How much training is enough for secrecy beamforming with artificial noise

In this paper, we consider the joint design of training and data transmission signals for wiretap channels where the transmitter is to send a secrect massage to the receiver without being intercepted by the eavesdropper. The celebrated secrecy beamforming scheme, which may or may not be assisted by artificial-noise (AN), is adopted in the data transmission phase to achieve this task. The achievable secrecy rate for practical systems with channel estimation error is first derived. Based on the achievable secrecy rate, we find the optimal tradeoff between the energy used for training and data signals. The optimal solutions in the low and high energy regimes are characterized analytically. We show that AN does not provide any advantages in the low energy regime, while it may have significant impact in the high energy regime. Numerical results are presented to verify our theoretical claims.