In this paper, the dimension of artificial noise (AN) and corresponding transmit power in multiple-input multiple-output single-eavesdropper channels are investigated. It is widely known that AN is transmitted in the null space of the channel matrix of a legitimate link between a source and a destination. Here, the secrecy outage probabilities are derived for various dimensions of AN. Recognizing the fact that the secrecy outage performance depends on the dimension of the AN , an optimization problem is formulated to maximize the secrecy rate under a secrecy outage constraint. The optimal power splitting factor between the information and AN signals is then derived. Furthermore, the asymptotic behaviors of the optimal power splitting factor and the resulting maximum secrecy rate are examined. Through asymptotic analyses and numerical verification, it is formally shown that the full-dimension AN maximizes the secrecy rate under a secrecy outage constraint . Because the complexity of AN design increases as the dimension of the AN increases, we can achieve a tradeoff between secrecy performance and AN design complexity by determining the dimension of the AN. This study can provide a guideline of AN design specifically pertaining to the dimension of the AN.

中文翻译：

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安全通信系统人工噪声的功率和维数设计

本文研究了多输入多输出单窃听器信道中人工噪声(AN)的维数和相应的发射功率。众所周知，AN 在源和目的地之间的合法链路的信道矩阵的零空间中传输。此处，针对 AN 的各个维度导出了保密中断概率。认识到这样一个事实保密中断性能取决于AN的维度 ，优化问题被公式化以最大化保密中断约束下的保密率。然后导出信息和 AN 信号之间的最佳功率分配因数。此外，研究了最佳功率分配因子的渐近行为和由此产生的最大保密率。通过渐近分析和数值验证，正式表明全维AN在保密中断约束下最大化保密率 . 由于 AN 设计的复杂度随着 AN 维度的增加而增加，我们可以通过确定 AN 的维度来实现保密性能和 AN 设计复杂度之间的权衡。这项研究可以提供专门针对 AN 尺寸的 AN 设计指南。