Performance of RIS-Assisted Systems in Mixed Fading Conditions

This paper presents a general framework for deriving the statistics of RIS-based communication systems under diverse fading conditions. Specifically, the probability density function (PDF) and higher-order moments are derived considering direct and RIS-assisted links from the source to the destination. Recognizing the analytical challenges of these derivations in the context of RIS-assisted systems, we employ a more practical yet tractable and notably accurate α-μ approximation, which offers a simple and closed-form solution, producing results virtually indistinguishable from those obtained through simulations for various realistic communication scenarios of interest. This approach is a valuable tool for evaluating system performance metrics such as outage probability and average symbol error rate since such an approximation significantly outperforms the one derived from the widely employed central limit theorem, even when dealing with a reasonably large number of elements. We subsequently apply this general framework to investigate the achievable RIS performance in different realistic fading environments, including α-μ, κ-μ, and Extended η-μ, both individually and combined. Specifically, we derive reasonably simple and functional closed-form asymptotic expressions, in terms of well-known special functions, for each case study, contributing to a deeper understanding of how each fading parameter affects the system’s performance regarding coding gain and diversity gain. In particular, we demonstrate that the diversity order is directly determined by the number of reflecting elements, the density of multipath clusters, and the degree of non-linearity in the propagation medium, with higher values of these parameters leading to clear improvements in performance. The offered results enable the development of valuable insights on RIS-based communications, which will be useful in future system designs and deployments.