Interference alignment via minimizing projector distances of interfering subspaces

A novel interference alignment (IA) algorithm is presented. Interference alignment solutions can be obtained in closed-form for special cases only. In general, iterative algorithms need to be used. Most of these algorithms are based on a joint design of precoders at the transmitter side and receive filters at the receiver side, while the proposed method achieves IA with a precoder design only. We present a new formulation, with more geometrical insights to the IA problem. A design based on precoders simplifies the problem structure and allows receive filters to be designed independently of the IA conditions. We show that optimal precoders lie in complex Grassmannian manifolds. Consequently, the proposed algorithm is an alternating optimization algorithm on the Grassmannian manifold. Simulation results show that a precoder based scheme does not lead to any performance degradation and that the same degrees of freedom as state-of-the-art methods are achieved.