In this letter, we derive exact closed-form expressions for the level crossing rate (LCR) and average fade duration (AFD) of the signal envelope in $\mathcal {F}$ composite fading channels. Using the novel expressions, we then investigate the behavior of the LCR and AFD for different multipath fading and shadowing conditions. It is shown that multipath fading has a more significant effect on the LCR at lower fade levels while shadowing tends to have a discernible impact on higher threshold levels. In contrast, shadowing has a more noticeable effect on the AFD compared to multipath fading at both lower and higher levels. Approximate expressions for the LCR and AFD are also provided, and shown to be in good agreement with the exact LCR and AFD as they approach lower and higher threshold levels. The offered results are expected to be useful in the design of emerging systems such as device-to-device communications.

中文翻译：

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F复合衰落信道中的电平交叉率和平均衰落持续时间

在这封信中，我们推导出了 $\mathcal {F}$ 复合衰落通道中信号包络的电平交叉率 (LCR) 和平均衰落持续时间 (AFD) 的精确闭式表达式。使用新颖的表达式，然后我们研究了 LCR 和 AFD 在不同多径衰落和阴影条件下的行为。结果表明，多径衰落在较低的衰落电平下对 LCR 具有更显着的影响，而阴影往往对较高的阈值电平产生明显的影响。相比之下，与较低和较高级别的多径衰落相比，阴影对 AFD 的影响更为明显。还提供了 LCR 和 AFD 的近似表达式，并且当它们接近较低和较高的阈值水平时，表明它们与确切的 LCR 和 AFD 非常吻合。