On Feasibility of Interference Alignment in MIMO Interference Networks

Abstract

The degrees of freedom of MIMO interference networks with constant channel\ncoefficients are not known in general. Determining the feasibility of a linear\ninterference alignment solution is a key step toward solving this open problem.\nOur approach in this paper is to view the alignment problem as a system of\nbilinear equations and determine its solvability by comparing the number of\nequations and the number of variables. To this end, we divide interference\nalignment problems into two classes - proper and improper. An interference\nalignment problem is called proper if the number of equations does not exceed\nthe number of variables. Otherwise, it is called improper. Examples are\npresented to support the intuition that for generic channel matrices, proper\nsystems are almost surely feasible and improper systems are almost surely\ninfeasible.\n