The Effect of Noise Correlation on MMSE Channel Estimation in One-Bit Quantized Systems

TL;DR

This paper investigates how spatially correlated noise affects MMSE channel estimation in one-bit quantized MIMO systems, deriving a new analytical expression that reveals complex impacts of noise correlation on estimation accuracy.

Contribution

It introduces a novel analytical expression for MMSE channel estimation with correlated noise in one-bit MIMO systems, considering arbitrary correlation structures.

Findings

Noise correlation can make the estimator linear despite correlation.

At low-to-medium SNR, noise correlation improves uncorrelated channel estimation.

Strong channel correlation combined with noise correlation degrades estimation performance.

Abstract

This paper analyzes the impact of spatially correlated additive noise on the minimum mean-square error (MMSE) estimation of multiple-input multiple-output (MIMO) channels from one-bit quantized observations. Although additive noise can be correlated in practical scenarios, e.g., due to jamming, clutter, or other external disturbances, the effect of such correlation on the MMSE channel estimator in this setting remains unexplored in prior work. Against this backdrop, we derive a novel analytical expression for the general MIMO MMSE channel estimator, which is inherently nonlinear in one-bit observations, and accommodates arbitrary channel and noise correlation structures. To further characterize the impact of noise correlation, we subsequently specialize the general MMSE expression to certain tractable multi antenna configurations in which both the channel and the noise assume single-parameter constant correlation structures. Our analyses reveal nontrivial, noise-correlation-induced scenarios in which the estimator remains linear despite non-zero channel and noise correlation parameters. Moreover, the results indicate that, at low-to-medium signal-to-noise ratio, noise correlation improves the MMSE performance when channels are uncorrelated, but degrades performance when channels are strongly correlated.