On Completing the Degrees of Freedom Characterization of MIMO Interference Networks with No CSIT

The two-user multi-input, multi-output (MIMO) interference and cognitive radio channels are studied under the assumption of no channel state information at the transmitter (CSIT) from the degrees of freedom (DoF) region perspective. With M-i and N-i denoting the number of antennas at transmitter i and receiver i respectively, the DoF region of the MIMO interference channel was recently characterized by Huang et al., Zhu and Guo, and by the authors of this paper for all values of the 4-tuple (M-1, M-2, N-1, N-2), except when min (M-1, N-1) > N-2 > M-2 (or min(M-2, N-2) > N-1 > M-1). This latter case was solved more recently by Zhu and Guo, who provided a tight outer-bound. Here, a simpler and more widely applicable proof of that outer-bound is given based on the idea of interference localization. Using it, the DoF region is also established for the class of MIMO cognitive radio channels (under certain restrictions on the fading distributions) when min (M-1 + M-2, N-1) > N-2 > M-2 (with the second transmitter cognitive) - the only class for which the inner and outer bounds previously obtained by the authors were not tight.