Gaussian-Chebyshev Quadrature Approximation for Analyzing RIS-Assisted Communications

Analyzing the impact of cascaded channels in reconfigurable intelligent surfaces (RIS)-assisted wireless communication systems presents significant challenges, particularly due to the varying channel models associated with different links. In this paper, we investigate the relationship between the rate coverage and RIS under specific channel conditions by deriving closed-form expressions for rate coverage, offering a robust solution to manage the complexity of these heterogeneous channels. The systems consider both direct and RIS-assisted links, with distinct fading models for each, including Rayleigh, Nakagami, and Rician distributions. The proposed approximation method provides a tight upper bound for rate coverage. Extensive Monte Carlo simulations validate the accuracy of the derived expressions. This study offers practical guidance for deploying RIS in future wireless networks, particularly in scenarios where varying propagation environments complicate signal transmission.