The deployment of reconfigurable intelligent surfaces (RIS) in millimeter-wave (mmWave) multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems is usually hindered by the dual challenges of high-dimensional channel estimation and prohibitive control phase-shift overhead. To reduce channel estimation complexity and feedback overhead, this paper constructs a unified tensor-based framework. First, by exploiting the sparsity of mmWave channels and the Vandermonde structure of antenna arrays, we formulate the received signals as a canonical polyadic (CP) model characterized by tensor decomposition uniqueness. Subsequently, a closed-form channel estimation algorithm is proposed to fit the constructed CP model and extract channel parameters. To further reduce the feedback overhead, we propose a tensor-based low-rank RIS feedback scheme. By exploiting the inherent Kronecker-structure of the optimal RIS phase-shift vector, the proposed scheme approximates it using a low-rank tensor representation, thereby enabling compression based on the estimated channel state information (CSI). Simulation results validate that the proposed framework achieves high-precision and low-complexity channel estimation while maintaining nearoptimal spectral efficiency with reduced feedback bits, particularly in line-of-sight (LoS)-dominant scenarios.

In this paper, we develop a tensor-based joint multi-dimensional (polarization, angle, and time delay) channel parameter estimation algorithm for single-input multiple-output (SIMO) communication systems equipped with an electromagnetic vector sensor (EMVS) linear array. By considering the EMVS array structure and multi-path propagation environment, the received signals at the base station (BS) are constructed into a third-order parallel factor (PARAFAC) tensor model. By decomposing the constructed tensor, we design a joint structured tensor decomposition algorithm (STDA) and bilinear alternating least squares (BALS) fitting algorithm using the Vandermonde structure of the array to estimate the factor matrices containing angles, polarization, and time delay. Based on the estimated factor matrices, we employ a closed-form algorithm to extract the two-dimensional direction of arrival (2D-DoA), polarization parameters, and time delay. In addition, to provide a quantitative assessment of the proposed algorithm’s performance, we calculate the Cramér-Rao bound (CRB) as a benchmark for comparison. Simulation results indicate that the proposed algorithm achieves superior estimation accuracy and is closer to the CRB compared with the existing tri-polarized algorithms.

In this paper, we propose a tensor-based framework for multi-user reconfigurable intelligent surface (RIS)-assisted integrated sensing and communication (ISAC), designed to enable efficient data transmission and accurate localization across far- and near-field communications. The proposed scheme introduces a two-phase nested tensor-based ISAC transmission protocol, comprising the precoding phase and the joint symbol detection and target localization (JSDTL) phase. During the precoding phase, a third-order tensor is constructed to extract angle information from the far-field base station (BS)-RIS channel links, which is then utilized to design a precoding strategy that mitigates inter-user interference. In the JSDTL phase, the received signals are constructed into a fourth-order nested tensor incorporating angular, temporal, and coding dimensions. The algebraic structure of the nested tensor, combined with the second-order Fresnel approximation for the near-field channel model between the RIS and user equipment (UE), is leveraged to perform data recovery and target localization. Simulation results confirm that the proposed scheme achieves superior ISAC performance with reduced computational complexity, outperforming benchmark algorithms.

In this article, we propose a novel integrated sensing and communication (ISAC) algorithm for massive multiple-input-multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems with spatial-frequency wideband (SFW) effects. To obtain high accuracy of channel state information (CSI), the proposed algorithm initially utilizes a deep neural network (DNN) for channel estimation. Then, the estimated channel is expressed as a third-order low-rank tensor model, on which the canonical polyadic (CP) decomposition is performed to obtain three factor matrices. These factor matrices hold the information pertaining to channel parameters. By fitting the constructed tensor model, channel parameters, such as Angles of Departure (AoDs), Angles of Arrival (AoAs), time delay, and complex gains, can be extracted. Ultimately, the positions of mobile station (MS) and scattering points are determined by utilizing the mapping relationship between the channel parameters and position coordinates. In contrast to existing algorithms, the proposed algorithm delivers greater precision in both channel estimation and positioning. The simulation results demonstrate that the proposed algorithm maintains outstanding ISAC performance, persisting even with diminished compression rate. Furthermore, the proposed algorithm proves effective in more complex scenarios lacking a line-of-sight (LOS) path.

