In this work, we have comprehensively investigated the impact of non-linearity (α − μ) and shadowing (inverse gamma) collectively over the wireless channel. To this effect, an approximate closed-form probability density function (PDF) expression is derived over α − μ/inverse gamma fading channel by employing Gauss–Laguerre quadrature polynomial. The accuracy of the proposed approximate solution is validated through the Kullback–Leibler divergence test. Subsequently, the proposed solution is utilized in the development of various fundamental statistics like commutative distribution function (CDF), moment generating function (MGF) and nth moment. This contribution also includes the derivation of coding gain and diversity gain to study average symbol error probability (SEP) with MRC and EGC diversity. It is observed that diversity gain is independent of shadowing and as the channel condition improves, the coding gain decreases. Finally, the closed-form solutions of spectral efficiency under different adaptive transmission policies are also developed specifically, optimal power and rate adaptation (OPRA) and effective capacity along with simpler low- and high-power expressions. Monte-Carlo simulations are utilized to validate the proposed analytical and numerical results.

中文翻译：

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α − μ 阴影衰落信道上无线信道的近似统计分析

在这项工作中，我们全面研究了非线性 ( α  -  μ ) 和阴影（逆伽马）对无线信道的共同影响。为此，通过使用 Gauss-Laguerre 正交多项式，在α  -  μ /逆伽马衰落信道上推导出近似封闭形式的概率密度函数 (PDF) 表达式。通过 Kullback-Leibler 散度测试验证了所提出的近似解的准确性。随后，所提出的解决方案用于开发各种基本统计数据，如交换分布函数 (CDF)、矩生成函数 (MGF) 和n那一刻。这一贡献还包括推导编码增益和分集增益，以研究具有 MRC 和 EGC 分集的平均符号错误概率 (SEP)。据观察，分集增益与阴影无关，并且随着信道条件的改善，编码增益会降低。最后，还专门开发了不同自适应传输策略下频谱效率的封闭形式解决方案，优化功率和速率自适应（OPRA）和有效容量以及更简单的低功率和高功率表达式。蒙特卡罗模拟被用来验证所提出的分析和数值结果。