Capacity Optimization using Reconfigurable Intelligent Surfaces: A Large System Approach

TL;DR

This paper derives asymptotic expressions for the mutual information in large multi-antenna systems with multiple RISs, revealing how channel correlation near RISs influences optimization gains and providing closed-form solutions for RIS configuration.

Contribution

It introduces a large-system analytical framework for optimizing RISs in multi-antenna systems, including closed-form expressions for optimal RIS responses.

Findings

Correlated channels near RISs significantly enhance communication gains.

Optimal RIS configurations can be derived in closed form, avoiding brute-force methods.

RIS optimization is especially beneficial when the reflection deviates from geometrical optics.

Abstract

Reconfigurable Intelligent Surfaces (RISs), comprising large numbers of low-cost and passive metamaterials with tunable reflection properties, have been recently proposed as an enabler for programmable radio propagation environments. However, the role of the channel conditions near the RISs on their optimizability has not been analyzed adequately. In this paper, we present an asymptotic closed-form expression for the mutual information of a multi-antenna transmitter-receiver pair in the presence of multiple RISs, in the large-antenna limit, using the random matrix and replica theories. Under mild assumptions, asymptotic expressions for the eigenvalues and the eigenvectors of the channel covariance matrices are derived. We find that, when the channel close to an RIS is correlated, for instance due to small angle spread, the communication link benefits significantly from the RIS optimization, resulting in gains that are surprisingly higher than the nearly uncorrelated case. Furthermore, when the desired reflection from the RIS departs significantly from geometrical optics, the surface can be optimized to provide robust communication links. Building on the properties of the eigenvectors of the covariance matrices, we are able to find the optimal response of the RISs in closed form, bypassing the need for brute-force optimization.