# Deep Graph Unfolding for Beamforming in MU-MIMO Interference Networks

arXiv: https://arxiv.org/abs/2304.00446 · HTML: https://mlsanity.com/paper/2304.00446/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 61 references that are in the map.
- First posted on arXiv 2 Apr 2023.

## Builds on (most cited first, 30 of 33)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Network In Network](https://mlsanity.com/paper/1312.4400/) (2013)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks](https://mlsanity.com/paper/1909.01865/) (2019)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [Unfolding WMMSE using Graph Neural Networks for Efficient Power Allocation](https://mlsanity.com/paper/2009.10812/) (2020)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)
- [Deep Unfolding for Communications Systems: A Survey and Some New Directions](https://mlsanity.com/paper/1906.05774/) (2019)
- [Deep Unfolded Robust PCA with Application to Clutter Suppression in Ultrasound](https://mlsanity.com/paper/1811.08252/) (2018)
- [Iterative Algorithm Induced Deep-Unfolding Neural Networks: Precoding Design for Multiuser MIMO Systems](https://mlsanity.com/paper/2006.08099/) (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 Learning Markov Random Field for Semantic Segmentation](https://mlsanity.com/paper/1606.07230/) (2016)
- [Link Scheduling using Graph Neural Networks](https://mlsanity.com/paper/2109.05536/) (2021)
- [Deep Learning based Wireless Resource Allocation with Application to Vehicular Networks](https://mlsanity.com/paper/1907.03289/) (2019)
- [Sampling of graph signals with successive local aggregations](https://mlsanity.com/paper/1504.04687/) (2015)
- [Annealed Langevin Dynamics for Massive MIMO Detection](https://mlsanity.com/paper/2205.05776/) (2022)
- [An Algorithm Unrolling Approach to Deep Image Deblurring](https://mlsanity.com/paper/1902.05399/) (2019)
- [Data-Driven Symbol Detection via Model-Based Machine Learning](https://mlsanity.com/paper/2002.07806/) (2020)
- [Coordinated Sum-Rate Maximization in Multicell MU-MIMO with Deep Unrolling](https://mlsanity.com/paper/2202.10371/) (2022)
- [Unsupervised Learning of Sampling Distributions for Particle Filters](https://mlsanity.com/paper/2302.01174/) (2023)
- [Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer?](https://mlsanity.com/paper/1403.6150/) (2014)
- [Learning to Continuously Optimize Wireless Resource In Episodically Dynamic Environment](https://mlsanity.com/paper/2011.07782/) (2020)
- [Efficient power allocation using graph neural networks and deep algorithm unfolding](https://mlsanity.com/paper/2012.02250/) (2020)
- [ML-aided power allocation for Tactical MIMO](https://mlsanity.com/paper/2109.06992/) (2021)

## Built on by (most cited first, 6 of 6)

- [Deep Unfolding: Recent Developments, Theory, and Design Guidelines](https://mlsanity.com/paper/2512.03768/) (2025)
- [Biased Backpressure Routing Using Link Features and Graph Neural Networks](https://mlsanity.com/paper/2407.09753/) (2024)
- [Generative Diffusion Models of Stochastic Graph Signals](https://mlsanity.com/paper/2607.06833/) (2026)
- [Learning Non-myopic Power Allocation in Constrained Scenarios](https://mlsanity.com/paper/2401.10297/) (2024)
- [Adaptive Anomaly Detection in Network Flows with Low-Rank Tensor Decompositions and Deep Unrolling](https://mlsanity.com/paper/2409.11529/) (2024)
- [Agentic AI for Bilevel Long-Term Optimization of Policy-Driven Physical Layer Systems](https://mlsanity.com/paper/2606.24416/) (2026)

## Abstract (arXiv)

We develop an efficient and near-optimal solution for beamforming in multi-user multiple-input-multiple-output single-hop wireless ad-hoc interference networks. Inspired by the weighted minimum mean squared error (WMMSE) method, a classical approach to solving this problem, and the principle of algorithm unfolding, we present unfolded WMMSE (UWMMSE) for MU-MIMO. This method learns a parameterized functional transformation of key WMMSE parameters using graph neural networks (GNNs), where the channel and interference components of a wireless network constitute the underlying graph. These GNNs are trained through gradient descent on a network utility metric using multiple instances of the beamforming problem. Comprehensive experimental analyses illustrate the superiority of UWMMSE over the classical WMMSE and state-of-the-art learning-based methods in terms of performance, generalizability, and robustness.