Joint Design of Altitude and Channel Statistics Based Energy Beamforming for UAV-Enabled Wireless Energy Transfer

In recent years, UAV-enabled wireless energy transfer (WET) has attracted significant attention for its ability to provide ground devices with efficient and stable power by flexibly navigating three-dimensional (3D) space and utilizing favorable line-of-sight (LoS) channels. At the same time, energy beamforming utilizing multiple antennas, in which energy beams are focused toward devices in desirable directions, has been highlighted as a key technology for substantially enhancing radio frequency (RF)-based WET efficiency. Despite its significant utility, energy beamforming has not been studied in the context of UAV-enabled WET system design. In this paper, we propose the joint design of UAV altitude and channel statistics based energy beamforming to minimize the overall charging time required for all energy-harvesting devices (EHDs) to meet their energy demands while reducing the additional resources and costs associated with channel estimation. Unlike previous works, in which only the LoS dominant channel without small-scale fading was considered, we adopt a more general air-to-ground (A2G) Rician fading channel, where the LoS probability as well as the Rician factor is dependent on the UAV altitude. To tackle this highly nonconvex and nonlinear design problem, we first examine the scenario of a single EHD, drawing insights by deriving an optimal energy beamforming solution in closed form. We then devise efficient methods for jointly designing altitude and energy beamforming in scenarios with multiple EHDs. Our numerical results demonstrate that the proposed joint design considerably reduces the overall charging time while significantly lowering the computational complexity compared to conventional methods.