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.

中文翻译：

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基于高斯混合模型的渐近MSE最优估计器


本文在具有加性高斯噪声的线性逆问题的背景下研究了基于高斯混合模型 (GMM) 的信道估计器。我们将 GMM 拟合给定的通道样本，以获得近似于真实通道 PDF 的解析概率密度函数 (PDF)。然后，以封闭形式计算与该近似PDF相对应的条件均值估计器（CME），并将其用作基于真实通道PDF的最佳CME的近似。这个最佳 CME 无法通过分析计算，因为真实的通道 PDF 通常是未知的。我们提出了温和的条件，使我们能够证明随着 GMM 分量数量的增加，基于 GMM 的 CME 可以收敛到最优 CME。此外，我们研究了估计器的计算复杂性，并根据常见的基于模型的见解提出了简化。此外，我们研究了估计器在数值实验中的行为，包括多输入多输出（MIMO）和宽带系统。