The Degrees of Freedom Regions of MIMO Broadcast, Interference, and Cognitive Radio Channels with No CSIT

Abstract

The degrees of freedom (DoF) regions are characterized for the multiple-input multiple-output (MIMO) broadcast channel (BC), interference channels (IC) (including X and multi-hop interference channels) and the cognitive radio channel (CRC), when there is perfect and no channel state information at the receivers and the transmitter(s) (CSIR and CSIT), respectively. For the K-user MIMO BC, the exact characterization of the DoF region is obtained, which shows that a simple time-division-based transmission scheme is DoF-region optimal. Using the techniques developed for the MIMO BC, the corresponding problems for the two-user MIMO IC and the CRC are addressed. For both of these channels, inner and outer bounds to the DoF region are obtained and are seen to coincide for a vast majority of the relative numbers of antennas at the four terminals, thereby characterizing DoF regions for all but a few cases. Finally, the DoF regions of the $K$-user MIMO IC, the CRC, and X networks are derived for certain classes of these networks, including the one where all transmitters have an equal number of antennas and so do all receivers. The results of this paper are derived for distributions of fading channel matrices and additive noises that are more general than those considered in other simultaneous related works. The DoF regions with and without CSIT are compared and conditions on the relative numbers of antennas at the terminals under which a lack of CSIT does, or does not, result in the loss of DoF are identified, thereby providing, on the one hand, simple and robust communication schemes that don't require CSIT but have the same DoF performance as their previously found CSIT counterparts, and on the other hand, identifying situations where CSI feedback to transmitters would provide gains that are significant enough that even the DoF performance could be improved.

49 pages, 11 figures, under review, IEEE Trans. Inform. Th. Submitted Sept. 2009, Revised Jan. 2011

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• The Degrees of Freedom Regions of Two-User and Certain Three-User MIMO Broadcast Channels with Delayed CSIT
• The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel with Delayed CSI
• The Degrees of Freedom Region of the MIMO Interference Channel with Shannon Feedback
• The Degrees of Freedom of the 2-Hop, 2-User Interference Channel with Feedback
• The DoF Region of the Multiple-Antenna Time Correlated Interference Channel with Delayed CSIT
• A New Outer-Bound via Interference Localization and the Degrees of Freedom Regions of MIMO Interference Networks with no CSIT
• Degrees of Freedom Regions of Two-User MIMO Z and Full Interference Channels: The Benefit of Reconfigurable Antennas
• On the Degrees of Freedom Regions of Two-User MIMO Z and Full Interference Channels with Reconfigurable Antennas
• A Large-System Analysis of the Imperfect-CSIT Gaussian Broadcast Channel with a DPC-based Transmission Strategy