In terahertz (THz) communication systems, extremely large scale arrays can effectively compensate for the limited communication distance problem. In this article, we consider the near-field channel estimation (CE) problem for an extremely large reconfigurable intelligence surface (XL-RIS)-assisted multi-user THz communication system. We first construct a near-field channel model based on a second-order Fresnel approximation derivation. Utilizing the spatial structure of the derived channel model, we sample the covariance matrix of the received signals. Then, we propose a tensor decomposition-based algorithm to estimate the angular parameters, and establish a truncated singular value decomposition (T-SVD) algorithm for the distance estimation. In the end, we estimate the path losses through the least squares (LS) method and recover the complete channel. Moreover, to further reduce the computational overhead, we construct a low-complexity tensor completion-based scheme for the angular parameters’ estimation. Simulation results indicate that the proposed tensor-based CE schemes outperform the conventional subspace-based approaches in terms of accuracy and computational complexity.

In this paper, we investigate the channel estimation and user localization problems for multi-user integrated sensing and communication (ISAC) systems empowered by the reconfigurable intelligent surface (RIS) technology. In order to perceive environmental information more deeply, we propose a spherical RIS architecture with spherically arranged unit cells. Based on the principle of phase mode excitation, we customize the design of RIS profiles and recover the equivalent channel parameters via subspace estimation tools. By exploring the characteristics of RIS array manifold and free-space propagation, we develop a decoupling framework of three-dimensional channel parameters, which is not supported by conventional planar RIS topologies. Each user can achieve a self-localization by analyzing the signals transmitted from other active users. Simulation results indicate that the spherical RIS can enable joint channel estimation, user localization and data transmission with remarkable performance that approaches the theoretical Cramér-Rao bounds.

In this paper, we investigate the channel estimation and localization problems for integrated sensing and communication (ISAC) systems empowered by the reconfigurable intelligent surface (RIS) technology. We propose a cylindrical RIS architecture that arranges reflecting elements on a curved substrate, where the three-dimensional array manifold can not only offer a 360° coverage but also perceive the environmental information more deeply. The conformal RIS topology can fit the deployment scenarios more flexibly, which, however, incurs a potential issue of shadowing effect, i.e., signal waves from/to certain directions can only be observed by a part of reflectors due to the shielding of the substrate curvature, yielding different visibility regions (VRs) for multiple users on the RIS array manifold. In order to address this problem, we propose a tensorial channel estimation approach, where the cascaded channel is transformed into the beamspace domain and modeled as a canonical polyadic tensor. By leveraging the principle of tensor completion, we can eliminate the RIS training profiles to deconstruct the channel in the element domain. Then, we develop a VR detection strategy based on the sliding windows, retrieving equivalent channel parameters from the effective signal responses. Finally, by exploring the characteristics of the cylindrical RIS architecture, we develop a decoupling framework to uniquely recover the exact channel parameters, based on which each user can locate itself and other interacting ones. Simulation results indicate that the proposed cylindrical RIS can enable the channel estimation, user localization and data transmission simultaneously, exhibiting remarkable performance under the shadowing effect interference.

We consider the problem of channel estimation for multi-reconfigurable intelligence durface (RIS) assisted orthogo-nal frequency division multiplexing (OFDM) systems. To detect the higher-rank signals reflected by multiple RISs, we divide the total RISs into several groups and propose a training protocol for filtering the signal components belonging to different groups. By concatenating the training signals on different subcarriers, we construct a low-rank third-order tensor model and develop a canonical polyadic decomposition (CPD) method to estimate the channel parameters. Simulation results indicate that the proposed tensor-based method effectively improves the estimation accuracy. The RIS grouping strategy trades off the training overhead and algorithm performance.

Integrated sensing and communication (ISAC) is emerging as a key enabler to address the increasing demands of spectrum and throughput for ubiquitous sensing and communication. Hereafter, we consider the channel estimation and localization for multi-user ISAC systems assisted by the reconfigurable intelligent surface (RIS) technology. In order to acquire precise environmental information, we propose a novel circular RIS architecture with circularly arranged reflecting unit cells. By modeling the training signal as a low-rank third-order canonical polyadic tensor, we transform the channel estimation problem into a tensor deconstruction task. By leveraging the phase mode excitation principle, we develop a customized RIS training pattern, and retrieve the equivalent channel parameters by subspace estimation algorithms. By exploring the characteristics of RIS array manifolds and free-space propagation, we implement a unique decoupling of channel parameters for user localization, which cannot be supported by traditional linear RIS topologies. Moreover, the design degrees of freedom in the spatial and frequency dimensions are also exploited to further enhance the proposed algorithms. Simulation results indicate that the circular RIS-enabled channel estimation schemes can recover the propagation information with remarkable accuracy, thereby offering a high-level resolution of localization.

