Beamforming of Amplify-and-Forward Relays under Individual Power Constraints

This paper investigates a distributive beamforming scheme for the amplify-and-forward (AF) protocol when the second-order statistics, i.e., the mean and variance, of the channel state information (CSI) are available to relay networks. For maximizing the signal-to-noise ratio (SNR) of a destination node, we derive an analytical solution and the maximum achievable SNR when there is an individual power constraint for each relay. Based on the derived results, a greedy algorithm is proposed to sequentially find beamforming weights. It is shown that the complexity is linear to the number of relays per iteration, and the number of iterations is less than or equal to the number of relays. The necessary condition and sufficient condition are analyzed, respectively, for the proposed algorithm to be optimal. The derived analytical solution and the proposed algorithm generalize the previous results in the literature, which are optimal for particular cases. Simulation results show that the performance of the proposed algorithm is near to that achieved using semidefinite programming (SDP).