Channel Estimation via Tensor Decomposition for Dynamic Metasurface Antennas with Known Mutual Coupling: Algorithms and Experiments

Dynamic metasurface antennas (DMAs) are an emerging hybrid-MIMO technology distinguished by an ultrathin form factor, low cost, and low power consumption. In real-world DMA prototypes, mutual coupling (MC) between meta-elements is generally non-negligible; some architectures even deliberately exploit strong MC to enhance wave-domain flexibility. In this paper, we address channel estimation (CE) for DMAs with known MC by formulating it as a tensor-decomposition problem. We develop a generalized block Tucker alternating least squares (BTALS) algorithm, together with specialized variants for cases with known direct and/or feed channel. We also develop a reciprocity-aware bilinear factorization method for the case with known direct channel. We experimentally validate our algorithms using an 18 GHz DMA prototype whose 7 feeds and 96 meta-elements are strongly coupled via a chaotic cavity. Our general BTALS algorithm reaches an accuracy of 43.1 dB, only 0.3 dB below the upper bound imposed by experimental noise. All proposed algorithms generally outperform the prior-art reference scheme thanks to the superior noise rejection enabled by the tensor-based framework. We further study the minimum number of required measurements as a function of the number of feeds and demonstrate the importance of MC awareness by comparison with an MC-unaware benchmark. Finally, we apply BTALS to a second setup enabling the prediction of the DMA's full dual-polarization 3D radiation diagram. We also measure the latter for DMA configurations optimized for channel-gain enhancement based on the estimated channels. Altogether, our work establishes the practical relevance of MC-aware tensor methods; beyond DMAs, it applies to all wireless systems with wave-domain programmability enabled by tunable lumped elements.

Semi-Blind Channel Estimation for Downlink Communications Based on Dynamic Metasurface Antennas

Dynamic metasurface antennas (DMAs) are emerging as a promising technology to enable energy-efficient, large array-based multi-antenna systems. This paper presents a simple channel estimation scheme for the downlink of a multiple-input single-output orthogonal frequency division multiplexing (MISO-OFDM) communication system exploiting DMAs. The proposed scheme extracts separate estimates of the wireless channel and the unknown waveguide propagation vector using a simple iterative algorithm based on the parallel factor (PARAFAC) decomposition. Obtaining decoupled estimates of the wireless channel and inner waveguide vector enables the isolation and compensation for its effect when designing the DMA beamformer, regardless of the wireless channel state, which evolves much faster due to its shorter coherence time and bandwidth. Additionally, our solution operates in a data-aided manner, delivering estimates of useful data symbols jointly with channel estimates, without requiring sequential pilot and data stages. To the best of our knowledge, this is the first work to explore this CE approach. Numerical results corroborate the notable performance of the proposed scheme.

Performance Evaluation of Beyond Diagonal RIS under Hardware Impairments

Beyond diagonal reconfigurable intelligent surface (BD-RIS) improves the traditional reconfigurable intelligent surface (RIS) architecture functionality by interconnecting elements for advanced wave control. However, real-world implementations face hardware imperfections, such as impedance mismatches and varactor nonidealities, which can degrade overall system performance. In this paper, we propose three hardware impairment models that directly affect the BD-RIS scattering matrix structure and evaluate their impact on the channel estimation accuracy using the normalized mean square error (NMSE) as a performance metric. The proposed impairment models consider imperfections affecting self-impedances, mutual impedances, or both. Our results reveal how each impairment type degrades the system performance, allowing us to identify scenarios where the traditional RIS can outperform the BD-RIS.

