Linear Degrees-of-Freedom for the $M\times N$ MIMO Interference Channels With Constant Channel Coefficients

This paper analyzes the linear degrees of freedom (LDoF) for K-user M ×N MIMO interference channels with constant channel coefficients. In this correspondence, we interpret the interference alignment problem as a multivariate polynomial system in terms of properness. The properness provides a LDoF upperbound for interference alignment. With this approach, we propose a method to obtain the upperbound for total LDoF achievable by linear interference alignment. The LDoF upperbound for properness condition results have two different cases which depend on the number of users, the number of transmit antennas, and the number of receive antennas. A key contribution of this paper is that it provides a closed-form LDoF upperbound for M ×N MIMO interference channels where the LDoF of each user may be different.