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.
翻译:重新配置的智能表面(RIS)由大量低成本和被动的具有金枪鱼可反射特性的低成本和被动元材料组成,最近被提议作为可编程的无线电传播环境的助推器;然而,尚未充分分析RIS附近频道条件在可优化性方面的作用;在本文件中,我们展示了一种无孔封闭式的表达方式,用于多个IRS、大安全帽限制、使用随机矩阵和复制理论的相互信息。在轻度假设下,可导出igen值和频道共变矩阵的偏振性表达方式。我们发现,当离RIS近的频道具有关联性时,例如由于角扩散小,通信连接从RIS优化中大大获益,结果出乎意料地高于几乎不相干的情况。此外,当RIS的预期反射从几何光学模型和复制理论大幅偏离时,可以推断出频道共变异性矩阵的无源表达式表达方式。我们发现,当接近RIS的频道与它相关时,例如由于角扩散小,通信联系会大大受益于RIS的优化,因此其收益比几乎不相关的情况要高。此外,当RIS的预期的反射反射离离离离离强的反光仪时,地面的反射力可以提供我们最优化的反射力的反射线的地面为最优化的反射力。