Joint Channel and Symbol Estimation for Communication Systems with Movable Antennas

Communication systems aided by movable antennas have been the subject of recent research due to their potentially increased spatial degrees of freedom offered by optimizing the antenna positioning at the transmitter and/or receiver. In this context, a topic that deserves attention is channel estimation. Conventional methods reported recently rely on pilot-assisted strategies to estimate the channel coefficients. In this work, we address the joint channel and symbol estimation problem for an uplink multi-user communication system, where the base station is equipped with a movable antenna array. A semi-blind receiver based on the PARAFAC2 model is formulated to exploit the tensor decomposition structure for the received signals, from which channel and symbol estimates can be jointly obtained via an alternating estimation algorithm. Compared with reference schemes, our preliminary numerical simulations yield remarkable results for the proposed method.

Circuit-Based Modeling Approach for Channel Estimation in RIS-Assisted Communications

Reconfigurable intelligent surface (RIS) has been explored as a supportive technology for wireless communication since around 2019. While the literature highlights the potential of RIS in different modern applications, two key issues have gained significant attention from the research community: channel estimation and phase shift optimization. The performance gains of RIS-assisted systems rely heavily on optimal phase shifts, which, in turn, depend on accurate channel estimation. Several studies have addressed these challenges under different assumptions. Some works consider a range of continuous phase shifts, while others propose a limited number of discrete phase values for the RIS elements. Many studies present an idealized perspective, whereas others aim to approximate more practical aspects by considering circuit system responses and employing phase shifts derived from a Discrete Fourier Transform (DFT) or other lookup tables. However, to our knowledge, no study has examined the influence of circuit system parameters on channel estimation and subsequent phase shift optimization. This paper models each RIS element as an equivalent resonant circuit composed of resistance, capacitance, and inductance. We propose that resistance and capacitance parameters can be dynamically and independently configured, leading to the formulation of an impedance matrix. Furthermore, we construct a circuit-based RIS phase shift matrix that accounts for the response of the resonant circuit, which changes with variations in the physical parameters of resistance and capacitance. We investigate the impact of this circuit-based RIS phase shift within a tensor-based channel estimation approach. Our results indicate a performance loss compared to ideal scenarios, such as those using the DFT design. However, we found that increasing the training time can mitigate this performance degradation.

Joint Downlink-Uplink Channel Estimation for Non-Reciprocal RIS-Assisted Communications

Reconfigurable intelligent surface (RIS) is a recent low-cost and energy-efficient technology with potential applicability for future wireless communications. Performance gains achieved by employing RIS directly depend on accurate channel estimation (CE). It is common in the literature to assume channel reciprocity due to the facilities provided by this assumption, such as no channel feedback, beamforming simplification, and latency reduction. However, in practice, due to hardware limitations at the RIS and transceivers, the channel non-reciprocity may occur naturally, so such behavior needs to be considered. In this paper, we focus on the CE problem in a non-reciprocal RIS-assisted multiple-input multiple-output (MIMO) wireless communication system. Making use of a novel closed-loop three-phase protocol for non-reciprocal CE estimation, we propose a two-stage fourth-order Tucker decomposition-based CE algorithm. In contrast to classical time-division duplexing (TDD) and frequency-division duplexing (FDD) approaches the proposed method concentrates all the processing burden for CE on the base station (BS) side, thereby freeing hardware-limited user terminal (UT) from this task. Our simulation results show that the proposed method has satisfactory performance in terms of CE accuracy compared to benchmark FDD LS-based and tensor-based techniques.

A Decoupled Channel Estimation Method for Beyond Diagonal RIS

Beyond diagonal reconfigurable intelligent surface (BD-RIS) is a new architecture for RIS where elements are interconnected to provide more wave manipulation flexibility than traditional single connected RIS, enhancing data rate and coverage. However, channel estimation for BD-RIS is challenging due to the more complex multiple-connection structure involving their scattering elements. To address this issue, this paper proposes a decoupled channel estimation method for BD-RIS that yields separate estimates of the involved channels to enhance the accuracy of the overall combined channel by capitalizing on its Kronecker structure. Starting from a least squares estimate of the combined channel and by properly reshaping the resulting filtered signal, the proposed algorithm resorts to a Khatri-Rao Factorization (KRF) method that teases out the individual channels based on simple rank-one matrix approximation steps. Numerical results show that the proposed decoupled channel estimation yields more accurate channel estimates than the classical least squares scheme.

