As an effective way to enhance the physical layer security (PLS) for the broadcast channel (BC), regularized zero-forcing (RZF) precoding has attracted much attention. However, the reliability performance, i.e., secrecy outage probability (SOP), of RZF is not well investigated in the literature. In this paper, we characterize the secrecy performance of RZF precoding in the large multiple-input single-output (MISO) broadcast system. For this purpose, we first consider a central limit theorem (CLT) for the joint distribution of the users' signal-to-interference-plus-noise ratio (SINR) and the eavesdropper's (Eve's) signal-to-noise ratio (ESNR) by leveraging random matrix theory (RMT). The result is then utilized to obtain a closed-form approximation for the ergodic secrecy rate (ESR) and SOP of three typical scenarios: the case with only external Eves, the case with only internal Eves, and that with both. The derived results are then used to evaluate the percentage of users in secrecy outage and the required number of transmit antennas to achieve a positive secrecy rate. It is shown that, with equally-capable Eves, the secrecy loss caused by external Eves is higher than that caused by internal Eves. Numerical simulations validate the accuracy of the theoretical results.

翻译：作为增强广播信道物理层安全（PLS）的有效手段，正则化迫零（RZF）预编码技术备受关注。然而，现有文献尚未充分研究RZF的可靠性性能指标，即保密中断概率（SOP）。本文针对大规模多输入单输出（MISO）广播系统，刻画了RZF预编码的保密性能。为此，我们首先基于随机矩阵理论（RMT），推导了用户信干噪比（SINR）与窃听者信噪比（ESNR）联合分布的中心极限定理（CLT）。进而利用该结果，针对三种典型场景（仅存在外部窃听者、仅存在内部窃听者、以及两者共存），获得了遍历保密速率（ESR）与SOP的闭式近似表达式。利用推导结果，我们评估了处于保密中断状态的用户比例，以及实现正保密速率所需的天线数量。研究表明，当窃听者具备同等能力时，外部窃听者造成的保密性能损失高于内部窃听者。数值仿真验证了理论结果的准确性。