An Asymptotically MSE-Optimal Estimator Based on Gaussian Mixture Models

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