Optimization of Beyond Diagonal RIS: A Universal Framework Applicable to Arbitrary Architectures

Reconfigurable intelligent surfaces (RISs) are envisioned as a promising technology for future wireless communication systems due to their ability to control the propagation environment in a hardware- and energy-efficient way. Recently, the concept of RISs has been extended to beyond diagonal RISs (BD-RISs), which unlock the full potential of RISs thanks to the presence of tunable interconnections between RIS elements. While various algorithms have been proposed for specific BD-RIS architectures, a universal optimization framework applicable to arbitrary architectures is still lacking. In this paper, we bridge this research gap by proposing an architecture-independent framework for BD-RIS optimization, with the main focus on sum-rate maximization and transmit power minimization in multiuser multi-input single-output (MU-MISO) systems. Specifically, we first incorporate BD-RIS architectures into the models by connecting the scattering matrix with the admittance matrix and introducing appropriate constraints to the admittance matrix. The formulated problems are then solved by our custom-designed partially proximal alternating direction method of multipliers (pp-ADMM) algorithms. The pp-ADMM algorithms are computationally efficient, with each subproblem either admitting a closed-form solution or being easily solvable. We further explore the extension of the proposed framework to general utility functions and multiuser multi-input multi-output (MU-MIMO) systems. Simulation results demonstrate that the proposed approaches achieve a better trade-off between performance and computational efficiency compared to existing methods. We also compare the performance of various BD-RIS architectures in MU-MISO systems using the proposed approach, which has not been explored before due to the lack of an architecture-independent framework.

Dual-Polarized Beyond Diagonal RIS

Beyond diagonal reconfigurable intelligent surface (BD-RIS) is a family of RIS architectures more flexible than conventional RIS. While BD-RIS has been primarily analyzed assuming uni-polarized systems, modern wireless deployments are dual-polarized. To address this gap, this paper investigates the fundamental limits of dual-polarized BD-RIS-aided systems. We derive the scaling laws governing the performance of BD-RIS and the Pareto frontier of the trade-off between performance and circuit complexity enabled by BD-RIS. Theoretical results show that the group-connected RIS with group size 2 provides remarkable gains over conventional RIS in both Rayleigh and line-of-sight (LoS) channels, while maintaining a reduced circuit complexity.

Rate-Splitting Multiple Access for Integrated Sensing and Communications: A First Experimental Study

A canonical use case of Integrated Sensing and Communications (ISAC) in multiple-input multiple-output (MIMO) systems involves a multi-antenna transmitter communicating with $K$ users and sensing targets in its vicinity. For this setup, precoder and multiple access designs are of utmost importance, as the limited transmit power budget must be efficiently directed towards the desired directions (users and targets) to maximize both communications and sensing performance. This problem has been widely investigated analytically under various design choices, in particular (a) whether or not a dedicated sensing signal is needed, and (b) for different MIMO multiple access techniques, such as Space Division Multiple Access (SDMA) and Rate-Splitting Multiple Access (RSMA). However, a conclusive answer on which design choice achieves the best ISAC performance, backed by experimental results, remains elusive. We address this vacuum by experimentally evaluating and comparing RSMA and SDMA for communicating with two users $(K = 2)$ and sensing (ranging) one target. Over three scenarios that are representative of \emph{vehicular} ISAC, covering different levels of inter-user interference and separation/integration between sensing and communications, we show that RSMA without a dedicated sensing signal achieves better ISAC performance -- i.e., higher sum throughput (upto $50\%$ peak throughput gain) for similar radar SNR (between $20$ to $24{\rm dB}$) -- than SDMA with a dedicated sensing signal. This first-ever experimental study of RSMA ISAC demonstrates the feasibility and the superiority of RSMA for future multi-functional wireless systems.

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.

Non-reciprocal Beyond Diagonal RIS: Sum-Rate Maximization in Full-Duplex Communications

Reconfigurable intelligent surface (RIS) has been envisioned as a key technology in future wireless communication networks to enable smart radio environment. To further enhance the passive beamforming capability of RIS, beyond diagonal (BD)-RIS has been proposed considering reconfigurable interconnections among different RIS elements. BD-RIS has a unique feature that cannot be enabled by conventional diagonal RIS; it can be realized by non-reciprocal circuits and thus enables an asymmetric scattering matrix. This feature provides the capability to break the wireless channel reciprocity, and has the potential to benefit full-duplex (FD) systems. In this paper, we model the BD RIS-assisted FD systems, where the impact of BD-RIS non-reciprocity and that of structural scattering, which refers to the specular reflection generated by RIS when the RIS is turned OFF, are explicitly captured. To assess the benefits of non-reciprocal BD-RIS, we optimise the scattering matrix, precoder and combiner to maximize the DL and UL sum-rates in the FD system. To tackle this optimization problem, we propose an iterative algorithm based on block coordination descent (BCD) and penalty dual decomposition (PDD). Numerical results demonstrate surprising benefits of non-reciprocal BD-RIS that it can achieve much higher DL and UL sum-rates in the FD scenario than reciprocal BD-RIS and conventional diagonal RIS.

