Time-sharing solutions in MIMO broadcast channel utility maximization

The problem of maximizing a utility function over the set of achievable rate vectors in a MIMO broadcast channel is considered. If the optimum rate vector lies in a time-sharing region, it is necessary to identify a set of corner points of the time-sharing region such that the optimum rate vector is a convex combination of these corner points. In a K user MIMO BC, the maximum number of corner points is K!, thus enumerating all corner points is only feasible for small K. In this work, an efficient algorithm for identifying a subset of relevant corner points is proposed. Simulation results show that in a scenario where the time-sharing region has K! corner points, out of which K are required to construct the optimum rate, the proposed algorithm on average computes less than K + 1 corner points until convergence.