Orthogonal Time–Frequency Space Modulation

Recently proposed orthogonal time frequency space (OTFS) modulation has been considered as a promising candidate for accommodating various emerging communication and sensing applications in high-mobility environments. In this paper, we propose a novel cross domain iterative detection algorithm to enhance the error performance of OTFS modulation. Different from conventional OTFS detection methods, the proposed algorithm applies basic estimation/detection approaches to both the time domain and delay-Doppler (DD) domain and iteratively updates the extrinsic information from two domains with the unitary transformation. In doing so, the proposed algorithm exploits the time domain channel sparsity and the DD domain symbol constellation constraints. We evaluate the estimation/detection error variance in each domain for each iteration and derive the state evolution to investigate the detection error performance. We show that the performance gain due to iterations comes from the non-Gaussian constellation constraint in the DD domain. More importantly, we prove that the proposed algorithm can indeed converge and, in the convergence, the proposed algorithm can achieve almost the same error performance as the maximum-likelihood sequence detection even in the presence of fractional Doppler shifts. Furthermore, the computational complexity associated with the domain transformation is low, thanks to the structure of the discrete Fourier transform (DFT) kernel. Simulation results are consistent with our analysis and demonstrate a significant performance improvement compared to conventional OTFS detection methods.

This paper presents a linear complexity iterative rake detector for the recently proposed orthogonal time frequency space (OTFS) modulation scheme. The basic idea is to extract and combine the received multipath components of the transmitted symbols in the delay-Doppler grid using linear diversity combining schemes like maximal ratio combining (MRC), equal gain combining and selection combining to improve the SNR of the combined signal. We reformulate the OTFS input-output relation in the vector form by placing some null symbols in the delay-Doppler grid thereby exploiting the block circulant property of the channel matrix. Using the new input-output relation we propose a low complexity iterative detector based on the MRC scheme. The bit error rate (BER) performance of the proposed detector will be compared with the state of the art message passing detector and orthogonal frequency division multiplexing (OFDM) scheme employing a single tap minimum mean square error (MMSE) equalizer. We also show that the frame error rate (FER) performance of the MRC detector can be improved by employing error correcting codes operating in the form of a turbo decision feedback equalizer (DFE).

In this article, a successive interference cancellation (SIC) based minimum mean squared error (MMSE) signal detection is investigated for orthogonal time frequency space (OTFS) modulation. In this proposed detection technique, the transmit symbols will be detected on the basis of layers, and different multipath components of the same layer signal together with its interference will be coherently combined and suppressed through MMSE filtering. The performance will be further improved from an iterative operation on SIC-MMSE detection. The complexity of calculating MMSE filter coefficients can be reduced when detection is performed in the time domain due to its simpler channel structures. Simulation shows that our proposed SIC-MMSE detection can outperform maximum-ratio-combing (MRC) thanks to its inherent balances on matched filter and zero-forcing detector.

The upcoming sixth-generation (6 G) communications is expected to support reliable communications for dense wireless networks even with high-mobility users. Integrating sparse code multiple access (SCMA) aided cell-free massive MIMO (CF-mMIMO) with orthogonal time frequency space (OTFS) modulation, i.e., SCMA-based CF-mMIMO-OTFS, potentially addresses these demands. Such a system can leverage the high-density network capabilities of SCMA-based CF-mMIMO and the robustness of OTFS in time-varying channels. This paper studies the error performance of a downlink (DL) user in such a system. We first derive the pairwise error probability (PEP) of a DL user and then an upper bound on the PEP. Based on this upper bound, we derive the maximum diversity order of the DL user. Our analysis highlights the need for better multi-user interference mitigation and provides insights into how the error performance is affected by the multiple access scheme and system/channel parameters. Simulation results validate the analytical findings, demonstrating significant error performance improvements of SCMA-assisted schemes over standard CF-mMIMO-OTFS and orthogonal multiple access (OMA)-based CF-mMIMO schemes.

In this paper, we investigate the use of a new modulation scheme recently introduced in the RF domain, called orthogonal time frequency space (OTFS) modulation, in an indoor visible light communication (VLC) setting. In particular, we consider VLC systems that employ dual-LED schemes for transmission. The following dual-LED schemes are considered: 1) non-DC biased (NDC) scheme, and 2) dual-LED complex modulation (DCM) scheme. The proposed NDC-OTFS scheme uses 2-dimension (2D) Hermitian symmetry operation to convert complex signals to positive, real-valued signals suitable for transmission in the optical domain, and the proposed DCM-OTFS scheme achieves this by exploiting the polar representation of complex signals. We obtain analytical upper bounds on the bit error performance of the proposed NDC-OTFS and DCM-OTFS schemes, which are found to be tight at high signal-to-noise ratios (SNR). Our analytical and simulation results show that the proposed NDC-OTFS and DCM-OTFS schemes achieve better performance, respectively, compared to NDC-OFDM and DCM-OFDM schemes known in the VLC literature. Further, using the ratio of the minimum distance of different normalized received signal sets as a metric, we quantify the spatial distribution of the SNR gain of the proposed NDC-OTFS/DCM-OTFS schemes compared to NDC-OFDM/DCM-OFDM schemes.

