High Resolution Compressed Sensing Radar Using Difference Set Codes

TL;DR: In this article, a sub-Nyquist sampling method based on difference sets (DS) was proposed to create dictionaries with highly incoherent atoms, and the coherence of the dictionary reached the Welch minimum bound.

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.1 Two low-complexity recovery methods are developed and sufficient condition of target recovery with specific resolution obtained theoretically for noisy and noiseless conditions. We also propose a new waveform, called DS-frequency coded modulated 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 $\text{2}{\%}$ of Nyquist samples and recover targets without resolution degradation in comparison to the conventional Nyquist processing.