Exact closed‐form capacity and outage probability of physical layer security in shadowed fading channels

Abstract

In this study, the secrecy performance of physical layer when both the main and wiretap channels undergo κ − μ shadowed fading conditions is analysed. In particular, the average secrecy capacity, secure outage probability (SOP), the lower bound of SOP (SOP L ), and the probability of strictly positive secrecy capacity are derived by using the classic Wyner's wiretap model. Two different scenarios for the fading parameters, namely, μ and m, which represent the real extension of the number of the multipath clusters and the shadowing index, respectively, have been studied. These parameters are chosen first as arbitrary numbers, thus the performance metrics are given in exact closed-form in terms of the extended generalised bivariate Fox's H-function that has been widely implemented in the open literature using various software packages. In the second scenario, both the fading parameters are assumed to be integer numbers to obtain the derived results in simple exact closed-form mathematically tractable expressions in terms of some analytic functions. The numerical results of this analysis are verified via the Monte Carlo simulations.