Orthogonal Space Research Articles

Doubly-Iterative Sparsified MMSE Turbo Equalization for OTFS Modulation

Currently, orthogonal time frequency space (OTFS) modulation has drawn much attention to reliable communications in high-mobility scenarios. This paper proposes a doubly-iterative sparsified minimum mean square error (DI-S-MMSE) turbo equalizer, which iteratively exchanges the extrinsic information between a soft-input-soft-input (SISO) MMSE estimator and a SISO decoder. Our proposed equalizer does not suffer from short loops and approaches the performance of the near-optimal symbol-wise maximum a posteriori (MAP) algorithm. To exploit the inherent sparsity of OTFS system, we resort to graph theory to investigate the sparsity pattern of the channel matrix, and propose two sparsification guidelines to reduce the complexity of calculating the matrix inverse at the MMSE estimator. Then, we apply two iterative algorithms to MMSE estimation, i.e., the Generalized Minimal Residual (GMRES) and Factorized Sparse Approximate Inverse (FSPAI) algorithms. The former is used at the initial turbo iteration, whose global convergence is proven in our equalizer, while the latter is used at the subsequent turbo iterations with the help of our proposed guidelines. Simulation results demonstrate that our equalizer can achieve a good bit-error-rate (BER) performance regardless of the fractional Doppler, and only has a linear order of complexity.

On the Characterizations of OTFS Modulation Over Multipath Rapid Fading Channel

Orthogonal time frequency space (OTFS) modulation has been confirmed to provide significant performance advantages against Doppler in high-mobility scenarios. The core feature of OTFS is that the time-variant channel is converted into a non-fading 2D channel in the delay-Doppler (DD) domain so that all symbols experience the same channel gain. In available literature, the channel is assumed to be quasi-static over an OTFS frame. As for more practical scenarios, the Doppler shift is dynamic and the channel gain could be time-variant as the environment or medium changes. In this paper, we analyze the characterizations of OTFS modulation over a more general multipath channel, where the signal in each propagation path has experienced a unique rapid fading. First, we derive the explicit input-output relationship of OTFS in the DD domain for the case of ideal pulse and rectangular pulse. It is shown that the rapid fading will produce extra Doppler dispersion without impact on delay domain. We next demonstrate that OTFS can be interpreted as an efficient time diversity technology that combines space-time encoding and interleaving against the rapid fading. Simulation results reveal that OTFS is insensitive to rapid fading and still outperforms conventional multicarrier systems in these channels.

Joint Compensation of TX/RX IQ Imbalance and Channel Parameters for OTSM Systems

Orthogonal time sequency multiplexing (OTSM), robust to doubly-selective fading channel, performs similar to orthogonal time frequency space (OTFS) system with less modulation/demodulation complexity. Direct conversion OTSM system suffers from hardware impairments such as in-phase and quadrature phase (IQ) imbalance at the transmitter (TX) and receiver (RX). At high frequencies, hardware imperfections are inevitable and should be compensated for better performance. In this Letter, we propose joint estimation of TX and RX IQ imbalance and estimate channel parameters in the delay time domain using pseudo noise based training sequence approach. The mean square error of the estimated channel parameters reduce with increase in training sequence length and power. With matched filtered Gauss-Seidel iterative method of detection of low complexity, it is shown that the compensated system performs close to ideal system under fractional delay and fractional Doppler.

ViterbiNet-Based Signal Detection for OTFS System

Recently, orthogonal time frequency space (OTFS) was presented to combat high Doppler shifts in wireless communication systems. Most studies on OTFS signal detection require channel state information (CSI). However, it is quite difficult to describe the channel model mathematically for some communication systems. This letter proposes a low-complexity ViterbiNet-based OTFS signal detection algorithm. A neural network (NN) is used in the ViterbiNet to replace the log-likelihood calculation that requires CSI in the Viterbi algorithm. Therefore, the proposed ViterbiNet-based scheme can perform signal detection without CSI in OTFS systems. Meanwhile, since it is a model-driven network, the proposed ViterbiNet-based scheme requires only a small size NN and a small amount of training data to achieve great performance. Moreover, the softplus function is utilized as the activation function, which smoothen the training of the ViterbiNet. Through experiments, simulation results prove the performance of the presented ViterbiNet-based OTFS signal detection algorithm.

Optical characterization of the psychophysical surface gloss space in the presence of surface haze

An unanimous framework for surface gloss perception does not exist yet, although an orthogonal two-dimensional gloss space (distinctness-of-image and contrast gloss) has already been proposed. Haze, a rarely studied attribute of glossiness, is considered in this study and introduced into this existing space. A set of samples with surface haziness is psychophysically and optically characterized. The perceived glossiness correlates with the visual dimension of contrast gloss, and with metrics based on “contrast” - between the specular highlight and sample background – obtained from measurements with different optical instruments. The suitability and advantages of the image-based gloss meter (iGM), introduced earlier by the authors [J Coat Technol Res. 19, 1567 (2022)10.1007/s11998-022-00630-0OCPOBG2770-0208], are thereby illustrated in comparison to the conventional gloss meter standards.

