Matched-filter loss from time-varying rough-surface reflection with a small ensonified area

Active sonar sensing often entails propagation paths that include a surface reflection, particularly in shallow-water scenarios. Models predicting surface reflection loss, which degrades sonar performance, are generally derived assuming the surface shape is not varying over the time in which the pulse is reflecting from it and that the ensonified region of the surface is large in extent relative to the spatial correlation length of the surface. While these models are often appropriate for short-duration, narrowband pulses, they are not necessarily applicable to long-duration, broadband pulses which are the focus of this paper. By assuming the effective ensonified area is smaller in extent than the spatial correlation length, the surface reflection loss after matched filtering (MF) is derived as a function of pulse duration relative to surface wave period when the net surface displacement is Gaussian distributed. Closed-form results are obtained when the pulse is long relative to the surface-wave period and under the assumption that the bandwidth is small relative to the center frequency (i.e., a narrow-band model). As might be expected, the MF loss for the small-ensonifiedarea scenario increases with the Rayleigh roughness, the number of consecutive surface reflections, and the ratio between pulse duration and the surface wave period. With respect to the latter, the loss is predicted to saturate when the pulse duration exceeds one surface wave period. Finally, the models were found to compare favorably with real data measurements. The models presented in this paper should be useful in sonar-equation analysis for predicting surface reflection loss with broadband waveforms when pulse duration is on par with or exceeds the surface wave period.