Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Learning to Unfold Fractional Programming for Multi-Cell MU-MIMO Beamforming with Graph Neural Networks

Zihan Jiao, Xinping Yi, Shi Jin

TL;DR

This work tackles weighted sum-rate beamforming in multi-cell MU-MIMO by enhancing fractional programming (FP) with a graph neural network (GNN) based unfolding. It introduces GNNFP, which reformulates the FP beamforming update into a standard quadratic form and solves it with a structure-aware GNN that shares parameters across iterations, enabling generalization to varying problem sizes and iteration counts. Empirical results show GNNFP achieves near FP performance with significantly faster convergence, smaller model size, and robust generalization across different numbers of users per cell, outperforming FastFP and DeepFP in early iterations. The approach offers a practical, scalable learning-based framework for constrained multi-variable quadratic programs in wireless beamforming.

Abstract

In the multi-cell multiuser multi-input multi-output (MU-MIMO) systems, fractional programming (FP) has demonstrated considerable effectiveness in optimizing beamforming vectors, yet it suffers from high computational complexity. Recent improvements demonstrate reduced complexity by avoiding large-dimension matrix inversions (i.e., FastFP) and faster convergence by learning to unfold the FastFP algorithm (i.e., DeepFP).

Learning to Unfold Fractional Programming for Multi-Cell MU-MIMO Beamforming with Graph Neural Networks

TL;DR

This work tackles weighted sum-rate beamforming in multi-cell MU-MIMO by enhancing fractional programming (FP) with a graph neural network (GNN) based unfolding. It introduces GNNFP, which reformulates the FP beamforming update into a standard quadratic form and solves it with a structure-aware GNN that shares parameters across iterations, enabling generalization to varying problem sizes and iteration counts. Empirical results show GNNFP achieves near FP performance with significantly faster convergence, smaller model size, and robust generalization across different numbers of users per cell, outperforming FastFP and DeepFP in early iterations. The approach offers a practical, scalable learning-based framework for constrained multi-variable quadratic programs in wireless beamforming.

Abstract

In the multi-cell multiuser multi-input multi-output (MU-MIMO) systems, fractional programming (FP) has demonstrated considerable effectiveness in optimizing beamforming vectors, yet it suffers from high computational complexity. Recent improvements demonstrate reduced complexity by avoiding large-dimension matrix inversions (i.e., FastFP) and faster convergence by learning to unfold the FastFP algorithm (i.e., DeepFP).
Paper Structure (15 sections, 31 equations, 1 figure, 2 tables)

This paper contains 15 sections, 31 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. FP-Based Algorithms
  4. Classical FP Algorithm FPPart1FPPart2
  5. FastFP Algorithm FastFP
  6. DeepFP Algorithm DeepFP
  7. Proposed GNNFP Algorithm
  8. Problem Reformulation
  9. GNN Structure Design
  10. Experimental Results
  11. Experimental Setup
  12. WSR Comparison with Other FP-based Algorithms
  13. Computational and Model Size Evaluation
  14. Generalization Performance
  15. Conclusion

Figures (1)

  • Figure 1: The weighted Sum-Rate performance of 4 FP-Based algorithms