Exact statistics and tight approximations for RIS-assisted communications in generalized fading environments

Reconfigurable Intelligent Surfaces (RISs) are considered a key candidate technology for next-generation 6G wireless systems, promising to extend network coverage, enhance spectral efficiency, and effectively mitigate interference. RISs will achieve this by controlling the propagation environment, enabled by carefully altering the reflective properties of their elements. In this context, this work presents a general framework for deriving the exact probability density function (PDF) and higher-order moments of the signal-to-ratio (SNR) in a RIS system, considering the direct transmission and RIS-assisted links from source to destination. Recognizing the analytical challenges associated with obtaining exact statistics for RIS-assisted systems, which persist in both common and more generalized fading models, the proposed contribution is realized with the aid of the suitable α-μ fading model. To that end, we derive accurate approximations for the κ-μ and the extended η-μ distributions, which constitute effective and versatile multipath fading models. Based on this, the achieved results are virtually indistinguishable from those obtained through simulations for various environmental settings. This renders the proposed framework a valuable tool for evaluating the performance of RIS systems, particularly in terms of the corresponding average symbol error rate (ASER). Tractable closed-form asymptotic expressions are also derived and utilized to provide a deeper understanding of the system's behavior.