In this letter, we propose a Gaussian mixture model (GMM)-based channel estimator which is learned on imperfect training data, i.e., the training data are solely comprised of noisy and sparsely allocated pilot observations. In a practical application, recent pilot observations at the base station (BS) can be utilized for training. This is in sharp contrast to state-of-theart machine learning (ML) techniques where a training dataset consisting of perfect channel state information (CSI) samples is a prerequisite, which is generally unaffordable. In particular, we propose an adapted training procedure for fitting the GMM which is a generative model that represents the distribution of all potential channels associated with a specific BS cell. To this end, the necessary modifications of the underlying expectation-maximization (EM) algorithm are derived. Numerical results show that the proposed estimator performs close to the case where perfect CSI is available for the training and exhibits a higher robustness against imperfections in the training data as compared to state-of-the-art ML techniques.

翻译：本文提出一种基于高斯混合模型（GMM）的信道估计器，该估计器利用不完美训练数据进行学习，即训练数据仅包含含噪声且稀疏分配的导频观测值。在实际应用中，基站（BS）处最近的导频观测值可用于训练。这与现有机器学习（ML）技术形成鲜明对比：后者要求训练数据集包含完美的信道状态信息（CSI）样本作为先决条件，而这通常难以实现。具体而言，我们提出了一种适配的训练流程来拟合GMM——这是一种生成模型，可表示与特定BS小区相关的所有潜在信道的分布。为此，推导了底层期望最大化（EM）算法所需的必要修正。数值结果表明，所提估计器的性能接近于使用完美CSI进行训练的情况，并且与现有ML技术相比，其对训练数据中的不完美性表现出更高的鲁棒性。