期刊
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY
卷 8, 期 11, 页码 1760-1774出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIFS.2013.2278936
关键词
Secrecy capacity; degrees of freedom; MIMO-X channels; feedback; channel state information
资金
- European Commission in the framework of the FP7 Network of Excellence in Wireless Communications (NEWCOM)
- Concerted Research Action, SCOOP
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 antennas each, and the receivers are equipped with 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 the presence of asymmetric output feedback and delayed CSIT, the sum SDoF region of the MIMO X-channel is the same as the SDoF region of a two-user MIMO BC with antennas at the transmitter, 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 the same as the DoF region of a two-user MIMO BC with antennas at the transmitter, antennas at each receiver, and delayed CSIT. We illustrate our results with some numerical examples.
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