# Precoder Design in Multi-User FDD Systems with VQ-VAE and GNN

arXiv: https://arxiv.org/abs/2510.09495 · HTML: https://mlsanity.com/paper/2510.09495/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 10 Oct 2025.

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

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [A Vision of 6G Wireless Systems: Applications, Trends, Technologies, and Open Research Problems](https://mlsanity.com/paper/1902.10265/) (2019)
- [Blockwise Self-Supervised Learning at Scale](https://mlsanity.com/paper/2302.01647/) (2023)
- [Variational Autoencoder Leveraged MMSE Channel Estimation](https://mlsanity.com/paper/2205.05345/) (2022)
- [Multidimensional Graph Neural Networks for Wireless Communications](https://mlsanity.com/paper/2212.11531/) (2022)
- [Role of Deep Learning in Wireless Communications](https://mlsanity.com/paper/2210.02596/) (2022)
- [Learning the CSI Denoising and Feedback Without Supervision](https://mlsanity.com/paper/2104.05002/) (2021)
- [Evaluation of a Gaussian Mixture Model-based Channel Estimator using Measurement Data](https://mlsanity.com/paper/2207.14150/) (2022)
- [A Statistical Characterization of Wireless Channels Conditioned on Side Information](https://mlsanity.com/paper/2406.04282/) (2024)
- [Millimeter-Wave Beamformed Full-dimensional MIMO Channel Estimation Based on Atomic Norm Minimization](https://mlsanity.com/paper/1709.03843/) (2017)
- [Feedback Design with VQ-VAE for Robust Precoding in Multi-User FDD Systems](https://mlsanity.com/paper/2408.04505/) (2024)
- [Statistical Precoder Design in Multi-User Systems via Graph Neural Networks and Generative Modeling](https://mlsanity.com/paper/2412.07519/) (2024)

## Abstract (arXiv)

Robust precoding is efficiently feasible in frequency division duplex (FDD) systems by incorporating the learnt statistics of the propagation environment through a generative model. We build on previous work that successfully designed site-specific precoders based on a combination of Gaussian mixture models (GMMs) and graph neural networks (GNNs). In this paper, by utilizing a vector quantized-variational autoencoder (VQ-VAE), we circumvent one of the key drawbacks of GMMs, i.e., the number of GMM components scales exponentially to the feedback bits. In addition, the deep learning architecture of the VQ-VAE allows us to jointly train the GNN together with VQ-VAE along with pilot optimization forming an end-to-end (E2E) model, resulting in considerable performance gains in sum rate for multi-user wireless systems. Simulations demonstrate the superiority of the proposed frameworks over the conventional methods involving the sub-discrete Fourier transform (DFT) pilot matrix and iterative precoder algorithms enabling the deployment of systems characterized by fewer pilots or feedback bits.