Artificial noise (AN) is a key physical-layer security scheme for wireless communications over multiple-input multiple-output wiretap channels. Recently, artificial noise elimination (ANE) has emerged as a strategy to mitigate the impact of AN on eavesdroppers. However, the influence of ANE on the secrecy rate when counteracting AN has not been investigated. In this paper, we address this issue by establishing scaling laws for both average and instantaneous secrecy rates in the presence of AN and ANE. Based on the scaling laws, several derived corollaries provide insights into the mutual constraints between the number of transmit antennas, receive antennas, and antennas at eavesdroppers, revealing the interplay between these factors. A key corollary reveals that when the eavesdropper possesses more than twice as many antennas as the transmitter, secure communication may no longer be guaranteed. Additionally, by comparing scenarios where ANE counteracts AN with those where AN is not employed, this study identifies sufficient conditions under which AN remains effective. Finally, the derived secrecy rates provide guidelines for system design, even in the presence of advanced ANE countermeasures implemented by the eavesdropper.

翻译：人工噪声（AN）是多输入多输出窃听信道无线通信中一种关键的物理层安全方案。近年来，人工噪声消除（ANE）作为一种减轻AN对窃听者影响的策略而出现。然而，当对抗AN时，ANE对保密速率的影响尚未得到研究。在本文中，我们通过建立存在AN和ANE情况下的平均与瞬时保密速率的标度律来解决这一问题。基于这些标度律，几个推导出的推论揭示了发射天线数量、接收天线数量以及窃听者天线数量之间的相互制约关系，阐明了这些因素之间的相互作用。一个关键推论表明，当窃听者拥有的天线数量超过发射机的两倍时，安全通信可能不再得到保证。此外，通过比较ANE对抗AN与未使用AN的场景，本研究确定了AN仍能保持有效的充分条件。最后，推导出的保密速率为系统设计提供了指导，即使在窃听者实施了先进的ANE对抗措施的情况下也是如此。