# Gridless Variational Bayesian Channel Estimation for Antenna Array Systems with Low Resolution ADCs

## TL;DR

This paper introduces a grid-less variational Bayesian method for channel estimation in mm-wave antenna systems with low-resolution ADCs, effectively handling sparse angular channels without grid mismatch issues.

## Contribution

It proposes the GL-QVBCE algorithm, a novel grid-less Bayesian approach that outperforms traditional methods and approaches the CRB in low-resolution ADC scenarios.

## Key findings

- GL-QVBCE outperforms least squares in simulations.
- The algorithm approaches the Cramér Rao bound asymptotically.
- Effective for sparse mm-wave channel estimation with low-res ADCs.

## Abstract

Employing low-resolution analog-to-digital converters (ADCs) coupled with large antenna arrays at the receivers has drawn considerable interests in the millimeter wave (mm-wave) system. Since mm-wave channels are sparse in angular dimensions, exploiting the structure could reduce the number of measurements while achieve acceptable performance at the same time. Motivated by the variational Bayesian line spectral estimation (VALSE) algorithm which treats the angles as random parameters, in contrast with previous works which confine the estimate to the set of grid angle points and induce grid mismatch, this paper proposes the grid-less quantized variational Bayesian channel estimation (GL-QVBCE) algorithm for antenna array systems with low resolution ADCs. Compared to the traditional least squares (LS) approach, numerical results show that GL-QVBCE performs significantly better and asymptotically approaches the Cram\`{e}r Rao bound (CRB).