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In this paper, an energy harvesting scheme for a multi-usermultiple-input-multiple-output (MIMO) secrecy channel with artificial noise(AN) transmission is investigated. Joint optimization of the transmitbeamforming matrix, the AN covariance matrix, and the power splitting ratio isconducted to minimize the transmit power under the target secrecy rate, thetotal transmit power, and the harvested energy constraints. The originalproblem is shown to be non-convex, which is tackled by a two-layerdecomposition approach. The inner layer problem is solved through semi-definiterelaxation, and the outer problem, on the other hand, is shown to be a single-variable optimization that can be solved by one-dimensional (1- D) line search.To reduce computational complexity, a sequential parametric convexapproximation (SPCA) method is proposed to find a near-optimal solution. Thework is then extended to the imperfect channel state information case withnorm-bounded channel errors. Furthermore, tightness of the relaxation for theproposed schemes are validated by showing that the optimal solution of therelaxed problem is rank-one. Simulation results demonstrate that the proposedSPCA method achieves the same performance as the scheme based on 1-D but withmuch lower complexity.

Beamforming and Power Splitting Designs for AN-aided Secure Multi-user MIMO SWIPT Systems