[论文解读] Intelligent User Clustering and Robust Beamforming Design for UAV-NOMA Downlink

Yanqing Xu, Fang Fang+2 more|arXiv (Cornell University)|Jun 10, 2020

UAV Applications and Optimization参考文献 32被引用 4

一句话总结

该论文提出了一种在信道状态信息（CSI）不完美条件下的无人机-非正交多址接入（UAV-NOMA）下行链路系统中，基于智能用户聚类与鲁棒波束成形的设计方法。该方法采用基于k-means++的聚类算法和基于半定规划松弛（SDR）的波束成形方法，并具备理论上的秩一解保证，实现了去中心化、低复杂度且节能的传输，同时在CSI不确定性条件下确保服务质量（QoS）。

ABSTRACT

In this work, we consider a downlink NOMA network with multiple single-antenna users and multi-antenna UAVs. In particular, the users are spatially located in several clusters by following the Poisson Cluster Process and each cluster is served by a hovering UAV with NOMA. For practical considerations, we assume that only imperfect CSI of each user is available at the UAVs. Based on this model, the problem of joint user clustering and robust beamforming design is formulated to minimize the sum transmission power, and meanwhile, guarantee the QoS requirements of users. Due to the integer variables of user clustering, coupling effects of beamformers, and infinitely many constraints caused by the imperfect CSI, the formulated problem is challenging to solve. For computational complexity reduction, the original problem is divided into user clustering subproblem and robust beamforming design subproblem. By utilizing the users' position information, we propose a k-means++ based unsupervised clustering algorithm to first deal with the user clustering problem. Then, we focus on the robust beamforming design problem. To attain insights on solving the robust beamforming design problem, we firstly investigate the problem with perfect CSI, and the associated problem is shown can be solved optimally. Secondly, for the problem in the general case with imperfect CSI, an SDR based method is proposed to produce a suboptimal solution efficiently. Moreover, we provide a sufficient condition under which the SDR based approach can guarantee to obtain an optimal rank-one solution, which is theoretically analyzed. Finally, an alternating direction method of multipliers based algorithm is proposed to allow the UAVs to perform robust beamforming design in a decentralized fashion efficiently. Simulation results demonstrate the efficacy of the proposed algorithms and transmission scheme.

研究动机与目标

• 解决在CSI不完美条件下的UAV-NOMA下行链路系统中联合用户聚类与鲁棒波束成形设计问题。
• 在CSI不确定性条件下，最小化总发射功率，同时保证所有用户的QoS。
• 通过将联合问题分解为用户聚类与波束成形子问题，降低计算复杂度。
• 通过交替方向乘子法（ADMM）算法实现去中心化的波束成形设计。
• 提供理论条件，确保基于SDR的波束成形解可实现秩一波束成形器，从而保证实际应用的可行性。

提出的方法

• 采用基于k-means++的无监督聚类算法，利用用户位置信息构建用户聚类。
• 将原始的混合整数非凸问题分解为两个子问题：用户聚类与鲁棒波束成形设计。
• 应用半定规划松弛（SDR）将鲁棒波束成形问题转化为具有无限多个约束的凸优化问题，以应对CSI不确定性。
• 利用S-lemma将鲁棒约束重述为线性矩阵不等式（LMI），从而实现高效的SDR求解。
• 推导出SDR解保证为秩一的充分条件，确保可实现的波束成形器用于实际部署。
• 设计基于ADMM的去中心化算法，使无人机能够独立计算波束成形器，无需集中协调。

实验结果

研究问题

• RQ1 在用户空间分布分散的UAV-NOMA系统中，如何高效地执行用户聚类？
• RQ2 在多无人机、多用户NOMA下行链路系统中，CSI不完美条件下最优的鲁棒波束成形设计是什么？
• RQ3 在何种条件下，基于SDR的波束成形解可实现秩一波束成形器，从而确保实际传输的可行性？
• RQ4 如何实现去中心化的波束成形设计，以减少信令开销？
• RQ5 在CSI不确定性条件下，所提方案在总功率降低与QoS保障方面的性能增益如何？

主要发现

• 基于k-means++的聚类算法能有效根据用户的空间分布进行分组，降低用户间干扰。
• 基于SDR的波束成形设计可获得次优解，并在充分条件下理论保证波束成形器为秩一。
• 秩一解的充分条件基于KKT条件以及波束成形器与对偶变量的结构推导得出。
• 基于ADMM的去中心化算法可实现无人机间高效、分布式波束成形计算，且协调开销极低。
• 仿真结果表明，所提方案在CSI不完美条件下显著降低了总发射功率，同时保持了QoS要求。
• 鲁棒波束成形设计能有效缓解CSI误差导致的性能退化，尤其在高移动性或高抖动的无人机环境中表现更优。