Secrecy Analysis for MISO Broadcast Systems with Regularized Zero-Forcing Precoding

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.