Unmanned aerial vehicle (UAV) with the intrinsic three-dimensional (3D) mobility provides an ideal platform for implementing aerial movable antenna (AMA) system enabled by UAV swarm cooperation. Besides, AMA system is readily to achieve an extremely large-scale array aperture, rendering the conventional far-field uniform plane wave (UPW) model no longer valid for aerial-to-ground links. This paper studies the UAV swarm enabled near-field AMA communication, by taking into account the non-uniform spherical wave (NUSW) model, where UAV swarm trajectory simultaneously influences the channel amplitude and phase. We formulate a general optimization problem to maximize the minimum average communication rate over user equipments (UEs), by jointly optimizing the 3D UAV swarm trajectory and receive beamforming for all UEs. To draw useful insights, the special case of single UE is first studied, and successive convex approximation (SCA) technique is proposed to efficiently optimize the UAV swarm trajectory. For the special case of placement optimization, the optimal placement positions of UAVs for cases of single UAV and two UAVs are derived in closed-form. Then, for the special case of two UEs, we show that an inter-UE interference (IUI)-free communication can be achieved by symmetrically placing an even number of UAVs along a hyperbola, with its foci corresponding to the locations of the two UEs. Furthermore, for arbitrary number of UEs, an alternating optimization algorithm is proposed to efficiently tackle the non-convex optimization problem. Numerical results validate the significant performance gains over the benchmark schemes.

翻译：无人机凭借其固有的三维机动性，为通过集群协作实现空中可移动天线系统提供了理想平台。此外，AMA系统易于实现极大尺度的阵列孔径，使得传统的远场均匀平面波模型不再适用于空地链路。本文研究了无人机集群赋能的近场AMA通信，考虑了非均匀球面波模型，其中无人机集群的轨迹同时影响信道幅度与相位。我们构建了一个通用的优化问题，旨在通过联合优化三维无人机集群轨迹和所有用户设备的接收波束成形，最大化用户设备间的最小平均通信速率。为获得有益见解，首先研究了单用户设备的特殊情况，并提出采用逐次凸逼近技术来高效优化无人机集群轨迹。针对位置优化的特殊情况，推导出了单无人机和双无人机情形下无人机最优放置位置的闭式解。随后，针对双用户设备的特殊情况，我们证明了通过将偶数个无人机沿一条双曲线对称放置（其焦点对应于两个用户设备的位置），可以实现无用户间干扰的通信。进一步地，针对任意数量的用户设备，提出了一种交替优化算法以有效处理该非凸优化问题。数值结果验证了相较于基准方案的显著性能提升。