Abstract
In this paper, we design relay factors for multiuser amplify-and-forward (AF) relay networks where each node in the network is equipped with one antenna. The relay factors are chosen to minimize the sum of mean square error (sum-MSE) at the destinations without considering the destinations' noise. Subsequently, a filter is designed for each receiver to cancel out the effect of the destination's noise. A closed form solution is provided and shown to outperform the zero-forcing (ZF) scheme available in literature. For the case where the number of users increases, an approximate closed form solution is provided that can be implemented distributively. We investigate the average transmit power of each relay and show that as the number of users increases, relay transmit power is inversely proportional with the number of users in the network. Finally, a modified solution is provided to address the effect of channel estimation error. Simulations are provided to verify the analysis and present the performance of the proposed scheme.