Complete characterization of the Pareto boundary of interference-coupled wireless systems with power constraints — The log-convex case

In this paper we analyze the structure of certain power-constrained utility sets, based on the axiomatic framework of log-convex interference functions. Log-convex interference functions contain convex and linear interference functions as a special case. We analyze the boundary of the set. It is shown how Pareto optimality of boundary points depends on the interference coupling between the users. Finally, we investigate feasible sets of signal-to-interference-plus-noise ratios for individual power constraints and a sum power constraint. We show certain properties that are desirable, e.g. in the context of cooperative game theory.