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A GNN Approach for Cell-Free Massive MIMO

Lou Salaun, Hong Yang, Shashwat Mishra, Chung Shue Chen

TL;DR

This work tackles the challenge of fast, fair downlink power control in cell-free massive MIMO with MRT precoding, where traditional SOCP-based solutions are computationally prohibitive for dynamic networks. It introduces a heterogeneous graph neural network that exploits permutation equivariance, representing the problem as MK nodes with AP- and UE-based interactions and using a graph transformer with multi-head attention. The GNN achieves near-optimal per-user SINR across diverse system sizes and deployment morphologies, while delivering substantially lower runtime than SOCP and better scalability than CNN-based approaches. Practically, the method enables real-time, scalable downlink power control in CFmMIMO, with strong generalization and competitive spectral efficiency improvements.

Abstract

Beyond 5G wireless technology Cell-Free Massive MIMO (CFmMIMO) downlink relies on carefully designed precoders and power control to attain uniformly high rate coverage. Many such power control problems can be calculated via second order cone programming (SOCP). In practice, several order of magnitude faster numerical procedure is required because power control has to be rapidly updated to adapt to changing channel conditions. We propose a Graph Neural Network (GNN) based solution to replace SOCP. Specifically, we develop a GNN to obtain downlink max-min power control for a CFmMIMO with maximum ratio transmission (MRT) beamforming. We construct a graph representation of the problem that properly captures the dominant dependence relationship between access points (APs) and user equipments (UEs). We exploit a symmetry property, called permutation equivariance, to attain training simplicity and efficiency. Simulation results show the superiority of our approach in terms of computational complexity, scalability and generalizability for different system sizes and deployment scenarios.

A GNN Approach for Cell-Free Massive MIMO

TL;DR

This work tackles the challenge of fast, fair downlink power control in cell-free massive MIMO with MRT precoding, where traditional SOCP-based solutions are computationally prohibitive for dynamic networks. It introduces a heterogeneous graph neural network that exploits permutation equivariance, representing the problem as MK nodes with AP- and UE-based interactions and using a graph transformer with multi-head attention. The GNN achieves near-optimal per-user SINR across diverse system sizes and deployment morphologies, while delivering substantially lower runtime than SOCP and better scalability than CNN-based approaches. Practically, the method enables real-time, scalable downlink power control in CFmMIMO, with strong generalization and competitive spectral efficiency improvements.

Abstract

Beyond 5G wireless technology Cell-Free Massive MIMO (CFmMIMO) downlink relies on carefully designed precoders and power control to attain uniformly high rate coverage. Many such power control problems can be calculated via second order cone programming (SOCP). In practice, several order of magnitude faster numerical procedure is required because power control has to be rapidly updated to adapt to changing channel conditions. We propose a Graph Neural Network (GNN) based solution to replace SOCP. Specifically, we develop a GNN to obtain downlink max-min power control for a CFmMIMO with maximum ratio transmission (MRT) beamforming. We construct a graph representation of the problem that properly captures the dominant dependence relationship between access points (APs) and user equipments (UEs). We exploit a symmetry property, called permutation equivariance, to attain training simplicity and efficiency. Simulation results show the superiority of our approach in terms of computational complexity, scalability and generalizability for different system sizes and deployment scenarios.
Paper Structure (13 sections, 17 equations, 4 figures, 2 tables)

This paper contains 13 sections, 17 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. Cell-Free Massive MIMO
  4. Downlink Max-Min SINR with MRT
  5. Graph Neural Network-Based Power Control
  6. Heterogeneous Graph Representation
  7. Data Preprocessing
  8. The Structure of the Neural Network
  9. Training and SINR Loss Function
  10. Numerical Results
  11. Comparison of GNN and CNN
  12. GNN Spectral Efficiency and Complexity
  13. Conclusion

Figures (4)

  • Figure 1: A typical node $\pi(m,k)=i\in V$ and its two types of neighbors
  • Figure 2: Spectral efficiency on urban scenarios
  • Figure 3: Spectral efficiency on urban scenarios with graph sizes (number of UEs and APs) that have not been seen by the GNN during training
  • Figure 4: FLOPs of GNN and SOCP as a function of $MK(M+K)$