Adaptive sub-nyquist sampling based on haar wavelet and compressive sensing in pulsed radar

The ultra wide band pulsed radar uses a very narrow pulse width. Sampling this narrow pulse at the Nyquist rate requires a high sampling rate which necessitates a high rate analog to digital converter. Recently, new approaches for sub-Nyquist rate sampling have been introduced. These approaches try to achieve the trade-off between the number of samples and the system's detection capabilities. In this paper, we present a proposed algorithm using the simple Haar wavelet bases to adaptively sample the signal at a sub-Nyquist rate based on compressive sensing. The proposed algorithm uses the previously received pulse interval as prior information for the present interval. Based on this information, the algorithm is able to sample the current interval at a low resolution and focus only on the target potential segments at high resolution. The introduced analysis shows that by using the proposed algorithm, the signal recovery speed is up to 387 times faster than competing approaches. The probability of detection is also improved at different signal-tonoise ratios. The simulation results demonstrate the feasibility and the competence of the proposed algorithm.