# Learning a Gaussian Mixture Model from Imperfect Training Data for Robust Channel Estimation

arXiv: https://arxiv.org/abs/2301.06488 · HTML: https://mlsanity.com/paper/2301.06488/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2023.

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

- [Channel Estimation for Quantized Systems based on Conditionally Gaussian Latent Models](https://mlsanity.com/paper/2309.04014/) (2023)
- [STAR-RIS-assisted Collaborative Beamforming for Low-altitude Wireless Networks](https://mlsanity.com/paper/2510.22108/) (2025)

## Abstract (arXiv)

In this letter, we propose a Gaussian mixture model (GMM)-based channel estimator which is learned on imperfect training data, i.e., the training data are solely comprised of noisy and sparsely allocated pilot observations. In a practical application, recent pilot observations at the base station (BS) can be utilized for training. This is in sharp contrast to state-of-theart machine learning (ML) techniques where a training dataset consisting of perfect channel state information (CSI) samples is a prerequisite, which is generally unaffordable. In particular, we propose an adapted training procedure for fitting the GMM which is a generative model that represents the distribution of all potential channels associated with a specific BS cell. To this end, the necessary modifications of the underlying expectation-maximization (EM) algorithm are derived. Numerical results show that the proposed estimator performs close to the case where perfect CSI is available for the training and exhibits a higher robustness against imperfections in the training data as compared to state-of-the-art ML techniques.