Abstract: This article is focused on secure relay beamformer design with a correlated channel model in the relay-eavesdropper network. In this network, a single-antenna source-destination pair transmits secure information with the help of an amplify-and-forward (AF) relay equipped with multiple antennas, and the legitimate and eavesdropping channels are correlated. The relay cannot obtain the instantaneous channel state information (CSI) of the eavesdropper, and has only the knowledge of correlation information between the legitimate and eavesdropping channels. Depending on this information, we derive the conditional distribution of the eavesdropping channel. Two beamformers at the relay are studied for the approximate ergodic secrecy rate: (1) the generalized match-and-forward (GMF) beamformer to maximize the legitimate channel rate, and (2) the general-rank beamformer (GRBF). In addition, one lower-bound-maximizing (LBM) beamformer at the relay is discussed for maximizing the lower bound of the ergodic secrecy rate. We find that the GMF beamformer is the optimal rank-one beamformer, that the GRBF is the iteratively optimal beamformer, and that the performance of the LBM beamformer for the ergodic secrecy rate gets close to that of the GRBF for the approximate secrecy rate. It can also be observed that when the relay has lower power or the channel gain of the second hop is low, the performance of the GMF beamformer surpasses that of the GRBF. Numerical results are presented to illustrate the beamformers’ performance.

Key words: Physical layer security, Relay beamforming, Correlated channels, Ergodic secrecy rate

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