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.

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.

In this letter, we derive a novel exact expression for the probability of false alarm (PFA) and an approximate closed-form solution for the probability of detection (PD) of a smallest of cell-averaging constant false alarm rate (SOCA-CFAR) detector operating over Weibull-distributed clutter. For the analysis, we consider an exponentially distributed target and allow arbitrary values for the shape parameter of clutter interference. To the best of our knowledge, there are no exact or approximate performance evaluations for an SOCA-CFAR detector considering arbitrary values for the shape parameter of the Weibull interference samples (i.e., different from 1) contained within the CFAR window. Therefore, our analytical derivations generalize previous performance evaluation studies and take a small step toward a better understanding of more realistic SOCA-CFAR detectors. Moreover, we obtain exact formulations for the probability density function (PDF) and the cumulative distribution function (CDF) for a minimum of two sums of independent and identically distributed (i.i.d.) Weibull random variables. Numerical results indicate that the system performance improves as the shape parameter of the Weibull interference increases. The validity of all our expressions is confirmed via Monte Carlo simulations.

In this letter, we provide a general cell-averaging constant false alarm rate (CA-CFAR) performance analysis considering homogeneous Weibull-distributed clutter environments. To do so, we provide generalized expressions for the probability of detection (PD) and probability of false alarm (PFA). Notably, these expressions permit arbitrary values for the shape parameter of the Weibull interference. So far, all CA-CFAR performance analyses were carried out by setting the shape parameter of the Weibull samples within the CFAR window equal to one, which narrows the overall evaluation spectrum. In this study, we allow the shape parameter to take values greater than or equal to one—regime of paramount importance in many practical applications—and still manage to derive manageable and easy-to-implement solutions. All our expressions are confirmed via Monte-Carlo simulations. Numerical results indicate that radar detection is improved as the shape parameter increases.