Optimal degree of freedom for MIMO interference channels with constant channel coefficients

This paper analyzes the optimal degrees of freedom (DoF) for K-user M × N MIMO interference channels with constant channel coefficients. In this paper, we use the methodology of interpreting the interference alignment problem as a multivariate polynomial system. The properness of the system enables us to determine the feasibility of interference alignment. Using this methodology, we propose an algorithm to obtain the optimal DoF, and compute the closed-form optimal DoF. We show that K min(M,N) is optimal DoF if δ ≥ min(M,N), where δ = ⌊M+N over K+1⌋. If δ < min(M,N), K M+N over K+1 is optimal DoF when M+N over K+1 is an integer, and ⌈K M+N over K+1⌉ − 1 is the optimal DoF when M+N over K+1 is not an integer. A key contribution of this paper is that it provides a closed-form optimal DoF for M × N MIMO interference channels when the DoF of each user can be different.