A simple approach to evaluate the ergodic capacity and outage probability of correlated Rayleigh diversity channels with unequal signal-to-noise ratios

In this article, we propose a novel method to derive exact closed-form ergodic capacity and outage probability expressions for correlated Rayleigh fading channels with receive diversity. Unlike the existing works, the proposed method employ a simple approach for the capacity and outage analysis for receiver diversity channels operating at different signal-to-noise ratios depicted in the diagonal elements of matrix Ω. With xbeing the channel gain vector, random variable of the form Y(a)=a + x Ωxis considered. Novelty of the work resides in the fact that the distribution of Y(a) is accurately determined by employing Fourier representation of unit step function followed by complex integration in a straight forward way. The ergodic channel capacity is thus calculated by using the first-order moment, , while the outage probability for a certain threshold γ0is evaluated using . Extensive experiments have been conducted demonstrating the accuracy of the proposed approach.