Magnetic resonant coupling (MRC) is a practically appealing method for realizing the near-field wireless power transfer (WPT). The MRC-WPT system with a single pair of transmitter and receiver has been extensively studied in the literature, while there is limited work on the general setup with multiple transmitters and/or receivers. In this paper, we consider a point-to-multipoint MRC-WPT system with one transmitter sending power wirelessly to a set of distributed receivers simultaneously. We derive the power delivered to the load of each receiver in closed-form expression, and reveal a "near-far" fairness issue in multiuser power transmission due to users' distance-dependent mutual inductances with the transmitter. We also show that by designing the receivers' load resistances, the near-far issue can be optimally solved. Specifically, we propose a centralized algorithm to jointly optimize the load resistances to minimize the power drawn from the energy source at the transmitter under given power requirements for the loads. We also devise a distributed algorithm for the receivers to adjust their load resistances iteratively, for ease of practical implementation.
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