# \(\alpha\)-Fluctuating Nakagami-\(m\) Fading Model for Wireless Communications
###### Abstract  
This research introduces and studies the performance of the \(\alpha\)-Fluctuating Nakagami-\(m\) model, which addresses the limitations of conventional models for wireless communications. For the assumed channel model, the research presents a complete first-order statistical description (including the probability density function (PDF), cumulative distribution function (CDF), moment generating function (MGF), and raw moments) and provides closed-form results for system performance (assessed in terms of outage probability, average bit error rate (ABER), and channel capacity). All of the expressions have the same numerical complexity as the base-line Fluctuating Nakagami-\(m\) model, and are accompanied by their high signal-to-noise ratio (SNR) asymptotics. The derived results helped to identify the amount of fading (AoF) and diversity/coding gain of the proposed channel model. In-depth analysis of the system performance was carried out for all possible fading channel parameter values. Numerical analysis of the proposed solutions demonstrated their high computational efficiency. The comparison with experimental results demonstrated that the model offers enhanced flexibility and better characterization of fading regimes. Numerical analysis and simulation results show a high degree of correspondence with the analytical work and help study the dependence of channel nonlinearity effects on overall system performance. fading channel; statistical description; Fluctuating Nakagami; error rate; outage; capacity; amount of fading; diversity gain  
89.70.+c; 84.40.Ua  
16 April 202524 May 202524 May 202527 May 202529 May 2025  
Nakagami [7] distributions. These approaches have a solid foundation (both analytical and experimental [19]), although they lead to very complex results regarding overall system performance (e.g., results expressed in terms of multivariate hypergeometric, multivariate Meijer G-, or Fox H-functions [20; 21; 22; 23; 24]). Recently, it was demonstrated that this issue can be circumvented by assuming a uniform distribution for shadowing of the multipath components [18]. Such an approach not only allows closed-form derivations of reasonable complexity but also makes it possible to account for heavy-tailed fading, which is valuable since it reflects poor propagation conditions. From a practical viewpoint, this model can be further improved--gaining new scope and flexibility--by introducing additional degrees of freedom (i.e., accounting for more effects). This can be achieved by assuming possible nonlinear wireless signal transformations, leading to the so-called \(\alpha\)-variate models. First introduced in [25], this approach has since gained sufficient traction by demonstrating its wide applicability in various practical scenarios [17; 26; 27; 28; 29; 30; 31]. It has led to several forms of \(\alpha\)-variate models (see, for example, [6; 17; 26; 29; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41]). The introduction of the \(\alpha\) parameter is typically motivated by the need for greater flexibility in characterizing real-world wireless propagation environments. Traditional fading models, including Nakagami-\(m\) and its extensions, have been successful in modeling a wide range of communication scenarios. However, empirical studies have repeatedly shown that standard fading distributions often fail to fully capture the statistical variations observed in practice. The \(\alpha\) parameter, first introduced in the \(\alpha\)-\(\mu\) fading model by [PERSON] [25], has been instrumental in accounting for nonlinearities and power-law characteristics in wireless channels--phenomena that classical models do not sufficiently represent. In wireless communications, propagation can rarely be assumed to be homogeneous [42; 43]. The presence of obstacles, scatterers, and varying atmospheric conditions introduces fluctuations that cause deviations from conventional Gaussian assumptions (which stem from the central limit theorem applied to multipath components).