as massive MIMO) by several dBs; for e.g., with 16 users, 128 antennas at the BS and 4 bpcu per user, SM-MIMO with 4 transmit antennas per user and 4-QAM outperforms massive MIMO with 1 transmit antenna per user and 16-QAM by about 4 to 5 dB at $10^{-3}$ uncoded BER. The SNR advantage of SM-MIMO over massive MIMO can be attributed to the following reasons: (i) because of the spatial index bits, SM-MIMO can use a lower-order QAM alphabet compared to that in massive MIMO to achieve the same spectral efficiency, and (ii) for the same spectral efficiency and QAM size, massive MIMO will need more spatial streams per user which leads to increased spatial interference.