Secure beamforming based on sparsity in multiple amplify-and-forward MIMO relay networks

In this paper, we study the secrecy rate maximization problem with the group-sparse penalty in the form of a mixed £f/£i regularization to design beamformers in Amplify-and-Forward (AF) relay networks. Resorting to such group-sparse penalty, we can efficiently choose a small size of relays to join in the secure transmission and reduce the cooperation overhead. In our work, the proximal gradient algorithm (PGA) is proposed to deal with the non-convexity and non-smoothness of the problem, which can converge to a local optimal solution in theory and parallelly calculate the beamformer of each relay. Simulation results show that the proposed algorithm can yield high level of secrecy rate performance with a small set of cooperative relays to reduce cooperation overhead and economize power.