Compressed Sensing Radar Detectors based on Weighted LASSO

TL;DR

This paper introduces a debiased weighted LASSO detector for compressed sensing radar systems that leverages prior information and statistical mechanics to improve detection performance over naive methods.

Contribution

It derives a debiased weighted LASSO estimator for row-orthogonal measurement matrices and constructs a detector with superior detection capabilities based on this estimator.

Findings

DWLD outperforms NWLD and DLD in detection probability.

Threshold setting based on false alarm rate improves detection accuracy.

Numerical experiments confirm the advantages of weight tuning in detection performance.

Abstract

The compressed sensing (CS) model can represent the signal recovery process of a large number of radar systems. The detection problem of such radar systems has been studied in many pieces of literature through the technology of debiased least absolute shrinkage and selection operator (LASSO). While naive LASSO treats all the entries equally, there are many applications in which prior information varies depending on each entry. Weighted LASSO, in which the weights of the regularization terms are tuned depending on the entry-dependent prior, is proven to be more effective with the prior information by many researchers. In the present paper, existing results obtained by methods of statistical mechanics are utilized to derive the debiased weighted LASSO estimator for randomly constructed row-orthogonal measurement matrices. Based on this estimator, we construct a detector, termed the debiased weighted LASSO detector (DWLD), for CS radar systems and prove its advantages. The threshold of this detector can be calculated by false alarm rate, which yields better detection performance than the naive weighted LASSO detector (NWLD) under the Neyman-Pearson principle. The improvement of the detection performance brought by tuning weights is demonstrated by numerical experiments. With the same false alarm rate, the detection probability of DWLD is obviously higher than those of NWLD and the debiased (non-weighted) LASSO detector (DLD).