In this work, we study the performance of energy detector (ED) over generalized fading channels expressed in terms of Fox’s H-function over the air-to-ground (A2G) and ground-to-ground (G2G) networks. Firstly, the closed-form expression for the probability of missed-detection (PM) is derived. Then utilizing it, a unified and novel closed-form expression for the average area under the receiver operating characteristic curve (AUC) is proposed for Fox’s H-fading distribution. The proposed formulation is expressed in terms of bivariate Fox’s H-function. Also, we provide the closed-form result for the derivative of PM that helps in obtaining the optimized value of the threshold. The channel model presented here subsumes many fading models of practical interest. To get the simplified expressions of the performance parameters, the asymptotic analysis of the proposed framework has been provided. The diversity gain and coding gain of the performance metrics over the generalized fading channel and its special cases have been evaluated. Lastly, we provide a comparison of the derived expressions with the Monte-Carlo simulations to validate the accuracy of the proposed solutions.

在这项工作中，我们研究了能量检测器 (ED) 在空对地 (A2G) 和地对地 (G2G) 网络上以 Fox 的 H 函数表示的广义衰落信道上的性能。首先，推导出漏检概率（PM）的闭式表达式。然后利用它，为 Fox 的 H 衰落分布提出了接收器操作特征曲线 (AUC) 下平均面积的统一且新颖的封闭形式表达式。建议的公式用二元 Fox 的 H 函数表示。此外，我们提供了 PM 导数的封闭形式结果，有助于获得阈值的优化值。这里介绍的信道模型包含了许多具有实际意义的衰落模型。为了得到性能参数的简化表达式，已提供对拟议框架的渐近分析。已经评估了广义衰落信道上的性能度量的分集增益和编码增益及其特殊情况。最后，我们将导出的表达式与蒙特卡洛模拟进行比较，以验证所提出解决方案的准确性。