  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.
