The Analysis of Channel Capacity in Reconfigurable Intelligent Surface-Aided Wireless Communication Systems

This work analyzes the capacity of the Reconfigurable Intelligent Surface (RIS)-aided wireless communication system deploying linear RIS. We propose modeling the cascade channel with a mixed product of random Vandermonde matrices and a random diagonal matrix. A challenging problem that has yet to be addressed is the lack of a concise and accurate expression for the capacity of this channel due to the absence of spectral properties of the Vandermonde matrix. In this paper, we tackle this problem by expressing the capacity as a series expansion and obtaining the exact moment expression of the channel covariance matrix. Simulations indicate that the derived moments provide a good prediction of the true values. The approximate expression for the channel capacity, using finite terms, is simple enough to offer valuable insights and matches the simulation results well.