Envelope Distribution of Two Correlated Complex Gaussian Random Variables and Application to the Performance Evaluation of RIS-Assisted Communications

Abstract

The operation of point-to-point communication assisted with reconfigurable intelligent surface, where the multi-hop channels between the source and the destination are subject to Rician fading but are not necessarily independent, is investigated. Considering binary phase-shift keying signaling for the data transmission and optimal maximum-likelihood detection at the receiver, a system performance evaluation is conducted in terms of reliability and capacity. For such, the distributions of the magnitude of the product of the complex channel gains are first obtained for both, the case when the channel gains are independent and the case when they are correlated. Subsequently, expressions of the system’s error rate and the upper-bounds on the average capacity are obtained for the said correlated and uncorrelated channel cases. Numerical results corroborating the analysis are also presented. In particular, it is revealed that correlation between the channels has negligible effect on the error rate when the fading is Rayleigh distributed, and that an increase in the value of the Rician parameter pertaining to the channel between the receiver pair has reduced impact on the reduction of the error rate, which provides practical guidelines for system deployments with high reliability.