# \(\alpha\)-Fluctuating Nakagami-\(m\) Fading Model for Wireless Communications
## 6 Conclusions  
This research introduces the \(\alpha\)-Fluctuating Nakagami-\(m\) (\(\alpha\)-FN) fading model as a robust extension of the baseline Fluctuating Nakagami-\(m\) model, addressing the limitations of conventional fading models in wireless communication analysis. The proposed model incorporates a nonlinear envelope transformation parameter \(\alpha\), which enhances statistical flexibility and improves the fit to empirical fading scenarios. The study provides a complete first-order statistical characterization of the \(\alpha\)-FN model, including closed-form expressions for the PDF, CDF, MGF, and raw moments, all with manageable computational complexity. The results demonstrate strong agreement with both numerical integration and Monte Carlo simulations, confirming the analytical derivations' accuracy. A comparative performance analysis reveals that increasing \(\alpha\) significantly reduces outage probability and average bit error rate (ABER), with improvements of several orders of magnitude observed at moderate SNRs. For instance, at \(\gamma=25\) dB, increasing \(\alpha\) from 1 to 4 lowers the outage probability from \(10^{-1}\) to \(10^{-4}\), reflecting greater link reliability. Similarly, ABER performance for BPSK and 16-QAM improves notably with \(\alpha\), and coherent modulation consistently outperforms non-coherent schemes. The ergodic capacity also scales positively with \(\alpha\), with \(\alpha=3\) yielding twice the capacity of \(\alpha=1\) at \(\gamma=10\) dB. These trends confirm that \(\alpha\) serves as an effective control parameter for optimizing system performance under diverse propagation conditions. The model's high-SNR asymptotics simplify system evaluation and provide reliable upper bounds on performance. Experimental validation with D2D data shows that the \(\alpha\)-FN model outperforms existing models such as IPL and F-Nak in capturing deep fading effects, with the lowest MSE. This flexibility is essential for wireless sensor networks (WSNs), where nodes often operate under harsh and unpredictable fading. The model's closed-form expressions enable rapid analysis of critical metrics, facilitating real-time adaptation in resource-constrained WSNs. Applications in D2D, mmWave, and THz communications further demonstrate its relevance to emerging technologies. The joint evaluation of fading, shadowing, and nonlinear transformation establishes the \(\alpha\)-FN model as a comprehensive statistical tool. Overall, the \(\alpha\)-Fluctuating Nakagami-\(m\) model offers a powerful, empirically validated framework for modeling complex wireless channels and optimizing network performance.  
**Funding:** This work was supported by the Russian Science Foundation under grant 24-29-00516 ([[https://rscf.ru/en/project/24-29-00516/](https://rscf.ru/en/project/24-29-00516/)]([https://rscf.ru/en/project/24-29-00516/](https://rscf.ru/en/project/24-29-00516/)), accessed on 25 May 2025).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.  
**Conflicts of Interest:** The author declares no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.