Optimization of the MIMO Compound Capacity

In this paper, we consider the optimization of the compound capacity in a rank one Ricean multiple input multiple output channel using partial channel state information at the transmitter side. We model the channel as a deterministic matrix within a known ellipsoid, and address the compound capacity defined as the maximum worst case mutual information in the set. We find that the optimal transmit strategy is always beamforming, and can be found using a simple one dimensional search. Similar results are derived for the worst case sum-rate of a multiple access channel with individual power constraints and a total power constraint. In this multiuser setting we assume equal array response at the receiver for all users. These results motivate the growing use of systems using simple beamforming transmit strategies