Zhang Tong, Chen Gaojie, Wang Shuai, Wang Rui
The Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
5GIC & 6GIC, Institute for Communication Systems, University of Surrey, Guildford GU2 7XH, UK.
Entropy (Basel). 2021 Nov 10;23(11):1484. doi: 10.3390/e23111484.
In this article, the sum secure degrees-of-freedom (SDoF) of the multiple-input multiple-output (MIMO) X channel with confidential messages (XCCM) and arbitrary antenna configurations is studied, where there is no channel state information (CSI) at two transmitters and only delayed CSI at a multiple-antenna, full-duplex, and decode-and-forward relay. We aim at establishing the sum-SDoF lower and upper bounds. For the sum-SDoF lower bound, we design three relay-aided transmission schemes, namely, the relay-aided jamming scheme, the relay-aided jamming and one-receiver interference alignment scheme, and the relay-aided jamming and two-receiver interference alignment scheme, each corresponding to one case of antenna configurations. Moreover, the security and decoding of each scheme are analyzed. The sum-SDoF upper bound is proposed by means of the existing SDoF region of two-user MIMO broadcast channel with confidential messages (BCCM) and delayed channel state information at the transmitter (CSIT). As a result, the sum-SDoF lower and upper bounds are derived, and the sum-SDoF is characterized when the relay has sufficiently large antennas. Furthermore, even assuming no CSI at two transmitters, our results show that a multiple-antenna full-duplex relay with delayed CSI can elevate the sum-SDoF of the MIMO XCCM. This is corroborated by the fact that the derived sum-SDoF lower bound can be greater than the sum-SDoF of the MIMO XCCM with output feedback and delayed CSIT.
本文研究了具有保密消息的多输入多输出（MIMO）X 信道（XCCM）在任意天线配置下的和保密自由度（SDoF），其中两个发射机没有信道状态信息（CSI），且在一个多天线、全双工、解码转发中继处只有延迟 CSI。我们旨在建立和 SDoF 的上下界。对于和 SDoF 下界，我们设计了三种中继辅助传输方案，即中继辅助干扰方案、中继辅助干扰和单接收机干扰对齐方案以及中继辅助干扰和双接收机干扰对齐方案，每种方案对应一种天线配置情况。此外，还分析了每种方案的安全性和解码情况。和 SDoF 上界是借助具有保密消息的两用户 MIMO 广播信道（BCCM）以及发射机处延迟信道状态信息（CSIT）的现有 SDoF 区域提出的。结果，得出了和 SDoF 的上下界，并刻画了当中继具有足够多天线时的和 SDoF。此外，即使假设两个发射机没有 CSI，我们的结果表明具有延迟 CSI 的多天线全双工中继可以提高 MIMO XCCM 的和 SDoF。这一点得到了如下事实的证实：所推导的和 SDoF 下界可能大于具有输出反馈和延迟 CSIT 的 MIMO XCCM 的和 SDoF。
