Robust relay beamforming for multiple-antenna amplify-and-forward relay system in the presence of eavesdropper

The problem of robust relay beamforming for the multiple-antenna amplify-and-forward (AF) relay network in the presence of an eavesdropper is studied in the paper, with the partial eavesdropper´s channel side information (ECSI) scenario being considered. In our work, the uncertainty of ECSI is modeled by using a bounded region, which imposes independent constraints on the channel gain and direction. We propose a new rank-2 relay beamformer with a special singular value decomposition (SVD) structure, whose optimal solution for the worst-case secrecy rate maximization problem can be derived via simple line searching. Furthermore, the asymptotic optimality of the proposed rank-2 beamformer is proved in the high-relay-power region under certain condition, with the performance of the proposed beamformer being verified by using numerical experiments.