A New Outer Bound via Interference Localization and the Degrees of Freedom Regions of MIMO Interference Networks With No CSIT

The two-user multiple-input multiple-output (MIMO) interference and cognitive radio channels are considered, where the
i
th transmitter and the
i
th receiver have
M
_i
and
N
_i
antennas, respectively. In particular, the degrees of freedom (DoF) regions of these channels are studied under the assumption of having no channel state information at the transmitters. Making certain assumptions about the distributions of channel matrices of increasing generality respectively, Huang, Zhu and Guo, and the authors of this paper characterized the DoF region of the MIMO interference channel for all values of the four-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
. More recently, for isotropic fading distributions, Zhu and Guo have solved this latter case by providing a tight outer bound to the DoF region. Here, a simpler and more widely applicable proof of that outer bound is given based on the idea of interference localization. Using the same idea, under Rayleigh fading, the DoF region is then also established for the MIMO cognitive radio channel (when the second transmitter is cognitive) with min(
M
₁
+
M
₂
,
N
₁
) >;
N
₂
>;
M
₂
-the only class for which the inner and outer bounds previously reported by the authors were not tight-thereby completing the DoF region characterization of this channel under Rayleigh fading for all values of (
M
₁
,
M
₂
,
N
₁
,
N
₂
).