On optimal artificial-noise assisted secure beamforming for the fading eavesdropper channel

We consider secure transmission in fading channels with only the statistics of the eavesdropper´s channel state information known at the transmitter. We optimize the celebrated artificial-noise (AN) assisted beamforming, which was studied by Goel and Negi using heuristically selected AN and beamforming directions. We find that Goel and Negi´s AN selection is strictly sub-optimal. On the contrary, one may inject AN to the beam direction of the message to improve the secrecy rate performance. We prove that for a multiple-input, single-output, single-antenna-eavesdropper system, the optimal transmission scheme is a beamformer which is aligned to the direction of the legitimate channel. We then prove that, for the part of the AN in the null space of the legitimate channel, uniform power allocation is optimal. We also provide the necessary condition for the proposed AN selection to be optimal. Simulation results show that our AN selection outperforms Goel and Negi´s, especially when the legitimate user´s channel quality is poor. In particular, when AN assisted beamforming is applied, the region with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of secure networks.