A Penalty-Dual Learning Framework for Multi-User QoS-Constrained Beamforming

This paper investigates a novel deep learning framework for general nonconvex quality-of-service (QoS)-constrained beamforming design problems in multi-user systems. While existing deep learning-based methods have shown great success for beamforming design with simple constraints, it is still challenging to tackle more complicated QoS constraints, where the beam-formers and the wireless channels are commonly coupled. To fill this gap, this paper proposes an augmented Lagrangian based penalty-dual training algorithm, which alternatingly trains two individual neural networks to infer the beamformers and the corresponding Lagrange multipliers, respectively. This framework is then applied for learning the energy-efficient beamformers, with judiciously designed neural network architectures based on the solution structures of the problem. Simulations demonstrate the superiority of the proposed approach over both state-of-the-art deep learning and optimization-based approaches.