Robust secrecy beamforming with energy-harvesting eavesdroppers

This letter considers simultaneous wireless information and power transfer (SWIPT) in multiple-input-single-output downlink systems in which a multiantenna transmitter sends a secret message to a single-antenna information receiver (IR) with multiple single-antenna energy receivers (ERs). We aim to maximize the harvested energy by the ERs while maintaining the signal-to-interference-and-noise ratio (SINR) threshold at the IR and keeping the message secure from possible eavesdropping by the ERs by suppressing their SINRs. Both scenarios of perfect and imperfect channel state information at the transmitter are studied. Using semidefinite relaxation techniques, we show that there always exists a rank-one optimal solution for the IR, i.e., transmit beamforming is optimal for the IR.