The extraction of range and Doppler from fourth-order spectra

A method for extracting range and Doppler information from a Doppler-spread active sonar echo is proposed. The Doppler spreading is based on Van Trees´ model, and the method is based on the fourth-order cumulant spectrum. Specifically, from the envelope of an amplitude modulated coded pulse train the spectrum and fourth-order cumulant spectrum are derived. It is demonstrated by analysis and simulation that, due to Doppler-spreading, the conventional method cannot extract range and Doppler shift frequencies of the return pulse without degradation. However, under the same conditions the method based on the fourth-order cumulant spectrum can. It is also shown that a special case of this method is independent of the covariance of the Doppler spreading function