Requirement-Driven Magnetic Beamforming for MIMO Wireless Power Transfer Optimization

In magnetic resonant coupling (MRC) enabled wireless power transfer (WPT) systems, the multiple-input multiple-output (MIMO) based technique, termed as ``magnetic beamforming", is used to enhance the efficiency of simultaneous power transfer to multiple receivers (RXs). In this paper, we study the requirement driven magnetic beamforming design in an MIMO MRC-WPT system, which is formulated as a weighted sum-power maximization (WSPMax) problem. We relax the peak current/voltage constraints, and prove that the optimal solution to the relaxed subproblem is choosing the transmitter current as an eigenvector of a constructed matrix. By discussing the WSPMax problem under special cases with limited power budget, we derive a close- form theoretical bound of the \textbf{WSPMax} problem, and demonstrate that the power transfer efficiency maximization problem can be solved through a transmitter-only method, i.e., without any communication feedback from RXs. More than just evaluation through simulation results, we also verify the proposed algorithm after prototyping the system with off-the-shelf components. Our results suggest the efficiency of the proposed algorithm, and its ability to performing requirement-driven power distribution among receivers.