Graph Neural Networks for Resource Allocation in Interference-limited Multi-Channel Wireless Networks with QoS Constraints

Meeting minimum data rate constraints is a significant challenge in wireless communication systems, particularly as network complexity grows. Traditional deep learning approaches often address these constraints by incorporating penalty terms into the loss function and tuning hyperparameters empirically. However, this heuristic treatment offers no theoretical convergence guarantees and frequently fails to satisfy QoS requirements in practical scenarios. Building upon the structure of the WMMSE algorithm, we first extend it to a multi-channel setting with QoS constraints, resulting in the enhanced WMMSE (eWMMSE) algorithm, which is provably convergent to a locally optimal solution when the problem is feasible. To further reduce computational complexity and improve scalability, we develop a GNN-based algorithm, JCPGNN-M, capable of supporting simultaneous multi-channel allocation per user. To overcome the limitations of traditional deep learning methods, we propose a principled framework that integrates GNN with a Lagrangian-based primal-dual optimization method. By training the GNN within the Lagrangian framework, we ensure satisfaction of QoS constraints and convergence to a stationary point. Extensive simulations demonstrate that JCPGNN-M matches the performance of eWMMSE while offering significant gains in inference speed, generalization to larger networks, and robustness under imperfect channel state information. This work presents a scalable and theoretically grounded solution for constrained resource allocation in future wireless networks.