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, multiple transmitters are deployed to enhance the efficiency of power transfer to a single receiver by jointly adapting their source currents/voltages so as to constructively combine the induced magnetic fields at the receiver, a technique known as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">magnetic beamforming</i> . In practice, since the transmitters (power chargers) are usually at fixed locations and the receiver (e.g., mobile phone) 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 power coverage, the transmitters need to be optimally placed in the region such that a minimum charging power can be achieved for the receiver regardless of its location, which motivates this paper. First, we derive 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 sum-power constraint at all transmitters. By applying adaptive magnetic beamforming based on this optimal solution, 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 formulated problem is nonconvex, we propose an iterative algorithm for solving it efficiently. Extensive simulation results are provided that show the significant performance gains by the proposed design with optimized transmitter locations and magnetic beamforming as compared to other benchmark schemes with nonadaptive and/or heuristic transmitter current allocation and node placement. Last, we extend the node placement problem to the case of 2D region, and propose efficient designs for this case.