Reconfigurable intelligent surface (RIS) technology is emerging as a promising technique for performance enhancement for next-generation wireless networks. This paper investigates the physical layer security of an RIS-assisted multiple-antenna communication system in the presence of random spatially distributed eavesdroppers. The RIS-to-ground channels are assumed to experience Rician fading. Using stochastic geometry, exact distributions of the received signal-to-noise-ratios (SNRs) at the legitimate user and the eavesdroppers located according to a Poisson point process (PPP) are derived, and closed-form expressions for the secrecy outage probability (SOP) and the ergodic secrecy capacity (ESC) are obtained to provide insightful guidelines for system design. First, the secrecy diversity order is obtained as $\frac{2}{\alpha_2}$, where $\alpha_2$ denotes the path loss exponent of the RIS-to-ground links. Then, it is revealed that the secrecy performance is mainly affected by the number of RIS reflecting elements, $N$, and the impact of the number of transmit antennas and transmit power at the base station is marginal. In addition, when the locations of the randomly located eavesdroppers are unknown, deploying the RIS closer to the legitimate user rather than to the base station is shown to be more efficient. Moreover, it is also found that the density of randomly located eavesdroppers, $\lambda_e$, has an additive effect on the asymptotic ESC performance given by $\log_2{\left({1}/{\lambda_e}\right)}$. Finally, numerical simulations are conducted to verify the accuracy of these theoretical observations.

翻译：可重构智能表面（RIS）技术正成为提升下一代无线网络性能的一种前景广阔的技术方案。本文研究了存在随机空间分布窃听者时，RIS辅助多天线通信系统的物理层安全性。假设RIS到地面信道经历莱斯衰落。利用随机几何理论，推导了合法用户以及服从泊松点过程分布的窃听者处接收信噪比的精确分布，并获得了保密中断概率和遍历保密容量的闭式表达式，为系统设计提供了具有洞察力的指导准则。首先，得到保密分集阶数为$\frac{2}{\alpha_2}$，其中$\alpha_2$表示RIS到地面链路的路径损耗指数。然后，揭示出保密性能主要受RIS反射单元数量$N$的影响，而基站发射天线数量和发射功率的影响则微乎其微。此外，当随机分布窃听者的位置未知时，将RIS部署在更靠近合法用户而非基站的位置被证明更为有效。进一步研究发现，随机窃听者密度$\lambda_e$对渐近遍历保密容量产生加性影响，该渐近容量由$\log_2{\left({1}/{\lambda_e}\right)}$给出。最后，通过数值仿真验证了这些理论观测结果的准确性。