Full-Duplex Secure Relay Beamforming Design for Systems With Perfect and Partial CSI

Considering that wireless unidirectional full-duplex (FD) transmission is one of the FD transmissions over 5G mobile wireless networks, this paper proposes a joint receive and transmit relay beamformer design for systems consisting of a source, a FD relay, an intended destination, and an eavesdropper. The source and destination are single-antenna nodes, whereas the FD relay is a multi-antenna node. Assuming that full channel state information (CSI) is available and the eavesdropper processes two blocks of received data at a time, the joint optimization problem is reformulated as a semidefinite relaxation (SDR) problem (in terms of relay transmit beamformer), which is tight in the sense that the rank-one beamformer can always be recovered from the SDR solution. In order to significantly minimize the computational cost of the SDR implementation, a novel semi-analytical approach based on dual optimization is proposed to obtain the optimum transmit beamformer. When the number of data blocks is arbitrary, we propose a successive convex approximation approach for solving the original non-convex optimization problem and show that a stationary solution can be efficiently obtained. We then propose a distributionally robust beamformer design for the case of an arbitrary number of blocks, assuming that the means and covariance matrices of the eavesdropper's channels are known. Computer simulations show that the proposed semi-analytical solution matches with that obtained from numerical optimization of the SDR problem, the FD scheme significantly outperforms its half-duplex counterpart, and the proposed robust design provides robustness against CSI uncertainty.