Optimality of the Bussgang Linear MMSE Channel Estimator for MIMO Systems with 1-Bit ADCs
Abstract
In this paper, we study the optimality of the Bussgang linear minimum mean squared error (BLMMSE) channel estimator for multiple-input multiple-output systems with 1-bit analog-to-digital converters. We compare the BLMMSE with the optimal minimum mean squared error (MMSE) channel estimator, which is generally non-linear, and we develop a novel framework based on the orthant probability of a multivariate normal distribution to compute the MMSE channel estimate. Then, we analyze the equivalence of the MMSE and BLMMSE channel estimators under specific assumptions on the channel correlation or pilot symbols. Interestingly, the BLMMSE channel estimator turns out to be optimal in several specific cases. Our study culminates with the presentation of a necessary and sufficient condition for the BLMMSE channel estimator to be optimal.
Keywords
Cite
@article{arxiv.2407.13921,
title = {Optimality of the Bussgang Linear MMSE Channel Estimator for MIMO Systems with 1-Bit ADCs},
author = {Minhua Ding and Italo Atzeni and Antti Tölli and A. Lee Swindlehurst},
journal= {arXiv preprint arXiv:2407.13921},
year = {2024}
}
Comments
Presented at the IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) 2024