# Stability Analysis of Unfolded WMMSE for Power Allocation

arXiv: https://arxiv.org/abs/2110.07471 · HTML: https://mlsanity.com/paper/2110.07471/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 14 Oct 2021.

## Builds on (most cited first, 18 of 18)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks](https://mlsanity.com/paper/1909.01865/) (2019)
- [Graph Neural Networks: Architectures, Stability and Transferability](https://mlsanity.com/paper/2008.01767/) (2020)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Unfolding WMMSE using Graph Neural Networks for Efficient Power Allocation](https://mlsanity.com/paper/2009.10812/) (2020)
- [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)
- [HodgeNet: Graph Neural Networks for Edge Data](https://mlsanity.com/paper/1912.02354/) (2019)
- [Distributed Scheduling using Graph Neural Networks](https://mlsanity.com/paper/2011.09430/) (2020)
- [A Graph Neural Network Approach for Scalable Wireless Power Control](https://mlsanity.com/paper/1907.08487/) (2019)
- [Adaptive Contention Window Design using Deep Q-learning](https://mlsanity.com/paper/2011.09418/) (2020)
- [Data-Driven Symbol Detection via Model-Based Machine Learning](https://mlsanity.com/paper/2002.07806/) (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)
- [Deep unfolding of the weighted MMSE beamforming algorithm](https://mlsanity.com/paper/2006.08448/) (2020)

## Built on by (most cited first, 2 of 2)

- [Deep Graph Unfolding for Beamforming in MU-MIMO Interference Networks](https://mlsanity.com/paper/2304.00446/) (2023)
- [Learning Non-myopic Power Allocation in Constrained Scenarios](https://mlsanity.com/paper/2401.10297/) (2024)

## Abstract (arXiv)

Power allocation is one of the fundamental problems in wireless networks and a wide variety of algorithms address this problem from different perspectives. A common element among these algorithms is that they rely on an estimation of the channel state, which may be inaccurate on account of hardware defects, noisy feedback systems, and environmental and adversarial disturbances. Therefore, it is essential that the output power allocation of these algorithms is stable with respect to input perturbations, to the extent that the variations in the output are bounded for bounded variations in the input. In this paper, we focus on UWMMSE -- a modern algorithm leveraging graph neural networks --, and illustrate its stability to additive input perturbations of bounded energy through both theoretical analysis and empirical validation.