Structure of Utility Optimization in Regular and Irregular Wireless Scenarios

We investigate the factors in a wireless configuration that determine the effectiveness of techniques for Intercell Interference Coordination (ICIC). Due to the increased density of current and future cellular deployments and the trend towards heterogeneous networks, interference levels are increasing and so there are significant research efforts that aim to mitigate the effects of this interference. In particular, Fractional Frequency Reuse algorithms adjust the power levels on different resource blocks in order to optimize the performance of the mobile users. 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 questions we propose a metric that measures how many points in a scenario benefit from a higher-order reuse scheme. We use this metric to argue that for many natural examples it is hard to beat a simple reuse-1 scheme. Hence for these examples the gains from more sophisticated ICIC algorithms are limited.