The infeasible SIR region is not a convex set

This paper deals with the geometry of a feasible SIR region, which is defined as a set of all signal-to-interference ratios that can be supported in a power-controlled wireless network when no link scheduling is involved. It was conjectured that the complement of the feasible SIR region, a so-called infeasible SIR region, is in general a convex set under a total power constraint. The conjecture was supported by some partial results and the fact that the infeasible SIR region is a convex set in the 2 dimensional case. This paper disproves this conjecture, thereby showing that the geometry of the infeasible SIR region is more complicated than it was supposed to be. The paper discusses some possible implications of these results on optimal link scheduling policies