Sparse Beamforming in Multiple Multi-Antenna Amplify-and-Forward Relay Networks

To reduce cooperation overhead in Amplify-and-Forward (AF) relay networks, a group-sparse penalty is introduced into the objective function to design beamformers for balancing the size of active relays and the signal-to-noise ratio (SNR) at the destination. To deal with the non-convexity and non-smoothness of the problem, the proximal gradient algorithm (PGA) is proposed, which can converge to a local optimal solution in theory. The simulation results show that the proposed algorithm can yield the high level of SNR performance with a small set of cooperative relays to reduce cooperation overhead and economize power.