Optimal Relay Selection and Beamforming Strategy in Cooperative Systems with Limited Feedback and Asymptotically Large Number of Relays

Abstract

Abstract-We consider a cooperative wireless network with a single source, a single destination, and M cooperative relays. We show that, with only limited feedback, MB bits, from the destination, using all the relays to perform beamforming may not be optimal. Assuming that the destination selects the relays whose power gains exceed a threshold and feeds back MB bits to specify a precoding matrix from a randomly generated precoder codebook, we find the optimal threshold that maximizes the capacity of a Decode-and-Forward (DF) system for a given B, asymptotically in the number of relays, M . We show that the system using the optimal threshold has a higher capacity than a system using all relays for allB, especially for small values ofB. Furthermore, using a fixed fraction (β * which is obtained from the optimal threshold) of relays in systems with finite number of relays also leads to a significant improvement in outage probability, comparing to that of the systems using all relays, in both DF and Amplify-and-Forward (AF) cooperating schemes.