An Analytical Approach to the Outage Probability of Amplify-and-Forward Relaying with an MRC Receiver

A novel analytical approach is proposed for the performance analysis of AF relaying systems with MRC receiver in the destination. We first derive PDF and CDF of equivalent SNR of the equivalent S-R-D channel. However, both the PDF and CDF include modified Bessel functions which are not easily tractable. In order to derive an analytical statistical model for the PDF of the total SNR at the output of MRC receiver, a novel approach is introduced to rewrite the modified Bessel function of second kind in the form of infinite series using simple elementary functions. By substituting novel series representation of modified Bessel function in the PDF of equivalent S-R-D channel, the performance of the overall system which includes MRC combining in the destination is analytically studied and closed form expressions are derived for the outage probability of the system. Interestingly, the infinite series approaches its asymptotic result rather accurately with a few terms only. Numerical simulations are provided to verify the accuracy of the novel theoretical approach.