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Reconfigurable intelligent surface (RIS) is an emerging technology to enhancewireless communication in terms of energy cost and system performance byequipping a considerable quantity of nearly passive reflecting elements. Thisstudy focuses on a downlink RIS-assisted multiple-input multiple-output (MIMO)wireless communication system that comprises three communication links ofRician channel, including base station (BS) to RIS, RIS to user, and BS touser. The objective is to design an optimal transmit covariance matrix at BSand diagonal phase-shifting matrix at RIS to maximize the achievable ergodicrate by exploiting the statistical channel state information at BS. Therefore,a large-system approximation of the achievable ergodic rate is derived usingthe replica method in large dimension random matrix theory. This large-systemapproximation enables the identification of asymptotic-optimal transmitcovariance and diagonal phase-shifting matrices using an alternatingoptimization algorithm. Simulation results show that the large-system resultsare consistent with the achievable ergodic rate calculated by Monte Carloaveraging. The results verify that the proposed algorithm can significantlyenhance the RIS-assisted MIMO system performance.

Large System Achievable Rate Analysis of RIS-Assisted MIMO Wireless Communication with Statistical CSIT