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) multiantenna multirelay network. Considering that the channel state information (CSI) from relays to a 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 differ in their complexity and performances. The optimal joint source and 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.