Phase-Tailored OTFS Waveform with Reduced Sidelobes for ISAC Systems

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.

Next generation wireless communication systems are considering orthogonal time frequency space (OTFS) waveform as an alternative to the existing orthogonal frequency division multiplexing (OFDM) waveform. It is more robust to high Doppler and high carrier frequencies. Multiple recent papers have evaluated OTFS at higher Doppler with long term evolution (LTE) system, to show its performance benefits over OFDM. In this paper, we provide the performance evaluation of OTFS waveform at mmWave frequencies using the third generation partnership project (3GPP) 5G new radio (NR) transmit-receive chain for different quadrature amplitude modulation (QAM) schemes. We compare the OTFS performance with that of OFDM, for 3GPP defined tapped delay line (TDL) and cluster delay line (CDL) channel models at multiple mobility conditions. We analyze the performance difference between OTFS and OFDM using both minimum mean-squared error (MMSE) and decision feedback equalizers (DFE) at the receiver, and show the need for DFE at higher modulation order, to compensate the inter symbol interference. We show that the OTFS has 10 dB gain in signal to noise ratio (SNR) over OFDM, for TDL-C channel with delay spread of 300 ns, at high speed train mobility of 500 kmph for 64-QAM, when evaluated with DFE. We further present the computational complexity of OTFS system, in comparison to OFDM.

Orthogonal time sequency multiplexing (OTSM) modulation is a new single-carrier modulation scheme proposed in recent years, which has higher performance gain than traditional orthogonal frequency division multiplexing (OFDM) and similar performance to orthogonal time frequency space (OTFS). However, the design complexity of the transmitter and receiver is greatly reduced by using the Walsh-Hadamard transform. In this paper, the OTSM modulation scheme is introduced and analyzed from the basic principle, and the modulator of OTSM system is designed and implemented by using Verilog hardware description language in QuartusII environment using field programmable gate array technology, and the effectiveness of the design is verified by Modelsim software simulation.

In this dissertation, new vehicular communication (V2V, V2X) scenarios are going to be studied. Under this context, against common and well known radar systems, new joint radar and communications techniques are taking part of the current literature. These system are mainly focused on the transmission of useful information towards the targets, which are, thus, not only “passively” detected, and a single equipment is able to perform both operational modes, avoiding to split the functionalities between two distinct subsystems (with increased cost and complexity). The choice of the multi-carrier modulation for joint radar and communication falls into two distinct waveforms, i.e., orthogonal frequency-division multiplexing (OFDM) modulation and orthogonal time frequency space (OTFS) modulation. OFDM is the most popular multi-carrier modulation of recent years, widely studied and standardized in most of the current communication standards, including 5G. The motivation of this choice is simple: thanks to the application of a cyclic prefix between symbols, i.e., a guard interval to prevent inter-symbol interference, and under the assumption of absence of inter-carrier interference, which holds under reasonable amount of the Doppler effect and subcarrier spacing, the communication channel can be diagonalized and symbol-by-symbol detection performed. Clearly, the appealing simplicity of detection makes OFDM the best choice for modern digital communications. On the other hand, OTFS is a modulation waveform with two big differences with respect to its direct competitor. First, it does not necessitate the insertion of the cyclic prefix, achieving a better communications rate, i.e., more information is sent over a time-frequency window, but at the cost of a more complex detection approach, working blockwise and not symbol-by-symbol. Second, OTFS is not sensitive to delay and Doppler shifts, meaning that its performance is kept constant whatever the distance and the speed between transmitter and (target) receiver. This feature is very appealing for joint radar and communication tasks, being the scenario very dynamical, with possible remarkable Doppler shifts and delays, increased by considering the round-trip time between radar transmitter and target. Based on the aforementioned analysis, in this dissertation we take care of a fair comparison between the two digital modulation formats, from the point of view of radar, parameter estimation, achievable communication rate, channel estimation, and more other tasks, to determine their positive and negative aspects, such that a system designer is able to choose the most suitable waveform for a given scenario or application.

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.

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.

Orthogonal time frequency space (OTFS) modulation is often declared to be superior to its direct concurrent, i.e., orthogonal frequency division multiplexing (OFDM) modulation. However, the comparison is often performed under favorable conditions for OTFS as, for instance, the assumption of extremely high Doppler shifts and/or the approximation of delay and Doppler shifts to be integer multiples of the Doppler-delay resolution of OTFS modulation. In order to provide a fair comparison, this paper addresses a comparison in terms of the information-theoretic achievable rate under practical separate detection and decoding, explicitly considering the pilot overhead necessary to acquire the channel state information, the accuracy of the channel estimation, and any other possible additional loss. We do not claim to establish in a definitive way which is the best modulation format, since the choice thereof depends on many other features which are outside the scope of this work (e.g., legacy, intellectual property, ease and know-how for implementation, and many other criteria). Nevertheless, we provide the foundations to properly compare multi-carrier communication systems in terms of their information theoretic achievable rate potential, within meaningful and sensible assumptions on the channel models and on the receiver complexity (both in terms of channel estimation and in terms of soft-output symbol detection).

Orthogonal time frequency space (OTFS) modulation has been proved to have better bit error rate (BER) performance over orthogonal frequency division multiplexing (OFDM) under high-mobility conditions. In this letter, a new transmission scheme, called OTFS with dual-mode index modulation (OTFS-DM-IM), is proposed to balance the transmission reliability and spectral efficiency. Moreover, a modified log-likelihood ratio (LLR) detector based on the minimum Hamming distance is designed for demodulation. Then, the theoretical BER analysis of the proposed OTFS-DM-IM is presented. Simulation results highlight the performance advantage of OTFS-DM-IM over classical OTFS and the existing OTFS systems based on index modulation (OTFS-IM), and also confirm the superiority of the modified LLR detector compared to maximum likelihood detector and conventional LLR detector.

