PACE: Pilot Agnostic Channel Estimation for OTFS-based Multistatic ISAC System

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.

Power-line noise is mainly comes from power systems and has become one of the most common noises during the acquisition of magnetotelluric (MT) signal, its components including a fundamental frequency signal and a lot of odd harmonics. There are trap circuits designed in most of the acquisition instruments to separate these noise, however, the fundamental frequency of the power line noise will fluctuate with the changing of load current, but the center frequency of the trap circuits are fixed, hence the MT data are still seriously disturbed by the power line noise. To mitigate the disturbance of power line noise, a novel denoising method was proposed based on orthogonal matching pursuit (OMP) algorithm. Semisynthetic experiments and real data obtained from Lu-Zong ore-concentration district illustrate that the proposed method can effectively suppress the power line noise while remain the useful MT signal, the apparent resistivity and phase curves are greatly improved over previous.

The intensities (i.e., number of protons in monitor unit [MU]) of deliverable proton spots need to be either zero or meet a minimum-MU (MMU) threshold, which is a nonconvex problem. Since the dose rate is proportionally associated with the MMU threshold, higher-dose-rate proton radiation therapy (RT) (e.g., efficient intensity modulated proton therapy (IMPT) and ARC proton therapy, and high-dose-rate-induced FLASH effect needs to solve the MMU problem with larger MMU threshold, which however makes the nonconvex problem more difficult to solve. This work will develop a more effective optimization method based on orthogonal matching pursuit (OMP) for solving the MMU problem with large MMU thresholds, compared to state-of-the-art methods, such as alternating direction method of multipliers (ADMM), proximal gradient descent method (PGD), or stochastic coordinate descent method (SCD). The new method consists of two essential components. First, the iterative convex relaxation (ICR) method is used to determine the active sets for dose-volume planning constraints and decouple the MMU constraint from the rest. Second, a modified OMP optimization algorithm is used to handle the MMU constraint: the non-zero spots are greedily selected via OMP to form the solution set to be optimized, and then a convex constrained subproblem is formed and can be conveniently solved to optimize the spot weights restricted to this solution set via OMP. During this iterative process, the new non-zero spots localized via OMP will be adaptively added to or removed from the optimization objective. The new method via OMP is validated in comparison with ADMM, PGD and SCD for high-dose-rate IMPT, ARC, and FLASH problems of large MMU thresholds, and the results suggest that OMP substantially improved the plan quality from PGD, ADMM and SCD in terms of both target dose conformality (e.g., quantified by max target dose and conformity index) and normal tissue sparing (e.g., mean and max dose). For example, in the brain case, the max target dose for IMPT/ARC/FLASH was 368.0%/358.3%/283.4% respectively for PGD, 154.4%/179.8%/150.0% for ADMM, 134.5%/130.4%/123.0% for SCD, while it was <120% in all scenarios for OMP; compared to PGD/ADMM/SCD, OMP improved the conformity index from 0.42/0.52/0.33 to 0.65 for IMPT and 0.46/0.60/0.61 to 0.83 for ARC. A new OMP-based optimization algorithm is developed to solve the MMU problems with large MMU thresholds, and validated using examples of IMPT, ARC, and FLASH with substantially improved plan quality from ADMM, PGD, and SCD.

In this paper, the estimation of doubly spread underwater acoustic (UWA) channels is investigated. The UWA channels are characterized by severe delay spread and significant Doppler effects, and can be well modeled as a multi-scale multi-lag (MSML) channel. Furthermore, exploiting the sparsity of UWA channels, MSML channel estimation can be transformed into the estimation of parameter sets (amplitude, Doppler scale factor, time delay). Based on this, the orthogonal matching pursuit (OMP) algorithm has been widely used. However, the estimation accuracy of OMP depends on the size of the dictionary, which is related with both delay spread and Doppler spread. Thus it requires high computational complexity. This paper proposes a new method, called wavelet transform (WT) based algorithm, for the UWA channel estimation. Different from OMP algorithm which needs to search in both time domain and Doppler domain, WT-based algorithm only needs to search in time domain by using the Doppler invariant characteristic of hyperbolic frequency modulation (HFM) signal. The performance of the proposed algorithm is evaluated by computer simulations based on BELLHOP. The simulation results show that WT-based algorithm performs slightly better than OMP algorithm in low signal to noise ratio (SNR) while can greatly reduce computational complexity.

