Rate optimal limited feedback policies for the MIMO downlink

This paper introduces and solves the sum rate maximization problem at the multiple-input multiple-output (MIMO) downlink as a function optimization problem subject to feedback constraints at the uplink. It is first shown that this optimization problem can be reduced to a finite dimensional non-convex optimization problem. Then, the resulting problem can be solved by investigating Schur-concavity of the aggregate communication rate across multiple traffic flows. Necessary and sufficient conditions for the rate optimality of homogenous threshold feedback policies are established. With some surprise, it is shown that homogenous thresholding is not always rate-wise optimal even if mobile users experience the same channel conditions statistically. Applications of these results are illustrated for Rayleigh fading channels.