Beamforming maximizes the rank one Ricean MIMO compound capacity

In this paper, we consider the optimization of the compound capacity in a rank one Ricean multiple input multiple output channels using partial channel state information at the transmitter side. We model the channel as a deterministic matrix within a known ellipsoid, and maximize the compound capacity defined as the worst case capacity within this set. We find that the optimal transmit strategy is always beamforming, and can be found using a simple one dimensional search. These results motivate the growing use of systems using simple beamforming transmit strategies.