Optimal relay selection and beamforming strategy in cooperative systems with limited feedback and asymptotically large number of relays

We consider a cooperative wireless network with a single source, a single destination, and M cooperative relays. We show that, with only limited feedback, M B̄ 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 M B̄ 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 B̄, 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 all B̄, especially for small values of B̄. 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.