TenSIM: Tensor-Based Channel Estimation for MIMO Systems with Stacked Intelligent Metasurfaces

Stacked intelligent metasurfaces (SIMs) are emerging as a promising architecture for the sixth generation (6G) and beyond of wireless systems, enabling richer electromagnetic-wave manipulation than conventional single-layer metasurfaces. However, realizing these gains requires accurate and scalable channel estimation under the strong inter-layer coupling and multilinear parameter interactions introduced by the stacked programmable metasurface layers. This paper proposes TenSIM, a tensor-based channel-estimation framework for SIM-assisted multiple-input multiple-output (MIMO) systems. By exploiting a structured SIM training protocol, TenSIM derives two parity-dependent observation models: a PARAllel FACtor (PARAFAC) model for odd-layer SIMs and a Tucker model for even-layer SIMs. These formulations decouple the transmitter-SIM and SIM-receiver channels while explicitly accounting for inter-layer wave coupling. Based on the resulting tensor models, we develop alternating least squares estimators, establish identifiability conditions using the associated design matrices, and characterize practical sufficient conditions for full-column-rank training designs, including those involving scaling ambiguities. The proposed framework is validated through extensive numerical experiments and reveals the main operating trade-offs. We show that both TenSIM-PARAFAC and TenSIM-Tucker outperform unstructured least squares baselines by exploiting the tensor structure of the SIM cascade. Moreover, TenSIM-PARAFAC offers better scalability, lower computational complexity, and stronger robustness to inter-layer spacing, while TenSIM-Tucker can provide more accurate channel reconstruction when sufficient training and strong layer coupling are available. Finally, it is shown that the proposed TenSIM framework remains effective under imperfect or blind SIM training when additional pilot diversity is available.

A Near-Field Compatible Model for 2D Waveguide-Fed Metasurfaces

This paper presents a novel physically consistent analytical model for two-dimensional (2D) waveguide-fed metasurface antennas that is based on the discrete dipole approximation. The proposed framework extends previous works deriving power-consistent constraints on the magnetic polarizability tensor, leading to closed-form expressions for the effective polarizabilities. The model is validated through full-wave simulations for multi-feed settings, and is extended to a near-field compatible~formulation enabling accurate predictions in the radiating near-field.

Near-Field Beam Focusing Characterization for 2D Waveguide-Fed Metasurface Antennas

Two-dimensional (2D) waveguide-fed metasurfaces enable scalable antenna apertures through guided wave excitation of distributed radiating elements. However, the resulting non-uniform excitation challenges classical interpretations of near-field characteristics. Using a physics-compliant model, this paper analyzes the near-field beam focusing behavior of such architectures. We derive asymptotic scaling laws for the beamforming gain, showcasing that the power-normalized gain scales linearly with the number of radiating elements. Furthermore, we introduce a normalized beam-depth formulation and obtain a compact analytic expression that characterizes the transition to far-field-like behavior. The presented analysis is validated against simulations based on the full electromagnetic model, confirming the accuracy of the derived scaling laws and beam-depth limits.

Robust Beamforming for Cell-Free Systems with Parallel-Plate-Waveguided Dynamic Metasurfaces

Dynamic Metasurface Antennas (DMAs) constitute a promising solution for extremely large antenna arrays, requiring lower power consumption and reduced hardware cost as compared to conventional phased arrays. In this paper, we consider a cell-free Orthogonal Frequency Division Multiplexing (OFDM) system comprising multiple Base Stations (BSs) equipped with parallel-plate-waveguided DMAs, which aims to serve multiple users in the downlink direction. Focusing on a realistic frequency-selective model for the response-tunable elements of each DMA panel, and targeting to surpass the necessity of centralized designs that rely on a central processing unit with high computational power, we present a distributed optimization framework with minimal control information exchange for the frequency-selective analog and digital beamforming matrices of the multiple BSs, having the system spectral efficiency maximization as the design objective. Considering imperfect Channel State Information (CSI) availability at each BS, we devise a parallel decomposition framework for the configuration of the tunable parameters of each DMA-based BS. Our numerical results showcase the robustness of the proposed distributed beamforming design over different CSI conditions, and quantify the critical role of taking into account mutual coupling during the DMA design process.

