On the Mutual Information of Multi-RIS Assisted MIMO: From Operator-Valued Free Probability Aspect

TL;DR

This paper analyzes the asymptotic mutual information of multi-RIS assisted MIMO channels using operator-valued free probability, revealing conditions under which multiple RIS panels significantly enhance data rates in Rician fading environments.

Contribution

It introduces a theoretical framework for evaluating mutual information in multi-RIS MIMO channels under Rician fading using operator-valued free probability theory.

Findings

Mutual information scales linearly with antennas and SNR in dB at high SNR.

Large Rician factors improve the effectiveness of multi-RIS deployment.

Few RIS panels suffice when reflected links have similar angles, leveraging spatial degrees of freedom.

Abstract

The reconfigurable intelligent surface (RIS) is useful to effectively improve the coverage and data rate of end-to-end communications. In contrast to the well-studied coverage-extension use case, in this paper, multiple RIS panels are introduced, aiming to enhance the data rate of multi-input multi-output (MIMO) channels in presence of insufficient scattering. Specifically, via the operator-valued free probability theory, the asymptotic mutual information of the large-dimensional RIS-assisted MIMO channel is obtained under the Rician fading with Weichselberger's correlation structure, in presence of both the direct and the reflected links. Although the mutual information of Rician MIMO channels scales linearly as the number of antennas and the signal-to-noise ratio (SNR) in decibels, numerical results show that it requires sufficiently large SNR, proportional to the Rician factor, in order to obtain the theoretically guaranteed linear improvement. This paper shows that the proposed multi-RIS deployment is especially effective to improve the mutual information of MIMO channels under the large Rician factor conditions. When the reflected links have similar arriving and departing angles across the RIS panels, a small number of RIS panels are sufficient to harness the spatial degree of freedom of the multi-RIS assisted MIMO channels.