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In this article, we investigate a multi-user multiple-input-single-output full-duplex system with simultaneous wireless information and power transfer under the non-linear energy harvesting model, where channel state information is imperfect. Since the channel estimation error is considered in our proposed system, the self-interference cannot be canceled perfectly. For such a system, a robust optimization problem that maximizes the minimum average total harvested power by jointly optimizing the uplink and downlink beamforming matrices is formulated. As the problem is non-linear and non-convex under channel estimation errors, a novel Newton method based iterative optimization algorithm is proposed to solve it efficiently. In each iteration, the semidefinite relaxation technique and S-Procedure method are applied to obtain the optimal beamforming vectors, which are proved to be optimal solutions with rank-one. Simulation results reveal that the proposed robust design can achieve better system performance than the non-robust scheme, both of which are based on the non-linear energy harvesting model.

Robust Beamforming for Multi-User MISO Full-Duplex SWIPT System Under Non-Linear Energy Harvesting Model