Abstract
Robust artificial noise (AN) aided secure precoding for an amplify-and-forward multiple-input multiple-output untrusted relay system is studied, where the relay is untrusted and willing to help forwarding multiple data streams from the source to destination. We consider that the available channel state information is imperfect and modeled by the worst case model. Our objective is to maximize the worst case secrecy rate under the robust transmit power constraints at the source and relay, by jointly designing the signal and AN precoding matrices at the source and the precoding matrix at the relay. The robust secure precoding problem is nonconvex and hard to solve. To overcome this difficulty, we propose the weighted minimum mean square error based method, where the sign-definiteness lemma is used to eliminate the channel uncertainties and an effective iterative optimization algorithm is developed. Simulation results are provided to demonstrate the effectiveness of the proposed scheme.