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.

中文翻译：

---

用于节能无人机非线性无线功率传输的联合模拟波束成形和轨迹规划


在本文中，我们考虑了一种具有非线性无线功率传输（WPT）功能的无人机（UAV）多用户网络，其中多个用户传感器分布在地面上。无人机作为能源，在固定高度运行，并通过无线信号将能量传输到多个传感器节点（SN）。为了更有效地收集能量（EH），无人机上安装了具有三维（3D）均匀线性阵列（ULA）结构的天线阵列，使无人机能够进行模拟波束成形以实现功率集中。考虑到无人机能耗并考虑实际的非线性 EH 模型，我们特别针对 WPT 任务来表征无人机能源效率，并随后提出效率最大化问题，其中模拟波束成形和无人机轨迹规划与发射功率一起共同确定控制方案。为了处理非凸联合优化问题，我们首先对复杂的 3D ULA 天线方向图提出了一种基于余弦的近似，并证明了凸性质。结合已证明的非线性EH模型的凸性，通过一系列的数学分析，构造了基于任意可行点的凸子问题，求解保证了能量效率的提高。然后，提出了一种迭代算法来迭代解决联合设计，直到收敛到次优解。通过模拟，我们验证了我们提出的迭代解决方案的收敛性和性能优势。在该解决方案中，针对不同的天线阵列规模，还观察到关于波束覆盖范围扩大和功率集中的不同波束形成偏好。