Low PAPR preamble-based channel estimation for OTFS systems on static multipath channels

In this paper we propose two preamble-based channel estimation methods for orthogonal time frequency space (OTFS) modulation. These new methods allow a robust channel estimation in noisy scenarios and static multipath channels. Moreover, the proposed preambles exhibit a strong resilience to nonlinearities introduced by high power amplifiers (HPA). We demonstrate that our proposed methods outperform the existing techniques in the literature, allowing the HPA to work at a low input backoff (IBO). To the best of the authors' knowledge, this is the first paper that addresses a study of HPA linearity in OTFS systems. Finally, we show that the complexity of our channel estimators is low enough for an efficient hardware implementation.

Wold-type decomposition for [formula omitted]-twisted contractions

Let n>1, and {Uij} for 1≤i<j≤n be (n2) commuting unitaries on a Hilbert space H such that Uji:=Uij⁎. An n-tuple of contractions (T1,…,Tn) on H is called Un-twisted contraction with respect to a twist {Uij}i<j if T1,…,Tn satisfyTiTj=UijTjTi;Ti⁎Tj=Uij⁎TjTi⁎andTkUij=UijTk for all i,j,k=1,…,n and i≠j. We obtain a recipe to calculate the orthogonal spaces of the Wold-type decomposition for Un-twisted contractions on Hilbert spaces. As a by-product, a new proof as well as complete structure for U2-twisted (or pair of doubly twisted) and Un-twisted isometries have been established.

Persistent Homology Approach for Human Presence Detection from 60 GHz OTFS Transmissions.

Orthogonal Time Frequency Space (OTFS) is a new, promising modulation waveform candidate for the next-generation integrated sensing and communication (ISaC) systems, providing environment-awareness capabilities together with high-speed wireless data communications. This paper presents the original results of OTFS-based person monitoring measurements in the 60 GHz millimeter-wave frequency band under realistic conditions, without the assumption of an integer ratio between the actual delays and Doppler shifts of the reflected components and the corresponding resolution of the OTFS grid. As the main contribution of the paper, we propose the use of the persistent homology technique as a method for processing gathered delay-Doppler responses. We highlight the advantages of the persistent homology approach over the standard constant false alarm rate target detector for selected scenarios.

Hybrid autoencoder with orthogonal latent space for robust population structure inference

Analysis of population structure and genomic ancestry remains an important topic in human genetics and bioinformatics. Commonly used methods require high-quality genotype data to ensure accurate inference. However, in practice, laboratory artifacts and outliers are often present in the data. Moreover, existing methods are typically affected by the presence of related individuals in the dataset. In this work, we propose a novel hybrid method, called SAE-IBS, which combines the strengths of traditional matrix decomposition-based (e.g., principal component analysis) and more recent neural network-based (e.g., autoencoders) solutions. Namely, it yields an orthogonal latent space enhancing dimensionality selection while learning non-linear transformations. The proposed approach achieves higher accuracy than existing methods for projecting poor quality target samples (genotyping errors and missing data) onto a reference ancestry space and generates a robust ancestry space in the presence of relatedness. We introduce a new approach and an accompanying open-source program for robust ancestry inference in the presence of missing data, genotyping errors, and relatedness. The obtained ancestry space allows for non-linear projections and exhibits orthogonality with clearly separable population groups.

Orthogonal latent space learning with feature weighting and graph learning for multimodal Alzheimer's disease diagnosis.

Recent studies have shown that multimodal neuroimaging data provide complementary information of the brain and latent space-based methods have achieved promising results in fusing multimodal data for Alzheimer's disease (AD) diagnosis. However, most existing methods treat all features equally and adopt nonorthogonal projections to learn the latent space, which cannot retain enough discriminative information in the latent space. Besides, they usually preserve the relationships among subjects in the latent space based on the similarity graph constructed on original features for performance boosting. However, the noises and redundant features significantly corrupt the graph. To address these limitations, we propose an Orthogonal Latent space learning with Feature weighting and Graph learning (OLFG) model for multimodal AD diagnosis. Specifically, we map multiple modalities into a common latent space by orthogonal constrained projection to capture the discriminative information for AD diagnosis. Then, a feature weighting matrix is utilized to sort the importance of features in AD diagnosis adaptively. Besides, we devise a regularization term with learned graph to preserve the local structure of the data in the latent space and integrate the graph construction into the learning processing for accurately encoding the relationships among samples. Instead of constructing a similarity graph for each modality, we learn a joint graph for multiple modalities to capture the correlations among modalities. Finally, the representations in the latent space are projected into the target space to perform AD diagnosis. An alternating optimization algorithm with proved convergence is developed to solve the optimization objective. Extensive experimental results show the effectiveness of the proposed method.

