A multicycle sub-Nyquist sampling system for pulse streams with Doppler shift

Pulse streams with Doppler shift exists widely in radar, communications, and many other time-variant linear systems. One central task in identifying these systems is to recover the delay-Doppler pairs. However, the classic methods require high sampling rate for wideband pulse. In this paper, a multicycle sub-Nyquist sampling system to recover delay-Doppler pairs symmetrically is proposed. Using finite rate of innovation (FRI) theory, the unknown parameters can be estimated from the directly sampled Fourier coefficients, where FRI refers to that the sampled signals have finite degrees of freedom per unit time. Based on the sparse common support (SCS) model and symmetry of the delay-Doppler pairs, the samples from each pulse repeat interval (PRI) can be jointly used to estimate parameters, where PRI is the time interval of the transmitted pulses, and SCS refers to that each PRI of the received signal has common non-zero supports but different weights. The number of PRIs and samples required for signals with both different and identical parameters are demonstrated mathematically. When the SNR is 10 dB, the NMSEs of the estimated delay-Doppler parameters are -10 dB and -5 dB or more higher than several advanced methods respectively, which demonstrate the effectiveness of the proposed method.