[Paper Review] 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 Optimization32 references4 citations

TL;DR

This paper proposes an intelligent user clustering and robust beamforming design for UAV-NOMA downlink systems under imperfect channel state information (CSI). It uses a k-means++-based clustering algorithm and a semidefinite relaxation (SDR)-based beamforming method with theoretical rank-one solution guarantees, enabling decentralized, low-complexity, and power-efficient transmission while ensuring QoS under CSI uncertainty.

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.

Motivation & Objective

• Address the joint user clustering and robust beamforming design problem in UAV-NOMA downlink systems with imperfect CSI.
• Minimize total transmission power while guaranteeing quality of service (QoS) for all users under CSI uncertainty.
• Reduce computational complexity by decomposing the joint problem into user clustering and beamforming subproblems.
• Enable decentralized beamforming design via an alternating direction method of multipliers (ADMM) algorithm.
• Provide theoretical conditions under which the SDR-based beamforming solution achieves a rank-one beamformer, ensuring practical applicability.

Proposed method

• Uses a k-means++-based unsupervised clustering algorithm that leverages user position information to form user clusters.
• Decomposes the original mixed-integer, non-convex problem into two subproblems: user clustering and robust beamforming design.
• Applies semidefinite relaxation (SDR) to transform the robust beamforming problem into a convex optimization problem with infinitely many constraints due to CSI uncertainty.
• Employs the S-Lemma to reformulate the robust constraints into linear matrix inequalities (LMIs), enabling efficient SDR-based solution.
• Derives a sufficient condition under which the SDR solution is guaranteed to be rank-one, ensuring a feasible beamformer for practical implementation.
• Develops an ADMM-based decentralized algorithm allowing UAVs to independently compute beamformers without centralized coordination.

Experimental results

Research questions

• RQ1 How can user clustering be efficiently performed in a UAV-NOMA system with spatially distributed users?
• RQ2 What is the optimal robust beamforming design under imperfect CSI in a multi-UAV, multi-user NOMA downlink system?
• RQ3 Under what conditions can the SDR-based beamforming solution achieve a rank-one beamformer, ensuring practical transmission?
• RQ4 How can the beamforming design be performed in a decentralized manner to reduce signaling overhead?
• RQ5 What is the performance gain of the proposed scheme in terms of sum power reduction and QoS guarantee under CSI uncertainty?

Key findings

• The k-means++-based clustering algorithm effectively groups users based on spatial distribution, reducing inter-cluster interference.
• The SDR-based beamforming design achieves a suboptimal solution with a theoretical guarantee of rank-one beamformers under a sufficient condition.
• The sufficient condition for rank-one solutions is derived based on the KKT conditions and the structure of the beamformer and dual variables.
• The ADMM-based decentralized algorithm enables efficient, distributed beamforming computation across UAVs with minimal coordination.
• Simulation results confirm that the proposed scheme achieves significant sum power reduction while maintaining QoS requirements under imperfect CSI.
• The robust beamforming design effectively mitigates performance degradation caused by CSI errors, especially in high-mobility or high-jitter UAV environments.