Variational Autoencoder for Channel Estimation: Real-World Measurement Insights

TL;DR

This work tackles the challenge of accurate channel estimation in real-world scenarios by proposing a variational autoencoder (VAE) based estimator that learns an approximate MMSE predictor from noisy observations alone. The method parameterizes the conditional mean and covariance of the channel via a latent variable z, enabling an MMSE-like estimator $\hat{h}_{VAE}(y) = t_\theta(z=\mu_\phi(y),y)$ with $t_\theta(z,y) = \mu_\theta(z) + C_\theta(z)(C_\theta(z) + \varsigma^2 I)^{-1}(y - \mu_\theta(z))$. The approach is evaluated on real measurement data and synthetic QuaDRiGa data, showing significant performance gains over state-of-the-art estimators on real data, while synthetic pretraining substantially reduces the amount of measurement data required for high-quality estimates. The results highlight the practical potential of MB-DL with VAEs for real-world channel estimation and the value of synthetic data to mitigate data collection costs in wireless deployments, with site-specific considerations evident in cross-dataset transfers.

Abstract

This work utilizes a variational autoencoder for channel estimation and evaluates it on real-world measurements. The estimator is trained solely on noisy channel observations and parameterizes an approximation to the mean squared error-optimal estimator by learning observation-dependent conditional first and second moments. The proposed estimator significantly outperforms related state-of-the-art estimators on real-world measurements. We investigate the effect of pre-training with synthetic data and find that the proposed estimator exhibits comparable results to the related estimators if trained on synthetic data and evaluated on the measurement data. Furthermore, pre-training on synthetic data also helps to reduce the required measurement training dataset size.

Figures (6)

• Figure 1: Structure of a VAE with CG distributions $q_{{\bm{\phi}}}({\bm{z}}{\,|\,}{\bm{y}})$ and $p_{{\bm{\theta}}}({\bm{y}}{\,|\,}{\bm{z}})$. The encoder and decoder represent dnn.
• Figure 2: Measurement setup on the Nokia campus in Stuttgart, Germany.
• Figure 3: nmse for different numbers of training samples at an SNR of 20 dB for the measurement data channels.
• Figure 4: Evaluation of the nmse for the measurement test dataset. The proposed methods are displayed with solid linestyles.
• Figure 5: Evaluation of the nmse for the measurement test dataset, which were pre-trained on QuaDRiGa channel data.