In this paper, a localization algorithm based on Bayesian tensor decomposition is proposed for frequency diverse array multiple-input multiple-output (FDA-MIMO) radar, which successfully achieves vehicle localization in intelligent transportation systems (ITSs). Considering that the FDA-MIMO radar array may suffer from unknown mutual coupling (UMC), the proposed algorithm first constructs selection matrices for elimination, and then models the received signals as a third-order complex-valued tensor. To reduce the computational complexity of tensor decomposition, real-valued processing and compression techniques are employed to transform the complex-valued tensor into a real-valued compressed one. Subsequently, the factor matrices are obtained by Bayesian tensor decomposition, from which the direction of arrival (DOA) and range of the vehicle are extracted. Finally, the vehicle location is determined through geometric relationships. Besides, the Cramér-Rao bounds (CRBs) for DOA and range are derived as a performance benchmark. The proposed algorithm is applicable to the manifolds of uniform linear arrays (ULAs) and uniform planar arrays (UPAs) with UMC. Unlike existing algorithms requiring prior knowledge of target numbers, the proposed algorithm realizes accurate vehicle localization under both known and unknown target numbers. Simulation results demonstrate the effectiveness and robustness of the proposed algorithm.

In the sixth-generation (6G) Internet of Everything (IoE) environment, integrated sensing and communication (ISAC) can improve the utilization of radio resources. The application of reconfigurable intelligent surface (RIS) and millimeter wave (mmWave) can improve the performance of the ISAC. In this article, we propose an ISAC algorithm for RIS-assisted multiuser mmWave multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. The proposed ISAC algorithm can achieve simultaneous channel estimation, positioning and environment mapping. Considering the limited robustness of the traditional algorithms to noise, the proposed algorithm first uses a complex-valued depth residual convolution neural network (C-DRCNN)-assisted channel estimation algorithm by using the powerful computational power of deep learning. Further, the sparsity of the mmWave channel can be utilized by the parallel factor (PARAFAC) tensor decomposition for obtaining the factor matrices, which contain the channel parameters, such as direction-of-arrival (DOA), direction-of-departure (DOD), time delay (TD), and complex path gain. Finally, the multiuser positioning and environment mapping are realized according to the geometric relationship between the position and channel parameters. The simulation results demonstrate that the proposed algorithm achieves better channel estimation, multiuser positioning and environment mapping performance compared with the state-of-the-art algorithm. In addition, since the proposed algorithm integrates the deep neural network and tensor decomposition, it still has excellent ISAC performance even at low signal-to-noise ratio (SNR).

In this paper, we propose a novel vehicle positioning method for commodity multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) WIFI systems in indoor parking lots. To address the limitation of the small number of WIFI antennas, the proposed method first utilizes signal model rearrangement techniques, in which the abundant carrier frequency resources of WIFI are expanded into space resources. Then a rearranged off-grid sparse Bayesian learning (ROG-SBL) algorithm is developed for parameters estimation to achieve vehicle positioning. Specifically, by resorting to the Bayesian inference and Newton method, the position-related parameters are estimated iteratively by fitting the channel state information (CSI) measurement model, and thus the vehicle positioning is realized according to the geometric relationship. Moreover, we derive the Cramér-Rao bound (CRB) as a performance reference for the proposed algorithm. Compared with the existing algorithms, the proposed one improves the positioning performance of the vehicle with fewer carrier numbers and has more stable performance. Simulation results show that the performance curves of the proposed algorithm for parameters estimation are close to the corresponding CRBs, and the proposed algorithm can cope with more challenging cases when the line-of-sight (LOS) path does not exist.

In this paper, an effective simultaneous channel estimation and sensing algorithm is proposed for millimeter wave (mmWave) multiple-input multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) systems. The proposed algorithm consists of a two-stage channel estimation scheme and a reliable sensing scheme, which enables high-quality channel estimation and precise sensing in three-dimensional (3D) space. Specifically, the proposed algorithm first puts forward an improved simultaneous orthogonal matching pursuit algorithm that utilizes structural relation between the sparse basis and indexes to implement coarse estimation of multiple parameters. Subsequently, taking the obtained coarse parameters as initial values, optimization of channel parameters is achieved using the idea of maximum likelihood and gradient descent algorithm. Finally, we develop a reliable sensing scheme to realize user localization and mapping of scattering environment in various scenarios. Cramér-Rao bounds (CRBs) of the parameters and positions are also derived and used as a benchmark in simulations. Simulation results demonstrate that compared with the existing algorithms, the proposed algorithm has better channel estimation and sensing performance and is closer to CRBs. Moreover, even in challenging environment with unknown user orientation and clock bias, the proposed algorithm can achieve precise user localization and mapping of scattering environment.

