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

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.