Abstract: This paper investigates the secrecy energy efficiency optimization for simultaneous wireless information and power transfer in the multiple-input-multiple-output wiretapping system which consists of  multiple eavesdroppers (Eves). In the presence of imperfect channel estimation ,the beamforming matrix, the artificial noise covariance matrix and the power splitting ratio are jointly designed to maximize the worst-case secrecy energy efficiency under the maximum transmit power and the minimum harvested energy constraints. Due to the non-convexity of this problem, the objective function is recast into an equivalent parametric problem by exploiting the fractional programming theory, and then the non-convex equivalent problem is approximated as a convex optimization problem by means of the S-Procedure and first order Taylor series  expansion. Furthermore, a two level optimization iterative algorithm is proposed based on the Dinkelbach method. Finally, simulation results are provided  to show the effectiveness and convergence of  the proposed algorithm.

Key words: physical-layer security, secrecy energy efficiency, simultaneous wireless information and power transfer