1. Introduction
Interference alignment (IA) is a cooperative transmission strategy for the interference channel that results in a linearly scaling sum-rate with the number of users in the system in the high SNR regime [1]. IA is based only on linear precoding at the transmitters and zero-forcing at the receivers but requires extensive channel knowledge in order to sufficiently suppress the interference at all receivers simultaneously [2]. The key idea of IA is to use precoding matrices at all transmitters such that the interference aligns at each receiver and spans only a subspace of the receive space, thus providing interference free subspaces for the desired signals. In some simple scenarios there exist closed-form solutions of the IA problem [1]. For scenarios with arbitrary number of users, transmit and receive antennas as well as number of spatial streams, iterative algorithms were introduced in [3]–[5]. In [6] IA feasibility conditions were derived for certain scenarios, while they are still unknown for arbitrary scenarios.