Interference alignment via alternating minimization

Using interference alignment, it has been shown that the number of degrees of freedom in the interference channel scales linearly with the number of users. Unfortunately, closed-form solutions for interference alignment over constant-coefficient channels with more than 3 users are difficult to derive. This paper proposes an algorithm for interference alignment in the MIMO interference channel with an arbitrary number of users, antennas, or spatial streams. The algorithm is an alternating minimization over the precoding matrices at the transmitters and the interference subspaces at the receivers, and is proven to converge. Numerical results show how the algorithm is useful for simulation and can give insight into the limitations of interference alignment.