# \(\alpha\)-Fluctuating Nakagami-\(m\) Fading Model for Wireless Communications
## 5 Simulation and Results' Analysis
### Model Experimental Verification and Positioning  
Figure 1 presents the probability density function (PDF) fitting of the \(\alpha\)-Fluctuating Nakagami-\(m\) model against real-world experimental data obtained from device-to-device (D2D) wireless measurements. The proposed model is compared with two conventional fading models: the Fluctuating Nakagami-\(m\) (denoted as F-Nak) model and the Inverse Power Lomax (denoted as IPL) model. The plot shows that the \(\alpha\)-Fluctuating Nakagami-\(m\) model achieves the closest match to empirical data across a wide range of signal variations. The fitting quality is quantitatively assessed using the mean squared error (MSE), where the proposed model exhibits the lowest MSE value of approximately \(4.69\times 10^{-4}\), compared to \(5.12\times 10^{-4}\) for F-Nak and \(6.05\times 10^{-4}\) for IPL. This indicates that the \(\alpha\)-Fluctuating Nakagami-\(m\) model provides a more flexible statistical representation of real-world fading conditions. The figure further illustrates that traditional models tend to underestimate the probability of deep fades, particularly in the hyper-Rayleigh region, whereas the proposed model accurately captures these effects. The fitting curves show that the deviation between the theoretical and empirical distributions is minimal at moderate signal levels, confirming the robustness of the statistical framework. The high accuracy of the proposed model confirms its applicability in modern wireless communication system analysis, particularly in environments characterized by severe multipath effects. Figure 2 presents a detailed comparison between analytically derived and simulated probability density functions (PDFs) of the \(\alpha\)-Fluctuating Nakagami-\(m\) model under various channel parameters. The figure contrasts numerically evaluated PDFs (using the derived expressions) with results obtained from Monte Carlo simulations, validating the theoretical framework. Multiple parameter sets are illustrated to cover different fading conditions, as was stated earlier. For instance, for \(m=3.5\), \(\alpha=1\), and \(m_{s}=10\), the simulated and numerical curves align almost perfectly, demonstrating a robust model behavior under low shadowing conditions. In contrast, for \(m=0.5\) and \(m_{s}=2\), a scenario associated with heavier fading, the PDFs exhibit longer tails, yet maintain high consistency between theory and simulation. This consistency across a wide range of parameters affirms the model's stability and accuracy. Compared to Figure 1, which focused on empirical fitting with real-world D2D data, Figure 2 emphasizes the model's analytical integrity through synthetic validation. While Figure 1 highlighted the \(\alpha\)-FN model's superiority in empirical fitting over other fading models like IPL and Fluctuating Nakagami-\(m\), Figure 2 further confirms that the theoretical framework is computationally sound and matches stochastic behavior even in challenging fading environments. These results support the model's usability for performance prediction across practical wireless scenarios. Figure 3 illustrates the positioning of the \(\alpha\)-Fluctuating Nakagami-\(m\) (\(\alpha\)-FN) model in terms of its cumulative distribution function (CDF), compared to several well-known multipath fading models. These include the standard Nakagami-\(m\) model [48], Fluctuating Nakagami-\(m\)[18], Inverse Power Lomax [17], Hoyt [48], Lomax [16], and \(\alpha-u\)[25] fading  
Figure 1: PDF fitting with experimental data from D2D measurements (see [50]). Fluctuating Nakagami (F-Nak) is fitted with the parameters presented in [18], and Inverse Power Lomax (IPL) with parameters presented in [17]. Figure 2: PDF comparison of numerical evaluation and numerical simulation across various channel parameters. models. The parameters are fixed such that \(\alpha=1.1\), \(m=0.5\), and \(m_{s}=2\) for the \(\alpha\)-FN and Fluctuating Nakagami-\(m\) models, with appropriate configurations for the others to ensure a fair comparison.