Non-reciprocal BD-RIS in Full-duplex Communications: A Perspective on Sum-rate Maximization

Reconfigurable intelligent surface (RIS) has been envisioned as a key technology in future wireless communication networks to enable smart radio environment. To further enhance the passive beamforming capability of RIS, beyond diagonal (BD)-RIS has been proposed considering interconnections among different RIS elements. BD-RIS has a unique feature that cannot be enabled by conventional diagonal RIS; it can be realized by non-reciprocal circuits and thus has asymmetric scattering matrix. This feature provides probability to break the wireless channel reciprocity, and thus has potential to benefit the full-duplex (FD) system. In this paper, we model the BD RIS-assisted FD systems, where the impact of BD-RIS non-reciprocity and that of structural scattering, which refers to the virtual direct channel constructed by RIS when the RIS is turned OFF, are explicitly captured. To visualize the analysis, we propose to design the scattering matrix, precoder and combiner to maximize the DL and UL sum-rates in the FD system. To tackle this optimization problem, we propose an iterative algorithm based on block coordination descent (BCD) and penalty dual decomposition (PDD). Numerical results demonstrate surprising benefits of non-reciprocal BD-RIS that it can achieve higher DL and UL sum-rates in the FD scenario than reciprocal BD-RIS and conventional diagonal RIS.

Robust Max-Min Fair Beamforming Design for Rate Splitting Multiple Access-aided Visible Light Communications

This paper addresses the robust beamforming design for rate splitting multiple access (RSMA)-aided visible light communication (VLC) networks with imperfect channel state information at the transmitter (CSIT). In particular, we first derive the theoretical lower bound for the channel capacity of RSMA-aided VLC networks.Then we investigate the beamforming design to solve the max-min fairness (MMF) problem of RSMA-aided VLC networks under the practical optical power constraint and electrical power constraint while considering the practical imperfect CSIT scenario.To address the problem, we propose a constrained-concave-convex programming (CCCP)-based beamforming design algorithm which exploits semidefinite relaxation (SDR) technique and a penalty method to deal with the rank-one constraint caused by SDR.Numerical results show that the proposed robust beamforming design algorithm for RSMA-aided VLC network achieves a superior performance over the existing ones for space-division multiple access (SDMA) and non-orthogonal multiple access (NOMA).

Global Optimal Closed-Form Solutions for Intelligent Surfaces With Mutual Coupling: Is Mutual Coupling Detrimental or Beneficial?

Reconfigurable Intelligent Surface (RIS) is a breakthrough technology enabling the dynamic control of the propagation environment in wireless communications through programmable surfaces. To improve the flexibility of conventional diagonal RIS (D-RIS), beyond diagonal RIS (BD-RIS) has emerged as a family of more general RIS architectures. However, D-RIS and BD-RIS have been commonly explored neglecting mutual coupling effects, while the global optimization of RIS with mutual coupling, its performance limits, and scaling laws remain unexplored. This study addresses these gaps by deriving global optimal closed-form solutions for BD-RIS with mutual coupling to maximize the channel gain, specifically fully- and tree-connected RISs. Besides, we provide the expression of the maximum channel gain achievable in the presence of mutual coupling and its scaling law in closed form. By using the derived scaling laws, we analytically prove that mutual coupling increases the channel gain on average under Rayleigh fading channels. Our theoretical analysis, confirmed by numerical simulations, shows that both fully- and tree-connected RISs with mutual coupling achieve the same channel gain upper bound when optimized with the proposed global optimal solutions. Furthermore, we observe that a mutual coupling-unaware optimization of RIS can cause a channel gain degradation of up to 5 dB.

Non-Reciprocal Beyond Diagonal RIS: Multiport Network Models and Performance Benefits in Full-Duplex Systems

Beyond diagonal reconfigurable intelligent surfaces (BD-RIS) is a new advance in RIS techniques that introduces reconfigurable inter-element connections to generate scattering matrices not limited to being diagonal. BD-RIS has been recently proposed and proven to have benefits in enhancing channel gain and enlarging coverage in wireless communications. Uniquely, BD-RIS enables reciprocal and non-reciprocal architectures characterized by symmetric and non-symmetric scattering matrices. However, the performance benefits and new use cases enabled by non-reciprocal BD-RIS for wireless systems remain unexplored. This work takes a first step toward closing this knowledge gap and studies the non-reciprocal BD-RIS in full-duplex systems and its performance benefits over reciprocal counterparts. We start by deriving a general RIS aided full-duplex system model using a multiport circuit theory, followed by a simplified channel model based on physically consistent assumptions. With the considered channel model, we investigate the effect of BD-RIS non-reciprocity and identify the theoretical conditions for reciprocal and non-reciprocal BD-RISs to simultaneously achieve the maximum received power of the signal of interest in the uplink and the downlink. Simulation results validate the theories and highlight the significant benefits offered by non-reciprocal BD-RIS in full-duplex systems. The significant gains are achieved because of the non-reciprocity principle which implies that if a wave hits the non-reciprocal BD-RIS from one direction, the surface behaves differently than if it hits from the opposite direction. This enables an uplink user and a downlink user at different locations to optimally communicate with the same full-duplex base station via a non-reciprocal BD-RIS, which would not be possible with reciprocal surfaces.

Physics-Compliant Modeling and Scaling Laws of Multi-RIS Aided Systems

Reconfigurable intelligent surface (RIS) is a revolutionary technology enabling the control of wireless channels and improving coverage in wireless networks. To further extend coverage, multi-RIS aided systems have been explored, where multiple RISs steer the signal toward the receiver via a multi-hop path. However, deriving a physics-compliant channel model for multi-RIS aided systems is still an open problem. In this study, we fill this gap by modeling multi-RIS aided systems through multiport network theory, and deriving the scaling law of the physics-compliant channel gain. The derived physics-compliant channel model differs from the widely used model, where the structural scattering of the RISs is neglected. Theoretical insights, validated by numerical results, show a significant discrepancy between the physics-compliant and the widely used models. This discrepancy increases with the number of RISs and decreases with the number of RIS elements, reaching 200% in a system with eight RISs with 128 elements each.