Secure transmission for multi-antenna wireless powered communication with co-channel interference and self-energy recycling

In this paper, we investigate secure transmission resource allocation problem for multi-antenna wireless powered communication networks (WPCNs) where a full-duplex (FD) wireless device (WD) sends confidential signals to an information receiver (IR), and an energy transmitter (ET) is employed to provide radio energy to the FD WD and to jam the multiple eavesdroppers at the same time. In order to improve energy efficiency, the FD WD also collects energy from its own loop interference signals. The energy FD WD harvested is supplied to its information transmission in the same time slot. We aim to maximize the achievable secrecy rate at the IR by designing the transmit covariances of the WD and ET under the energy harvesting constraint of WD and transmit power constraints of WD and ET, respectively. Firstly, we consider perfect channel state information (CSI) of all links. Due to the non-convexity of the optimization problem, we propose a two-level optimization algorithm, the inner level optimization problem is a semi-definite programming (SDP) problem and the outer level optimization problem is a single-variable optimization problem. The optimal solution is derived and the sufficient condition to ensure that transmit beamforming having rank-one structure is also provided. Then, we consider robust secure transmit scheme design where the CSI uncertainties are molded by the worst-case model, and S-procedure and its extension are employed to transform the semi-infinite constraint problem into finite constraint problem. Similarly, the optimal robust solution and the sufficient condition to ensure that robust transmit beamforming is optimal are provided. Simulation results demonstrate the effectiveness of our proposed strategies.