Design of the Power and Dimension of Artificial Noise for Secure Communication Systems

In this paper, the dimension of artificial noise (AN) and corresponding transmit power in multiple-input multiple-output single-eavesdropper channels are investigated. It is widely known that AN is transmitted in the null space of the channel matrix of a legitimate link between a source and a destination. Here, the secrecy outage probabilities are derived for various dimensions of AN. Recognizing the fact that the secrecy outage performance depends on the dimension of the AN, an optimization problem is formulated to maximize the secrecy rate under a secrecy outage constraint. The optimal power splitting factor between the information and AN signals is then derived. Furthermore, the asymptotic behaviors of the optimal power splitting factor and the resulting maximum secrecy rate are examined. Through asymptotic analyses and numerical verification, it is formally shown that the full-dimension AN maximizes the secrecy rate under a secrecy outage constraint. Because the complexity of AN design increases as the dimension of the AN increases, we can achieve a tradeoff between secrecy performance and AN design complexity by determining the dimension of the AN. This study can provide a guideline of AN design specifically pertaining to the dimension of the AN.