Multiuser interference balancing for general interference functions - A convergence analysis

We address the problem of maximizing the minimum signal-to-interference ratio (SIR) in a multiuser system. In the context of resource allocation, this is referred to as max-min fairness. Moreover, the balanced SIR margin is an indicator for feasibility, so the problem also plays a fundamental role for the characterization of the SIR achievable region and related regions. In this paper, we propose an iterative solution for max-min SIR balancing under the assumption of convex interference functions. It is proven that the proposed iteration always finds the unique global optimum. Similar results in the beamforming context [1] differ in two respects: Firstly, a much more general interference model is used. Secondly, the results a found by using a different analytical approach, which allows to show convergence directly, without the need of compactness arguments. This way, uniqueness of the optimum can be shown. Finally, we show that Yates' fixed-point iteration [2], which is successfully used in a different context, does generally not converge to the max-min optimum, unless an additional scaling is introduced.