We consider the channel estimation and environment mapping problems in multiple-input multiple-output orthogonal frequency division multiplexing systems empowered by intelligent reconfigurable surfaces (IRSs). In order to acquire more in-depth environmental information, as well as, to flexibly take into account existing real-life infrastructure, we propose a novel three-dimensional conformal IRS architecture consisting of reflective unit cells distributed on curved surfaces. We model the training signal as a third-order canonical polyadic tensor and construct a tensor factorization problem. Given specific conditions on the allocated temporal-frequency training resources, we develop four channel estimation approaches, i.e., least squares, direct, wideband direct and wideband subspace methods, by leveraging tensor techniques and nonlinear system solvers. By fully exploiting the characteristics of conformal IRSs, we propose two decoupling modes to precisely recover the multipath parameters without ambiguities, which cannot be supported by the traditional IRS planar topologies. We implement scatterer mapping and user positioning tasks based on precise parameter estimates. Simulation results indicate that the proposed conformal IRS structure and estimation schemes can recover the channel state information with remarkable accuracy, thereby offering a centimeter-level resolution of environment mapping.

We consider the channel estimation problem and the channel-based wireless applications in multiple-input multiple-output orthogonal frequency division multiplexing systems assisted by intelligent reconfigurable surfaces (IRSs). To obtain the necessary channel parameters, i.e., angles, delays and gains, for environment mapping and user localization, we propose a novel twin-IRS structure consisting of two IRS planes with a relative spatial rotation. We model the training signal from the user equipment to the base station via IRSs as a third-order canonical polyadic tensor with a maximal tensor rank equal to the number of IRS unit cells. We present four designs of IRS training coefficients, i.e., random, structured, grouping and sparse patterns, and analyze the corresponding uniqueness conditions of channel estimation. We extract the cascaded channel parameters by leveraging array signal processing and atomic norm denoising techniques. Based on the characteristics of the twin-IRS structures, we formulate a nonlinear equation system to exactly recover the multipath parameters by two efficient decoupling modes. We realize environment mapping and user localization based on the estimated channel parameters. Simulation results indicate that the proposed twin-IRS structure and estimation schemes can recover the channel state information with remarkable accuracy, thereby offering a centimeter-level resolution of user positioning.

We consider the channel estimation problem in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems assisted by intelligent reconfigurable surfaces (IRSs). To avoid the inherent estimation ambiguities of the two-hop channels from mobile stations (MS) to the base station (BS), we adopt a hybrid IRS architecture composed of passive reflectors and active sensors, and establish two independent subproblems of estimating the MS-to-IRS and BS-to-IRS channels. By leveraging the sparse characteristics of high-frequency propagation, we model the training signals as multi-dimensional canonical polyadic decomposition (CPD) tensors with missing fibers or slices. We develop algebraic algorithms to solve the tensor completion problems and recover channel multipath parameters, i.e., angles of arrival, time delays and path gains. Our methods require neither random initialization nor iterative operations, and for these reasons they can perform robustly with a low computational complexity. Moreover, we investigate the uniqueness condition of CPD tensor completion, which can be utilized to inform both the physical design of hybrid IRSs and the time-frequency resource allocation of training strategies. Simulation results indicate that the proposed schemes outperform the traditional counterparts in terms of accuracy, robustness and complexity, especially for the case of low-complexity IRSs with limited number of active sensing elements.

We consider the channel estimation problem in millimeter wave (mmWave) multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with hybrid analog-digital architectures. Leveraging the spatial- and frequency-wideband (dual-wideband) effects in massive MIMO scenarios, we derive a spatial-frequency channel model with dual-wideband effects that incorporates the multipath parameters, i.e., time delay, complex gain, angle of departure/arrival. We adopt a successive beam training scheme and formulate the training OFDM signal as a third-order low-rank tensor fitting a canonical polyadic (CP) model with factor matrices containing the channel parameters. Exploiting the Vandermonde nature of factor matrices, we propose a structured CP decomposition-based channel estimation strategy aided by the spatial smoothing method, where two dedicated algorithms with particular tensor modeling and parameter recovery operations are developed. The proposed scheme leverages standard linear algebra, and, hence, avoids the random initialization problem and iterative procedure. An analysis of the uniqueness condition of CP decomposition is also pursued. Simulation results indicate that the proposed strategy achieves enhanced estimation performance, which outperforms the traditional approaches in terms of accuracy, robustness and complexity.

Hybrid transceiver designs for millimeter wave massive multiple-input multiple-output systems are feasible candidates to reduce the volume of radio frequency (RF) chains, decomposing the signal processing into the analog and digital domains. The existing schemes heavily depend on the singular value decomposition to obtain subchannels with uneven power gains, causing bit error rate (BER) performance degradation. In this paper, we propose a hybrid transceiver design based on the uniform channel decomposition (UCD), yielding subchannels with identical gains to improve the BER performance. Inspired by the UCD concept, we derive an equivalent optimization problem and propose two schemes, namely, phase-extraction and iterative update, to determine the RF beamformers, yielding an effective baseband channel with the greatest possible geometric mean of singular values. We apply the UCD with a minimum mean squared error criterion to complete the baseband beamforming. Finally, we combine the hybrid UCD beamforming with the vertical-Bell Labs layered space-time and dirty paper coding, to eliminate the inter-subchannel interference. An asymptotic analysis of the scheme performance is also pursued. The simulation results show that the proposed hybrid scheme outperforms the conventional schemes on the transmission BER, which achieves a spectral efficiency close to that of the fully-digital counterpart.