  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.
