Interference Alignment as a Rank Constrained Rank Minimization

The authors show that the maximization of the sum degrees of-freedom for the static flat-fading Multiple-Input Multiple-Output (MIMO) interference channel is equivalent to a rank constrained rank minimization problem, when the signal spaces span all available dimensions. The rank minimization corresponds to maximizing Interference Alignment (IA) such that interference spans the lowest dimensional subspace possible. The rank constraints account for the useful signal spaces spanning all available spatial dimensions. That way, they reformulate all IA requirements to requirements involving ranks.