Optimal Correlation Estimators for Quantized Signals

TL;DR

This paper derives optimal correlation estimators for quantized Gaussian signals using maximum-likelihood, addressing issues with traditional estimators and providing insights for digital correlator implementation.

Contribution

It introduces new maximum-likelihood-based correlation estimators for quantized signals, analyzing their bias, noise, and optimality in different correlation regimes.

Findings

Traditional estimators have large noise at high correlation.

Estimators are fully optimal when correlation is near zero.

Bias and noise characteristics are quantified for different estimators.

Abstract

Using a maximum-likelihood criterion, we derive optimal correlation strategies for signals with and without digitization. We assume that the signals are drawn from zero-mean Gaussian distributions, as is expected in radio-astronomical applications, and we present correlation estimators both with and without a priori knowledge of the signal variances. We demonstrate that traditional estimators of correlation, which rely on averaging products, exhibit large and paradoxical noise when the correlation is strong. However, we also show that these estimators are fully optimal in the limit of vanishing correlation. We calculate the bias and noise in each of these estimators and discuss their suitability for implementation in modern digital correlators.