Robust beamforming optimization for magnetic resonance coupling wireless power transfer systems

Magnetic Resonance Coupling (MRC) wireless power transfer (WPT) is a promising technique for portable devices and Internet of Things applications, which can transfer power to energy-constrained terminals in mid-range with relatively high efficiency. To enhance the transfer performance, by applying more coils in transceivers, multiple-input single-output (MISO) MRC-WPT system has attracted much attention in recent years. In this paper, a MISO MRC-WPT system with multiple transmitters (TXs) and a single receiver (RX) is studied and its robust magnetic beamforming problem is investigated. The optimal robust beamforming design of the currents of TXs is investigated to maximize the power received by RX with the mutual inductance error between TXs and RX, whereas the total power required is less than a certain value and each TXs has a certain limited transmitting power. By using certain transformation techniques, the optimization problem is converted into a relaxed semidefinite programming (SDP) problem which can be solved efficiently. We further prove that the solution of the relaxed SDP problem is always rank-one, which indicates that the relaxation is tight, and the optimal solution for the problem was obtained. Numerical results demonstrate that the proposed beamforming design can achieve up to 97% transfer efficiency by reducing the measurement errors. (paper)