# Variational Bayes for Joint Channel Estimation and Data Detection in Few-Bit Massive MIMO Systems

arXiv: https://arxiv.org/abs/2212.01717 · HTML: https://mlsanity.com/paper/2212.01717/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 4 Dec 2022.

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

- [LoRD-Net: Unfolded Deep Detection Network with Low-Resolution Receivers](https://mlsanity.com/paper/2102.02993/) (2021)
- [White Paper on Broadband Connectivity in 6G](https://mlsanity.com/paper/2004.14247/) (2020)
- [SVM-based Channel Estimation and Data Detection for One-Bit Massive MIMO Systems](https://mlsanity.com/paper/2003.10678/) (2020)
- [Linear and Deep Neural Network-based Receivers for Massive MIMO Systems with One-Bit ADCs](https://mlsanity.com/paper/2008.03757/) (2020)
- [Robust Data Detection for MIMO Systems with One-Bit ADCs: A Reinforcement Learning Approach](https://mlsanity.com/paper/1903.12546/) (2019)
- [Deep Learning for Estimation and Pilot Signal Design in Few-Bit Massive MIMO Systems](https://mlsanity.com/paper/2107.11958/) (2021)
- [Gridless Variational Bayesian Channel Estimation for Antenna Array Systems with Low Resolution ADCs](https://mlsanity.com/paper/1906.00576/) (2019)
- [Neural Network-Optimized Channel Estimator and Training Signal Design for MIMO Systems with Few-Bit ADCs](https://mlsanity.com/paper/2003.09007/) (2020)
- [A Variational Bayesian Perspective on Massive MIMO Detection](https://mlsanity.com/paper/2205.11649/) (2022)
- [Linearized Binary Regression](https://mlsanity.com/paper/1802.00430/) (2018)
- [Supervised and Semi-Supervised Learning for MIMO Blind Detection with Low-Resolution ADCs](https://mlsanity.com/paper/1906.04090/) (2019)
- [A Simple Variational Bayes Detector for Orthogonal Time Frequency Space (OTFS) Modulation](https://mlsanity.com/paper/1911.12538/) (2019)

## Built on by (most cited first, 2 of 2)

- [MIMO Detection with Spatial Sigma-Delta ADCs: A Variational Bayesian Approach](https://mlsanity.com/paper/2410.03891/) (2024)
- [Variational Bayesian Channel Estimation and Data Detection for Cell-Free Massive MIMO with Low-Resolution Quantized Fronthaul Links](https://mlsanity.com/paper/2506.18863/) (2025)

## Abstract (arXiv)

Massive multiple-input multiple-output (MIMO) communications using low-resolution analog-to-digital converters (ADCs) is a promising technology for providing high spectral and energy efficiency with affordable hardware cost and power consumption. However, the use of low-resolution ADCs requires special signal processing methods for channel estimation and data detection since the resulting system is severely non-linear. This paper proposes joint channel estimation and data detection methods for massive MIMO systems with low-resolution ADCs based on the variational Bayes (VB) inference framework. We first derive matched-filter quantized VB (MF-QVB) and linear minimum mean-squared error quantized VB (LMMSE-QVB) detection methods assuming the channel state information (CSI) is available. Then we extend these methods to the joint channel estimation and data detection (JED) problem and propose two methods we refer to as MF-QVB-JED and LMMSE-QVB-JED. Unlike conventional VB-based detection methods that assume knowledge of the second-order statistics of the additive noise, we propose to float the noise variance/covariance matrix as an unknown random variable that is used to account for both the noise and the residual inter-user interference. We also present practical aspects of the QVB framework to improve its implementation stability. Finally, we show via numerical results that the proposed VB-based methods provide robust performance and also significantly outperform existing methods.