2D Waveguide-Fed Metasurfaces: Physically Consistent Modeling, Validation, and Optimization

Antenna array architectures based on programmable metasurfaces are emerging as a promising solution for scalable implementations of the eXtremely Large Multiple-Input Multiple-Output (XL-MIMO) systems paradigm, envisioned for 6-th Generation (6G), and beyond, wireless networks. However, their accurate modeling, quantifying the role of key structural features, such as strong mutual coupling and guided-wave excitation, remains challenging, amplifying the need for physically consistent representations of the constituent metamaterial elements. In this paper, capitalizing on the coupled dipole formulation, we develop a comprehensive electromagnetics-compliant framework for 2-Dimensional (2D) waveguide-fed metasurface antennas. The proposed model extends relevant existing modeling approaches by incorporating both electric and magnetic dipoles' responses, accounting for multiple excitation feeds, and enabling accurate characterization in both the near- and far-field regimes. Radiation-reaction corrections based on passivity constraints are derived and shown to ensure the passivity of the overall dipole system. In addition, we present a novel input impedance model for the considered architecture enabling explicit computation of the accepted power, and facilitating efficient beamforming design under realistic power constraints. All modeling components developed in this paper are validated against full-wave electromagnetic simulations. Furthermore, the analytical structure of the proposed model enables the formulation of a differentiable beamforming design optimization problem over both the considered metasurface geometry and its feed excitations. The presented numerical results demonstrate the effectiveness of the proposed modeling framework in achieving both directive beamforming and sector-wide coverage.

Low-Complexity Learning-Based Beamforming for Ultra-Massive MIMO THz Communications

Terahertz (THz) communications have emerged as a key technology for escalating data rates in future generation wireless networks. However, severe propagation losses at THz frequencies pose significant challenges, which can be mitigated via ultra-massive multiple-input multiple-output (UM-MIMO) systems employing highly directional transmissions. To this end, codebook-based analog beamforming constitutes a realistic solution, eliminating the need for explicit channel estimation. However, in UM-MIMO systems, the use of extremely narrow beams makes beam training and alignment increasingly challenging, leading to a substantial increase in the number of codewords to be tested and, thus, to high computational complexity. In this paper, a novel artificial neural network architecture for low-complexity beam training in UM-MIMO THz systems is presented, which does not require a constant feedback link between transmitter and receiver to obtain the best beamformer and combiner pair. An inception and residual network, which is trained based on the received signal powers using the transmit and receive codewords generated from predefined hierarchical codebooks, is designed. Our numerical investigations demonstrate that the proposed machine learning approach significantly reduces the complexity of UM-MIMO transmit and receive beamforming design, as compared to the standard exhaustive and hierarchical beam searching methods.

Wideband Sensing with Dynamic Metasurface Antennas under Realistic Phase Response Modeling

This paper investigates the impact of practical features of the emerging antenna array technology of Dynamic Metasurface Antennas (DMAs) when used for wideband sensing. By adopting a realistic DMA response model capturing frequency selective magnetic polarizability, finite resonant frequency tuning, and waveguide phase and leakage effects, we first present a compact observation model for user localization and multiple scattering points sensing through DMA-based analog combining of Orthogonal Frequency Division Multiplexing (OFDM) pilots transmitted in the uplink direction. Building on this model, we derive the Fisher Information Matrix (FIM), the equivalent FIM, and the corresponding Cramer-Rao Bounds (CRBs) for the relevant spatitemporal parameters estimation. The analysis reveals that frequency selectivity reduces the effective information bandwidth and distorts the DMA-based reception manifold, while waveguide attenuation decreases both the coherent combining gain and the effective aperture, thereby degrading estimation accuracy. Numerical results validate the analysis and confirm the resulting inflation in the delay, angle, and position error bounds.

