A New Outer-Bound via Interference Localization and the Degrees of Freedom Regions of MIMO Interference Networks with no CSIT

TL;DR

This paper derives a new outer-bound for the degrees of freedom region of MIMO interference networks without CSIT using interference localization, completing the characterization of the DoF region for these channels.

Contribution

It introduces a simpler proof of an existing outer-bound and extends the DoF region characterization to MIMO cognitive radio channels with no CSIT.

Findings

Established the DoF region for the previously unresolved antenna configuration.

Provided a simplified proof of the tight outer-bound using interference localization.

Extended the DoF region results to MIMO cognitive radio channels with no CSIT.

Abstract

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.