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

TL;DR

This paper introduces a GMM-based channel estimator trained on noisy, imperfect data, offering a practical alternative to traditional methods that require perfect CSI, and demonstrates robustness and near-optimal performance.

Contribution

It develops an adapted EM algorithm for fitting GMMs with imperfect training data, enabling robust channel estimation without perfect CSI.

Findings

Performs close to ideal estimators with perfect CSI

Outperforms existing ML techniques in robustness

Effective with noisy and sparse pilot data

Abstract

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.