# Learning Optimal Linear Precoding for Cell-Free Massive MIMO with GNN

arXiv: https://arxiv.org/abs/2406.04456 · HTML: https://mlsanity.com/paper/2406.04456/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 24 references that are in the map.
- First posted on arXiv 6 Jun 2024.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Degree-Quant: Quantization-Aware Training for Graph Neural Networks](https://mlsanity.com/paper/2008.05000/) (2020)
- [Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks](https://mlsanity.com/paper/1909.01865/) (2019)
- [Graph Neural Networks for Wireless Communications: From Theory to Practice](https://mlsanity.com/paper/2203.10800/) (2022)
- [Scalable Cell-Free Massive MIMO Systems](https://mlsanity.com/paper/1908.03119/) (2019)
- [Heterogeneous graph neural network for power allocation in multicarrier-division duplex cell-free massive MIMO systems](https://mlsanity.com/paper/2205.00546/) (2022)
- [A GNN Approach for Cell-Free Massive MIMO](https://mlsanity.com/paper/2403.12062/) (2024)
- [Joint User Association and Power Control for Cell-Free Massive MIMO](https://mlsanity.com/paper/2401.02701/) (2024)
- [Energy-Efficient Power Allocation in Cell-Free Massive MIMO via Graph Neural Networks](https://mlsanity.com/paper/2401.14281/) (2024)
- [Joint optimal beamforming and power control in cell-free massive MIMO](https://mlsanity.com/paper/2208.01385/) (2022)

## Abstract (arXiv)

We develop a graph neural network (GNN) to compute, within a time budget of 1 to 2 milliseconds required by practical systems, the optimal linear precoder (OLP) maximizing the minimal downlink user data rate for a Cell-Free Massive MIMO system - a key 6G wireless technology. The state-of-the-art method is a bisection search on second order cone programming feasibility test (B-SOCP) which is a magnitude too slow for practical systems. Our approach relies on representing OLP as a node-level prediction task on a graph. We construct a graph that accurately captures the interdependence relation between access points (APs) and user equipments (UEs), and the permutation equivariance of the Max-Min problem. Our neural network, named OLP-GNN, is trained on data obtained by B-SOCP. We tailor the OLP-GNN size, together with several artful data preprocessing and postprocessing methods to meet the runtime requirement. We show by extensive simulations that it achieves near optimal spectral efficiency in a range of scenarios with different number of APs and UEs, and for both line-of-sight and non-line-of-sight radio propagation environments.