The supportable QOS region of a multiuser system with log-convex interference functions

We address the problem of interference coupling and achievability of SIR targets in a multiuser system. Interference is modeled by an axiomatic framework, with log-convex interference functions. There are efficient algorithms which perform optimization over the boundary of the SIR region, but they typically require that the boundary is achievable. We show that achievability is closely linked to the interference coupling in the system. This effect is already known from power control theory, where achievability is commonly ensured by assuming an irreducible coupling matrix. In this paper, we consider a more general interference model which is based on an axiomatic framework. In order to describe the interference coupling in the system, the concept of a dependency matrix is introduced. It is shown that the achievability of the boundary only depends on the combinatorial structure of this matrix. Necessary and sufficient conditions are derived.