Symbol Error Analysis for Fluid Antenna Systems with One- and Two-Dimensional Modulation Schemes

This paper considers a Fluid Antenna (FA) system comprising a single-antenna transmitter that communicates with a receiver equipped with an FA array with $N$ ports. The transmitter is assumed to deploy any of the modulation schemes: \textit{i}) two-sided $M$-ary amplitude-shift keying, \textit{ii}) $M$-ary phase-shift keying, iii) $M$-ary quadrature-amplitude modulation, and \textit{iv}) binary frequency-shift keying, the channels between its antenna and the receiver ports are subjected to Rayleigh fading, and the receiver chooses the best $K$ out of its $N$ ports for symbol detection. Considering that the receiver combines the signals from the best $K$ ports using maximal-ratio combining, the optimal reception structures for all the considered signaling schemes are obtained. We also present novel exact closed-form expressions for the respective symbol error probabilities (SEPs) of the FA system, as well as asymptotic approximations valid at high signal-to-noise ratios. The presented analysis is corroborated through comparisons with simulation results, showcasing the critical role of various system parameters on the SEP performance.

Multi-User Symbol Detection with XL Reception: Dynamic Metasurface Antennas with Low Resolution ADCs

Dynamic Metasurface Antennas (DMAs) have been recently proposed as a cost- and energy-efficient front-end solution for eXtremely Large (XL) antenna array systems, supporting scalable Analog and Digital (A/D) beamforming while using a reduced number of Radio-Frequency (RF) chains. This array architecture is commonly realized as partially connected hybrid A/D beamformers, in which non-overlapping subarrays are linked to separate RF chains, each attached to a waveguide hosting multiple metamaterials. In this work, we study uplink multi-user communications where each RF chain of an XL DMA receiver is equipped with a $b$-bit resolution Analog-to-Digital Converter (ADC). We cast a Mean Squared Error (MSE) minimization problem for the design of the hybrid A/D combiner aimed at multi-user symbol detection, which is intrinsically non-convex due to the structural constraints imposed by the DMA hardware. By exploiting the Bussgang decomposition and a tractable modeling framework, we propose an efficient joint design of the hybrid A/D combining parameters. Our numerical evaluations showcase that XL DMA receivers can perform highly accurate multi-user symbol detection, revealing attractive trade-offs between hardware complexity and MSE performance.

Secret Key Rate Analysis of RIS-Assisted THz MIMO CV-QKD Systems under Localized and Global Eavesdropping

A multiple-input multiple-output (MIMO) system operating at terahertz (THz) frequencies and consisting of a transmitter, Alice, that encodes secret keys using Gaussian-modulated coherent states, which are communicated to a legitimate receiver, Bob, under the assistance of a reconfigurable intelligent surface (RIS) is considered in this paper. The composite wireless channel comprising the direct Alice-to-Bob signal propagation path and the RIS-enabled reflected one is modeled as a passive linear Gaussian quantum channel, allowing for a unitary dilation that preserves the canonical commutation relations. The security of the considered RIS-empowered MIMO system is analyzed under collective Gaussian entangling attacks, according to which an eavesdropper, Eve, is assumed to have access to environmental modes associated with specific propagation segments. We also study, as a benchmark, the case where Eve has access to the purification of the overall channel. The legitimate receiver, Bob, is designed to deploy homodyne detection and reverse reconciliation for key extraction. Novel expressions for the achievable secret key rate (SKR) of the system are derived for both the considered eavesdropping scenarios. Furthermore, an optimization framework is developed to determine the optimal RIS phase configuration matrix that maximizes the SKR performance. The resulting optimization problem is efficiently solved using particle swarm optimization. Numerical results are presented to demonstrate the system's performance with respect to various free parameters. It is showcased that the considered RIS plays a crucial role in enhancing the SKR of the system as well as in extending the secure communication range. This establishes RIS-assisted THz MIMO CV-QKD as a promising solution for next generation secure wireless networks.