Learning to Optimize QoS-Constrained Beamforming in Multi-User Systems: A Penalty-Dual Framework

This paper investigates a novel deep learning framework for the general nonconvex quality-of-service (QoS)-constrained beamforming design problems in multi-user systems. While existing deep learning-based approaches have shown great success for various power allocation and beamforming design problems, most of the considered problems are equipped with simple constraints (e.g., power budget constraints), which can be satisfied by a simple projection operation. However, it is still a challenge to tackle the more complicated QoS constraints, in which the beamformers and the wireless channels are commonly coupled. To fill this gap, this paper proposes an augmented Lagrangian based penalty-dual training algorithm, which trains two individual neural networks for inferring the beamformers and the corresponding Lagrange multipliers alternatingly. Furthermore, we apply the proposed penalty-dual learning framework to optimize the energy-efficient unicast beamformers and the power-minimized multicast beamformers, respectively. The neural network architectures are judiciously designed based on the solution structures of the two problems. Simulation results on the two applications demonstrate that the proposed penalty-dual approach outperforms state-of-the-art learning approaches and optimization-based algorithms in terms of the constraint violation and the computational time, respectively.