Phase Transitions in Frequency Agile Radar Using Compressed Sensing

TL;DR

This paper analyzes phase transitions in frequency agile radar using compressed sensing, deriving practical curves to optimize target recovery, especially for extended targets, and validating these with simulations.

Contribution

It derives closed-form phase transition curves for block sparse recovery in FAR and provides approximations for practical radar parameter design.

Findings

Block sparse recovery outperforms standard sparse recovery for extended targets.

The derived phase transition curves are validated through simulations.

Approximate curves facilitate practical application in radar system design.

Abstract

FAR has improved anti-jamming performance over traditional pulse-Doppler radars under complex electromagnetic circumstances. To reconstruct the range-Doppler information in FAR, many compressed sensing (CS) methods including standard and block sparse recovery have been applied. In this paper, we study phase transitions of range-Doppler recovery in FAR using CS. In particular, we derive closed-form phase transition curves associated with block sparse recovery and complex Gaussian matrices, based on prior results of standard sparse recovery under real Gaussian matrices. We further approximate the obtained curves with elementary functions of radar and target parameters, facilitating practical applications of these curves. Our results indicate that block sparse recovery outperforms the standard counterpart when targets occupy more than one range cell, which are often referred to as extended targets. Simulations validate the availability of these curves and their approximations in FAR, which benefit the design of the radar parameters.