Structured Covariance Matrix Estimation for Noise-Type Radars

TL;DR

This paper develops and compares two methods for estimating the structured covariance matrix parameters in noise-type radars, providing statistical properties and applying them to target detection performance analysis.

Contribution

It introduces two estimation techniques for the covariance matrix parameters in noise radars and derives their statistical distributions, enhancing detection analysis.

Findings

Both estimators are equivalent and optimal under the proposed methods.

Explicit PDFs and approximate PDFs for the estimators are derived.

Application to target detection yields ROC curve expressions.

Abstract

Standard noise radars, as well as noise-type radars such as quantum two-mode squeezing radar, are characterized by a covariance matrix with a very specific structure. This matrix has four independent parameters: the amplitude of the received signal, the amplitude of the internal signal used for matched filtering, the correlation between the two signals, and the relative phase between them. In this paper, we derive estimators for these four parameters using two techniques. The first is based on minimizing the Frobenius norm between the structured covariance matrix and the sample covariance matrix; the second is maximum likelihood parameter estimation. The two techniques yield the same estimators. We then give probability density functions (PDFs) for all four estimators. Because some of these PDFs are quite complicated, we also provide approximate PDFs. Finally, we apply our results to the problem of target detection and derive expressions for the receiver operating characteristic curves of two different noise radar detectors.