Nonconcave Utility Maximisation in the MIMO Broadcast Channel

The problem of determining an optimal parameter setup at the physical layer in multi-user, multiantenna downlink is considered. An aggregate utility, which is assumed to depend on the users’ rates, is used as performance metric. It is not assumed that the utility function is concave, allowing for more realistic utility models of applications with limited scalability. Due to the structure of the underlying capacity region, a two step approach is necessary: First, an optimal rate vector is determined. Second, the optimal parameter setup is derived from the optimal rate vector. Two methods for computing an optimal rate vector are proposed: First, based on the differential manifold structure offered by the boundary of the MIMO BC capacity region, a gradient projection method on the boundary is developed. Being a local algorithm, the method converges to a rate vector which is not guaranteed to be a globally optimal solution. Second, the monotonic structure of the rate space problem is exploited to compute a globally optimal rate vector with an outer approximation algorithm. While the second method yields the global optimum, the first method is shown to provide an attractive trade-off between utility performance and computational complexity.