Secrecy Rate Analysis of Dual-Hop Triple Selection AF Relaying Over Nakagami Fading Channels

This paper analyzes the secrecy rate of dual-hop triple selection amplify-and-forward (AF) relaying over Nakagami fading channels. The triple selection chooses transmit antenna, relay node and user node with the maximum received signal to noise ratio (SNR) using feedback information from each node. In this study, we use selection combing (SC) and maximum ratio combining (MRC) to derive new exact closed-form expressions for the cumulative distribution function (CDF) and probability density function (PDF) of the received SNR for triple selection. To derive the secrecy rate, this paper presents the alternative exact analytical expressions for CDF and PDF using fractional and calculus mathematics. Using the alternative distribution, this work evaluates new exact and approximate analytical expressions of the triple selection for the secrecy rate. Using the asymptotic analysis, the power offset and the slope are quantified for the secrecy rate. Using asymptotic and numerical results, we demonstrate that the high SNR slope for the secrecy rate is constant regardless of authorizer’s parameters and eavesdropper’s parameters as well as fading index of channel. We also confirm that the high SNR power offset is affected by the parameters of the authorizer and the eavesdropper, whereas the fading index is not affected.