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Learning-based Multiuser Beamforming for Holographic MIMO~Systems

Shiyong Chen, Shengqian Han

TL;DR

This paper tackles the challenge of real-time beamforming in HMIMO downlinks by deriving a learning-based policy that exploits permutation equivariance. It introduces a gradient-based GNN (GGNN) that learns an equivalent beamformer $\mathbf{V}_{e}=\mathbf{M}_{\mathrm{p}}\mathbf{V}$, followed by two projection modules to recover the digital beamformer while satisfying the power constraint, thereby reducing output dimensionality and inference latency. The proposed 3DPE/PEPI-aware architecture outperforms alternating optimization and existing learning-based baselines in spectral efficiency and generalization, with notably lower inference latency. This approach enables scalable, low-latency HMIMO beamforming suitable for real-time deployment in multiuser settings.

Abstract

Holographic multiple-input multiple-output (HMIMO) is a potential technique for improving spectral efficiency (SE) while maintaining low hardware cost and power consumption. Although conventional alternating optimization (AO) methods are widely adopted for optimizing the digital and holographic beamformers, their high computational complexity hinders real-time deployment. Deep learning provides an alternative with low inference latency, where graph neural networks (GNNs) have attracted considerable attention due to their ability to exploit permutation equivariance (PE) properties. In HMIMO systems, the optimal beamforming policy exhibits PE properties across multiple dimensions, which can be leveraged by GNNs. However, designing a single GNN to exploit the PE properties in all dimensions results in large model sizes and substantial training complexity. To address this issue, we first transform the beamforming optimization problem to optimize an equivalent beamformer and the holographic beamformer. Then, we propose a novel network architecture consisting of a gradient-based graph neural network (GGNN) followed by two projection modules, which first learns the equivalent beamformer and holographic beamformer and subsequently recovers the digital beamformer from the equivalent beamformer. Simulation results demonstrate that the proposed method achieves higher SE with reduced inference latency than the AO baseline and exhibits superior generalization performance compared with existing learning-based approaches.

Learning-based Multiuser Beamforming for Holographic MIMO~Systems

TL;DR

This paper tackles the challenge of real-time beamforming in HMIMO downlinks by deriving a learning-based policy that exploits permutation equivariance. It introduces a gradient-based GNN (GGNN) that learns an equivalent beamformer , followed by two projection modules to recover the digital beamformer while satisfying the power constraint, thereby reducing output dimensionality and inference latency. The proposed 3DPE/PEPI-aware architecture outperforms alternating optimization and existing learning-based baselines in spectral efficiency and generalization, with notably lower inference latency. This approach enables scalable, low-latency HMIMO beamforming suitable for real-time deployment in multiuser settings.

Abstract

Holographic multiple-input multiple-output (HMIMO) is a potential technique for improving spectral efficiency (SE) while maintaining low hardware cost and power consumption. Although conventional alternating optimization (AO) methods are widely adopted for optimizing the digital and holographic beamformers, their high computational complexity hinders real-time deployment. Deep learning provides an alternative with low inference latency, where graph neural networks (GNNs) have attracted considerable attention due to their ability to exploit permutation equivariance (PE) properties. In HMIMO systems, the optimal beamforming policy exhibits PE properties across multiple dimensions, which can be leveraged by GNNs. However, designing a single GNN to exploit the PE properties in all dimensions results in large model sizes and substantial training complexity. To address this issue, we first transform the beamforming optimization problem to optimize an equivalent beamformer and the holographic beamformer. Then, we propose a novel network architecture consisting of a gradient-based graph neural network (GGNN) followed by two projection modules, which first learns the equivalent beamformer and holographic beamformer and subsequently recovers the digital beamformer from the equivalent beamformer. Simulation results demonstrate that the proposed method achieves higher SE with reduced inference latency than the AO baseline and exhibits superior generalization performance compared with existing learning-based approaches.
Paper Structure (14 sections, 1 theorem, 19 equations, 3 figures, 1 table)

This paper contains 14 sections, 1 theorem, 19 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Learning the Beamforming Policy with GNNs
  4. Properties of the optimal beamforming policy
  5. Problem Transformation
  6. Overall Network Architecture
  7. Design of GGNN
  8. Simulation Results
  9. Simulation Setup
  10. Learning Performance
  11. Dimension Generalizability
  12. Inference and Training Complexity
  13. Conclusions
  14. Proof of Proposition \ref{['proposition1']}

Key Result

Proposition 1

When the inputs of the beamforming policy are permuted as $\hat{\mathbf{H}}=\boldsymbol{\Pi}_{N_t}^{\mathsf{T}}\mathbf{H}\boldsymbol{\Pi}_{K}$, $\hat{\mathbf{M}}_{\mathrm{p}}=\boldsymbol{\Pi}_{N_t}^{\mathsf{T}}\mathbf{M}_{\mathrm{p}}\boldsymbol{\Pi}_{\mathrm{RF}}$, then the beamformers $\hat{\mathbf

Figures (3)

  • Figure 1: Overall network architecture.
  • Figure 2: Performance comparison under different parameters.
  • Figure 3: Generalization performance versus $K$.

Theorems & Definitions (1)

  • Proposition 1