In this work, we propose to utilize a variational autoencoder (VAE) for channel estimation (CE) in underdetermined (UD) systems. The basis of the method forms a recently proposed concept in which a VAE is trained on channel state information (CSI) data and used to parameterize an approximation to the mean squared error (MSE)-optimal estimator. The contributions in this work extend the existing framework from fully-determined (FD) to UD systems, which are of high practical relevance. Particularly noteworthy is the extension of the estimator variant, which does not require perfect CSI during its offline training phase. This is a significant advantage compared to most other deep learning (DL)-based CE methods, where perfect CSI during the training phase is a crucial prerequisite. Numerical simulations for hybrid and wideband systems demonstrate the excellent performance of the proposed methods compared to related estimators.

翻译：本文提出利用变分自编码器（VAE）进行欠定（UD）系统中的信道估计（CE）。该方法的基础是最近提出的一个概念，即基于信道状态信息（CSI）数据训练VAE，并用其参数化对均方误差（MSE）最优估计器的近似。本文的贡献在于将现有框架从全确定（FD）系统扩展到具有高度实际相关性的UD系统。特别值得注意的是，估计器变体的扩展在离线训练阶段不需要完美的CSI，这相较于大多数其他基于深度学习（DL）的信道估计方法（其训练阶段以完美CSI为关键前提）具有显著优势。针对混合系统和宽带系统的数值仿真表明，所提方法与相关估计器相比具有优异性能。