SIR Balancing for strongly connected interference networks — Existence and uniqueness of a solution

In this paper we revisit the problem of SIR Balancing which was extensively studied in the wireless communication literature. We generalize existing results by showing conditions for the existence and uniqueness of a max-min optimizer. It is shown that a unique positive optimizer exists if the underlying asymptotic coupling matrix is irreducible and the interference functions are strictly monotonic on the dependency set. We also show how the solution can be extended to include power constraints.