Improper Gaussian Signalings for Secure Non-Orthogonal Multiple Access

Abstract

This paper studies a downlink single-input-single-output (SISO) non-orthogonal multiple access (NOMA) systems in which a transmitter and a pair of legitimate receivers communicate with each other by using improper Gaussian signalings. There is an eavesdropper who overhears the information transmitted to the pair of legitimate receivers. Proper Gaussian signalings have been known as optimal on channels without interference, due to which proper Gaussian signalings have been widely used in many areas. Recently, it has been shown that improper Gaussian signalings improve achievable rates of NOMA systems. In this paper, we extend the application of improper Gaussian signalings to the secure NOMA systems. More specifically, we derive closed-form expressions of secrecy outage probability for users and analyze the effects of impropriety on the secrecy outage probability. Based on the mathematical analysis, we propose an algorithm to find the optimal impropriety degree for the secure NOMA. To confirm the analytic results, we perform extensive numerical evaluations and show that the analytic and numerical results are well matched each other. In addition, the NOMA systems based on improper and proper Gaussian signalings are compared in terms of the secrecy outage probability. The comparison substantiates our claim that a better secrecy performance is achievable with the improper Gaussian signalings.