  In this paper, an energy harvesting scheme for a multi-user
multiple-input-multiple-output (MIMO) secrecy channel with artificial noise
(AN) transmission is investigated. Joint optimization of the transmit
beamforming matrix, the AN covariance matrix, and the power splitting ratio is
conducted to minimize the transmit power under the target secrecy rate, the
total transmit power, and the harvested energy constraints. The original
problem is shown to be non-convex, which is tackled by a two-layer
decomposition approach. The inner layer problem is solved through semi-definite
relaxation, and the outer problem 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 convex approximation (SPCA)
method is proposed to find a near-optimal solution. Furthermore, tightness of
the relaxation for the 1-D search method is validated by showing that the
optimal solution of the relaxed problem is rank-one. Simulation results
demonstrate that the proposed SPCA method achieves the same performance as the
scheme based on 1-D search method but with much lower complexity.
