Least Squares Approach to Joint Beam Design for Interference Alignment in Multiuser Multi-Input Multi-Output Interference Channels

In this correspondence, the problem of interference alignment for
K
-user time-invariant multi-input multi-output interference channels is considered. The necessary and sufficient conditions for interference alignment are converted to a system of linear equations that have dummy variables. Based on this linear system, a new algorithm for beam design for interference alignment is proposed by minimizing the overall
interference misalignment
. The proposed algorithm consists of solving a least squares problem iteratively. The convergence of the proposed algorithm is established, and its complexity is analyzed. The performance of the proposed algorithm is also evaluated numerically. It is shown that the proposed algorithm has faster convergence and lower complexity than the previous method with a comparable sum rate performance in the most practical case of two receive antennas.