RIS-Assisted Sensing: A Nested Tensor Decomposition-Based Approach

We study a monostatic multiple-input multiple-output sensing scenario assisted by a reconfigurable intelligent surface using tensor signal modeling. We propose a method that exploits the intrinsic multidimensional structure of the received echo signal, allowing us to recast the target sensing problem as a nested tensor-based decomposition problem to jointly estimate the delay, Doppler, and angular information of the target. We derive a two-stage approach based on the alternating least squares algorithm followed by the estimation of the signal parameters via rotational invariance techniques to extract the target parameters. Simulation results show that the proposed tensor-based algorithm yields accurate estimates of the sensing parameters with low complexity.

Semi-Blind Receivers for Hybrid Reflecting and Sensing RIS

Recent research has delved into advanced designs for reconfigurable intelligent surfaces (RIS) with integrated sensing functions. One promising concept is the hybrid RIS (HRIS), which blends sensing and reflecting meta-atoms. This enables HRIS to process signals, aiding in channel estimation (CE) and symbol detection tasks. This paper formulates semi-blind receivers for HRIS-aided wireless communications that enable joint symbol and CE at the HRIS and BS. The proposed receivers rely on a new tensor modeling approach for the signals received at both the HRIS and BS while exploiting a tensor signal coding scheme at the transmit side. Specifically, by capitalizing on the multilinear structures of the received signals, we develop iterative and closed-form receiver algorithms for joint estimation of the uplink channels and symbols at both the HRIS and the BS. Enabling joint channel and symbol estimation functionalities, the proposed receivers offer symbol decoding capabilities to the HRIS and ensure ambiguity-free separate CE without requiring an a priori training stage. We also study identifiability conditions ensuring a unique joint channel and symbol recovery and discuss the computational complexities and tradeoffs involved by the proposed semi-blind receivers. Our findings demonstrate the competitive performances of the proposed algorithms at the HRIS and the BS and uncover distinct performance trends based on the possible combinations of HRIS-BS receiver pairs. Finally, extensive numerical results elucidate the interplay between power splitting, symbol recovery, and CE accuracy in HRIS-assisted communications. Such insights are pivotal for optimizing receiver design and enhancing system performance in future HRIS deployments.

Channel Estimation for Beyond Diagonal RIS via Tensor Decomposition

This paper addresses the channel estimation problem for beyond diagonal reconfigurable intelligent surface (BD-RIS) from a tensor decomposition perspective. We first show that the received pilot signals can be arranged as a three-way tensor, allowing us to recast the cascaded channel estimation problem as a block Tucker decomposition problem that yields decoupled estimates for the involved channel matrices while offering a substantial performance gain over the conventional (matrix-based) least squares (LS) estimation method. More specifically, we develop two solutions to solve the problem. The first one is a closed-form solution that extracts the channel estimates via a block Tucker Kronecker factorization (BTKF), which boils down to solving a set of parallel rank-one matrix approximation problems. Exploiting such a low-rank property yields a noise rejection gain compared to the standard LS estimation scheme while allowing the two involved channels to be estimated separately. The second solution is based on a block Tucker alternating least squares (BTALS) algorithm that directly estimates the involved channel matrices using an iterative estimation procedure. We discuss the uniqueness and identifiability issues and their implications for training design. We also propose a tensor-based design of the BD-RIS training tensor for each algorithm that ensures unique decoupled channel estimates under trivial scaling ambiguities. Our numerical results shed light on the tradeoffs offered by BTKF and BTALS methods. Specifically, while the first enjoys fast and parallel extraction of the channel estimates in closed form, the second has a more flexible training design, allowing for a significantly reduced training overhead compared to the state-of-the-art LS method.