  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
eavesdropper's channel state information at the transmitter. For the
multiple-input, single-output, single-antenna eavesdropper systems, we
generalize Goel and Negi's 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 Negi's 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 Negi's,
especially when the quality of legitimate channel is much worse than that of
eavesdropper's. 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.
