Degrees of freedom of 2-user and 3-user rank-deficient MIMO interference channels

We study the degrees of freedom (DoF) of 2-user and 3-user multiple input multiple output (MIMO) interference channels with rank deficient channel matrices. Only achievable DoF results and trivial outer bounds were previously available for these problems, restricted to symmetric settings. For the 2-user rank deficient MIMO interference channel we prove the optimality of previously known achievable DoF in the symmetric case and generalize the result to fully asymmetric settings. For the 3-user rank deficient MIMO interference channel, we improve the achievable DoF and provide a tight outer bound to establish optimality. Linear precoding based achievable schemes are found to be DoF optimal in both cases.