Characterization of a Class of "Convexificable" Resource Allocation Problems

This paper investigates the possibility of having convex formulations of optimization problems for interference coupled wireless systems. An axiomatic framework for interference functions proposed by Yates in 1995 is used to model interference coupling in our paper. The paper shows, that under certain very natural assumptions -- the exponential mapping is the unique transformation (up to a constant), for ``convexification'' of resource allocation problems for linear interference functions. The paper shows that it is sufficient to check for the joint convexity of the sum of weighted utility functions of inverse signal--to--interference (plus noise)--ratio, if we would like the resulting resource allocation problem to be convex. The paper characterizes the largest class of interference functions, which allow a convex formulation of a problem for interference coupled wireless systems. It extends previous literature on log--convex interference functions and provides boundaries on the class of problems in wireless systems, which are jointly convex and hence can be efficiently solved at least from a numerical perspective.