# Unfolding WMMSE using Graph Neural Networks for Efficient Power Allocation

arXiv: https://arxiv.org/abs/2009.10812 · HTML: https://mlsanity.com/paper/2009.10812/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2020.

## Built on by (most cited first, 30 of 61)

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- [Edge Artificial Intelligence for 6G: Vision, Enabling Technologies, and Applications](https://mlsanity.com/paper/2111.12444/) (2021)
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- [Graph Neural Networks for Wireless Communications: From Theory to Practice](https://mlsanity.com/paper/2203.10800/) (2022)
- [Link Scheduling using Graph Neural Networks](https://mlsanity.com/paper/2109.05536/) (2021)
- [Graph-based Deep Learning for Communication Networks: A Survey](https://mlsanity.com/paper/2106.02533/) (2021)
- [Machine Learning for Large-Scale Optimization in 6G Wireless Networks](https://mlsanity.com/paper/2301.03377/) (2023)
- [Scalable Power Control/Beamforming in Heterogeneous Wireless Networks with Graph Neural Networks](https://mlsanity.com/paper/2104.05463/) (2021)
- [Wide and Deep Graph Neural Network with Distributed Online Learning](https://mlsanity.com/paper/2107.09203/) (2021)
- [State-Augmented Learnable Algorithms for Resource Management in Wireless Networks](https://mlsanity.com/paper/2207.02242/) (2022)
- [Modular Meta-Learning for Power Control via Random Edge Graph Neural Networks](https://mlsanity.com/paper/2108.13178/) (2021)
- [GraphMAD: Graph Mixup for Data Augmentation using Data-Driven Convex Clustering](https://mlsanity.com/paper/2210.15721/) (2022)
- [Federated Learning and Meta Learning: Approaches, Applications, and Directions](https://mlsanity.com/paper/2210.13111/) (2022)
- [Stability to Deformations of Manifold Filters and Manifold Neural Networks](https://mlsanity.com/paper/2106.03725/) (2021)
- [Stability of Neural Networks on Manifolds to Relative Perturbations](https://mlsanity.com/paper/2110.04702/) (2021)
- [Robust Stochastically-Descending Unrolled Networks](https://mlsanity.com/paper/2312.15788/) (2023)
- [Fast Power Control Adaptation via Meta-Learning for Random Edge Graph Neural Networks](https://mlsanity.com/paper/2105.00459/) (2021)
- [Graph Neural Networks Meet Wireless Communications: Motivation, Applications, and Future Directions](https://mlsanity.com/paper/2212.04047/) (2022)
- [Unsupervised Learning of Sampling Distributions for Particle Filters](https://mlsanity.com/paper/2302.01174/) (2023)
- [Message Passing Meets Graph Neural Networks: A New Paradigm for Massive MIMO Systems](https://mlsanity.com/paper/2302.06896/) (2023)
- [Node-Variant Graph Filters in Graph Neural Networks](https://mlsanity.com/paper/2106.00089/) (2021)
- [Power Allocation for Wireless Federated Learning using Graph Neural Networks](https://mlsanity.com/paper/2111.07480/) (2021)
- [A Bipartite Graph Neural Network Approach for Scalable Beamforming Optimization](https://mlsanity.com/paper/2207.05364/) (2022)
- [Deep Unfolding: Recent Developments, Theory, and Design Guidelines](https://mlsanity.com/paper/2512.03768/) (2025)
- [Deep Graph Unfolding for Beamforming in MU-MIMO Interference Networks](https://mlsanity.com/paper/2304.00446/) (2023)
- [Solving Linear Inverse Problems using Higher-Order Annealed Langevin Diffusion](https://mlsanity.com/paper/2305.05014/) (2023)
- [Stochastic Unrolled Federated Learning](https://mlsanity.com/paper/2305.15371/) (2023)
- [Graph-based Algorithm Unfolding for Energy-aware Power Allocation in Wireless Networks](https://mlsanity.com/paper/2201.11799/) (2022)
- [ENGNN: A General Edge-Update Empowered GNN Architecture for Radio Resource Management in Wireless Networks](https://mlsanity.com/paper/2301.00757/) (2022)
- [Unrolling Particles: Unsupervised Learning of Sampling Distributions](https://mlsanity.com/paper/2110.02915/) (2021)

## Abstract (arXiv)

We study the problem of optimal power allocation in a single-hop ad hoc wireless network. In solving this problem, we depart from classical purely model-based approaches and propose a hybrid method that retains key modeling elements in conjunction with data-driven components. More precisely, we put forth a neural network architecture inspired by the algorithmic unfolding of the iterative weighted minimum mean squared error (WMMSE) method, that we denote by unfolded WMMSE (UWMMSE). The learnable weights within UWMMSE are parameterized using graph neural networks (GNNs), where the time-varying underlying graphs are given by the fading interference coefficients in the wireless network. These GNNs are trained through a gradient descent approach based on multiple instances of the power allocation problem. We show that the proposed architecture is permutation equivariant, thus facilitating generalizability across network topologies. Comprehensive numerical experiments illustrate the performance attained by UWMMSE along with its robustness to hyper-parameter selection and generalizability to unseen scenarios such as different network densities and network sizes.