# \(\alpha\)-Fluctuating Nakagami-\(m\) Fading Model for Wireless Communications
## 5 Simulation and Results' Analysis
### Model Experimental Verification and Positioning
The figure clearly shows that the \(\alpha\)-FN model provides a unique behavior that interpolates between light-tailed and heavy-tailed fading distributions. In particular, the CDF of the \(\alpha\)-FN model closely resembles that of hyper-Rayleigh fading, but with better adaptability across various regimes. The plot demonstrates that at low SNRs, the \(\alpha\)-FN model's curve rises more gradually than Nakagami-\(m\) and Fluctuating Nakagami-\(m\), indicating a heavier tail and higher probability of deep fades. Compared to the IPL and Hoyt models, the \(\alpha\)-FN distribution remains flexible, providing a better fit for a wide range of fading environments. This adaptability reinforces its value as a unified fading model capable of encompassing diverse real-world propagation characteristics. Monte Carlo simulations align well with the analytical CDF, validating the accuracy of the derived expressions. Overall, Figure 3 supports the conclusion that the \(\alpha\)-FN model generalizes and enhances traditional models by offering increased tunability and closer alignment with empirical fading statistics. As was mentioned, MGF is one of the key analytical tools used to further evaluate performance metrics such as average bit error rate and outage probability. In Figure 4, the solid lines represent the exact analytical expressions for the MGF derived using [PERSON]'s H-function-based formulations, while the markers correspond to numerical integration results that validate the theoretical expressions. The plot illustrates how the MGF behaves under varying values of the \(\alpha\) parameter, which controls the degree of nonlinearity in the fading envelope, as well as the \(m\) and \(m_{s}\) parameters that govern fading severity and shadowing intensity, respectively. It is evident that the rate of decay of the MGF curve varies significantly depending on the chosen parameters. For lower values of \(\alpha\), such as \(\alpha=0.1\), the MGF decays more slowly, suggesting higher variability in the channel and a greater likelihood of deep fades. This aligns with the interpretation that smaller \(\alpha\) values correspond to more severe nonlinear distortions in the propagation environment. Increasing the fading severity parameter \(m\) leads to a faster decay of the MGF, consistent  
Figure 3: \(\alpha\)-Fluctuating Nakagami-\(m\) model positioning (in terms of CDF) among different multipath channels: Nakagami-\(m\)[48], Fluctuating Nakagami-\(m\)[18], Inverse Power Lomax [17], Hoyt [48], Lomax [16], and \(\alpha-\mu\)[25]. with the behavior of the classical Nakagami-m model where larger \(m\) values correspond to less severe fading conditions. Similarly, increasing the shadowing parameter \(m_{s}\) results in slower MGF decay, indicating that stronger shadowing causes fading effects even at high SNR levels. The close match between the analytical curves and the numerical integration results confirms the correctness of the derived MGF expressions and supports their use in subsequent performance analysis. This also demonstrates the flexibility of the \(\alpha\)-Fluctuating Nakagami-m model in capturing both light and heavy fading scenarios by adjusting the \(\alpha\) parameter, thereby extending the applicability beyond conventional models. The results indicate that the MGF can be effectively used for deriving the system-level performance bounds (studied further) for wireless communication systems operating in complex propagation environments such as device-to-device (D2D) links, millimeter-wave (mmWave), and terahertz (THz) channels. Furthermore, the parametric control offered by \(\alpha\) allows for better fitting to empirical data in real-world scenarios where traditional models may fail to capture observed fading dynamics. The numerical validation reinforces the robustness of the analytical framework and supports its use in practical applications such as link budget calculations, adaptive modulation design, and diversity combining techniques.