Feasibility Conditions for Interference Alignment

TL;DR

This paper investigates the conditions under which interference alignment is feasible in MIMO networks with constant channels, proposing a classification based on the count of equations and variables to predict solvability.

Contribution

It introduces a new classification of interference alignment problems into proper and improper, linking feasibility to the balance of equations and variables.

Findings

Proper systems are almost surely feasible for generic channels.

Improper systems are almost surely infeasible for generic channels.

The approach simplifies feasibility analysis of interference alignment problems.

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.