Secure Relay Beamforming With Imperfect Channel Side Information

In this paper, we study the robust relay beamformer design problem in the relay-eavesdropper network with imperfect knowledge of the eavesdropper's channel. In this network, the half-duplexing relay is equipped with multiple antennas and employs the amplify-and-forward (AF) relaying protocol. Assuming static legitimate links, we consider the relay beamforming problem under two models for the eavesdropper's channel: 1) the Rician fading channel model, where only statistical information of the eavesdropper's channel is known by the legitimate nodes; and 2) the deterministic uncertainty model, where the uncertainty region of the eavesdropper's channel vector is modeled as a sphere. As for the optimization criteria, we use an approximation of the ergodic secrecy rate under the Rician fading model and the worst-case secrecy rate under the deterministic uncertainty model. Under both models, the optimal rank-1, match-and-forward (MF), and zero-forcing (ZF) beamformers are developed, and the equivalence of the optimal rank-1 beamformer and the optimal MF beamformer is also established. Under the Rician fading model, it is shown that the optimal ZF beamformer may have a rank greater than 1 and, therefore, could outperform the optimal MF beamformer, whereas under the deterministic uncertainty model, the optimal ZF beamformer must be rank-1. Numerical results are presented to verify the effectiveness of the proposed relay beamformers.