An Asymptotically MSE-Optimal Estimator based on Gaussian Mixture Models

TL;DR

This paper introduces a GMM-based channel estimator that converges to the optimal estimator as the number of mixture components increases, with demonstrated effectiveness in MIMO and wideband systems.

Contribution

It proposes a novel GMM-based estimator for linear inverse problems, proving its asymptotic MSE optimality and analyzing its computational complexity.

Findings

Estimator converges to the optimal CME with increasing GMM components

Provides conditions for convergence and complexity analysis

Validates performance through numerical experiments in MIMO and wideband systems

Abstract

This paper investigates a channel estimator based on Gaussian mixture models (GMMs) in the context of linear inverse problems with additive Gaussian noise. 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 estimator (CME) corresponding to this approximating PDF is computed in closed form and used as an approximation of the optimal CME based on the true channel PDF. This optimal CME cannot be calculated analytically because the true channel PDF is generally unknown. We present mild conditions which allow us to prove the convergence of the GMM-based CME to the optimal CME as the number of GMM components is increased. Additionally, we investigate the estimator's computational complexity and present simplifications based on common model-based insights. Further, we study the estimator's behavior in numerical experiments including multiple-input multiple-output (MIMO) and wideband systems.