  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.
