In this paper, we provide expressions for the secrecy outage probability (SOP) for suboptimal and optimal opportunistic scheduling schemes in a reconfigurable intelligent surface (RIS) aided {single antenna} system with multiple eavesdroppers in approximate closed form. A suboptimal scheduling (SS) scheme is analyzed, which is used when the channel state information (CSI) of the eavesdropping links is unavailable, and the optimal scheduling (OS) scheme is also analyzed, which is used when the global CSI is available. For each scheme, we provide a simplified expression for the SOP in the high signal-to-noise ratio (SNR) regime to demonstrate its behavior as a function of the key system parameters. At high SNR, the SOP saturates to a constant level which decreases exponentially with the number of RIS elements in the SS scheme and with the product of the number of RIS elements and the number of users in the OS scheme. We also show that the derived SOP of the SS scheme can directly provide the SOP for the best antenna-user pair scheduling scheme in a multiple antenna system. We compare the performance of the opportunistic user scheduling schemes with that of a non-orthogonal multiple access (NOMA) based scheduling scheme which chooses a pair of users in each time slot for scheduling and we show that the opportunistic schemes outperform the NOMA-based scheme. We also derive a closed-form expression for the SOP of a decode-and-forward (DF) relay-aided scheduling scheme in order to compare it with that of the RIS-aided system. It is found that the RIS-aided system outperforms the relay-aided systems when the number of RIS elements is sufficiently large. An increased number of RIS elements is required to outperform the relay-aided system at higher operating frequencies.

翻译：本文针对存在多个窃听者的可重构智能表面（RIS）辅助单天线系统，推导了次优与最优机会型调度方案的保密中断概率近似闭式表达式。分析了当窃听链路信道状态信息不可用时采用的次优调度方案，以及当全局信道状态信息可用时采用的最优调度方案。针对每种方案，我们给出了高信噪比条件下保密中断概率的简化表达式，以揭示其随关键系统参数变化的规律。在高信噪比区域，保密中断概率将饱和至恒定水平：在次优调度方案中该水平随RIS单元数量呈指数下降，而在最优调度方案中则随RIS单元数量与用户数量的乘积呈指数下降。研究还表明，所推导的次优调度方案保密中断概率可直接应用于多天线系统中的最优天线-用户对调度方案。通过将机会型用户调度方案与基于非正交多址接入的调度方案（该方案每时隙选择一对用户进行调度）进行性能对比，发现机会型方案性能更优。为与RIS辅助系统进行对比，本文进一步推导了解码转发中继辅助调度方案的保密中断概率闭式表达式。研究发现：当RIS单元数量足够大时，RIS辅助系统性能优于中继辅助系统；在更高工作频率下，需要更多RIS单元才能超越中继辅助系统的性能。