Masked Beamforming in the Presence of Energy-Harvesting Eavesdroppers

This paper considers a multiple-input single-output downlink system consisting of one multiantenna transmitter, one single-antenna information receiver (IR), and multiple single-antenna energy-harvesting receivers (ERs) for simultaneous wireless information and power transfer. The design is to keep the message secret to the ERs while maximizing the information rate at the IR and meeting the energy harvesting constraints at the ERs. Technically, our objective is to optimize the information-bearing beam and artificial noise energy beam for maximizing the secrecy rate of the IR subject to individual harvested energy constraints of the ERs for the case where the ERs can collude to perform joint decoding in an attempt to illicitly decode the secret message to the IR. As a by-product, we also solve the total power minimization problem subject to secrecy rate and energy harvesting constraints. Both scenarios of perfect and imperfect channel state information (CSI) at the transmitter are addressed. For the imperfect CSI case, we study both eavesdroppers' channel covariance-based and worst case-based designs. Using semidefinite relaxation (SDR) techniques, we show that there always exists a rank-one optimal transmit covariance solution for the IR. Furthermore, if the SDR results in a higher rank solution, we propose an efficient algorithm to always construct an equivalent rank-one optimal solution. Computer simulations are carried out to demonstrate the performance of the proposed algorithms.