Secrecy capacity of a multiple-antenna wiretap channel is studied in the low signal-to-noise ratio (SNR) regime. Expressions for the first and second derivatives of the secrecy capacity with respect to SNR at SNR = 0 are derived. Transmission strategies required to achieve these derivatives are identified. In particular, it is shown that it is optimal in the low-SNR regime to transmit in the maximal-eigenvalue eigenspace of φ = Hm† Hm - Nm/Ne He†He where Hm and He denote the channel matrices associated with the legitimate receiver and eavesdropper, respectively, and Nm and Ne are the noise variances at the receiver and eavesdropper, respectively. Energy efficiency is analyzed by finding the minimum bit energy required for secure and reliable communications, and the wideband slope. Increased bit energy requirements under secrecy constraints are quantified. Finally, the impact of fading is investigated, and the benefits of fading in terms of energy efficiency are shown.
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机译：在低信噪比（SNR）体制下研究了多天线窃听通道的保密容量。推导了在SNR = 0时相对于SNR的保密能力的一阶和二阶导数的表达式。确定了实现这些衍生物所需的传播策略。特别地，表明在低SNR体制中，在φ= H m † H m < / sub>-N m / N e H e † H e H m 和H e 分别表示与合法接收者和窃听者相关联的信道矩阵，而N m 和N e < / sub>分别是接收器和窃听器处的噪声方差。通过找到安全可靠的通信所需的最小比特能量以及宽带斜率来分析能效。在保密约束下增加的比特能量需求被量化。最后，研究了衰落的影响，并显示了在能量效率方面衰落的好处。
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