Optimal Transmit Antenna Deployment and Power Allocation for Wireless Power Supply in an Indoor Space

As Internet of Things (IoT) devices proliferate, sustainable methods for powering them are becoming indispensable. The wireless provision of power enables battery-free operation and is crucial for complying with weight and size restrictions. For the energy harvesting components of these devices to be small, a high operating frequency is necessary. In conjunction with an electrically large antenna, the receivers may be located in the radiating near-field (Fresnel) region, e.g., in indoor scenarios. In this paper, we propose a wireless power transfer system to ensure a reliable supply of power to an arbitrary number of mobile, low-power, and single-antenna receivers, which are located in a three-dimensional cuboid room. To this end, we formulate a max-min optimisation problem to determine the optimal allocation of transmit power among an infinite number of radiating elements of the system's transmit antenna array. Thereby, the optimal deployment, i.e, the set of transmit antenna positions that are allocated non-zero transmit power according to the optimal allocation, is obtained implicitly. Generally, the set of transmit antenna positions corresponding to the optimal deployment has Lebesgue measure zero and the closure of the set has empty interior. Moreover, for a one-dimensional transmit antenna array, the set of transmit antenna positions is proven to be finite. The proposed optimal solution is validated through simulation. Simulation results indicate that the optimal deployment requires a finite number of transmit antennas and depends on the geometry of the environment and the dimensionality of the transmit antenna array. The robustness of the solution, which is obtained under a line-of-sight (LoS) assumption between the transmitter and receiver, is assessed in an isotropic scattering environment containing a strong LoS component.