Channel Estimation for Quantized Systems based on Conditionally Gaussian Latent Models

TL;DR

This paper proposes novel channel estimators for coarse quantization systems using conditionally Gaussian latent models like GMMs, MFAs, and VAEs, which improve estimation accuracy by learning the channel distribution and leveraging the Bussgang decomposition.

Contribution

It introduces a new class of estimators based on generative latent models that can be trained directly from quantized data without ground-truth channels, enhancing performance in quantized systems.

Findings

Significant MSE reduction compared to existing methods

Improved achievable rate metrics in simulations

Effective learning of channel models from quantized observations

Abstract

This work introduces a novel class of channel estimators tailored for coarse quantization systems. The proposed estimators are founded on conditionally Gaussian latent generative models, specifically Gaussian mixture models (GMMs), mixture of factor analyzers (MFAs), and variational autoencoders (VAEs). These models effectively learn the unknown channel distribution inherent in radio propagation scenarios, providing valuable prior information. Conditioning on the latent variable of these generative models yields a locally Gaussian channel distribution, thus enabling the application of the well-known Bussgang decomposition. By exploiting the resulting conditional Bussgang decomposition, we derive parameterized linear minimum mean square error (MMSE) estimators for the considered generative latent variable models. In this context, we explore leveraging model-based structural features to reduce memory and complexity overhead associated with the proposed estimators. Furthermore, we devise necessary training adaptations, enabling direct learning of the generative models from quantized pilot observations without requiring ground-truth channel samples during the training phase. Through extensive simulations, we demonstrate the superiority of our introduced estimators over existing state-of-the-art methods for coarsely quantized systems, as evidenced by significant improvements in mean square error (MSE) and achievable rate metrics.