Intercept Probability and Secrecy Capacity Evaluation of RIS-Empowered Wireless Communications Over Nakagami-$m$ Fading

In this paper, we evaluate the secrecy performance of a wireless communication network empowered with the reconfigurable intelligent surface (RIS) over Nakagami-m fading channels. To be specific, we consider two different scenarios of a classical wiretap model where a source communicates with a receiver through an RIS, and simultaneously a passive eavesdropper tries to fetch the information either from the source or through the RIS. In the first scenario, the eavesdropper is snooping the information directly from the source, whereas in the second scenario, it overhears the information through an RIS. We first present the statistical characterization of the instantaneous end-to-end signal-to-noise ratios at the legitimate receiver and the eavesdropper under both scenarios by exploiting the tight Gamma distribution approximation over Nakagami-
$m$
fading. We then exploit these to derive the exact expressions for the intercept probability and the probability of non-zero secrecy capacity over Nakagami-m distribution. Finally, we validate our analytical outcomes with numerical and Monte-Carlo simulations.