Adaptive Doppler Shift Quantization Interval Scheme for OTFS

In this paper, a minimum mean squared error (MMSE) based turbo equalization scheme in delay-Doppler domain for a coded orthogonal time frequency space (OTFS) system is provided as a low complexity version requiring only a single matrix inversion. Also, we derived extrinsic log likelihood ratios (LLRs) for the turbo equalization, exploiting a priori information fed from a channel decoder, under the assumption that the equalized data symbol follows Gaussian distribution. We rigorously conducted link level evaluation to compare coded orthogonal frequency division multiplexing (OFDM) and OTFS over time-varying multipath channels (based on the channel model in 3GPP 5G New Radio) in 30 GHz band, which may cause severe inter-symbol interference (ISI) and/or inter-carrier interference (ICI) depending on numerology setup. The link level simulation verifies that OTFS is superior to OFDM in block error rate (BLER) performance, each being configured with the best numerology, over all the channel scenarios considered. OTFS shows better BLER performance with smaller subcarrier spacing (SCS) while OFDM has an intermediate SCS for the best BLER due to trade-off between ISI and ICI. Also, we measured normalized mean squared error (NMSE) to see how ISI and ICI affect the performance with respect to numerology, which is used to conjecture why the BLER performance has such peculiarity.

Known as a new promising waveform modulation technique, the orthogonal time-frequency space (OTFS) technique is considered a very important waveform modulation technique that modulates data in the delay-Doppler (DD) domain. The key difference between OTFS and the traditional multiplexing techniques is that it is two-dimensional modulation that converts between the time-frequency (TF) domain and delay-Doppler domain, these features enable dealing with the Doppler shift generated from high mobility objects which were ignored in the traditional modulation techniques such as orthogonal frequency division multiplexing (OFDM). The main objective of this survey is to provide an overview of this novel subject indicating its system model. Also, we review the main topics related to OTFS modulation as data detection techniques, channel estimation, MIMO, and multiuser systems. Then, the main research direction of OTFS on future wireless generation systems is given.

The orthogonal time frequency space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To enable efficient OTFS detection in the delay-Doppler (DD) domain, the DD domain channels need to be acquired accurately. To achieve the low latency requirement in future wireless communications, the time duration of the OTFS block should be small, therefore fractional Doppler shifts have to be considered to avoid significant modelling errors due to the assumption of integer Doppler shifts. However there lack investigations on the estimation of OTFS channels with fractional Doppler shifts in the literature. In this work, we develop a channel estimator for OTFS with particular attention to fractional Doppler shifts, and both bi-orthogonal waveform and rectangular waveform are considered. Instead of estimating the DD domain channel directly, we estimate the channel gains and (fractional) Doppler shifts that parameterize the DD domain channel. The estimation is formulated as a structured sparse signal recovery problem with a Bayesian treatment. Based on a factor graph representation of the problem, an efficient message passing algorithm is developed to recover the structured sparse signal (thereby the OTFS channel). The Cramer-Rao Lower Bound (CRLB) for the estimation is developed and the effectiveness of the algorithm is demonstrated through simulations.

Orthogonal time frequency space (OTFS) technique is a recent two-dimensional (2-D) modulation aiming to exploit both time and frequency selectivity of doubly dispersive wireless channel, which significantly affects the reliability of conventional wireless communication systems. In OTFS transmission, delay-Doppler domain is utilized for conveying the data symbols. Besides channel characteristics, the performance of wireless communications systems is severely limited due to the impairments at the RF front-end. One of these impairments is the in-phase and quadrature (IQ) imbalance that occurs due to inevitable imperfections existing between in-phase and quadrature branches at either transmitter (Tx) or receiver (Rx) architecture. The aim of this paper is to reveal and investigate the physical effect of IQ impairment in delay-Doppler domain, which is unknown in the literature. Hence, we provide theoretical models to explicitly understand the impact of IQ imbalance at different stages of OTFS-based communication systems including Tx, Rx, and jointly Tx-Rx. Importantly, we show that although the performance of OTFS transmission depends on both delay and Doppler axes, IQ imbalance leads to an interference originating only from the mirror Doppler axes, which we name mirror Doppler interference (MDI), along with power degradation. Moreover, we assess the performance of IQ imbalanced OTFS under various communication scenarios considering ideal and practical pulse shapes with maximum likelihood (ML) and minimum mean square error (MMSE) detectors, respectively.