The orthogonal matching pursuit (OMP) algorithm is widely used because of its simple algorithmic structure, the linear magnitude of its computational complexity and other advantages. Algorithms of improved and extended OMP types are continually emerging. To make the OMP algorithm more suitable for the new transmission requirements of the fifth-generation (5G) network, the orthogonal matching pursuit with multiple users (OMP_mu) algorithm is proposed for cell-free massive multi-input multi-output (MIMO) networks with multiuser spatial index modulation. The OMP_mu algorithm considers the constraint condition for the sparsity of each user on the basis of each iterative search in the OMP algorithm until all users meet the constraint. The simulation results show that compared with the original OMP algorithm, the OMP_mu algorithm has a greatly improved demodulation performance. Compared with the orthogonal matching pursuit step-by-step (OMP_step) algorithm, which takes the user sparsity constraint condition into account in two steps, the OMP_mu algorithm greatly reduces the operation time and number of iterations while achieving a slightly better performance. The OMP_mu algorithm provides an effective reference for the application of spatial index modulation in cell-free massive MIMO networks.

In this paper, a fast orthogonal matching pursuit (OMP) algorithm based on optimized iterative process is proposed for sparse time-varying underwater acoustic (UWA) channel estimation. The channel estimation consists of calculating amplitude, delay and Doppler scaling factor of each path using the received multi-path signal. This algorithm, called as OIP-FOMP, can reduce the computationally complexity of the traditional OMP algorithm and maintain accuracy in the presence of severe inter-carrier interference that exists in the time-varying UWA channels. In this algorithm, repeated inner product operations used in the OMP algorithm are removed by calculating the candidate path signature Hermitian inner product matrix in advance. Efficient QR decomposition is used to estimate the path amplitude, and the problem of reconstruction failure caused by inaccurate delay selection is avoided by optimizing the Hermitian inner product matrix. Theoretical analysis and simulation results show that the computational complexity of the OIP-FOMP algorithm is reduced by about 1/4 compared with the OMP algorithm, without any loss of accuracy.

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 matching pursuit (OMP) is a commonly used algorithm for recovery sparse signals due to its low complexity and simple implementation. We analyze the convergence property of OMP based on the restricted isometry property (RIP), and show that the OMP algorithm can exactly recover an arbitrary K-sparse signal using K steps provided that the sampling matrix Φ satisfies the RIP with parameter . In addition, we also give the convergence analysis of OMP for the case of inaccurate measurements. Moreover, a variant of OMP, referred to as multi-candidate OMP (MOMP) algorithm, is proposed to recover sparse signals, which can further reduce the computational complexity of OMP. The key point of MOMP is that at each step it selects multi-candidates adding to the optimal atom set, whilst OMP only selects one atom. We also present the convergence analysis of MOMP using the RIP. Finally, we testify the performance of the proposed algorithm using several numerical experiments.

FOMP algorithm for Direction of Arrival estimation

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.

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.

The favorable characteristics of the delay-Doppler domain in Orthogonal Time Frequency Space (OTFS) have led to its extensive research as a signal for integrated sensing and communication (ISAC). Many works have employed compressed sensing algorithms to estimate target parameters in OTFS; however, they have not considered the correlation between the atoms in the dictionary matrix. By exploiting this correlation, we propose the Gradient Descent Refinement (GDR) algorithm to estimate fractional delay and fractional Doppler shifts. Experimental results demonstrate that GDR achieves better estimation accuracy and lower computational complexity compared to conventional compressed sensing algorithms. When the channel contains numerous reflectors, the superposition of different paths causes inter-path interference. To mitigate this issue, we enhanced the GDR algorithm with interference cancelation. We also derive the Cramér-Rao lower bound (CRLB) for parameter estimation in the scenario where the transmitter and radar receiver are co-located and compare it with the performance of proposed algorithms.

Traditional orthogonal matching pursuit (OMP) algorithms for direction of arrival (DOA) estimation suffer from poor angular resolution and noise suppression. In this paper, we analyze the reason why the OMP algorithm has difficulties in resolving closely separated DOAs and conclude that it lies in the rules of support detection. Moreover, we propose a solution to this problem via developing the connection between the sparse reconstruction class algorithm and the subspace algorithm from the structure of the redundant dictionary. Based on the framework of the matching pursuit (MP) algorithm, the effective information of the signal and noise subspaces is integrated, and a noise subspace reprojection orthogonal matching pursuit (NSRomp) algorithm for DOA estimation is proposed. By adopting signal subspaces to reconstruct the original signal, the proposed NSRomp can reduce both the influence of noise on the selection of the support set and the computing time. By implementing the minimum norm method to optimize the noise subspace into a vector, which corrects the selection rules of the support set during each iteration, the angular resolution of the proposed algorithm is improved. From the simulation results, when the signal to noise ratio (SNR) is lower than or near 0, the angular resolution can be improved by > 15° using OMP algorithms to by > 5° using the proposed NSRomp algorithm.

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.

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.