Worst case robust downlink beamforming on the Riemannian manifold

In this paper we take a new perspective on the worst case robust multiuser downlink beamforming problem with imperfect second order channel state information at the transmitter. Recognizing that all channel covariance matrices form a Riemannian manifold, we propose to use a measure properly defined along this manifold in order to model the set of mismatched channel covariance matrices for which robustness shall be guaranteed. This leads to a new robust beamforming problem formulation for which a convex approximation is derived. Simulation results show a dramatically improved performance of the proposed scheme, both in terms of transmission power and constraint satisfaction, as compared to the previous methods.