On the Nuclear Norm Approach to Interference Alignment

This paper considers a K-user multiple-input multiple-output (MIMO) interference channel in which uncoordinated interference appears. Due to the uncoordinated interference, perfect interference alignment (IA) may be not attained. In order to maximize the achievable degrees-of-freedom (DoF) per user, the interference alignment is formulated as a rank constrained rank minimization (RCRM) problem which maximizes the rank of the interference matrix while keeping a full-rank constraint on the direct signal space. Because of the non-convexity of the optimization problem, we propose a new approach to provide a tight convex approximation for the rank function, instead of using the standard nuclear norm approximation. The optimum precoders and receiver subspaces are obtained iteratively via alternating minimizing approach, with convergence guaranteed. Simulation results are presented to validate the effectiveness of the proposed algorithms.