Effective Rate Evaluation of RIS-Assisted Communications Using the Sums of Cascaded α-μ Random Variates

This paper begins with the characterization of sum M versions cascaded α-μ (equivalently, N * (α-μ)) distributed random variates (RVs), and later on, explores feasibility applicability obtained results in recent proposed reconfigurable intelligent surface (RIS)-assisted communications. More specifically, RVs is exactly characterized by probability density function (PDF) expressed terms programmable multivariate Fox's H-function, approximated mixture Gaussian (MoG) distribution. The approximation accuracy further validated Kolmogorov-Smirnov (KS) goodness fit test. Based on statistical results, a promising application, i.e., RIS-assisted communication, considered evaluated from effective rate perspective. exact, asymptotic, are derived closed-form expressions. Finally, our analytical using Monte-Carlo simulation, their confirmed error indicator. One can conclude that (i) exact expression complex manner mathematical representation; (ii) MoG-based simple provides highly tight to expression, besides it indeed acts as upper bound for expression; (iii) solution outperforms H-function based approach reducing complexity.