Achieving Global Optimality for Joint Source and Relay Beamforming Design in Two-Hop Relay Channels

This paper deals with joint source and relay beamforming (BF) design for an amplify-and-forward (AF) multi-antenna multirelay network. Considering that the channel state information (CSI) from relays to destination is imperfect, we aim to maximize the worst case received signal-to-noise ratio (SNR). The associated optimization problem is then solved in two steps. In the first step, by fixing the source BF vector, a semi-closed form solution of the relay BF matrices is obtained, up to a power allocation factor. In the second step, the global optimal source BF vector is obtained based on the Polyblock outer Approximation (PA) algorithm. We also propose two low-complexity methods for obtaining the source BF vector, which are different in their complexities and performances. The optimal joint source-relay BF solution obtained by the proposed algorithms serves as the benchmark for evaluating the existing schemes and the proposed low-complexity methods. Simulation results show that the proposed robust design can significantly reduce the sensitivity of the channel uncertainty to the system performance.