An Asymptotically Optimal Approximation of the Conditional Mean Channel Estimator based on Gaussian Mixture Models

TL;DR

This paper proposes a GMM-based channel estimator that approximates the optimal conditional mean estimator, converging to it as the number of GMM components increases, with promising results in numerical experiments.

Contribution

It introduces a closed-form GMM-based approximation of the conditional mean channel estimator that converges to the optimal estimator as components increase.

Findings

Estimator converges to the optimal as GMM components increase

Numerical experiments show promising estimation accuracy with few components

Analytic PDF approximation enables closed-form estimator computation

Abstract

This paper investigates a channel estimator based on Gaussian mixture models (GMMs). We fit a GMM to given channel samples to obtain an analytic probability density function (PDF) which approximates the true channel PDF. Then, a conditional mean channel estimator corresponding to this approximating PDF is computed in closed form and used as an approximation of the optimal conditional mean estimator based on the true channel PDF. This optimal estimator cannot be calculated analytically because the true channel PDF is generally not available. To motivate the GMM-based estimator, we show that it converges to the optimal conditional mean estimator as the number of GMM components is increased. In numerical experiments, a reasonable number of GMM components already shows promising estimation results.