metasurface modeling

Conventional single-layer reconfigurable intelligent surfaces (RISs) offer limited electromagnetic control, insufficient to meet 6G’s demand for high-dimensional and flexible signal processing. This work presents a systematic review of stacked intelligent metasurfaces (SIMs), establishing— for the first time—a theoretical framework that positions SIMs as programmable electromagnetic processors. It introduces a novel wave-domain signal processing paradigm grounded in cascaded wave–matter interactions. By leveraging cascaded operator modeling, multi-port impedance analysis, and learning-driven control strategies, the study reveals the potential of SIMs in near-field communications, broadband transmission, and integrated sensing and communication. Furthermore, it identifies key research directions, including cross-layer co-design and network-level integration, thereby providing a comprehensive technical roadmap for programmable electromagnetic front-ends in 6G systems.

Static frequency-selective metaprisms (MTPs) face a fundamental trade-off between beamforming accuracy and physical realizability across multiple incident angles and operating frequencies. Method: This work proposes a multi-port equivalent modeling framework incorporating Foster circuit constraints, establishing—for the first time—a rigorous equivalence between MTPs and ideal scattering-parameter (S-parameter) models. A joint optimization strategy is then developed to simultaneously satisfy angular–spectral response requirements and hardware feasibility. Contribution/Results: Through combined angular–spectral analysis, Foster-type circuit synthesis, and full-wave simulations (CST/ANSYS), the method achieves high-precision multi-frequency beam separation and steering. The synthesized reflection amplitude–phase responses strictly obey causality and passivity. Compared to conventional simplified models, performance improves by over 37%, significantly reducing reconfiguration overhead for reconfigurable intelligent surfaces (RISs).

This work addresses the joint optimization of beamforming and surface geometry in reconfigurable intelligent metasurface-assisted integrated sensing and communication (ISAC) systems, aiming to minimize the Cramér-Rao bound while satisfying communication quality-of-service constraints. Tackling this non-convex optimization challenge, the study pioneers the incorporation of deformable surface geometry into the ISAC design framework and proposes a deep reinforcement learning approach based on Deep Deterministic Policy Gradient (DDPG). A constraint-aware reward mechanism is introduced to balance sensing accuracy and communication performance. Simulation results demonstrate that the proposed method significantly reduces the Cramér-Rao bound compared to conventional rigid arrays, while effectively maintaining required communication quality-of-service levels.

This work addresses integrated sensing and communication (ISAC) systems empowered by flexible intelligent metasurfaces (FIMs), focusing on jointly optimizing beamforming and the geometric shapes of transmit and receive FIM surfaces to minimize the Cramér–Rao bound (CRB)—the theoretical lower bound on sensing performance. It is the first to reveal how FIM geometric deformations influence the CRB, proposing instead to maximize the average Fisher information as a tractable surrogate objective. A decoupled cooperative optimization framework is developed, where the objective function is approximated via Gauss–Hermite quadrature, beamforming is optimized using Schur complement and penalty-based semidefinite relaxation, and the FIM shapes are updated via fixed-point equations and projected gradient methods. Simulations demonstrate that the proposed approach significantly reduces the average CRB, outperforms rigid arrays even in multi-target scenarios, and maintains robust communication performance.

This work addresses the challenges of slow convergence, high computational complexity, and lack of user prioritization in joint signal enhancement and suppression using reconfigurable intelligent surfaces (RIS) in multi-user wireless systems. To overcome these limitations, the authors propose a unified RIS optimization framework that incorporates adaptive gradient scaling for fast, parameter-free convergence, a low-complexity beamforming recovery method that avoids matrix decomposition, and a novel user prioritization mechanism based on RIS subarray allocation, complemented by a modular architecture supporting flexible addition or removal of components. Evaluated across three representative scenarios, the proposed scheme closely approaches theoretical performance bounds, significantly outperforms conventional semidefinite relaxation methods, and demonstrates near-optimality, scalability, and effectiveness in both cooperative and competitive multi-user environments under real-world channel conditions.

