Asymptotic performance of reconfigurable intelligent surface assisted MIMO communication for large systems using random matrix theory

Reconfigurable intelligent surface (RIS) can provide unprecedented spectral efficiency gains and excellent ability to manipulate electromagnetic waves. This article considered a RIS-assisted multiuser multiple-input multiple-output (MIMO) downlink system, where the beamforming at the base station and RIS are jointly designed to maximize the sum-rate. For the large dimension scenario and high-rank beamforming matrix, the accurate deterministic approximations from random matrix theory are then utilized to simplify the RIS-assisted MIMO systems. The asymptotical signal-to-interference-plus-noise ratio values obtained through random matrix theory is infinitely close to the theoretical limits calculated by accurately iteration. And the performance of the proposed algorithm computed via the sharing second-order channel statistics matches that of the RIS algorithm with sharing full channel state information asymptotically. The deterministic approximations are instrumental to get improvement into the structure of the optimal beamforming and to reduce the implementation complexity in large-scale MIMO system. Numerical simulations results are provided to evaluate and verify the accuracy of the asymptotic results obtained from the proposed algorithm in the finite system regime. With the complex operation process of large dimension matrix reducing to the deterministic approximations, a lower computational complexity can be obtained compared with other methods.