Performance of RIS-assisted systems in mixed fading conditions

This paper presents a general framework for deriving the statistics of RIS-based communication systems underdiverse fading conditions. Specifically, the probability densityfunction (PDF) and higher-order moments are derived considering direct and RIS-assisted links from the source to thedestination. Recognizing the analytical challenges of these derivations in the context of RIS-assisted systems, we employ a morepractical yet tractable and notably accurate α-µ approximation, which offers a simple and closed-form solution, producingresults virtually indistinguishable from those obtained throughsimulations for various realistic communication scenarios ofinterest. This approach is a valuable tool for evaluating systemperformance metrics such as outage probability and averagesymbol error rate since such an approximation significantlyoutperforms the one derived from the widely employed centrallimit theorem, even when dealing with a reasonably large numberof elements. We subsequently apply this general framework toinvestigate the achievable RIS performance in different realisticfading 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 fadingparameter affects the system’s performance regarding codinggain and diversity gain. In particular, we demonstrate that thediversity order is directly determined by the number of reflectingelements, the density of multipath clusters, and the degree ofnon-linearity in the propagation medium, with higher values ofthese 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 futuresystem designs and deployments.