A Riemannian distance for robust downlink beamforming

We examine the robust downlink beamforming design from the point of outage probability constraint. We further reason that since the estimated downlink channel correlation (DCC) matrices form a manifold in the signal space, the estimation error should be measured in terms of Riemannian distance (RD) instead of the commonly used Euclidean distance (ED). Applying this concept of measure to our design constraint, we transform the design problem into a convex optimization which can be solved efficiently by standard methods. Simulation results show that the performance of our design is superior to those of other robust beamformers recently developed.