Range and Doppler information from fourth-order spectra

In an active sonar system setting, a novel method is evaluated that extracts range and Doppler information from a Doppler-spread active sonar echo. The Doppler spreading is based on H. Van Trees' (1971) Gaussian amplitude modulating model, and the new method is based on the Fourier transform of a special case of the fourth-order cumulant. Specifically, from the envelope of the Gaussian amplitude modulated echo of a transmitted coded pulse train, the second-order spectrum and the Fourier transform of a special case of the fourth-order cumulant are derived and analyzed for this ability to extract range and Doppler information. It is shown that the method can theoretically extract range and Doppler information without degradation. The reason for this result is that a special case of the fourth-order cumulant is independent of the covariance of the Gaussian amplitude modulating function. These methods are also simulated and compared with the simulated results of the range-Doppler ambiguity function. This shows that the ambiguity function and the second-order spectrum are degraded due to the Gaussian amplitude modulation. The results are further demonstrated by simulating the three range-Doppler extraction methods for the received echo in noise