Continuous Reverberation Response and Comb Spectra Waveform Design

A model for the matched filter response to continuous reverberation from the transmission of broadband waveforms is developed. The application is for reverberation from a rough interface, based on perturbation theory. The model is developed for both the stationary rough bottom and the moving ocean surface interfaces. The mean reverberation is predicted as a function of the Doppler speed of the matched filter replica. Application is made to the design of waveforms with comb-like spectra. A uniform train of impulses produces a comb spectrum that is shown to significantly reject reverberation for a certain range of Doppler speeds. A similar low-reverberation response is produced from a continuous source emitting a wavetrain composed of adjacent hyperbolic-frequency-modulated (HFM) pulses. A waveform design technique is demonstrated to ensure continuity of the entire HFM wavetrain. Finally, waveforms with geometrically spaced comb spectra are considered. A new geometric comb waveform with constant amplitude is specified. However, this waveform requires a large bandwidth which may be difficult to obtain with practical high-power sources. Hard and soft-clipped versions of the comb spectra waveform are considered which provide useful compromises between the amount of reverberation suppression, the transmitted energy efficiency, and the utilization of available bandwidth.