Coherent matched-filter reflection loss from a moving rough surface as a function of pulse duration and ensonified area

Abstract

The loss incurred when matched filtering a sonar pulse after reflection from a rough surface depends on the ensonified area on the surface and the motion of the surface throughout the pulse. Simple solutions exist for the loss in the coherently reflected component when the ensonified area is either very large or very small. The large ensonified area (LEA) result is generally accurate for narrowband pulses while a small ensonified area (SEA) requires broadband waveforms. By assuming the reflection comprises a finite number of statistically independent surface heights and that the surface is Gaussian distributed with a narrowband spectrum, the loss can be determined as a function of both the pulse duration relative to the wave period and effective ensonified area (which depends on pulse bandwidth) using the spatial correlation function of the surface. The result is shown to be a convex combination of the LEA and SEA results. A one-dimensional example illustrates how surface reflection loss increases with pu...