Performance Analysis of Physical Layer Security over Fluctuating Beckmann Fading Channels

In this paper, we analyse the performance of physical layer security over Fluctuating Beckmann (FB) fading channel which is an extended model of both the $\kappa-\mu$ shadowed and the classical Beckmann distributions. Specifically, the average secrecy capacity (ASC), secure outage probability (SOP), the lower bound of SOP (SOP$^L$), and the probability of strictly positive secrecy capacity (SPSC) are derived in exact closed-form expressions using two different values of the fading parameters, namely, $m$ and $\mu$ which represent the multipath and shadowing severity impacts, respectively. Firstly, when the fading parameters are arbitrary values, the performance metrics are derived in exact closed-form in terms of the extended generalised bivariate Fox's $H$-function (EGBFHF) that has been widely implemented in the open literature. In the second case, to obtain simple mathematically tractable expressions in terms of analytic functions as well as to gain more insight on the behaviour of the physical layer security over Fluctuating Beckmann fading channel models, $m$ and $\mu$ are assumed to be integer and even numbers, respectively. The numerical results of this analysis are verified via Monte Carlo simulations.