Fixed point iteration for max-min sir balancing with general interference functions

This paper studies the convergence of a fixed point iteration algorithm for the problem of max-min signal-to-interference ratio (SIR) balancing. Differently from the existing work on the subject, the interference in the system is assumed to fall into the axiomatic framework of general interference functions. Monotonicity of the extremal SIR values during the iterations of the algorithm is shown. In the case of strictly monotonic interference functions, a novel sufficient condition for the convergence of the algorithm to an optimal solution is derived. The obtained condition is easily verifiable, and presents a generalization of a related requirement for the power method from matrix analysis. It is also shown how the results transfer to the power-constrained case and standard interference functions.