# Blind Channel Estimation and Joint Symbol Detection with Data-Driven Factor Graphs

arXiv: https://arxiv.org/abs/2401.12627 · HTML: https://mlsanity.com/paper/2401.12627/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 48 references that are in the map.
- First posted on arXiv 23 Jan 2024.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Loopy Belief Propagation for Approximate Inference: An Empirical Study](https://mlsanity.com/paper/1301.6725/) (2013)
- [Deep Learning Methods for Improved Decoding of Linear Codes](https://mlsanity.com/paper/1706.07043/) (2017)
- [Model-Driven Deep Learning for Physical Layer Communications](https://mlsanity.com/paper/1809.06059/) (2018)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences](https://mlsanity.com/paper/1609.00978/) (2016)
- [ViterbiNet: A Deep Learning Based Viterbi Algorithm for Symbol Detection](https://mlsanity.com/paper/1905.10750/) (2019)
- [Deep Learning for Wireless Communications: An Emerging Interdisciplinary Paradigm](https://mlsanity.com/paper/2007.05952/) (2020)
- [Neural Network Detection of Data Sequences in Communication Systems](https://mlsanity.com/paper/1802.02046/) (2018)
- [Discriminative and Generative Learning for Linear Estimation of Random Signals [Lecture Notes]](https://mlsanity.com/paper/2206.04432/) (2022)
- [Unsupervised Linear and Nonlinear Channel Equalization and Decoding using Variational Autoencoders](https://mlsanity.com/paper/1905.08795/) (2019)
- [Online Meta-Learning For Hybrid Model-Based Deep Receivers](https://mlsanity.com/paper/2203.14359/) (2022)
- [Data-Driven Factor Graphs for Deep Symbol Detection](https://mlsanity.com/paper/2002.00758/) (2020)
- [Low-complexity Near-optimum Symbol Detection Based on Neural Enhancement of Factor Graphs](https://mlsanity.com/paper/2203.16417/) (2022)
- [Blind Equalization and Channel Estimation in Coherent Optical Communications Using Variational Autoencoders](https://mlsanity.com/paper/2204.11776/) (2022)
- [Achievable Information Rates for Fiber Optics: Applications and Computations](https://mlsanity.com/paper/1709.10393/) (2017)
- [Neural Enhancement of Factor Graph-based Symbol Detection](https://mlsanity.com/paper/2203.03333/) (2022)
- [Learning Joint Detection, Equalization and Decoding for Short-Packet Communications](https://mlsanity.com/paper/2207.05699/) (2022)

## Built on by (most cited first, 4 of 4)

- [Data-Driven Symbol Detection for Intersymbol Interference Channels with Bursty Impulsive Noise](https://mlsanity.com/paper/2405.10814/) (2024)
- [Optimization of Iterative Blind Detection based on Expectation Maximization and Belief Propagation](https://mlsanity.com/paper/2408.02312/) (2024)
- [Robust Blind Channel Estimation for Bursty Impulsive Noise with a Constrained EM Approach](https://mlsanity.com/paper/2504.03685/) (2025)
- [Phase-Aware Code-Aided EM Algorithm for Blind Channel Estimation in PSK-Modulated OFDM](https://mlsanity.com/paper/2511.21340/) (2025)

## Abstract (arXiv)

We investigate the application of the factor graph framework for blind joint channel estimation and symbol detection on time-variant linear inter-symbol interference channels. In particular, we consider the expectation maximization (EM) algorithm for maximum likelihood estimation, which typically suffers from high complexity as it requires the computation of the symbol-wise posterior distributions in every iteration. We address this issue by efficiently approximating the posteriors using the belief propagation (BP) algorithm on a suitable factor graph. By interweaving the iterations of BP and EM, the detection complexity can be further reduced to a single BP iteration per EM step. In addition, we propose a data-driven version of our algorithm that introduces momentum in the BP updates and learns a suitable EM parameter update schedule, thereby significantly improving the performance-complexity tradeoff with a few offline training samples. Our numerical experiments demonstrate the excellent performance of the proposed blind detector and show that it even outperforms coherent BP detection in high signal-to-noise scenarios.