In this letter, we study the secure degrees-of-freedom (SDoF) characterization for the multiple-input multiple-output (MIMO) X channel with confidential messages and delayed channel state information at the transmitter (CSIT). In particular, we propose a transmission scheme, which can be regarded as a generalization of the state-of-the-art scheme without security and with delayed CSIT. The key of this generalization is performing the security analysis, by which we derive the optimal duration of the artificial noise transmission phase. As a result, we derive the sum-SDoF lower bound. Furthermore, we reveal that if the number of receive antennas, denoted by ${N}$ , is fixed, the minimum number of transmit antennas achieving the maximum of the lower bound is $\frac {7+\sqrt {33}}{8}N$ .

中文翻译：

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使用延迟 CSIT 保护 MIMO X 信道的自由度

在这封信中，我们研究了多输入多输出 (MIMO) X 信道的安全自由度 (SDoF) 特性，其中包含机密消息和发射机 (CSIT) 的延迟信道状态信息。特别是，我们提出了一种传输方案，可以将其视为没有安全性和延迟 CSIT 的最新方案的推广。这种概括的关键是执行安全性分析，通过它我们得出人工噪声传输阶段的最佳持续时间。因此，我们推导出 sum-SDoF 下界。此外，我们揭示了如果接收天线的数量，表示为 ${N}$ , 是固定的，达到下界最大值的最小发射天线数为 $\frac {7+\sqrt {33}}{8}N$ .