Level Crossing Rate and Average Fade Duration in <inline-formula> <tex-math notation="LaTeX">$\mathcal{F}$ </tex-math></inline-formula> Composite Fading Channels

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 <inline-formula> <tex-math notation="LaTeX">$\mathcal {F}$ </tex-math></inline-formula> 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.