Spectral Efficient Modem Design With OTFS Modulation for Vehicular-IoT System

A 5G network’s use-case in the Internet of Things (IoT) is a breakthrough, offering networks the ability to handle billions of connected devices with the proper blend of speed, latency, and cost. The IoT networks implemented in high-speed scenarios like intra and intervehicular communications in autonomous driving vehicles, high-speed vehicles, and trains will experience a Doppler effect. Orthogonal frequency-division multiplexing, the popular transmission technology for existing new-radio IoT (NR-IoT), is limited in providing reliable connections in high-speed vehicular scenarios. The performance of such system degrades with higher-order antenna configuration due to the lack of channel state information in highly mobile environments. The recently proposed orthogonal time-frequency space (OTFS) modulation is a strong contender that can handle high mobility but requires efficient transceiver design to be deployed in vehicular NR-IoT (V-IoT) systems. To conserve the resources and minimize the air time of the devices, we have proposed an embedded pilot design in the Delay–Doppler domain for the V-IoT systems. In the designed frame structure, the pilot’s position is optimized as per the vehicle speed to maximize the spectral efficiency of the system. The increase in spectral efficiency is at the cost of interference in the channel search region of the received Delay–Doppler domain OTFS signal. So a new joint estimator and the low-complex detector are proposed to handle the interference. The proposed efficient transceiver design with the spectral efficient pilot patterns allows us to conserve resources and remove complex encoder–decoders like the low-density parity check in NR-IoT.

OTFS-Based Joint Communication and Sensing for Future Industrial IoT

Effective wireless communications are increasingly important in maintaining the successful closed-loop operation of mission-critical Industrial Internet of Things (IIoT) applications. To meet the ever-increasing demands on better wireless communications for IIoT, we propose an orthogonal time-frequency space (OTFS) waveform-based joint communication and radio sensing (JCAS) scheme—an energy-efficient solution for not only reliable communications but also high-accuracy sensing. OTFS has been demonstrated to have higher reliability and energy efficiency than the currently popular IIoT communication waveforms. JCAS has also been highly recommended for IIoT, since it saves cost, power, and spectrum compared to having two separate radio frequency systems. Performing JCAS based on OTFS, however, can be hindered by a lack of effective OTFS sensing. This article is dedicated to filling this technology gap. We first design a series of echo preprocessing methods that successfully remove the impact of communication data symbols in the time-frequency domain, where major challenges, such as intercarrier and intersymbol interference and noise amplification, are addressed. Then, we provide a comprehensive analysis of the signal-to-interference-plus-noise ratio (SINR) for sensing and optimize a key parameter of the proposed method to maximize the SINR. The extensive simulations show that the proposed sensing method approaches the maximum-likelihood estimator with respect to the estimation accuracy of target parameters and manifests applicability to wide ranges of key system parameters. Notably, the complexity of the proposed method is only dominated by a 2-D Fourier transform.

A Complexity-Reduced QRD-SIC Detector for Interleaved OTFS

Signal detectors are quite important to attain the diversity of doubly-dispersive wireless channels. Detectors based on message-passing (MP) of factor graphs have been regarded as the way to achieve the near-optimal performance for OTFS. In this paper, by deriving the pattern of the multipath vectorized channel matrix of the orthogonal time frequency space (OTFS) system, it is shown that short girth (i.e. girth-4) may exist in the Tanner graphs, which will degrade the performance of MP detectors, especially with high modulation orders. By introducing interleavers at the transmitter and receiver, the vectorized channel matrix turns out to be a sparse upper block Heisenberg matrix, whose structure is beneficial for the computation of matrix QR decomposition (QRD). Successive interference canceling (SIC) detectors based on QRD and sorted QRD are constructed to eliminate the cross-symbol interference and improve the reliability of the symbol-level channel. Simulation results show that for 4QAM, the QRD-based SIC detectors can achieve about 4dB gain at 10−2 over the non-SIC detectors, while the sorted QRD-based SIC detectors can bring an additional 2dB at 10−3, which is only 1dB gap from the MP. For 16QAM, the sorted SIC detectors show superior BER performance than the MP method, and for 64QAM, the MP detector reaches the error floor while SIC detectors show their excellent performance in all configurations.