Although it is often used in the orthogonal frequency division multiplexing (OFDM) systems, application of massive multiple-input multiple-output (MIMO) over the orthogonal time frequency space (OTFS) modulation could suffer from enormous training overhead in high mobility scenarios. In this paper, we propose one uplink-aided high mobility downlink channel estimation scheme for the massive MIMO-OTFS networks. Specifically, we firstly formulate the time domain massive MIMO-OTFS signal model along the uplink and adopt the expectation maximization based variational Bayesian (EM-VB) framework to recover the uplink channel parameters including the angle, the delay, the Doppler frequency, and the channel gain for each physical scattering path. Correspondingly, with the help of the fast Bayesian inference, one low complex approach is constructed to overcome the bottleneck of the EM-VB. Then, we fully exploit the angle, delay and Doppler reciprocity between the uplink and the downlink and reconstruct the angles, the delays, and the Doppler frequencies for the downlink massive channels at the base station. Furthermore, we examine the downlink massive MIMO channel estimation over the delay-Doppler-angle domain. The channel dispersion of the OTFS over the delay-Doppler domain is carefully analyzed and is utilized to associate one given path with one specific delay-Doppler grid if different paths of any user have distinguished delay-Doppler signatures. Moreover, when all the paths of any user could be perfectly separated over the angle domain, we design the effective path scheduling algorithm to map different users' data into the orthogonal delay-Doppler-angle domain resource and achieve the parallel and low complex downlink 3D channel estimation. For the general case, we adopt the least square estimator with reduced dimension to capture the downlink delay-Doppler-angle channels. Various numerical examples are presented to confirm the validity and robustness of the proposed scheme.

This paper proposes an off-grid channel estimation scheme for orthogonal time-frequency space (OTFS) systems adopting the sparse Bayesian learning (SBL) framework. To avoid channel spreading caused by the fractional delay and Doppler shifts and to fully exploit the channel sparsity in the delay-Doppler (DD) domain, we estimate the original DD domain channel response rather than the effective DD domain channel response as commonly adopted in the literature. The OTFS channel estimation problem is formulated as an off-grid sparse signal recovery problem based on a virtual sampling grid defined in the DD space, where the on-grid and off-grid components of the delay and Doppler shifts are separated for estimation. In particular, the on-grid components of the delay and Doppler shifts are jointly determined by the entry indices with significant values in the recovered sparse vector. Then, the corresponding off-grid components are modeled as hyper-parameters in the proposed SBL framework, which can be estimated via the expectation-maximization method. Simulation results verify that compared with the on-grid approach, our proposed off-grid OTFS channel estimation scheme enjoys a 1.5 dB lower normalized mean square error.

Next-generation wireless systems face unique challenges in identifying high-mobility emitters/vehicles (HME/V), especially in the delay-Doppler domain, where existing technologies fall short. The orthogonal time-frequency space (OTFS) technique has recently been proposed to deal with challenges in the delay-Doppler domain. Hence, for the first time, this letter introduces a novel emitter identification (EI) framework using radio-frequency (RF) fingerprints of HME/V using OTFS. A convolutional neural network (CNN) is exploited to extract the RF fingerprints from in-phase and quadrature-phase (IQ) components of the received OTFS-modulated signal to identify different emitters accurately. Further, we also analyze the impact of the same/different set of digitally modulated baseband signals such as binary phase shift keying (BPSK), on-off keying (OOK), 4-amplitude shift keying (4ASK), and 8-amplitude shift keying (8ASK) within the OTFS, employed by the emitters. Experimental results depict the efficacy of the proposed EI framework for HME/V even under low signal-to-noise ratios (SNRs).

