A High-Performance Block LMMSE Equalizer for OTFS-MIMO Diversity and Multiplexing

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).

One of the promising techniques to achieve high-speed data transmission in limited bandwidth is multi-input multi-output (MIMO) multiplexing. In MIMO multiplexing, signal separation/detection is one of the most important signal processing parts, so that the signal separation/detection schemes have been vigorously researching. Recently, as a promising signal separation/detection scheme, frequency-domain iterative interference cancellation (FD-IIC) has been proposed. FD-IIC can achieve good transmission performance which is close to lower bound when QPSK is used. However, the accuracy of signal separation/detection significantly degrades in case of high data modulation. Therefore, in this paper, to improve the accuracy of signal separation/detection, we propose layered-symbol iterative interference cancellation (LSIC). We consider single-carrier (SC) MIMO multiplexing and the achievable frame error rate (FER) performances with LSIC are evaluated by computer simulation to show that LSIC can provide better FER performance than FD-IIC.

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.

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 coherently combine the received multipath components of the transmitted symbols in the delay-Doppler grid using maximal ratio combining (MRC) to improve the SNR of the combined signal. We reformulate the OTFS input-output relation in simple vector form by placing guard null symbols or zero padding (ZP) in the delay-Doppler grid and exploiting the resulting circulant property of the blocks of the channel matrix. Using this vector input-output relation we propose a low complexity iterative decision feedback equalizer (DFE) based on MRC. The performance and complexity of the proposed detector favorably compares with the state of the art message passing detector. An alternative time domain MRC based detector is also proposed for even faster detection. We further propose a Gauss-Seidel based over-relaxation parameter in the rake detector to improve the performance and the convergence speed of the iterative detection. We also show how the MRC detector can be combined with outer error-correcting codes to operate as a turbo DFE scheme to further improve the error performance. All results are compared with a baseline orthogonal frequency division multiplexing (OFDM) scheme employing a single tap minimum mean square error (MMSE) equalizer.

Channel estimation performance is an important evaluation parameter in Orthogonal Time Frequency Space (OTFS) modulated systems, in which the pilots in the delay-Doppler (DD)-domain are estimated at the receiver point. The proposed adjustment model will collect results of the history transmission progress and utilize these records to adjust the channel estimation path for the next transmission progress. A BP-based learning algorithm is introduced into the adjustment model, which completes the adjustment progress by analyzing pilot final channel selection and other not selected channels in history transmission. Feedback from the adjustment model is used in the next OTFS transmission for reducing channel estimation paths when data/signals with the same DD-domain index are transmitted in another transmission set. The simulation results indicate that the improvement of our proposal under classical Bit Error Rate(BER)-based scheme is competitive in various learning-based OTFS optimization solutions.

By selecting various active-silent combinations, classical frequency-domain index modulation (IM) generates numerous energy-free subcarriers dispersed across subblocks, which we refer to as the fragmented spectra. This letter proposes a novel IM approach aimed at collecting the fragmented spectra in subblocks to form a completely unused frequency band, called the IM-aided fragmented spectra centralization (IM-FSC). Specifically, within each subblock, if the last subcarrier is to be activated, we transfer this active position to the first unactivated subcarrier and employ a distinguishable constellation to modulate the symbol on this subcarrier. Through this approach, each subblock contributes one energy-free subcarrier, and the unused frequency band can be obtained accordingly by combining these fragmented spectra from multiple subblocks. We designate this unoccupied frequency band as zero padding (ZP) and guard interval for interference cancellation and channel estimation in orthogonal time frequency space (OTFS) system. The closed-form expressions of bit error rate (BER) and generalization guidelines are also derived. Simulation results demonstrate the promising communication capability and channel estimation accuracy of the proposed scheme.

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 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.

In this study, the Peak-to-Average Power Ratio (PAPR) and Bit Error Rate (BER) performance in Orthogonal Time Frequency Space (OTFS) modulation with Non-Orthogonal Multiple Access (NOMA) over Rayleigh fading channels were investigated. Simulations with 256-QAM and 512-QAM modulation schemes on 256 subcarriers evaluated several PAPR reduction techniques, including the Vandermonde matrix-based Partial Transmit Sequence with Companding (Vm-PTS+Companding), Vm-SLM+Companding, conventional PTS, Selective Mapping (SLM), Companding, and Clipping & Filtering (C&F). The proposed Vm-PTS+Companding achieves up to 9dB PAPR reduction for 256-QAM and 8.9dB for 512-QAM at a Complementary Cumulative Distribution Function (CCDF) of [Formula: see text], outperforming existing methods. Under a [Formula: see text] channel estimation error, the PAPR performance degrades, yet the proposed scheme maintains a 2.9-9.9dB gain over conventional approaches. BER analysis showed Signal-to-Noise Ratio (SNR) improvements of 3.5-13.7dB in ideal channels and up to 16dB under error conditions. Power Spectral Density (PSD) evaluation further confirmed the reduced spectral leakage, with the method achieving a level of [Formula: see text]dB. These results demonstrate that Vm-PTS+Companding effectively optimizes both the PAPR and BER in OTFS-NOMA systems, supporting high data rates in error-prone wireless environments.

A doppler delay-time frequency (DD-TF) cross-domain high-security transmission scheme based on orthogonal time frequency space (OTFS) is proposed, which is compatible with high-speed and large-capacity optical transmission systems. In this scheme, 36 sets of chaotic sequences are mapped out through a two-dimensional chaotic system with variable control parameters and variable initial values for optical physical layer encryption. The data modulated based on OTFS is encrypted by multiple sets of chaotic sequences, achieving cross-domain joint encryption in the DD domains and TF domains. This method improves security performance of the optical transmission system. An experiment is conducted, in which the encrypted 16-quadrature amplitude modulation (QAM) OTFS signals over 25km standard single-mode fiber (SSMF) is achieved, and the key space is 101140 to effectively prevent malicious attacks from illegal Optical Network Units (ONUs). This key space is the reported maximum key space of the physical layer of two-dimensional chaotic systems. Compared with orthogonal frequency division multiplexing (OFDM) encryption scheme, this scheme obtains better transmission performance. It is shown that OTFS system with cyclic prefix (CP) of 1/16 obtains 2.1dB gain than the OTFS system with CP of 1/32 in terms of receiver sensitivity when the bit error rate (BER) is 10-3. Due to its comprehensive advantages in error rate and security performance, this chaotic encryption based on OTFS has a high application prospect in low-cost and reliable optical access system.

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.

In this paper, we investigate the robustness of the Unique Word Orthogonal Frequency Division Multiplexing (UW-OFDM) technique for channel estimation issue. We consider the UW-OFDM technique instead of Zero-Padding (ZP) OFDM one to construct the OFDM symbols for MultiBand Orthogonal Frequency Division Multiplexing Ultra WideBand (MB-OFDM UWB) systems. Then, we propose a two-step LMMSE channel estimator. In the first step, by using the knowledge of UW sequence in the receiver side, the Channel Frequency Response (CFR) is estimated. In the second step, the Linear Minimum Mean-Squared Error (LMMSE) channel estimation is performed using the estimated CFR of the first step and the Channel Estimation Sequence (CES) included in the frame preamble. We evaluate the performance of the proposals in terms of Bit Error Rate (BER) by computer simulations. We show that the consideration of UW-OFDM technique provides, not only reduction of complexity, but also improvement in BER performance. Moreover, we show that the two-step LMMSE channel estimation does not affect the system performance mainly for low Signal-to-Noise Ratio (SNR).

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.

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.

PAPR analysis in OTFS using the centre phase sequence matrix based PTS method