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

arXiv: https://arxiv.org/abs/2509.06395 · HTML: https://mlsanity.com/paper/2509.06395/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Builds on (most cited first, 11 of 11)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019)
- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Graph Neural Networks for Scalable Radio Resource Management: Architecture Design and Theoretical Analysis](https://mlsanity.com/paper/2007.07632/) (2020)
- [Learning Optimal Resource Allocations in Wireless Systems](https://mlsanity.com/paper/1807.08088/) (2018)
- [Towards Optimal Power Control via Ensembling Deep Neural Networks](https://mlsanity.com/paper/1807.10025/) (2018)
- [Deep Reinforcement Learning-Based Channel Allocation for Wireless LANs with Graph Convolutional Networks](https://mlsanity.com/paper/1905.07144/) (2019)
- [Decentralized Channel Management in WLANs with Graph Neural Networks](https://mlsanity.com/paper/2210.16949/) (2022)
- [Graph Neural Networks for Power Allocation in Wireless Networks with Full Duplex Nodes](https://mlsanity.com/paper/2303.16113/) (2023)
- [Flex-Net: A Graph Neural Network Approach to Resource Management in Flexible Duplex Networks](https://mlsanity.com/paper/2301.11166/) (2023)
- [GNN-Based Joint Channel and Power Allocation in Heterogeneous Wireless Networks](https://mlsanity.com/paper/2408.03957/) (2024)

## Abstract (arXiv)

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.