Secure Multiantenna Transmission With an Unknown Eavesdropper: Power Allocation and Secrecy Outage Analysis

This paper investigates the power allocation problem for secure multiple-input single-output transmission with the injection of artificial noise (AN), in the presence of an unknown eavesdropper (Eve). Two power allocation schemes, the optimal adaptive power allocation (OAPA) and suboptimal fixed power allocation (SFPA) schemes, are proposed to enhance the physical layer security of the considered system. Since the noise power at Eve is unknown, both power allocation schemes are designed for the worst-case scenario in which the noise power at Eve is assumed to be zero, aiming to minimize the secrecy outage probability (SOP). To characterize the performance of the proposed power allocation schemes, approximate closed-form expressions for average SOP under a preset noise power level are derived by applying Gauss-Chebyshev quadrature. We also address the worst-case secrecy outage performance for the proposed OAPA and SFPA schemes. Our analytical and numerical results show that, compared with the exhaustive search method that requires Eve's prior information, the proposed OAPA scheme exhibits comparable secrecy outage performance without Eve's prior information. Additionally, the SFPA scheme, also without Eve's prior information, is capable of achieving almost the same worst-case SOP as the OAPA scheme, with a much lower implementation complexity.