  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.
