Scattering function for multiple-bounce underwater acoustic channels

The second statistical moment of a scattering channel involving several statistically independent bounces is computed, using the Fresnel-corrected Helmholtz integral formulation. The surface at all bounces is assumed to have a Gaussian probability density, and the surface correlation function is taken to be a cosine with a Gaussian envelope. The resulting second-moment function depends primarily on two reverberation time constants. One of these is shown to be simply the sum of reverberation time constants obtained for single bounces. The scattering function is also computed, and it is shown that the multiple bounces can destroy the narrow horseshoe shape of the scattering function found in earlier work on a single-bounce scatter channels.