IRS-Assisted High Mobility Communications Using OTFS Modulation

Intelligent reflecting surface (IRS) has emerged as a promising technology for fifth generation (5G) and beyond wireless networks that are expected to support high mobility applications. Supporting IRS-assisted high mobility communications is nonetheless challenging due to the cascade of doubly-dispersive transmitter-IRS and IRS-receiver channels. To address this issue, we propose a multiple-input multiple-output orthogonal time frequency space (MIMO-OTFS) IRS-assisted communications system with MMSE detection. We present a general time-domain input-output relation, which is also applicable to single-input single-output OTFS (SISO-OTFS). We then design the IRS phase shifts to maximize the received signal-to-noise (SNR) for both SISO and MIMO cases. Numerical results show significantly lower error rates than orthogonal frequency division multiplexing (OFDM) IRS-assisted systems for terrestrial and non-terrestrial high-Doppler communications.

A low complexity distributed differential scheme based on orthogonal space time block coding for decode-and-forward wireless relay networks

&lt;span lang="EN-US"&gt;This work proposes a new differential cooperative diversity scheme with high data rate and low decoding complexity using the decode-and-forward protocol. The proposed model does not require either differential encoding or channel state information at the source node, relay nodes, or destination node where the data sequence is directly transmitted and the differential detection method is applied at the relay nodes and the destination node. The proposed technique enjoys a low encoding and decoding complexity at the source node, the relay nodes, and the destination node. Furthermore, the performance of the proposed strategy is analyzed by computer simulations in quasi-static Rayleigh fading channel and using the decode-and-forward protocol. The simulation results show that the proposed differential technique outperforms the corresponding reference strategies.&lt;/span&gt;

New Fixed Point Results in Orthogonal B-Metric Spaces with Related Applications

In this article, we present the concept of orthogonal α-almost Istra˘tescu contraction of types D and D* and prove some fixed point theorems on orthogonal b-metric spaces. We also provide an illustrative example to support our theorems. As an application, we establish the existence and uniqueness of the solution of the fractional differential equation and the solution of the integral equation using Elzaki transform.

Parallel model order reduction methods based on structured matrix analysis for discrete-time systems with parametric uncertainty

This paper explores two novel parallel parametric model order reduction methods for discrete-time systems with parametric uncertainty. The proposed methods allow that the parametric dependence is non-affine. With the shift-transformation matrix of the discrete orthogonal polynomials, including Charlier polynomials and Krawtchouk polynomials, the expansion coefficients of state variable in discrete orthogonal polynomials space can be obtained by solving the system of linear algebraic equations (SLAE). By applying the structured matrix analysis of the SLAE, two parallel strategies based on the equivalent transformation of block bi-diagonal matrices and the block discrete Fourier transform of block ϵ-circulant matrices are proposed to solve the SLAE. Then, the projection matrix is constructed to reduce discrete-time parametric systems. Moreover, we analyze the properties of the proposed parallel methods, including the invariable coefficients, the invertibility, and the error analysis. Finally, the effectiveness of the proposed methods is illustrated by the numerical experiments.

Iterative receiver for orthogonal time frequency space with index modulation via structured prior-based hybrid belief and expectation propagation

Orthogonal Time Frequency Space (OTFS) signaling with index modulation (IM) is a promising transmission scheme characterized by high transmission efficiency for high mobility scenarios. In this paper, we study the receiver for coded OTFS-IM system. First, we construct the corresponding factor graph, on which the structured prior incorporating activation pattern constraint and channel coding is devised. Then we develop a iterative receiver via structured prior-based hybrid belief propagation (BP) and expectation propagation (EP) algorithm, named as Str-BP-EP, for the coded OTFS-IM system. To reduce the computational complexity of discrete distribution introduced by structured prior, Gaussian approximation conducted by EP is adopted. To further reduce the complexity, we derive two variations of the proposed algorithm by using some approximations. Simulation results validate the superior performance of the proposed algorithm.

Orthogonal Time Frequency Space Modulation—Part I: Fundamentals and Challenges Ahead

This letter is the first part of a three-part tutorial on orthogonal time frequency space (OTFS) modulation, which is a promising candidate waveform for future wireless networks. This letter introduces and compares two popular implementations of OTFS modulation, namely the symplectic finite Fourier transform (SFFT)- and discrete Zak transform (DZT)-based architectures. Based on these transceiver architectures, fundamental concepts of OTFS modulation, including the delay-Doppler (DD) domain, DD domain information multiplexing, and its potential benefits, are discussed. Finally, the challenges ahead for OTFS modulation are highlighted.

Guest editorial: Orthogonal time frequency space modulation in 6G era

Over the past decades, wireless technologies with reliable data transmissions and precise sensing ability in hostile environments are much less understood and significantly under-developed. The DD domain waveform, e.g., orthogonal time frequency space (OTFS), has been recognized globally for its great potential to achieve high-reliable communications and robust sensing performance under various channel conditions in 6G era.