The secrecy performance of continuous-aperture array (CAPA)-based wiretap channels in terms of secrecy rate and secrecy outage probability (SOP) is analyzed. First, the system models of CAPA systems with maximum-ratio transmission under a Rayleigh fading channel are established, and approximate probability density functions for the legitimate user Bob's signal-to-noise ratio (SNR) and the eavesdropper Eve's SNR are derived using Mercer's theorem and Landau's eigenvalue theorem. Three scenarios are considered, including a single Eve, multiple independent Eves, and multiple collaborative Eves. Next, the expressions of the secrecy rate and SOP under these three scenarios are derived, and the high-SNR slope, high-SNR power offset, diversity order, and array gain in Bob's high-SNR region are obtained. It is then theoretically proven that, in all three scenarios, the CAPA system achieves the same high-SNR slope and the same diversity order, with the latter being equal to the spatial degrees of freedom. Moreover, the CAPA system with a single Eve has the smallest high-SNR offset and the highest array gain, whereas the CAPA system with multiple collaborative Eves exhibits the largest high-SNR offset and the lowest array gain. Finally, the theoretical analyses of secrecy rate, SOP, high-SNR performance are validated by the simulation results, and a higher secrecy rate and a lower SOP are achieved by the CAPA systems compared to the spatially-discrete array systems with half-wavelength antenna spacing.

翻译：本文分析了基于连续孔径阵列的窃听信道在保密速率和保密中断概率方面的保密性能。首先，建立了瑞利衰落信道下采用最大比传输的连续孔径阵列系统模型，并利用Mercer定理和Landau特征值定理推导了合法用户Bob信噪比与窃听者Eve信噪比的近似概率密度函数。考虑了三种场景：单Eve窃听、多个独立Eve窃听以及多个协作Eve窃听。接着，推导了这三种场景下的保密速率与保密中断概率表达式，并获得了Bob高信噪比区域的高信噪比斜率、高信噪比功率偏移、分集阶数与阵列增益。随后从理论上证明：在所有三种场景中，连续孔径阵列系统均能达到相同的高信噪比斜率与相同的分集阶数，且后者等于空间自由度。此外，单Eve场景的连续孔径阵列系统具有最小的高信噪比偏移与最高的阵列增益，而多协作Eve场景则表现出最大的高信噪比偏移与最低的阵列增益。最后，仿真结果验证了关于保密速率、保密中断概率及高信噪比性能的理论分析，并且表明：与半波长天线间距的空间离散阵列系统相比，连续孔径阵列系统能够实现更高的保密速率与更低的保密中断概率。