In high-mobility scenarios envisioned for 6G communications, orthogonal time frequency space (OTFS) has emerged as a promising alternative to conventional orthogonal frequency division multiplexing (OFDM) schemes. To address the parameter estimation problem in OTFS-integrated radar and communication systems, we propose a two-stage parameter estimation framework based on sparse reconstruction and the Alternating Direction Method of Multipliers-Newton (ADMM-Newton), which exploits the sparsity of OTFS signals in the delay-Doppler (DD) domain to enable precise parameter estimation in high-mobility scenarios. In the first step, we construct an echo signal model for an OTFS-integrated radar-communication system and estimate the delay and Doppler integer grid values of the detected targets using a sparse reconstruction-based ADMM algorithm. In the second step, the estimates of the integer grid parameters are used as constraints for a more specific search. Fractional-precision estimations of the range and velocity parameters are obtained by iteratively solving for the Newton direction via the Newton algorithm. Finally, numerical simulations are executed to verify the proposed algorithm’s performance in parameter estimation in ISAC systems. The results demonstrate that the proposed algorithm achieves millimeter-level accuracy in velocity estimation under single-target simulation scenarios. Particularly in situations involving multiple sensing targets, the proposed method can estimate target range and velocity with centimeter-level accuracy. The proposed algorithm effectively eliminates notable differences between estimated and real values due to three targets interfering with one another, demonstrating strong estimation accuracy. Furthermore, in target conditions that are closely spaced, the proposed algorithm maintains robust estimation accuracy.

Orthogonal time frequency space (OTFS) modulations are robust to time-varying frequency-selective fading channels. OTFS modulations operate in the delay-Doppler domain whereas two-dimensional (2D) orthogonal frequency division multiplexing (OFDM) modulations operate in the time-frequency domain. For 2D OFDM modulations in time-varying frequency-selective fading channels, we investigate the pilot pattern design problem, which minimizes the mean square error (MSE) of channel estimation. The MSE lower bound (LB) is theoretically derived to provide the design criterion. Based on the criterion, we show that the LB achieving design can be found by exhaustive 2D pilot location search. Exhaustive 2D search has high computational complexity. To reduce the complexity, sufficient conditions on the existence of LB achieving design are provided to decouple the 2D problem into two one-dimensional (1D) problems. For the 1D problem, we propose the LB achieving design when the number of possible pilot locations is divisible by the number of pilots. Simulation results illustrate that our proposed LB achieving design is superior to the random pilot pattern design and the bilinear interpolation channel estimation method.

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.

Obtaining an efficient multicarrier signalling technique is an essential part in signal processing of the (6G) wireless networks. In order to achieve their intended objectives, the 6G mobile networks needs the utilization of a multicarrier scheme that possesses the ability to withstand multipath fading and inter-symbol interference (ISI), as well as exhibit resilience against inter-carrier interference (ICI) and Doppler spread. In recent research, several filter-based methods have been suggested, including Filter Bank Multicarrier (FBMC), as well as various Orthogonal Frequency Division Multiplexing (OFDM) based techniques such as Universal Filtered Multicarrier (UFMC). Orthogonal Time-Frequency Space (OTFS) technique has been identified as a promising candidate waveform for 6G, particularly in high-mobility scenarios, where it has demonstrated superior performance compared to traditional OFDM-based techniques. The OTFS method offers an advantage in that it can be considered the pre-and post-processing stages for techniques based on OFDM. This papaer presents the design (OTFS) using (UFMC) technique. Additionally, a novel structure is proposed for coded/uncoded UFMC-based OTFS technique, which combines the advantages of both strategies while mitigating their limitations. The results of our analysis demonstrate that the UFMC-based OTFS system exhibits superior performance in terms of error probability and time-spectral efficiency compared to the OFDM-based OTFS system.

Orthogonal time frequency space (OTFS) modulation exhibits excellent performance in time-varying channels with severe Doppler shifts. Diversity analysis is an effective method in predicting error performance of an OTFS system. Recent works have studied OTFS diversity in a time-varying channel assuming constant delay-Doppler (DD) channel realization per frame. However, in practice, DD channel realizations may vary in a frame due to the rapid changes in channel geometry relative to a frame duration, leading to a block time-varying (BTV) channel. This paper analyzes the OTFS diversity in such BTV channels. Specifically, we derive the pairwise error probability of the system and analyze its diversity by finding the minimum rank of the pairwise error matrix and its associated multiplicity. We also compare it with other known schemes and demonstrate its improved diversity. Finally, simulations are performed to validate the analytical results.

Orthogonal Time Frequency Space (OTFS) is a two-dimensional modulation technique designed in the delay-Doppler (DD) domain. Each symbol experiences a sparse channel with low variability in the DD domain rather than the time-varying multi-path channel in conventional orthogonal frequency division multiplexing systems. In practical applications, fractional Doppler shifts is unavoidable due to the limited frame duration. Channel dispersion caused by fractional Doppler shifts makes the channel estimation more difficult and causes data aliasing. In this paper, we propose an adaptive scheme to reduce fractional Doppler shifts. Doppler shift compensation is performed on time-domain signals and the number of time-domain symbols is changed to approximate the quantized Doppler shifts integers. With the proposed adaptive scheme, the overhead of the reference signal can be significantly reduced with the fractional Doppler shifts eliminated. Simulation results show that block error rate performance is not degraded and system throughput is improved with the proposed scheme.