A number of new results aiming at facilitating the use of the α-η-κ-μ fading model are presented. These results include: 1) fast convergent, with no recursions, series representations for the envelope probability density function (PDF) and cumulative distribution function (CDF); 2) higher order moments of the envelope; 3) moment generating function (MGF) of the envelope; 4) asymptotic behavior of the envelope PDF and also of the envelope CDF; 5) a procedure for parameter estimation; 6) new closed-form expressions for particular cases of the envelope distribution; 7) new mathematical identity for the generalized Laguerre polynomial and the generalized hypergeometric function; and 8) approximate, but tight, series representation for the phase PDF. As application examples, the following are given: 1) outage probability; 2) outage capacity; 3) amount of fading; and 4) bit error rate, for which the asymptotic behavior is also presented.

中文翻译：

---

α-η-κ-μ 衰落模型：新的基本结果

介绍了一些旨在促进使用 α-η-κ-μ 衰落模型的新结果。这些结果包括：1) 快速收敛，没有递归，包络概率密度函数 (PDF) 和累积分布函数 (CDF) 的级数表示；2) 包络线的高阶矩；3）包络的矩生成函数（MGF）；4) 包络 PDF 和包络 CDF 的渐近行为；5) 参数估计程序；6) 包络分布特殊情况的新封闭式表达式；7) 广义拉盖尔多项式和广义超几何函数的新数学等式；和 8) 相位 PDF 的近似但紧密的系列表示。作为应用实例，给出以下内容： 1) 中断概率；2) 停电能力；3) 褪色量；和 4) 误码率，其渐进行为也被提出。