Relay beamforming design for physical layer secure communication via line search algorithm

This paper considers a physical layer security model in wireless communications. Two legitimate users communicate through several relays with the presence of an eavesdropper. We jointly design the relay beamforming weights and minimize the total relay transmit power, while ensuring users' Quality of Services and preventing the information being eavesdropped at the same time. The problem is a robust optimization problem, because of the imperfect channel state information from users and relays to the eavesdropper. First the original problem is simplified, where the high order robust terms are omitted. Then we design an iterative algorithm based on line search, by solving two Quadratically Constrained Quadratic Programming subproblems and a one-dimensional subproblem. Simulation results indicate that the proposed algorithm outperforms the state of the arts.