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）。该方法基于近期提出的概念，即通过训练VAE学习信道状态信息（CSI）数据，并参数化均方误差（MSE）最优估计器的近似解。本文的贡献在于将现有框架从全定（FD）系统扩展至具有高度实践相关性的UD系统。特别值得注意的是，本文拓展了估计器变体，其离线训练阶段无需完美CSI。相比多数基于深度学习（DL）的信道估计方法（其中训练阶段完美CSI是必要条件），这一特性构成显著优势。针对混合系统与宽带系统的数值仿真表明，所提方法相较于相关估计器具有卓越性能。