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Statistical Precoder Design in Multi-User Systems via Graph Neural Networks and Generative Modeling

Nurettin Turan, Srikar Allaparapu, Donia Ben Amor, Benedikt Böck, Michael Joham, Wolfgang Utschick

TL;DR

The paper addresses sum-rate optimization in multi-user massive MIMO under practical constraints by introducing a GNN-based precoder framework that utilizes statistical channel information. It integrates a GMM-based limited feedback mechanism to handle approximate statistics in FDD systems, enabling flexible operation across different numbers of users and pilot overhead without retraining. Key contributions include a scalable, low-complexity GNN architecture that leverages the first-row covariance structure and a structured GMM prior for feedback, along with extensive simulations on SCM and real-world data showing superior performance to SWMMSE and DFT-based baselines, especially in low-pilot regimes. The work offers a practical pathway toward efficient, scalable precoding in future wireless systems with limited feedback and imperfect CSI, and points to future directions in alternative generative priors and end-to-end pilot optimization.

Abstract

This letter proposes a graph neural network (GNN)-based framework for statistical precoder design that leverages model-based insights to compactly represent statistical knowledge, resulting in efficient, lightweight architectures. The framework also supports approximate statistical information in frequency division duplex (FDD) systems obtained through a Gaussian mixture model (GMM)-based limited feedback scheme in massive multiple-input multiple-output (MIMO) systems with low pilot overhead. Simulations using a spatial channel model and measurement data demonstrate the effectiveness of the proposed framework. It outperforms baseline methods, including stochastic iterative algorithms and Discrete Fourier transform (DFT) codebook-based approaches, particularly in low pilot overhead systems.

Statistical Precoder Design in Multi-User Systems via Graph Neural Networks and Generative Modeling

TL;DR

The paper addresses sum-rate optimization in multi-user massive MIMO under practical constraints by introducing a GNN-based precoder framework that utilizes statistical channel information. It integrates a GMM-based limited feedback mechanism to handle approximate statistics in FDD systems, enabling flexible operation across different numbers of users and pilot overhead without retraining. Key contributions include a scalable, low-complexity GNN architecture that leverages the first-row covariance structure and a structured GMM prior for feedback, along with extensive simulations on SCM and real-world data showing superior performance to SWMMSE and DFT-based baselines, especially in low-pilot regimes. The work offers a practical pathway toward efficient, scalable precoding in future wireless systems with limited feedback and imperfect CSI, and points to future directions in alternative generative priors and end-to-end pilot optimization.

Abstract

This letter proposes a graph neural network (GNN)-based framework for statistical precoder design that leverages model-based insights to compactly represent statistical knowledge, resulting in efficient, lightweight architectures. The framework also supports approximate statistical information in frequency division duplex (FDD) systems obtained through a Gaussian mixture model (GMM)-based limited feedback scheme in massive multiple-input multiple-output (MIMO) systems with low pilot overhead. Simulations using a spatial channel model and measurement data demonstrate the effectiveness of the proposed framework. It outperforms baseline methods, including stochastic iterative algorithms and Discrete Fourier transform (DFT) codebook-based approaches, particularly in low pilot overhead systems.

Paper Structure

This paper contains 13 sections, 10 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Channel Data
  3. Data Transmission Phase
  4. Pilot Transmission Phase
  5. Channel Data
  6. Spatial Channel Model
  7. Real-World Channel Data
  8. Proposed Framework
  9. GNN-based Precoder Design given Perfect Statistics
  10. Combining GMMs and GNNs for Limited Feedback-based Precoder Design
  11. Baseline Schemes for Precoder Design
  12. Simulation Results
  13. Conclusion & Outlook

Figures (4)

  • Figure 1: Block diagram of the proposed GNN-based precoder design framework.
  • Figure 2: The sum-rate over the number of MT $J$ for a system with $B=6$ feedback bits, $n_\mathrm{p}=16$ pilots, and $\text{SNR}=10dB$ (spatial channel model).
  • Figure 3: The sum-rate over the SNR for a system with $B=6$ feedback bits, $J=16$MT, and (a) $n_\mathrm{p}=8$ pilots, or (b) $n_\mathrm{p}=16$ pilots. (spatial channel model).
  • Figure 4: The sum-rate over the SNR for a system with $B=6$ feedback bits, $J=8$MT, and $n_{\mathrm{p}}=8$ pilots (measured channel data).