Compressed Sensing Radar Detectors Under the Row-Orthogonal Design Model: A Statistical Mechanics Perspective

Siqi Na, Tianyao Huang, Yimin Liu, Takashi Takahashi, Yoshiyuki Kabashima, Xiqin Wang

Abstract: Compressed sensing (CS) model of complex-valued data can represent the signal recovery process of many types of radar systems, especially when the measurement matrix is row-orthogonal. Based on debiased least absolute shrinkage and selection operator (LASSO), the detection problem under the Gaussian random design model, i.e. the elements of the measurement matrix are drawn from a Gaussian distribution, is studied by literature. However, these approaches are unsuitable for the 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 a detector can analytically provide the threshold according to a 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. Compared with other debiased LASSO based detectors, simulation results indicate that the proposed approach can achieve a more accurate probability of false alarm when the measurement matrix is row-orthogonal, leading to better detection performance under the Neyman-Pearson principle.