On Physical Layer Security over Fox's $H$-Function Wiretap Fading Channels

Abstract: Most of the well-known fading distributions, if not all of them, could be encompassed by Fox's $H$-function fading. Consequently, we investigate the exact and asymptotic behavior of physical layer security (PLS) over Fox's $H$-function fading wiretap channels. In particular, closed-form expressions are derived for secrecy outage probability (SOP), probability of non-zero secrecy capacity (PNZ), and average secrecy capacity (ASC). These expressions are given in terms of either univariate or bivariate Fox's $H$-function. In order to show the comprehensive effectiveness of our derivations, three metrics are respectively listed over the following frequently used fading channels, including Rayleigh, Weibull, Nakagami-$m$, $\alpha-\mu$, Fisher-Snedecor (F-S) $\mathcal{F}$, and extended generalized-$\mathcal{K}$ (EGK). Our tractable results are more straightforward and general, besides that, they are feasible and applicable, especially the SOP, which was mostly limited to the lower bound in literature due to the difficulty of achieving closed-from expressions. In order to validate the accuracy of our analytical results, Monte-Carlo simulations are subsequently performed for the special case $\alpha-\mu$ fading channels. One can observe perfect agreements between the exact analytical and simulation results, and highly accurate approximations between the exact and asymptotic analytical results.