Compressed sensing radar detectors under the row-orthogonal design model: a statistical mechanics perspective

TL;DR

This paper develops a statistical mechanics-based approach for radar detection using compressed sensing with row-orthogonal measurement matrices, providing more accurate detection thresholds and improved performance over traditional LASSO detectors.

Contribution

It introduces a novel detection method tailored for row-orthogonal measurement matrices, deriving precise test statistics and thresholds, and demonstrating superior detection performance.

Findings

More accurate false alarm probability estimation.

Enhanced detection performance compared to traditional LASSO.

Analytical thresholds enable control of false alarm rates.

Abstract

Compressed sensing (CS) model of complex-valued data can represent the signal recovery process of a large amount types of radar systems, especially when the measurement matrix is row-orthogonal. Based on debiased least absolute shrinkage and selection operator (LASSO), detection problem under Gaussian random design model, i.e. the elements of measurement matrix are drawn from Gaussian distribution, is studied by literature. However, we find that these approaches are not suitable for row-orthogonal measurement matrices, which are of more practical relevance. In view of statistical mechanics approaches, we provide derivations of more accurate test statistics and thresholds (or p-values) under the row-orthogonal design model, and theoretically analyze the detection performance of the present detector. Such detector can analytically provide the threshold according to given false alarm rate, which is not possible with the conventional CS detector, and the detection performance is proved to be better than that of the traditional LASSO detector. Comparing with other debiased LASSO based detectors, simulation results indicate that the proposed approach can achieve more accurate probability of false alarm when the measurement matrix is row-orthogonal, leading to better detection performance under Neyman-Pearson principle.