Utility Maximization in the Multi-User MISO Downlink with Linear Precoding

The maximization of an increasing function over the set of achievable rates in a multi-user, multi-antenna downlink is addressed. In general, the set of rates achievable by linear precoding and treating interference as noise is nonconvex. As a result, the corresponding utility maximization problem is nonconvex. The rate region can be convexifled by time sharing, and the utility maximization over the convexifled region can be solved via Lagrange duality. Still, subproblems in the dual problem remain nonconvex. It is shown how all the aforementioned nonconvex problems can be solved to global optimality in the framework of monotonic optimization. Moreover, it is investigated to what extent utility is increased by time sharing. While all problems can be solved to global optimality, the resulting computational complexity is rather high, thus the proposed solution strategies mainly provide a benchmark for locally optimum, less complex methods. Numerical results demonstrate that a method which finds stationary points on the boundary of the rate region can provide close-to-optimum performance.