Node Placement and Distributed Magnetic Beamforming Optimization for Wireless Power Transfer

In multiple-input single-output (MISO) wireless power transfer (WPT) via magnetic resonant coupling (MRC), multiple transmitters are deployed to enhance the efficiency of power transfer to the electric load at a single receiver by jointly optimizing their source currents to constructively combine the induced magnetic fields at the receiver, known as magnetic beamforming. In practice, since the receiver is desired to be freely located in a target region for wireless charging, its received power can fluctuate significantly over locations even with adaptive magnetic beamforming applied. To achieve uniform coverage, the transmitters need to be optimally placed such that a minimum charging power can be achieved for the receiver regardless of its location in the region, which motivates this paper. First, we drive the optimal magnetic beamforming solution in closed-form for a distributed MISO WPT system with fixed locations of the transmitters and receiver to maximize the deliverable power to the receiver subject to a given sumpower constraint at all transmitters. With the optimal magnetic beamforming derived, we then jointly optimize the locations of all transmitters to maximize the minimum power deliverable to the receiver over a given one-dimensional (1D) region. Although the problem is non-convex, we propose an iterative algorithm for solving it efficiently. Extensive simulation results are provided which show the significant performance gains by the proposed design with optimized transmitter locations and magnetic beamforming as compared to other benchmark schemes with non-adaptive or heuristic currents allocation and transmitters placement. Last, we extend our approach to the general two-dimensional (2D) region case, and highlight the key insights for practical design. Index Terms Wireless power transfer, magnetic resonant coupling, magnetic beamforming, node placement optimization, uniform coverage.