In this paper, a stochastic geometry based analytical framework is proposed for secure simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted non-orthogonal multiple access (NOMA) transmissions, where legitimate users (LUs) and eavesdroppers are randomly distributed. Both the time-switching protocol (TS) and energy splitting (ES) protocol are considered for the STAR-RIS. To characterize system performance, the channel statistics are first provided, and the Gamma approximation is adopted for general cascaded $\kappa$-$\mu$ fading. Afterward, the closed-form expressions for both the secrecy outage probability (SOP) and average secrecy capacity (ASC) are derived. To obtain further insights, the asymptotic performance for the secrecy diversity order and the secrecy slope are deduced. The theoretical results show that 1) the secrecy diversity orders of the strong LU and the weak LU depend on the path loss exponent and the distribution of the received signal-to-noise ratio, respectively; 2) the secrecy slope of the ES protocol achieves the value of one, higher than the slope of the TS protocol which is the mode operation parameter of TS. The numerical results demonstrate that: 1) there is an optimal STAR-RIS mode operation parameter to maximize the secrecy performance; 2) the STAR-RIS-NOMA significantly outperforms the STAR-RIS-orthogonal multiple access.

翻译：本文提出了一种基于随机几何的分析框架，用于保障同时透射和反射可重构智能表面（STAR-RIS）辅助的非正交多址接入（NOMA）传输的安全性，其中合法用户（LUs）和窃听者随机分布。针对STAR-RIS，同时考虑了时间切换协议（TS）和能量分裂协议（ES）。为表征系统性能，首先给出了信道统计特性，并采用Gamma近似处理通用级联κ-μ衰落。随后，推导了保密中断概率（SOP）和平均保密容量（ASC）的闭式表达式。为进一步获得启示，推导了保密分集阶数和保密斜率的渐近性能。理论结果表明：1）强合法用户和弱合法用户的保密分集阶数分别取决于路径损耗指数和接收信噪比的分布；2）ES协议的保密斜率达到1，高于TS协议的斜率（后者为TS的模式操作参数）。数值结果证明：1）存在最优的STAR-RIS模式操作参数以最大化保密性能；2）STAR-RIS-NOMA显著优于STAR-RIS-正交多址接入。