Interference Alignment as a Rank Constrained Rank Minimization

Abstract--We show that the maximization of the sum degreesof-freedom for the static flat-fading multiple-input multipleoutput (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, we reformulate all IA requirements to requirements involving ranks. Then, we present a convex relaxation of the RCRM problem inspired by recent results in compressed sensing and low-rank matrix completion theory that rely on approximating rank with the nuclear norm. We show that the convex envelope of the sum of ranks of the interference matrices is the sum of their corresponding nuclear norms and introduce tractable constraints that are asymptotically equivalent to ...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Dimitris S. Papailiopoulos, Alexandros G. Dimakis
• Keywords: CORR 2010, Education, Interference Alignment, Rank Minimization, Rank Minimization Problem