In this manuscript, we propose to utilize the generative neural network-based variational autoencoder for channel estimation. The variational autoencoder models the underlying true but unknown channel distribution as a conditional Gaussian distribution in a novel way. The derived channel estimator exploits the internal structure of the variational autoencoder to parameterize an approximation of the mean squared error optimal estimator resulting from the conditional Gaussian channel models. We provide a rigorous analysis under which conditions a variational autoencoder-based estimator is mean squared error optimal. We then present considerations that make the variational autoencoder-based estimator practical and propose three different estimator variants that differ in their access to channel knowledge during the training and evaluation phase. In particular, the proposed estimator variant trained solely on noisy pilot observations is particularly noteworthy as it does not require access to noise-free, ground-truth channel data during training or evaluation. Extensive numerical simulations first analyze the internal behavior of the variational autoencoder-based estimators and then demonstrate excellent channel estimation performance compared to related classical and machine learning-based state-of-the-art channel estimators.

翻译：本文提出利用基于生成神经网络的变分自编码器进行信道估计。变分自编码器以一种新颖的方式将底层真实但未知的信道分布建模为条件高斯分布。所推导的信道估计器利用变分自编码器的内部结构对条件高斯信道模型下的均方误差最优估计器进行参数化近似。我们严格分析了变分自编码器估计器在何种条件下能达到均方误差最优。随后提出了使基于变分自编码器的估计器具有实用性的考量，并设计了三种在训练和评估阶段信道知识获取方式不同的估计器变体。其中，一种仅基于含噪导频观测训练的估计器变体尤为值得关注，它不需要在训练或评估阶段获取无噪声的真实信道数据。大量数值仿真首先分析了基于变分自编码器的估计器的内部行为，然后展示了其相比相关经典和基于机器学习的先进信道估计器具有优异的信道估计性能。