High Resolution Compressed Sensing Radar using Difference Set Codes

TL;DR

This paper introduces a novel sub-Nyquist radar sampling method using difference set codes, enabling high-resolution target detection with significantly fewer samples and improved noise robustness.

Contribution

It proposes a new DS-sampling technique with minimal dictionary coherence and a low complexity recovery method, advancing sub-Nyquist high-resolution radar technology.

Findings

Achieves target recovery with less than 2% of Nyquist samples.

Dictionary coherence reaches the Welch minimum bound with DS-sampling.

Enhanced noise robustness with the DS-FCM waveform.

Abstract

In this paper, we consider compressive sensing (CS)-based recovery of delays and Doppler frequencies of targets in high resolution radars. We propose a novel sub-Nyquist sampling method in the Fourier domain based on difference sets (DS), called DS-sampling, to create dictionaries with highly incoherent atoms. The coherence of the dictionary reaches the Welch minimum bound if the DS-sampling is employed. This property let us to implement sub-Nyquist high resolution radars with minimum number of samples. We also develop a low complexity recovery method, based on structured CS and propose a new waveform, called difference set--frequency coded modulated (DS-FCM) waveform, to boost the recovery performance of the sub-Nyquist radar in noisy environments. The proposed method solves some of the common problems in many CS-based radars and overcome disadvantages of the conventional Nyquist processing, i.e. matched filtering in high resolution radar systems. The proposed method allows us to design sub-Nyquist radars, which require less than 2% of Nyquist samples and recover targets without resolution degradation in comparison to the conventional Nyquist processing.