Orthogonal time-frequency space (OTFS) is a two-dimensional (2D) modulation technology for processing high mobility communication signals. The integer delay and Doppler shifts can lead to significant modeling error in the delay-Doppler (DD) domain. To obtain accurate estimation of fractional DD domain channel, we propose a novel two-step off-grid channel estimation using Bayesian compressive sensing (BCS) for OTFS systems. First, we analyze the vectorized form of fractional DD domain input-output relationship and derive a simplified expression form to adapt compressive sensing model. Then, to tackle the problem of fractional parameters estimation, we build an off-grid compressive model in light of high-order Taylor expansion. The channel parameters can be obtained by our proposed off-grid BCS (OG-BCS) algorithm, where we edge out the noise parameters and adopt a hierarchical Laplacian scale mixture (LSM) prior for OTFS signal. At the same time, based on likelihood maximization we derive the off-grid update expressions and incorporate it into our optimized BCS framework. To further reduce the computational complexity, we propose a fast BCS (FBCS) algorithm via LSM prior. In our proposed FBCS algorithm, the hyper-parameters modeling the sparse signal are separated for calculation, and only a single hyper-parameter is considered for updating in each iteration. Specially, we analyze the condition of maximization for obtaining the solution of hyper-parameters and derive its update expressions. Simulation results illustrate that our proposed algorithm has better computational efficiency and precise channel estimation performance.

Orthogonal time frequency and space (OTFS) modulation is a promising technology that satisfies high-Doppler requirements for future mobile systems. OTFS encodes information symbols and pilot symbols into the two-dimensional (2D) delay-Doppler (DD) domain. The received symbols suffer from inter-Doppler interference (IDI) in fading channels with fractional Doppler shifts sampled at noninteger indices in the DD domain. The IDI has been treated as an unavoidable effect because the fractional Doppler shifts cannot be obtained directly from the received pilot symbols. This paper provides a solution to channel estimation for fractional Doppler channels with lower computational complexity than a conventional channel estimation method using a pseudo sequence. The proposed estimation provides new insight into the OTFS input-output relation in the DD domain as a 2D circular convolution with a small approximation. According to the input-output relation, we also provide a low-complexity channel equalization method using the estimated channel information. We demonstrate the error performance of the proposed channel estimation and equalization in a high-Doppler channel by simulations. The simulation results show that the proposed channel estimation method outperforms the conventional channel estimation. The results also show that the proposed equalization method has a similar performance to the minimum mean square error equalizer using matrix inversion.

In this letter, we study the achievable rates adopting two delay-Doppler (DD) domain multiples access (MA) schemes for uplink orthogonal time frequency space (OTFS) transmissions, namely delay division multiple access (DDMA) and Doppler division multiple access (DoDMA). To shed light on the system performance, we establish the achievable rate upper-bounds for both DDMA and DoDMA in comparisons to that of the conventional orthogonal frequency division multiple access (OFDMA). In particular, we show that both DDMA and DoDMA have more robust signal-to-interference-plus-noise ratio (SINR) performances against channel fluctuations compared to OFDMA and this robustness leads to higher achievable rates for both DDMA and DoDMA. To be more specific, we find that the achievable rate upper-bounds for OTFS depend only on the channel fading coefficients of different paths and the multi-user interference (MUI), while the delay and Doppler shifts also have significant impacts on that of the conventional OFDMA. Our simulation results are consistent with our derivations and demonstrate a noticeable improvement of the achievable rates for both DDMA and DoDMA over OFDMA.

