面向智能超表面（SIM）辅助无人机的节能多用户波束成形与三维位置优化
Energy Efficient Multi-User Beamforming and 3D Position Optimization for SIM-Assisted UAVs
AI总结：
针对配备堆叠智能超表面的节能无人机多用户通信，提出联合优化数字预编码、SIM相移与无人机三维位置的算法，大幅提升能效并揭示关键设计权衡。
AI中文摘要：
本文研究配备堆叠智能超表面（stacked intelligent metasurfaces, SIM）的无人机（UAV）通信系统中节能的下行多用户传输，该系统通过多个级联超表面层实现波域模拟波束成形，同时使用有限数量的发射射频链执行低维数字预编码。该架构以降低的硬件复杂度实现灵活的电磁波操控，特别适用于能量受限的空中平台。我们构建了感知硬件的能效（energy-efficiency, EE）最大化问题，旨在在发射功率、SIM 运行及 UAV 部署约束下，联合优化数字预编码器、所有 SIM 层的相移以及 UAV 的三维位置。由于目标函数为分式形式、SIM 的级联结构、各组成超表面层的单位模相移约束，以及与 UAV 相关的非线性信道，所得问题具有高度非凸性。为应对这些挑战，我们开发了基于变换的交替优化框架，结合 Dinkelbach 方法、对偶变换与二次变换，以实现闭式数字波束成形、针对 SIM 相移的黎曼流形优化，以及针对 UAV 定位的逐次凸近似（successive convex approximation, SCA）。我们提供了收敛性与复杂度分析以表征所提算法。数值结果表明，与全数字及最大比传输基准方案相比，所提联合设计显著提升了能效，同时揭示了发射功率、SIM 尺寸及其组成堆叠层数之间的重要设计权衡。
英文摘要：
This paper studies energy-efficient downlink multi-user transmissions with unmanned aerial vehicle (UAV) communication systems equipped with stacked intelligent metasurfaces (SIM), enabling wave-domain analog beamforming through multiple cascaded metasurface layers, while low-dimensional digital precoding is carried out using a limited number of transmit radio-frequency chains. This architecture enables flexible electromagnetic wave manipulation with reduced hardware complexity, making it particularly suitable for energy-constrained aerial platforms. We formulate a hardware-aware energy-efficiency (EE) maximization problem aiming to jointly optimize the digital precoder, the phase shifts of all SIM layers, and the three-dimensional UAV position under transmit-power, SIM operation, and UAV deployment constraints. The resulting problem is highly non-convex due to the fractional objective, the cascaded SIM structure and the unit-modulus phase constraints of the constituent metasurface layers, as well as the non-linear UAV-dependent channel. To address these challenges, we develop a transform-based alternating optimization framework that combines Dinkelbach's method, dual and quadratic transforms, to enable closed-form digital beamforming, Riemannian manifold optimization for SIM phase shifts, and successive convex approximation (SCA) for UAV positioning. Convergence and complexity analyses are provided to characterize the proposed algorithm. The presented numerical results showcase that the proposed joint design significantly improves EE compared with fully digital and maximum ratio transmission benchmark schemes, while revealing important design trade-offs among transmit power, SIM size, and the number of its constituent stacked layers.
