Random Matrix Analysis of Secrecy Outage Probability for MISO Systems With RZF Precoding

With its capability to obtain a good tradeoff between complexity and performance, regularized zero-forcing (RZF) has been widely investigated to enhance the physical layer security. However, the associated reliability performance, i.e., secrecy outage probability (SOP), is not yet available in the literature. In this paper, we characterize the secrecy performance of RZF in the multi-user, downlink multiple-input single-output system. For this purpose, we first set up a central limit theorem for the joint distribution of users' signal-to-interference-plus-noise ratio and eavesdropper's signal-to-noise ratio by leveraging random matrix theory. The result is then utilized to obtain a closed-form approximation for the ergodic secrecy rate 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 and demonstrate the advantage of RZF over other linear transmitters such as ZF.