Sparse recovery and resolution of pulse-Doppler radar

The resolution of a pulse Doppler radar using matched filter banks is known to be constrained by the radar uncertainty principle. Recently, it has been proposed that sparse recovery techniques [4], [5], [10], [14] can be used to achieve high resolution in point target environments. These techniques assume the time-frequency dictionary of the radar signal satisfies certain incoherence requirements. In this paper, we relate the incoherence requirement to the ambiguity function and show that the resolution of common sparse recovery algorithms is also constrained by the uncertainty principle. Furthermore, using recovery bounds in [13], it is shown that even radar signals not meeting the incoherence requirement can be used for reconstructing certain target scenes. This is used to define a resolution plot for comparing the resolution of sparse recovery algorithms with different transmit signals.