In this paper we consider the secure transmission in fast Rayleigh fading channels with full knowledge of the main channel and only the statistics of the eavesdroppers channel state information at the transmitter. For the multiple-input, single-output, single-antenna eavesdropper systems, we generalize Goel and Negis celebrated artificial-noise (AN) assisted beamforming, which just selects the directions to transmit AN heuristically. Our scheme may inject AN to the direction of the message, which outperforms Goel and Negis scheme where AN is only injected in the directions orthogonal to the main channel. The ergodic secrecy rate of the proposed AN scheme can be represented by a highly simplified power allocation problem. To attain it, we prove that the optimal transmission scheme for the message bearing signal is a beamformer, which is aligned to the direction of the legitimate channel. After characterizing the optimal eigenvectors of the covariance matrices of signal and AN, we also provide the necessary condition for transmitting AN in the main channel to be optimal. Since the resulting secrecy rate is a non-convex power allocation problem, we develop an algorithm to efficiently solve it. Simulation results show that our generalized AN scheme outperforms Goel and Negis, especially when the quality of legitimate channel is much worse than that of eavesdroppers. In particular, the regime with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of the secure network when the proposed AN assisted beamforming is applied.
Download