  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 regions of the MIMO interference channel
were recently characterized by Huang et al., Zhu and Guo, and by the authors of
this paper for all values of numbers of antennas 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 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 -- thereby
completing the DoF region characterization of the general 2-user MIMO cognitive
radio channel as well.
