Matched-Filter Loss From Time-Varying Rough-Surface Reflection With a Small Effective Ensonified Area

Active sonar sensing often entails propagation paths that include a surface reflection, particularly in shallow-water scenarios. Surface reflection loss, which degrades sonar performance, depends on how rough the surface is with respect to the sensing wavelength and grazing angle. The Rayleigh roughness measure quantifies this relationship with small values representing an acoustically smooth surface and large values an acoustically rough surface. Models predicting surface reflection loss 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 after matched filtering is smaller in extent than the spatial correlation length, a surface-reflection-loss model is derived as a function of pulse duration relative to surface wave period when the net surface displacement is Gaussian distributed. As might be expected the matched filter loss for the small-ensonified-area 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. The model was compared with data measurements from the 2013 Target and Reverberation Experiment, as reported by Hines et al. (“The dependence of signal coherence on sea surface roughness for high and low duty cycle sonars in a shallow water channel,” IEEE J. Ocean. Eng., vol. 42, no. 2, pp. 298-318, Apr. 2017). The data represent both short- and long-duration pulses with respect to the surface wave period. For the short-duration pulses, the model corroborates the data analysis by Hines et al. in predicting a very small matched filter loss. It also compared very favorably with the data for the long-duration pulses in both level and slope as a function of surface roughness. 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.