# Channel Estimation for Quantized Systems based on Conditionally Gaussian Latent Models

arXiv: https://arxiv.org/abs/2309.04014 · HTML: https://mlsanity.com/paper/2309.04014/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 70 references that are in the map.
- First posted on arXiv 7 Sep 2023.

## Builds on (most cited first, 16 of 16)

- [High Dimensional Channel Estimation Using Deep Generative Networks](https://mlsanity.com/paper/2006.13494/) (2020)
- [An Asymptotically MSE-Optimal Estimator based on Gaussian Mixture Models](https://mlsanity.com/paper/2112.12499/) (2021)
- [Channel Estimation for One-Bit Multiuser Massive MIMO Using Conditional GAN](https://mlsanity.com/paper/2006.11435/) (2020)
- [Variational Autoencoder Leveraged MMSE Channel Estimation](https://mlsanity.com/paper/2205.05345/) (2022)
- [Deep Learning for Massive MIMO with 1-Bit ADCs: When More Antennas Need Fewer Pilots](https://mlsanity.com/paper/1910.06960/) (2019)
- [Channel Estimation based on Gaussian Mixture Models with Structured Covariances](https://mlsanity.com/paper/2205.03634/) (2022)
- [On the Mean Square Error Optimal Estimator in One-Bit Quantized Systems](https://mlsanity.com/paper/2212.04470/) (2022)
- [Massive MIMO Channel Estimation with Low-Resolution Spatial Sigma-Delta ADCs](https://mlsanity.com/paper/2005.07752/) (2020)
- [Plug-in Channel Estimation with Dithered Quantized Signals in Spatially Non-Stationary Massive MIMO Systems](https://mlsanity.com/paper/2301.04641/) (2023)
- [Variational Inference Aided Estimation of Time Varying Channels](https://mlsanity.com/paper/2210.17177/) (2022)
- [A Versatile Low-Complexity Feedback Scheme for FDD Systems via Generative Modeling](https://mlsanity.com/paper/2304.14373/) (2023)
- [Low-Rank Structured MMSE Channel Estimation with Mixtures of Factor Analyzers](https://mlsanity.com/paper/2304.14809/) (2023)
- [Evaluation of a Gaussian Mixture Model-based Channel Estimator using Measurement Data](https://mlsanity.com/paper/2207.14150/) (2022)
- [Learning a Gaussian Mixture Model from Imperfect Training Data for Robust Channel Estimation](https://mlsanity.com/paper/2301.06488/) (2023)
- [One-Bit Covariance Reconstruction with Non-zero Thresholds: Algorithm and Performance Analysis](https://mlsanity.com/paper/2303.16455/) (2023)
- [Amplitude Retrieval for Channel Estimation of MIMO Systems with One-Bit ADCs](https://mlsanity.com/paper/1907.11904/) (2019)

## Built on by (most cited first, 5 of 5)

- [Generative Diffusion Models for High Dimensional Channel Estimation](https://mlsanity.com/paper/2408.10501/) (2024)
- [Diffusion Models for Future Networks and Communications: A Comprehensive Survey](https://mlsanity.com/paper/2508.01586/) (2025)
- [Linear and Nonlinear MMSE Estimation in One-Bit Quantized Systems under a Gaussian Mixture Prior](https://mlsanity.com/paper/2407.01305/) (2024)
- [Enhancing Channel Estimation in Quantized Systems with a Generative Prior](https://mlsanity.com/paper/2405.03542/) (2024)
- [Mixture-of-Experts Diffusion Models for Adaptive Massive MIMO Channel Estimation via Variational Bayesian Inference](https://mlsanity.com/paper/2605.18325/) (2026)

## Abstract (arXiv)

This work introduces a novel class of channel estimators tailored for coarse quantization systems. The proposed estimators are founded on conditionally Gaussian latent generative models, specifically Gaussian mixture models (GMMs), mixture of factor analyzers (MFAs), and variational autoencoders (VAEs). These models effectively learn the unknown channel distribution inherent in radio propagation scenarios, providing valuable prior information. Conditioning on the latent variable of these generative models yields a locally Gaussian channel distribution, thus enabling the application of the well-known Bussgang decomposition. By exploiting the resulting conditional Bussgang decomposition, we derive parameterized linear minimum mean square error (MMSE) estimators for the considered generative latent variable models. In this context, we explore leveraging model-based structural features to reduce memory and complexity overhead associated with the proposed estimators. Furthermore, we devise necessary training adaptations, enabling direct learning of the generative models from quantized pilot observations without requiring ground-truth channel samples during the training phase. Through extensive simulations, we demonstrate the superiority of our introduced estimators over existing state-of-the-art methods for coarsely quantized systems, as evidenced by significant improvements in mean square error (MSE) and achievable rate metrics.