Secure Degrees of Freedom of MIMO X-Channels with Output Feedback and Delayed CSIT

Abstract

We investigate the problem of secure transmission over a two-user multi-input multi-output (MIMO) X-channel in which channel state information is provided with one-unit delay to both transmitters (CSIT), and each receiver feeds back its channel output to a different transmitter. We refer to this model as MIMO X-channel with asymmetric output feedback and delayed CSIT. The transmitters are equipped with M-antennas each, and the receivers are equipped with N-antennas each. For this model, accounting for both messages at each receiver, we characterize the optimal sum secure degrees of freedom (SDoF) region. We show that, in presence of asymmetric output feedback and delayed CSIT, the sum SDoF region of the MIMO X-channel is same as the SDoF region of a two-user MIMO BC with 2M-antennas at the transmitter, N-antennas at each receiver and delayed CSIT. This result shows that, upon availability of asymmetric output feedback and delayed CSIT, there is no performance loss in terms of sum SDoF due to the distributed nature of the transmitters. Next, we show that this result also holds if only output feedback is conveyed to the transmitters, but in a symmetric manner, i.e., each receiver feeds back its output to both transmitters and no CSIT. We also study the case in which only asymmetric output feedback is provided to the transmitters, i.e., without CSIT, and derive a lower bound on the sum SDoF for this model. Furthermore, we specialize our results to the case in which there are no security constraints. In particular, similar to the setting with security constraints, we show that the optimal sum DoF region of the (M,M,N,N)--MIMO X-channel with asymmetric output feedback and delayed CSIT is same as the DoF region of a two-user MIMO BC with 2M-antennas at the transmitter, N-antennas at each receiver, and delayed CSIT. We illustrate our results with some numerical examples.

To Appear in IEEE Transactions on Information Forensics and Security

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Cited by in corpus (9)

• Secure Degrees of Freedom of Wireless X Networks Using Artificial Noise Alignment
• On Cooperative Multiple Access Channels with Delayed CSI at Transmitters
• Blind MIMOME Wiretap Channel with Delayed CSIT
• Relay Broadcast Channel with Confidential Messages
• Secure Degrees-of-Freedom of the MIMO X Channel with Delayed CSIT
• Interplay Between Delayed CSIT and Network Topology for Secure MISO BC
• The DoF Region of Order-(K-1) Messages for the K-user MIMO Broadcast Channel with Delayed CSIT
• On-off Switched Interference Alignment for Diversity Multiplexing Tradeoff Improvement in the 2-User X-Network with Two Antennas
• On Secure Degrees of Freedom of the MIMO Interference Channel with Local Output Feedback