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.

This article proposes an extension to the η-μ fading model by including a parameter that quantifies the clustering imbalance between in-phase and quadrature components. The inclusion of such a parameter renders the model enormously flexible, extending its reach of application in a wider range of scenarios. Despite the inclusion of an additional parameter, the equations obtained remain as mathematically tractable as those for the original η-μ model. Several new closed-form expressions for important statistics are then obtained, including: (i) probability density functions for both envelope and phase; (ii) cumulative distribution functions for both envelope and phase; (iii) arbitrary moments for the envelope; (iv) moment generating function for the envelope; (v) average bit error rate for coherent binary systems; (v) level crossing rate, average fading duration, and phase crossing rate; and (vi) several other joint distributions encompassing envelope, phase, and their respective time derivatives. It is noteworthy that many of the closed-form formulations presented here are not available even for the simple η-μ model.

In this paper, we introduce a new fading model which is capable of characterizing both the shadowing of the dominant component and composite shadowing which may exist in wireless channels. More precisely, this new model assumes a κ-μ envelope where the dominant component is fluctuated by a Nakagami-m random variable (RV) which is preceded (or succeeded) by a secondary round of shadowing brought about by an inverse Nakagami-m RV. We conveniently refer to this as the double shadowed κ-μ fading model. In this context, novel closed-form and analytical expressions are developed for a range of channel related statistics, such as the probability density function, cumulative distribution function, and moments. All of the derived expressions have been validated through Monte-Carlo simulations and reduction to a number of well-known special cases. It is worth highlighting that the proposed fading model offers remarkable flexibility as it includes the κ-μ, η-μ, Rician shadowed, double shadowed Rician, κ-μ shadowed, κ-μ/inverse gamma and η-μ/inverse gamma distributions as special cases.

This paper presents exact, novel formulations for the probability density function and cumulative distribution function for the product of two independent and non-identically distributed α-μ, κ-μ, and η-μ variates. The expressions are given in terms of both 1) generalized Fox H-function and 2) easily computable series expansions. The formulations derived can be directly used to explore the performance of a number of wireless communication processes, including multihop systems, cascaded channels, radar communications, multiple-input multiple-output links, and others. Due to the high flexibility of the above-mentioned distributions, the results presented here comprise a substantial number of useful product distributions. As application examples, performance metrics for the cascaded fading channel are derived. The validity of the expressions is confirmed via Monte Carlo simulation. It is noteworthy that, because any composite multipath-shadowing fading model is obtained as a particular case of the product of two fading variables, the results given here provide a plethora of composite multipath-shadowing fading scenarios.

In this paper, we perform a systematic investigation of the statistics associated with the product of two independent and non-identically distributed κ-μ random variables. More specifically, we develop novel analytical formulations for many of the fundamental statistics of interest, namely, the probability density function, cumulative distribution function, and moment-generating function. Using these new results, closedform expressions are obtained for the higher order moments, amount of fading and channel quality estimation index, while analytical formulations are obtained for the outage probability, average channel capacity, average symbol error probability, and average bit error probability. These general expressions can be reduced to a number of fading scenarios, such as the double Rayleigh, double Rice, double Nakagami-m, κ-μ/Nakagami-m, and Rice/Nakagami-m, which all occur as special cases. Additionally, as a byproduct of the work performed here, formulations for the κ-μ/κ-μ composite fading model can also be deduced. To illustrate the efficacy of the novel expressions proposed here, we provide useful insights into the outage probability of a dualhop system used in body area networks, and demonstrate the suitability of the κ-μ/κ-μ composite fading for characterizing shadowed fading in device-to-device channels.

In this paper, we initially consider the product of two independent and non-identically distributed κ-μ variates, and obtain its probability density function (PDF) in novel analytical form. Following from this, the PDF for the κ-μ/κ-μ composite fading model is then deduced. Monte-Carlo simulations are performed to verify the derived results. It is worth highlighting that both sets of expressions can be reduced to a number of double and composite fading scenarios such as the double Rice, double Nakagami-m, κ-μ/Nakagami-m, and Rice/Nakagami-m. Finally, we illustrate the usefulness of the obtained formulations by characterizing the shadowed fading encountered in body area networks, device-to-device and vehicle-to-vehicle communication channels. To this end, it is shown that the κ-μ/κ-μ composite fading model provides an excellent fit to the measurement data.

In this paper, we obtain novel analytical formulations for the outage probability (OP) in scenarios with α-μ or κ-μ faded signals of interest (SoI), and κ-μ or α-μ faded co-channel interference (CCI). Both single and multiple interfering scenarios have been considered, and exact formulations are provided when the SoI experiences α-μ fading and the CCI experiences κ-μ fading. When the SoI is subject to κ-μ fading and the CCI is subject to α-μ fading, exact and highly accurate approximate OP expressions have been derived for the single and multiple interfering cases, respectively. We also analyze the asymptotic behavior of the OP when the average signal-to-noise-ratio (SNR) of the SoI is significantly larger or smaller than that of the interferers. Monte-Carlo simulations are performed to verify the derived results. It is worth highlighting that these general expressions are important as they unify the CCI for a number of previously disjoint fading scenarios.