This paper analyzes the performance of decode-and-forward (DF)-based multi-hop relaying communication systems over $\alpha -\kappa -\mu$ and $\alpha -\kappa -\mu$-Extreme fading channels. Analytical formulas for the probability density function (PDF) and the cumulative distribution function (CDF) of the received signal-to-noise ratio (SNR) as well as its moment generating function (MGF) are derived. Based on the derived PDFs, novel closed-form expressions for the outage probability (OP), bit error rate (BER) under coherent and non-coherent modulation schemes are derived. Additionally, asymptotic analyses of BER based on Poincare series expansions of SNR PDFs are carried out and results show good approximations for low SNR regimes. Simulations are performed to verify the accuracy and to show the tightness of the theoretical analysis.

本文分析了基于DF的多跳中继通信系统的性能 $\alpha --\kappa --\mu$ 和 $\alpha --\kappa --\mu$-极端的衰落通道。推导了接收信噪比（SNR）的概率密度函数（PDF）和累积分布函数（CDF）及其矩生成函数（MGF）的解析公式。基于派生的PDF，推导了相干和非相干调制方案下的中断概率（OP），误码率（BER）的新颖闭式表达式。此外，基于SNR PDF的Poincare级数展开对BER进行了渐近分析，结果显示了对于低SNR方案的良好近似。进行仿真以验证准确性并显示理论分析的紧密性。