The $\alpha$-$\eta$-$\kappa$-$\mu$ is one of the most generalized and flexible channel models having an excellent fit to experimental data from diverse propagation environments. The existing statistical results on the envelope of $\alpha$-$\eta$-$\kappa$-$\mu$ model contain an infinite series involving regularized hypergeometric function and generalized Laguerre polynomial, prohibiting its widespread application in the performance analysis of wireless systems. In this paper, we employ a novel approach to derive density and distribution functions of the envelope of the $\alpha$-$\eta$-$\kappa$-$\mu$ fading channel without an infinite series approximation. The derived statistical results are presented using a single Fox's H-function for tractable performance analysis and efficient numerical computations, especially for high-frequency mmWave and terahertz wireless transmissions. To gain insight into the distribution of channel envelope, we develop an asymptotic analysis using a more straightforward Gamma function converging to the exact within a reasonable range of channel parameters. To further substantiate the proposed analysis, we present the exact outage probability and average bit-error-rate (BER) performance of a wireless link subjected to the $\alpha$-$\eta$-$\kappa$-$\mu$ fading model using a single tri-variate Fox's H-function. We obtain the diversity order of the system by analyzing the outage probability at a high signal-to-noise (SNR) ratio. We use numerical and simulation analysis to demonstrate the significance of the developed statistical results compared with the existing infinite series representation for the envelope of the $\alpha$-$\eta$-$\kappa$-$\mu$ model.

翻译：$α$-$η$-$κ$-$μ$模型是最通用且最灵活的衰落信道模型之一，能够完美拟合多种传播环境下的实验数据。现有关于$α$-$η$-$κ$-$μ$模型包络的统计结果包含涉及正则化超几何函数和广义拉盖尔多项式的无穷级数，这限制了其在无线系统性能分析中的广泛应用。本文采用一种新颖方法推导了$α$-$η$-$κ$-$μ$衰落信道包络的密度函数和分布函数，无需进行无穷级数近似。所得统计结果采用单一的Fox H函数表示，便于进行可处理的性能分析和高效的数值计算，尤其适用于高频毫米波和太赫兹无线传输。为深入理解信道包络的分布特性，我们开发了一种渐近分析方法，采用更直接的Gamma函数，该函数在合理的信道参数范围内收敛于精确值。为进一步验证所提分析的有效性，我们利用单一的三变量Fox H函数，给出了受$α$-$η$-$κ$-$μ$衰落模型影响的无线链路的中断概率和平均误比特率性能。通过分析高信噪比下的中断概率，获得了系统的分集阶数。通过数值计算和仿真分析，我们展示了所建立统计结果相较于现有的$α$-$η$-$κ$-$μ$模型包络无穷级数表示的重要性。