In this paper, we present a new approach for unmanned aerial vehicle (UAV) positioning and reconfigurable intelligent surface (RIS) partitioning to enhance connectivity of uplink RIS-assisted UAV networks. To achieve this, our approach optimizes RIS-aided link selection, RIS partitioning, and UAV positions to maximize network connectivity characterized by its Fiedler value. Meanwhile, it maintains a specific signal-to-interference plus noise ratio (SINR) constraint for user equipment (UE), which is influenced by RIS partitioning and UAV reliability. The network connectivity optimization problem is formulated using the Fiedler value subject to RIS elements allocation and SINR constraints. This problem is a computationally expensive combinatorial optimization, necessitating an efficient iterative approach. In particular, we propose a perturbation method for RIS-aided link selection, and derive a closed-form solution for RIS partitioning, with each partition tailored to optimize SINR for individual UAV. For the given RIS-aided links and RIS partitioning, we then show that the problem of UAV positioning can be formulated as a low complexity semi-definite programming (SDP) optimization problem, which can be solved using off-the-shelf CVX solvers. Our simulations show the potential gain of UAV positioning and RIS partitioning compared to the benchmark schemes from the literature.

翻译：本文提出了一种新的无人机（UAV）定位与可重构智能表面（RIS）分区方法，以增强上行RIS辅助无人机网络的连通性。为此，我们的方法优化了RIS辅助链路选择、RIS分区和无人机位置，从而通过其Fiedler特征值最大化网络连通性。同时，该方法维持用户设备（UE）的特定信干噪比（SINR）约束，该约束受RIS分区和无人机可靠性的影响。网络连通性优化问题以Fiedler特征值为目标函数，并受限于RIS元素分配和SINR约束。该问题属于计算成本高昂的组合优化，需要高效的迭代求解方法。特别地，我们提出了一种用于RIS辅助链路选择的扰动方法，并推导出RIS分区的闭式解，每个分区针对单个无人机的SINR进行优化。对于给定的RIS辅助链路和RIS分区，我们进一步证明无人机定位问题可建模为低复杂度的半正定规划（SDP）优化问题，并可通过现成的CVX求解器求解。仿真结果表明，相较于文献中的基准方案，无人机定位与RIS分区能带来显著的性能增益。