Integrated Sensing and Communication (ISAC) systems combine radar sensing and communication to improve spectral and hardware efficiency in 6 G networks. The emerging Orthogonal Time Frequency Space (OTFS) modulation is wellsuited for ISAC due to its robustness in the Delay-Doppler (DD) domain compared to traditional Orthogonal Frequency Division Multiplexing (OFDM). Despite its advantages, OTFS exhibits high sidelobe levels that affect sensing performance. To further enhance the radar sensing aspect of an OTFS-based ISAC system, we design a phase matrix to optimize the OTFS waveform. Our goal is to reduce the sidelobe levels of the 2D Ambiguity Function (AF) for the phase-tailored OTFS waveform. Specifically, we formulate an optimization problem to minimize the AF Peak Sidelobe Level (PSL) by introducing an additional degree of freedom for each communication symbol, thereby improving sensing performance while preserving similar communication efficiency. We solve the related non-convex NP-hard optimization problem and propose an Alternative Optimization (AO)-based algorithm. By decomposing the problem into two subproblems, one convex and the other is solved using Projected Gradient Descent (PGD), we iteratively update the variables until convergence. This approach effectively minimizes the PSL, improving target resolution and reducing interference. Simulation results show that the proposed method efficiently reduces the sidelobe levels and improves the AF, leading to increased sensing performance.

As a promising modulation scheme for high mobility wireless communications, orthogonal time frequency space (OTFS) has received tremendous attention. In the case of bi-orthogonal waveforms, OTFS allows highly efficient detection in the delay-Doppler (DD) domain by exploiting the (circulant or sparsity) structures of the channel matrix. However, in the case of more practical waveforms, such as the rectangular waveform, the special structures do not exist. In the literature, to achieve low complexity detection, null symbols or cyclic prefixes (CPs) are frequently inserted to the OTFS signal block, which, however, leads to significant overhead. In this work, we partition the large channel matrix in the time domain into a number of small sub-matrices (blocks), and represent the system with a factor graph. Based on the graph representation, a message passing receiver is developed, where the unitary approximate message passing (UAMP) is used to handle the blocks. The proposed receiver does not require the frequent use of CPs or null symbols, while delivering promising performance.

Channel estimation and data detection schemes for Orthogonal Time Frequency Space massive MIMO systems

This work proposes a superimposed pilot (SP)-based channel estimation and data detection framework for orthogonal time-frequency space (OTFS) scheme, wherein low-powered pilots are superimposed on to data symbols in the delay-Doppler domain. We propose an iterative channel estimation and data detection design for SP-OTFS systems which, unlike the existing OTFS designs, does not designate any slots for pilots, which improves its spectral efficiency (SE). The proposed design iterates between message-passing-aided data detection and data-aided channel estimation. The data-detection and channel-estimation steps of the proposed design exploit the OTFS channel sparsity, which reduces its computational complexity. We numerically show that the proposed design has superior SE than the two state-of-the-art OTFS channel estimation and data detection designs.

Orthogonal Time–Frequency Space (OTFS) modulation has emerged as a promising waveform for high-mobility wireless channels because it maps information into the delay–Doppler domain and offers robustness against channel time-variations. However, like other multicarrier schemes, OTFS exhibits high peak-to-average power ratio (PAPR), which degrades transmitter power efficiency and causes nonlinear distortion when passed through power amplifiers. This paper surveys and compares three families of PAPR-reduction techniques adapted to OTFS — (1) precoding (symbol-domain transforms and optimization), (2) clipping and filtering (and variants such as iterative clipping & filtering), and (3) coding-based and selective mapping (including PTS/SLM and hybrid variants). For each family we review principles, implementation complexity, and reported PAPR reduction, and analyze the trade-off between PAPR mitigation and bit-error-rate (BER) degradation. We propose a unified evaluation framework and outline simulation experiments that quantify complementary strengths: precoding tends to lower PAPR with little BER loss at moderate complexity, clipping is simple and effective but introduces in-band distortion which elevates BER, and coding/SLM/PTS methods offer configurable PAPR–BER tradeoffs at the cost of side information or complexity. Finally, we provide best-practice recommendations for OTFS system designers and directions for future research, including hybrid methods and ML-assisted optimization.