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 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 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：本文针对可重构智能表面（RIS）辅助系统中存在多个窃听者的场景，给出了次优与最优机会调度方案下保密中断概率（SOP）的近似闭式表达式。分析了窃听链路信道状态信息（CSI）不可用时的次优调度（SS）方案，以及全局CSI可用时的最优调度（OS）方案。针对每种方案，我们提供了高信噪比（SNR）条件下SOP的简化表达式，以展示其随关键系统参数变化的特性。在高SNR下，SOP收敛至恒定水平，该水平在SS方案中随RIS单元数量呈指数递减，在OS方案中随RIS单元数量与用户数量的乘积呈指数递减。我们将机会用户调度方案与非正交多址接入（NOMA）调度方案（每时隙选择一对用户进行调度）的性能进行比较，结果表明机会方案优于NOMA方案。此外，为与RIS辅助系统进行对比，我们推导了解码转发（DF）中继辅助调度方案下SOP的闭式表达式。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性能。