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arXiv 2109.07754cs.ITcs.ETmath.IT
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使用可重构智能表面的容量优化:一种大系统方法

Capacity Optimization using Reconfigurable Intelligent Surfaces: A Large System Approach

Aris L. Moustakas, George C. Alexandropoulos, Mérouane Debbah

摘要:

可重构智能表面(RISs),包括大量的低成本和无源超材料与可调反射特性,最近已被提出作为可编程无线电传播环境的使能器。然而,RISs附近的信道条件对它们的可优化性的作用还没有得到充分的分析。在本文中,我们提出了一个渐进的封闭形式的表达式的互信息的多天线收发机对的存在多个RI,在大天线的限制,使用随机矩阵和副本理论。在适当的假设下,推导出了信道协方差矩阵特征值和特征向量的渐近表达式。我们发现,当接近RIS的信道相关时,例如由于小角度扩展,通信链路从RIS优化中显著受益,从而导致增益出人意料地高于几乎不相关的情况。此外,当来自RIS的期望反射显著偏离几何光学时,可以优化表面以提供鲁棒的通信链路。基于协方差矩阵的特征向量的性质,我们能够找到封闭形式的RIS的最佳响应,绕过了蛮力优化的需要。

英文摘要:

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.

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