Multivariate Correlated Rayleigh Fading With MRC and Applications to Wireless Secrecy

Abstract

This letter studies physical layer security of an outdated channel-state-information (oCSI) decode-and-forward (DaF) opportunistic-relay (OR) network under equal-correlated (equ.c.) Rayleigh fading with maximal ratio combining (MRC) deployment. By assuming that relays operate under equ.c. Rayleigh fading and wiretapper-Destination operate under exponential-correlated (exp.c.) Rayleigh fading, this work (i) derives an MRC output (MRCO) distribution of multivariate equ.c. Rayleigh fading, (ii) derives an MRCO distribution of bivariate exp.c. Rayleigh fading under oCSI conditions, and (iii) expresses the secrecy outage probability (SOP) in closed form. By considering oCSI severity, channel correlation among cooperative DaF ORs, Destination, wiretapper, and MRC deployment, this work's practicality can be significantly improved. Detailed discussions are given, in which the impact of several important parameters on the SOP is discussed. Monte Carlo simulation is shown to match theoretical predictions.