In this paper, we provide novel expressions of moment generating function (MGF) for Fisher–Snedocor $\mathcal{F}$ composite fading channels. Precisely, we derive the exact MGF and its approximated expression to incorporate the heavy as well as the light shadowed conditions. With the help of these expressions, it is shown that the MGF of the $\mathcal{F}$ distribution turn to be valid for the entire range of the composite fading parameters yielding finite results for each value of the average signal to noise ratio. The significance of these expressions is further explained by simplifying the key integrals which are used in the error computation of widely used efficient digital modulation schemes. The analytical framework is also validated with the help of Monte-Carlo simulations.

在本文中，我们为 Fisher–Snedocor 提供了矩生成函数 (MGF) 的新表达式 $\mathcal{F}$复合衰落信道。准确地说，我们推导出精确的 MGF 及其近似表达式，以结合重阴影和轻阴影条件。在这些表达式的帮助下，表明 MGF 的$\mathcal{F}$分布对整个复合衰落参数范围都有效，从而为平均信噪比的每个值产生有限结果。通过简化用于广泛使用的高效数字调制方案的误差计算的关键积分，进一步解释了这些表达式的重要性。分析框架也在蒙特卡罗模拟的帮助下得到验证。