Conventional single-layer reconfigurable intelligent surfaces (RIS) in multi-user MISO downlink systems suffer from limited wave-domain processing capability and rely heavily on digital beamforming and high-resolution DACs. Method: This paper proposes a stacked intelligent metasurface (SIM) architecture, deploying multiple cascaded reconfigurable metasurface layers at the base station to enable fully analog-domain beamforming. We formulate a novel wave-domain joint optimization model that co-designs transmit power allocation and discrete phase shifts—first of its kind—to maximize the system’s sum rate. An efficient algorithm is developed based on alternating optimization and electromagnetic scattering modeling. Contribution/Results: Under identical antenna count and power constraints, the proposed SIM architecture achieves approximately 200% higher sum rate than conventional MISO systems, while exhibiting significantly lower computational complexity compared to benchmark schemes.

This work addresses the weighted sum-rate maximization problem under per-cluster power constraints in downlink distributed antenna systems. By exploiting the fact that optimal beamformers lie in the low-dimensional subspace spanned by the channels of their respective antenna clusters, the original high-dimensional constrained optimization problem is reformulated—for the first time—as an unconstrained optimization over a product of ellipsoidal manifolds. The authors systematically develop the Riemannian geometry of this manifold, including its tangent space, metric, projection, and retraction operators, and design a tailored Riemannian conjugate gradient algorithm. The proposed method achieves solution quality comparable to that of WMMSE and conventional manifold-based approaches while significantly improving computational efficiency and scalability, with pronounced advantages as the number of antenna clusters increases.

This work addresses the challenge of rapidly escalating computational complexity in large-scale non-convex reconfigurable intelligent surface (RIS) configuration optimization, which intensifies with the number of scattering elements and architectural intricacy. To tackle this, the paper proposes a stochastic optimization framework that integrates continuous cross-entropy (CE) methods with Metropolis–Hastings (MH) sampling. The approach operates directly on continuous variables and incorporates relaxation and projection mechanisms to accommodate discrete RIS configurations, making it applicable to both nearly passive and active RIS architectures for optimizing spectral efficiency and energy efficiency. As the first systematic application of continuous stochastic optimization to RIS network design, the proposed method transcends the limitations of conventional discrete optimization, offering theoretical guarantees on convergence and computational efficiency. In representative scenarios, it achieves performance comparable to or better than state-of-the-art deterministic algorithms while reducing runtime by up to an order of magnitude.

This work addresses the limitations of conventional metasurface inverse design, which relies on time-consuming full-wave simulations and suffers from insufficient control accuracy and structural diversity in existing generative approaches. The authors propose a generative inverse design framework based on a progressively growing Wasserstein GAN, incorporating feature-wise linear modulation to achieve high-precision spectral conditioning. Physical consistency is ensured through a surrogate model–guided spectral alignment loss, while geometric diversity is enhanced via determinantal point process regularization. Evaluated over the 2–18 GHz band, the method achieves an average mean squared error of 0.0052, a diversity score of 0.8730, a band-alignment accuracy of 0.8533, and an effective design generation rate of 89.57%, significantly outperforming current state-of-the-art techniques.

This work addresses the challenge that metasurface inverse design heavily relies on domain experts to construct solver-compatible workflows and that existing language-driven approaches struggle to transfer knowledge across tasks. The authors propose an agent-based framework featuring context-level skill evolution, wherein a large language model–driven coding agent collaborates with a persistently evolving skill library and a physics-simulation–based deterministic evaluator. This enables cross-task, self-evolving optimization without modifying either the underlying model or the solver. Evaluated on in-distribution tasks, the method improves success rate from 38% to 74%, increases the达标 rate (task-completion metric) from 0.510 to 0.870, and reduces the average number of trials to 2.30. Furthermore, it demonstrates preliminary transferability to unseen task families.

This work addresses the bottlenecks in spectral efficiency and onboard hardware complexity faced by low Earth orbit (LEO) satellite constellations by introducing metasurface antennas into LEO satellite communications for the first time. The authors propose a mixed-integer nonlinear optimization framework that jointly optimizes user scheduling and passive beamforming. Leveraging an alternating optimization strategy, the approach employs minimum-cost maximum-flow (MCMF) to achieve polynomial-time-complexity user scheduling and integrates weighted minimum mean square error (WMMSE) with semidefinite relaxation (SDR) to design high-precision beamforming patterns that effectively suppress multiuser interference. Simulation results demonstrate that the proposed method significantly enhances both the system’s weighted sum rate and resource utilization efficiency.