A Riemannian Distance For Robust Downlink Beamforming

Abstract

<p>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 establish approximated outage probability constraints using multidimensional ball set and multidimensional cube set. We transform the design problem into a convex optimization problem which can be solved efficiently by standard methods. Our proposed methods apply to both Gaussian distribution assumption and uniform distribution assumption. Simulation results show that the performance of our design is superior to those of other robust beamformers recently developed.</p>