# \(\alpha\)-Fluctuating Nakagami-\(m\) Fading Model for Wireless Communications
###### Abstract
The aforementioned Fluctuating Nakagami-\(m\) model already provides an improvement over classical models by incorporating both line-of-sight (LoS) and non-line-of-sight (NLoS) conditions with a fluctuating power component. However, the introduction of the \(\alpha\) parameter further enhances this model by accounting for additional irregularities in the propagation environment. Specifically, it offers a more accurate representation of small-scale fading in complex scenarios. The \(\alpha\) parameter also plays an important role (as verified experimentally) in modeling modern wireless technologies (i.e., fitting the distribution of channel coefficients), including Device-to-Device (D2D) communication [36], underwater acoustic communication systems [36], cellular networks [17], indoor LoS and NLoS mm-Wave communications [44], THz communication for 6G [45], and more. In these contexts, the fading characteristics exhibit complex spatial and temporal variations that are better captured by the enhanced flexibility offered by \(\alpha\). Moreover, empirical data from various environments--such as urban microcells, vehicular communication systems, and D2D setups--have shown that fading distributions often exhibit heavy-tailed behaviors or non-Gaussian fluctuations. The \(\alpha\) parameter enables a more flexible characterization of these conditions [17], allowing the Fluctuating Nakagami-\(m\) (FN) model to be modified to better match measured data. Furthermore, the \(\alpha\) modification provides greater control over the severity of fading, which is crucial for optimizing wireless network performance [17; 40]. This flexibility proves useful for evaluating key system performance metrics, including bit error rate (BER), outage probability, and channel capacity. Thus, to extend the scope of the Fluctuating Nakagami-\(m\) model [18], this research presents and studies its \(\alpha\)-transformed variant, i.e., the \(\alpha\)-Fluctuating Nakagami-\(m\) (\(\alpha\)-FN) model. It should be specifically noted that the proposed \(\alpha\)-FN model, in addition to improving analytical tractability, maintains the mathematical structure and complexity level of the baseline model [18]. By incorporating an additional degree of freedom, it enables the derivation of more generalized expressions for performance metrics, thus facilitating efficient system design and optimization. The model unifies various existing distributions within a single mathematical framework. This unification is particularly valuable for designing adaptive communication systems that must operate across diverse propagation conditions. Additionally, the inclusion of \(\alpha\) helps bridge the gap between small-scale fading and shadowing effects. Many real-world environments exhibit composite fading, where large-scale shadowing overlaps with small-scale multipath fading. The \(\alpha\)-FN model can more accurately characterize such scenarios, leading to improved precision in system performance prediction. This is especially relevant in satellite and airborne communication systems, where signals traverse multiple atmospheric layers with varying densities and turbulence levels. The necessity of introducing the \(\alpha\) modification to the Fluctuating Nakagami-\(m\) model is justified by its ability to generalize existing models, enhance analytical tractability, improve empirical data fitting, and extend applicability to both modern and future wireless communication systems. By incorporating this additional parameter, researchers and engineers are equipped with a more versatile tool for modeling, analyzing, and optimizing wireless networks under diverse and challenging propagation conditions.