Secure Transmission over Fast Fading Multiple-Antenna Gaussian Broadcast Channel with Confidential Messages

In wiretap channels the eavesdropper's channel state information (CSI) is commonly assumed to be known at the transmitter, fully or partially. In practice, the eavesdropper may not be motivated to feedback correct CSI. In this paper we consider a more practical problem for the transmitter to have the eavesdropper's CSI. That is, the fast fading multiple-antenna Gaussian broadcast channels (FMGBC-CM) with confidential messages, where there are two receivers both legitimate and willing to feedback accurate CSI to the transmitter to maintain their secure transmission, and not to be eavesdropped by the other. We assume that only the statistics of the channel state information are known by the transmitter. We first derive the achievable rate region for the FMGBC-CM. After that we propose an iterative algorithm to solve the channel input covariance matrices and the inflation factor. Finally, numerical examples show that under perfect secrecy constraint both users can achieve positive rates simultaneously, which verifies our derived necessary condition. Numerical results also elucidate the effectiveness of the proposed algorithm in terms of the convergence speed.