Optimization of a class of non-convex objectives on the Gaussian MIMO multiple access channel: Algorithm development and convergence analysis

In this paper we develop an algorithm for computing the optimal transmission parameters, which include the transmission covariance, the time-shares and the user-orderings that minimize a particular class of objectives defined over the capacity region of Gaussian multiple antenna multiple access channels. This class includes objectives that are twice-differentiable, non-increasing and convex in the users´ rates, but not necessarily convex in the aforementioned transmission parameters. As such, this class includes design objectives that are non-convex and that, without the proposed algorithm, are difficult to solve in general. The proposed algorithm is iterative with polynomial complexity per iteration and with convergence to the global optimal guaranteed. The utility of this algorithm is illustrated via a numerical example for maximizing proportional fairness.