Outage Probability of Correlated RIS-Aided Communication Links

A second-order approximation of the Moment- Generating Function (MGF) for the sum of the product of corre- lated Rayleigh envelopes (a well-known problem in the literature) is presented in this paper. The MGF is applied to evaluate the outage probability of Reconfigurable Intelligent Surfaces (RIS) in both uncorrelated and correlated environments. Key contributions include the derivation of the MGF approximation and its application to outage probability assessment in different scenarios. The accuracy of the approximation is analyzed under two distinct correlation conditions, demonstrating its reliability in providing outage probability estimates. The results emphasize the effectiveness of the approximation as a practical tool for evaluating the outage probability in RIS-based systems, especially in correlated environments. These findings offer valuable insights for future research and practical implementations of RIS in wire- less communication systems, particularly in optimizing system performance in the presence of varying correlation conditions.