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.

中文翻译：

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使用可重构智能表面进行容量优化：一种大型系统方法

可重构智能表面 (RIS) 包含大量具有可调反射特性的低成本和无源超材料，最近已被提议作为可编程无线电传播环境的推动者。然而，RIS 附近的信道条件对其可优化性的作用尚未得到充分分析。在本文中，我们使用随机矩阵和复制理论，在大天线限制下，在存在多个 RIS 的情况下，提出了多天线发射器-接收器对互信息的渐近闭式表达式。在温和的假设下，导出了信道协方差矩阵的特征值和特征向量的渐近表达式。我们发现，当靠近 RIS 的通道相关时，例如由于小角度扩展，通信链路从 RIS 优化中受益匪浅，导致收益比几乎不相关的情况出奇地高。此外，当来自 RIS 的所需反射明显偏离几何光学时，可以优化表面​​以提供强大的通信链接。基于协方差矩阵的特征向量的属性，我们能够找到封闭形式的 RIS 的最佳响应，绕过了暴力优化的需要。