Structure of Utility Optimization in Regular and Irregular Wireless Scenarios

Power optimization has long been known to be a non-convex problem which suggests that finding the true maximum might be a computationally difficult problem. In this paper we investigate the geometry of power selection over multiple resource blocks and try to determine the true difficulty of the problem. In particular, we focus on two questions:•Are there local maxima? i.e. can a natural gradient ascent algorithm ever converge to a suboptimal solution?•For typical scenarios, how much can be gained in comparison to a simple solution that allocates power for each basestation uniformly over the resource blocks?In answer to the first question we show that local maxima can indeed exist and we investigate the performance of gradient ascent as well as other algorithms on such an example. In answer to the second question we propose a metric that measures how many points in a scenario benefit from a higher-order reuse scheme and we show that for a random arrangement it is hard to beat a simple reuse-1 scheme.