A Tutorial on Beyond-Diagonal Reconfigurable Intelligent Surfaces: Modeling, Architectures, System Design and Optimization, and Applications

2025-05-22

AI Summary

Conventional diagonal reconfigurable intelligent surfaces (D-RISs) are constrained by diagonal scattering matrices, severely limiting beamforming degrees of freedom. Method: This paper proposes beyond-diagonal RISs (BD-RISs), establishing the first general theoretical and technical framework enabling full non-diagonal scattering matrices—thereby achieving complete wavefront control and inter-element energy redistribution. We introduce a physically consistent multi-port network model, a non-reciprocal architecture, and a Pareto-optimal trade-off methodology balancing performance and hardware complexity, jointly accounting for practical impairments including discrete impedance tuning, mutual coupling, wideband distortion, and interconnect losses. Contribution/Results: The framework unifies transmission, reflection, hybrid, and multi-sector operational modes, delivering substantial gains across wireless communications, sensing, and power transfer. BD-RISs establish a new paradigm for intelligent electromagnetic environment control.

Technology Category

• Intelligent Robots: Multi-Robot Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Responsible Web: Consent frameworks and practices on the web

Abstract

Written by its inventors, this first tutorial on Beyond-Diagonal Reconfigurable Intelligent Surfaces (BD-RISs) provides the readers with the basics and fundamental tools necessary to appreciate, understand, and contribute to this emerging and disruptive technology. Conventional (Diagonal) RISs (D-RISs) are characterized by a diagonal scattering matrix $mathbf{Theta}$ such that the wave manipulation flexibility of D-RIS is extremely limited. In contrast, BD-RIS refers to a novel and general framework for RIS where its scattering matrix is not limited to be diagonal (hence, the ``beyond-diagonal'' terminology) and consequently, all entries of $mathbf{Theta}$ can potentially help shaping waves for much higher manipulation flexibility. This physically means that BD-RIS can artificially engineer and reconfigure coupling across elements of the surface thanks to inter-element reconfigurable components which allow waves absorbed by one element to flow through other elements. Consequently, BD-RIS opens the door to more general and versatile intelligent surfaces that subsumes existing RIS architectures as special cases. In this tutorial, we share all the secret sauce to model, design, and optimize BD-RIS and make BD-RIS transformative in many different applications. Topics discussed include physics-consistent and multi-port network-aided modeling; transmitting, reflecting, hybrid, and multi-sector mode analysis; reciprocal and non-reciprocal architecture designs and optimal performance-complexity Pareto frontier of BD-RIS; signal processing, optimization, and channel estimation for BD-RIS; hardware impairments (discrete-value impedance and admittance, lossy interconnections and components, wideband effects, mutual coupling) of BD-RIS; benefits and applications of BD-RIS in communications, sensing, power transfer.

Problem

• BD-RIS enhances wave manipulation flexibility beyond diagonal RIS limitations
• BD-RIS enables artificial coupling across surface elements for versatile wave control
• BD-RIS requires novel modeling, design, and optimization for transformative applications

Innovation

• BD-RIS uses non-diagonal scattering matrix
• BD-RIS enables inter-element wave coupling
• BD-RIS supports versatile intelligent surfaces