Power line communication is a critical component of smart grids, which are vulnerable to eavesdropping. To address this challenge, we investigate a cooperative relay hybrid power line and wireless communication system where multiple eavesdroppers are considered. We propose an elaborate artificial noise (AN)-aided beamforming (BF) scheme to improve physical layer security. Our scheme maximizes the outage-constrained secrecy rate (OCSR) of the legitimate link while restricting the capacity of the eavesdroppers to a reasonable region. However, due to the imperfect channel state information of the wiretap channel and secrecy outage probability constraint, the robust OCSR problem becomes intractable because of the non-concave secrecy objective function and the non-convex constraints. To solve this issue, we utilize semidefinite programming and Bernstein-type inequality to transform the robust OCSR nonconvex problem into two convex sub-problems, which a block-coordinated descent algorithm can solve. Simulation results showcase the effectiveness of our robust AN-aided secure BF scheme and show that the proposed scheme outperforms the benchmark scheme in a security performance gain under various channel conditions, even in the worst case.

In this paper, we investigate the physical layer security of a full-duplex decode-and-forward relay-aided system in the worst case, where all channel state informations are realistic imperfect. For the sake of confidentiality of signals transmitted from source to destination, a robust artificial noise (AN)-aided beamforming scheme is proposed. Explicitly, our objective function is that of maximizing the worst-case secrecy rate under the transmit power constraints, by jointly optimizing the beamforming matrix and AN at the source and the relay. To overcome the non-convexity of the robust AN-aided secure beamforming problem, we transform it into multi-block convex problems, where the semi-infinite linear matrix inequality is applied to eliminate the channel uncertainties. As a benefit, our proposed robust AN -aided secure beamforming scheme obtains substantial secrecy performance gains, which verifies the efficiency of the proposed scheme.