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）技术成为提升下一代无线网络性能的前沿方案。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能。假设RIS到地面链路经历莱斯衰落。利用随机几何方法，推导了合法用户与根据泊松点过程（PPP）分布的窃听者处接收信噪比的精确分布，并得到了保密中断概率（SOP）和遍历保密容量（ESC）的闭式表达式，为系统设计提供指导性准则。首先，获得保密分集阶数为$\frac{2}{\alpha_2}$，其中$\alpha_2$表示RIS到地面链路的路径损耗指数。其次，揭示安全性能主要受RIS反射单元数$N$影响，而基站发射天线数和发射功率的影响较小。此外，当随机分布窃听者位置未知时，将RIS部署在合法用户附近比部署在基站附近更有效。进一步发现，随机分布窃听者密度$\lambda_e$对渐近ESC性能产生加法性影响，其表达式为$\log_2{\left({1}/{\lambda_e}\right)}$。最后通过数值仿真验证了这些理论观测结果的准确性。