  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.
