An Asymptotically MSE-Optimal Estimator Based on Gaussian Mixture Models

作     者：Koller, Michael Fesl, Benedikt Turan, Nurettin Utschick, Wolfgang 

作者机构：Tech Univ Munich Methoden Signalverarbeitung D-80333 Munich Germany 

出 版 物：《IEEE TRANSACTIONS ON SIGNAL PROCESSING》 (IEEE Trans Signal Process)

年 卷 期：2022年第70卷

页      面：4109-4123页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 

基　　金：Deutsche Forschungsgemeinschaft [UT 36/21] 

主　　题：Channel estimation Probability density function Covariance matrices Statistics Numerical simulation Gaussian mixture model Signal processing algorithms Asymptotic convergence conditional mean channel estimation Gaussian mixture models machine learning spatial channel model 

摘      要：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.