Optimality of the Bussgang Linear MMSE Channel Estimator for MIMO Systems with 1-Bit ADCs

TL;DR

This paper investigates the conditions under which the Bussgang linear MMSE channel estimator is optimal for MIMO systems with 1-bit ADCs, providing a new framework and necessary criteria for optimality.

Contribution

It introduces a novel framework based on orthant probability to compare BLMMSE with the optimal MMSE estimator and identifies conditions for BLMMSE optimality.

Findings

BLMMSE is optimal under specific channel correlation or pilot symbol assumptions.

A new orthant probability-based framework for MMSE estimation is developed.

Necessary and sufficient conditions for BLMMSE optimality are established.

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.