Degrees of Freedom of Rank-Deficient MIMO Interference Channels

We characterize the degrees of freedom (DoF) of multiple-input and multiple-output (MIMO) interference channels with rank-deficient channel matrices. For the two-user rank-deficient MIMO interference channel, we provide a tight outer bound to show that the previously known achievable DoF in the symmetric case is optimal and generalize the result to fully asymmetric settings. For the K-user rank-deficient interference channel, we improve the previously known achievable DoF and provide a tight outer bound to establish optimality in symmetric settings. In particular, we show that for the K-user rank-deficient interference channel, when all nodes have M antennas, all direct channels have rank D₀, all cross channels are of rank D, and the channels are otherwise generic, the optimal DoF value per user is min(D₀, M - (min(M, (K - 1)D)/2)). Notably for interference channels, the rank-deficiency of direct channels does not help and the rank deficiency of cross-channels does not hurt. The main technical challenge is to account for the spatial dependences introduced by rank deficiencies in the interference alignment schemes that typically rely on the independence of channel coefficients.