Joint Analog Beamforming and Trajectory Planning for Energy-Efficient UAV-Enabled Nonlinear Wireless Power Transfer

In this paper, we consider an unmanned aerial vehicle (UAV)-enabled multi-user network with nonlinear wireless power transfer (WPT), where multiple user sensors are distributed on the ground. Acting as an energy source, the UAV operates at a fixed height and transfers energy to the multiple sensor nodes (SNs) via wireless signals. For more efficient energy harvesting (EH), an antenna array has been installed on UAV with a structure of three dimensional (3D) uniform linear array (ULA), which enables the UAV to perform analog beamforming for power concentration. Taking into account the UAV energy consumption and considering a practical nonlinear EH model, we characterize the UAV energy efficiency particularly for WPT task and subsequently formulate an efficiency maximization problem, in which the analog beamforming and UAV trajectory planning are jointly determined together with the transmit power control scheme. To deal with the nonconvex joint optimization problem, we first propose a cosine-based approximation for the complicated 3D ULA antenna pattern, in which a convex property is proved. Combining with the proved convexity in nonlinear EH model, through a series of mathematical analysis, we construct a convex subproblem based on any feasible point, solving which guarantees an improvement of the energy efficiency. Afterwards, an iterative algorithm is proposed for iteratively addressing the joint design until a convergence to a suboptimal solution. Via simulations, we verify the convergence and performance advantages of our proposed iterative solution. Among the solution, different beamforming preferences regarding the beam coverage enlargement and power concentration are also observed with respect to different antenna array scales.