Discrimination and identification of time-delay repeater jamming and target echo by basis pursuit

The basis pursuit algorithm of sparse decomposition is used to recover and discriminate the target echo and the jamming signal which have different time-delay and pulse width. The key is to construct an atomic dictionary. The recoveries in both the noiseless case and in the noisy case are considered. The noiseless case adopts linear programming. The noisy case adopts quadratic programming. Since the recovery is sensitive to the noise, the solution to the noisy case is unstable. More importantly, densely false targets, including the case that two signals are overlapped in the temporal domain, can also be recovered. Finally, simulations verifies the results.