Diversity Analysis of Relay Assignment in Cooperative Networks Based on Sum-Rate Criterion

In this paper, we consider relay assignment in cooperative networks based on the sum-rate criterion. We show that this scheme achieves full diversity, assuming that all the end-to-end (E2E) channels are independent. Our analysis is motivated by the fact that there are many algorithms in the literature to find the permutation that maximizes sum rate; however, the diversity order achieved by each user through the use of this criterion is not statistically analyzed. We perform this analysis in an amplify-and-forward (AF) relay network comprising N source-destination pairs and N relays where each relay can serve only one-source destination pair. However, the diversity analysis holds true for other network configurations where the E2E channels are independent Rayleigh fading channels. To perform this analysis, we first propose a new general method to calculate the diversity order of fading channels at a high SNR. In the previous method, the diversity order was expressed in terms of the Taylor expansion of the random SNR´s probability density function (pdf) at the origin, but that method fails to calculate the diversity when the pdf is not well behaved at the origin. (The pdf is finite, but its derivative is not defined.) Our proposed method is a unifying method that works wherever the previous method works and also where the pdf of SNR is not well behaved.