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 . With x being the channel gain vector, random variable of the form Y(a) = a+ x∗ x is 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, E[ log2(Y(1))], while the outage probability for a certain threshold γ0 is evaluated using ∫ γ0 0 fY(0)(y)dy. Extensive experiments have been conducted demonstrating the accuracy of the proposed approach.