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 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...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2022, Vol.70, p.4109-4123
Main Authors: Koller, Michael, Fesl, Benedikt, Turan, Nurettin, Utschick, Wolfgang
Format: Article
Language:English
Subjects:
Approximation
Asymptotic convergence
Channel estimation
conditional mean channel estimation
Covariance matrices
Gaussian mixture model
Gaussian mixture models
Inverse problems
machine learning
Mathematical analysis
Numerical simulation
Probabilistic models
Probability density function
Probability density functions
Random noise
Signal processing algorithms
spatial channel model
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Summary: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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2022.3194348