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/voltages to constructively combine the induced magnetic fields at the receiver, known as magnetic beamforming. 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 coverage, the transmitters need to be optimally placed in the region, which motivates this paper. First, we derive the optimal magnetic beamforming solution in closed-form for a distributed MISO WPT system with given locations of the transmitters and receiver to maximize the deliverable power to the receiver load subject to a given sum-power constraint at all transmitters. With the optimal magnetic beamforming solution, we then jointly optimize the locations of all transmitters to maximize the minimum power deliverable to the receiver when it is being moved over a given one-dimensional (1D) region, i.e., a line of finite length. Although the formulated node placement 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 the node placement problem to the more general case of two-dimensional (2D) region, and draw the key insights. 
Mohammad R. Vedady Moghadam and Rui Zhang
cs.SY