Robust Beamforming for AN Aided MISO SWIPT System with Unknown Eavesdroppers and Non-Linear EH Model

This work studies a beamforming design for down-link transmission of a multi-user multiple-input single-output (MISO) system where each legitimate user employs a power splitting (PS) based simultaneous wireless information and power transfer (SWIPT) technique. The transmitter intends to send confidential information to its legitimate users in the presence of purely unknown eavesdroppers. Since the transmitter does not have any knowledge of the eavesdroppers' channel state information (CSI), we consider an artificial noise (AN) approach to establishing secure communication. This beamforming design is developed by maximizing the AN power to interfere with the eavesdropper as much as possible. Based on the assumption of imperfect CSI of legitimate users at the transmitter, two robust design approaches for the joint beamforming and PS ratio have been studied to maximize the AN power under both energy harvesting (EH) and signal-to-interference-plus-noise ratio (SINR) requirements at each legitimate user. In the first robust design, we consider the bounded channel uncertainties, and employ semidefinite relaxation (SDR) and a linear matrix inequality (LMI) representation to transform the original problem into a semidefinite program (SDP). In the second robust design, we consider the statistical channel uncertainties, and show that the proposed problem can be reformulated into another form of SDP through both SDR and Bernstein-type inequality. In addition, the non-linear energy harvesting (EH) model is incorporated in this work as it could reflect the characteristics of practical radio frequency(RF)-EH conversion circuit. Simulation results have been provided to demonstrate the performance of our proposed robust designs.