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Considering worst-case channel uncertainties, we investigate the robust secure beamforming design problem in multiple-input-single-output full-duplex two-way secure communications. Our objective is to maximize worst-case sum secrecy rate under weak secrecy conditions and individual transmit power constraints. Since the objective function of the optimization problem includes both convex and concave terms, we propose to transform convex terms into linear terms. We decouple the problem into four optimization problems and employ alternating optimization algorithm to obtain the locally optimal solution. Simulation results demonstrate that our proposed robust secure beamforming scheme outperforms the non-robust one. It is also found that when the regions of channel uncertainties and the individual transmit power constraints are sufficiently large, because of self-interference, the proposed two-way robust secure communication is proactively degraded to one-way communication.

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