On Feasibility of Interference Alignment in MIMO Interference Networks

TLDR

The degrees of freedom of MIMO interference networks with constant channel coefficients remain largely unknown. The study aims to determine the feasibility of linear interference alignment to advance understanding of MIMO interference network degrees of freedom. The authors formulate alignment as a system of bilinear equations, classifying problems as proper or improper based on whether equations outnumber variables. Examples show that for generic channel matrices, proper systems are almost surely feasible while improper systems are almost surely infeasible.

Abstract

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