A Likelihood Ratio-Based Detector for QTMS Radar and Noise Radar

TL;DR

This paper develops a likelihood ratio-based detector for QTMS and noise radars, providing explicit formulas, approximations, and ROC analysis, revealing regimes where alternative detectors may outperform LR tests.

Contribution

It introduces a new LR detector for QTMS and noise radars, with explicit and approximate formulas, and analyzes its performance through theoretical and simulation-based ROC curves.

Findings

LR detector derived and explicit formula provided

Approximate detector function for difficult detection scenarios

In some regimes, alternative detectors outperform LR, challenging optimality assumptions

Abstract

We derive a detector function for quantum two-mode squeezing (QTMS) radars and noise radars that is based on the use of a likelihood ratio (LR) test for distinguishing between the presence and absence of a target. In addition to an explicit expression for the LR detector, we derive a detector function which approximates the LR detector in the limit where the target is small, far away, or otherwise difficult to detect. When the number of integrated samples is large, we derive a theoretical expression for the receiver operating characteristic (ROC) curve of the radar when the LR detector is used. When the number of samples is small, we use simulations to understand the ROC curve behavior of the detector. One interesting finding is there exists a parameter regime in which a previously-studied detector outperforms the LR detector, contrary to the intuition that LR tests are optimal. This is because neither the Neyman-Pearson lemma, nor the Karlin-Rubin theorem which generalizes the lemma, hold in this particular problem. However, the LR detector remains a good choice for target detection.