Compressive nonstationary spectral estimation using parsimonious random sampling of the ambiguity function

We propose a compressive estimator for the discrete Rihaczek spectrum (RS) of a time-frequency sparse, underspread, nonstationary random process. The new estimator uses a compressed sensing technique to achieve a reduction of the number of measurements. The measurements are randomly located samples of the ambiguity function of the observed signal. We provide a bound on the mean-square estimation error and demonstrate the performance of the estimator by means of simulation results. The proposed RS estimator can also be used for estimating the Wigner-Ville spectrum (WVS) since for an underspread process the RS and WVS are almost equal.