Covert communication aims to hide the existence of wireless transmissions which provides a strong security guarantee for wireless networks. This paper investigates the covert communacation performance of Orthogonal Time Frequency Space (OTFS) frame. The transmitter transmits messages to the receiver through OTFS modulation, where an eveasdropper tries to detect its existence. Different from the binary hypothesis test based the radio meter detection framework considered in prior works, we adopted sequential change-point detection (SCPD) framework and derives the closed-form expression for the average run length ratio (ARLR). In simulation results, we analyze the conditional average detection delay (CADD) reflecting the covert communication performance for the OTFS frame structure on the covert performance. Our results indicate that the closer the guard interval position is to the detection start position, the better the covert performance can achieve, while the pilot has the opposite effect.

Non-Contiguous Orthogonal Time Frequency Space Modulation for Cognitive Radio to Enhance Spectrum Sharing in High Doppler Channels

Multi and single carrier waveforms are utilized in cellular systems for high-speed data transmission. In The Fifth Generation (5G) system, several waveform techniques based on multi carrier waveforms are proposed. However, the Peak to Average Power Ratio (PAPR) is seen as one of the significant concerns in advanced waveforms as it degrades the efficiency of the framework. The proposed article documents the study, progress, and implementation of PAPR reduction algorithms for the 5G radio framework. We compare the PAPR algorithm performance for advanced and conventional waveforms. The simulation results reveal that the advanced Partial Transmission Sequence (PTS) and Selective Mapping (SLM) methods enhanced the throughput and gain of the 5G waveforms. Furthermore, we have also analyzed the performance of Orthogonal Time Frequency Space Modulation (OTFSM) based on a single carrier system and found that PAPR is significantly low and is best suited to fading environments. It is seen that the conventional algorithms lower the PAPR but increase the complexity. The proposed PTS and SLM have shown good performance with low computational complexity.

Symbiotic radio (SR) holds promise for large-scale Internet of Things (IoT) networks by allowing both primary and secondary systems to share spectrum resources for mutually beneficial transmission. However, in high-mobility scenarios, rapidly changing channels pose significant challenges for reliable and low-latency communications. To enable SR transmission over high-mobility channels, this paper explores the secondary transmission and equivalent channel estimation problems in intelligent reflecting surface (IRS)-SR systems utilizing orthogonal time frequency space (OTFS) modulation. The IRS is divided into multiple groups, each attached with informative frequencies, for secondary transmission. Exploiting the spectrum structure induced by the secondary information, a deep learning (DL)-based secondary information detector is proposed. Moreover, after transforming the channel estimation problem into a compressed sensing (CS) problem, a DL-sparse Bayesian learning (SBL) network is proposed to improve the estimation accuracy and ease the computational afford by avoiding the large amount of iterations in conventional CS algorithms, e.g. the SBL algorithm. Finally, numerical results are provided to illustrate the superiority of the proposed detector and estimator over several benchmarks.

In this paper, we model M × N orthogonal time frequency space modulation (OTFS) over a P-path doubly dispersive channel with delays less than τ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> and Doppler shifts in the range (ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> ,ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> ). 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.

Recently, orthogonal time frequency space modulation with index modulation (OTFS-IM) has been proposed, which can achieve better bit error rate (BER) performance than conventional OTFS. In this letter, a new transmission scheme, OTFS with in-phase and quadrature index modulation (OTFS-I/Q-IM), is presented to increase the spectral efficiency of OTFS-IM, in which additional information bits are carried through the grid index of OTFS block in in-phase and quadrature dimensions. Furthermore, the analytical expressions of average bit error probability (ABEP) and the maximum peak to average power ratio (PAPR) are derived to evaluate the performance of the proposed scheme. Simulation results demonstrate the enhanced performance of the proposed scheme in high-mobility scenarios.

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 &amp; 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 a recently introduced modulation which has been shown to perform better than OFDM in RF wireless communications. In this paper, we investigate OTFS in multi-LED indoor visible light wireless communications. We propose two multi-LED OTFS schemes, namely, quadrature spatial modulation OTFS (QSMOTFS) scheme and dual mode index modulation OTFS (DMIMOTFS) scheme. The proposed schemes use dual-LED complex modulation as the basic building block and offer enhanced rates compared to conventional index modulation schemes. The schemes also have the advantage of not requiring Hermitian symmetry and DC bias operations to obtain real, positive-valued signals suited for intensity modulation of LEDs. We obtain upper bounds on the bit error rate performance of the proposed schemes, which are tight at high signal-to-noise ratios. The proposed OTFS schemes are shown to perform better than their OFDM counterparts known in the literature. In addition, the spatial distribution of the performance gap between OTFS and OFDM across the room is captured using the ratio of the minimum distance of normalized received signal sets of the considered schemes as a metric.

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.

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.