Pulse spreading and correlation loss in shallow water environments with rough sea surfaces and bottoms

Active sonar pulses suffer time-spreading, distortion, and de-correlation due to multipath propagation and reflections from rough boundaries. Correlation of the received distorted pulse with the transmitted pulse leads to degradation in pulse compression gain in comparison to the ideal case of a received pulse being simply a time-shifted, amplitude-scaled replica propagated along a single direct path. We assess the degradation by first simulating the propagation of linear frequency-modulated (LFM) pulses in shallow water through Fourier synthesis of parabolic equation solutions, and then characterising the time spreading of the pulse envelope after correlation. Rough seafloor interfaces are modelled as random statistical realisations of power-law spectra. Doppler-spreading effects from sea surface motion are ignored, and rough sea surfaces are modelled as frozen statistical realisations of Pierson–Moskowitz spectra. The variation of correlation loss with sound speed profile, sensor depth, pulse bandwidth, and pulse time duration is investigated and discussed in terms of propagation physics. For performance prediction of broadband active sonar, the conventional active sonar equation needs to be revised by including time-spreading or correlation-loss terms, or by modifying the transmission loss term.