This paper proposes an effective algorithm for gain-phase error (GPE) and angle estimation in multiple-input multiple-output (MIMO) radar. First, the received signals are constructed into a third-order tensor model containing information such as GPE in transmitting arrays (Tx) and receiving arrays (Rx), directions-of-departures (DODs) and directions-of-arrivals (DOAs). Then, a tensor-based two-stage estimation algorithm to estimate GPE and angles is developed. In the first stage, GPE and angle information are obtained by the least squares Khatri-Rao factorization (LS-KRF) separation. In the second stage, the GPE in Tx and Rx is estimated by a two-step GPE estimation scheme, while the DODs and DOAs are estimated by a non-iterative angle estimation scheme based on the spatial smoothing preprocessing. Simulation results show the superiority of the proposed GPE and angle estimation algorithm.

In this study, the authors present a novel channel estimation algorithm for three‐hop multi‐input multi‐output (MIMO) relay systems using the PARATUCK2 tensor model. At the destination, the proposed algorithm exploits a unified formulation of the received signal as a PARATUCK2 model, and jointly estimates all of the channel matrices involved in the communication. Compared with existing algorithms, the proposed algorithm only requires the source to transmit the channel training sequences, does not need relays to perform any task of channel estimation, and yields smaller estimation error. Moreover, the proposed algorithm can be extended to multi‐hop MIMO relay systems with any number of hops. Numerical examples are shown to demonstrate the effectiveness of the PARATUCK2‐based channel estimation algorithm.

In this study, the authors consider a new space‐time coding scheme for two‐hop amplify‐and‐forward (AF) relay multiple‐input multiple‐output (MIMO) relay communication systems. This scheme, called multiple Khatri–Rao space‐time coding, which combines symbol stream blocking, spatial precoding and time‐domain spreading. The authors show that the received signals at the destination node can be formulated as two parallel factor (PARAFAC) models, and then a novel semi‐blind receiver is derived using a two‐stage iterative fitting algorithm for joint symbol and channel estimation. Under the assumption that channel state information (CSI) is not available neither at the relay nodes nor at the destination node, the proposed semi‐blind receiver operates close to the zero forcing receiver with perfect CSI. Moreover, without any channel training sequence, the proposed semi‐blind receiver provides the destination node with full knowledge of all channel matrices involved in the transmission. Simulation results illustrate the performance of the proposed semi‐blind receiver in comparison with alternative approaches.

In this study, the authors present a novel channel estimation scheme for a two‐hop non‐regenerative multiple‐input multiple‐output relay system. The proposed scheme has two stages. In the first stage, the source node transmits channel training sequence to the relay node. The relay node amplifies the received signal and forwards it to the destination node. During the second stage, the relay node amplifies the pre‐received signal with another amplification matrix, and forwards it to the destination node. Based on the proposed scheme, by using parallel factor (PARAFAC) analysis, they further propose a low complexity channel estimation algorithm, where full knowledge of all channel matrices involved in the communication can be estimated at the destination node. Compared with existing algorithms, the proposed algorithm yields smaller channel estimation error with lower complexity. Numerical examples are shown to demonstrate the effectiveness of the low complexity PARAFAC‐based channel estimation algorithm.

Distributed space‐time block coding (STBC) is a promising technique for future broadband wireless communication system, because of its substantially improving the reliability of wireless channel by exploiting cooperative spatial diversity. In this study, the authors propose a novel two time slots distributed time‐reversal STBC scheme for amplify‐and‐forward relay‐assisted single‐carrier (SC) block transmissions over frequency‐selective fading channel. They first exploit the discrete Fourier transform extended properties to construct a linear precoding matrix. They then employ a low‐complexity suboptimal frequency domain decision feedback equalisation (FD‐DFE) to collect potential multipath diversity at high signal‐to‐noise ratio. Simulation results demonstrate that the proposed scheme provides better performance than the conventional distributed SC‐STBC scheme with minimum‐mean‐square error FD linear equalisation.