Sampling theorems for Doppler-stretched wide-band signals

The paper deals with Doppler-stretched wide-band signals occurring in mobile communications and in radar/sonar problems in the presence of moving targets in the case of constant relative radial speeds. Loève bifrequency spectrum and cross-spectrum are used to characterize in the spectral domain the received signal and to jointly characterize the transmitted and received signals. It is shown that, even if both the transmitted and received signals are singularly almost-cyclostationary (ACS), they are not jointly ACS but, rather, jointly spectrally correlated. The problem of uniformly sampling these nonstationary signals is addressed. It is shown that, unlike the case of the wide-sense stationary signals, several kind of aliasing effects occur for the various spectral (cross-)statistical functions used to characterize these signals. Lower bounds on the sampling frequency are derived to avoid these aliasing effects.