Magnetic MIMO Signal Processing and Optimization for Wireless Power Transfer

In magnetic resonant coupling (MRC) enabled multiple-input multiple-output (MIMO) wireless power transfer (WPT) systems, multiple transmitters (TXs) are used to enhance the efficiency of simultaneous power transfer to multiple receivers (RXs) by constructively combining their induced magnetic fields, a technique termed “magnetic beamforming”. In this paper, we study the optimal magnetic beamforming design in a multiuser MIMO MRC-WPT system. We introduce and characterize the multiuser power region, which constitutes all the achievable power tuples for all RXs, subject to the given total power constraint over all TXs as well as their individual peak voltage and current constraints. For the special case without TX peak voltage and current constraints, we derive the optimal TX current allocation for the single-RX setup in closed-form and that for the multi-RX setup by applying the techniques of semidefinite relaxation (SDR) and time-sharing. In general, the problem is a nonconvex quadratically constrained quadratic programming (QCQP), which is difficult to solve. For the case of one single RX, we show that the SDR of the problem is tight and thus solve the problem efficiently. For the general case with multiple RXs, based on SDR we obtain two approximate solutions by applying the techniques of time-sharing and randomization, respectively. Moreover, we propose a new method to estimate the magnetic MIMO channel between TXs and RXs for practical implementation of magnetic beamforming. Numerical results show that our proposed magnetic channel estimation and adaptive beamforming schemes are practically effective and can significantly improve the power transfer efficiency and multiuser performance tradeoff in MIMO MRC-WPT systems compared with the benchmark scheme of uncoordinated WPT with fixed identical TXs' current.