Moment characterization of a doubly spread surface-scatter channel at high Rayleigh parameters

Many communication channels involving distortion due to random time-varible surface scattering suffer from extremely acute time and frequency smear. This is particularly true for sonar and low or medium frequeacy electromagnetic propaption where Fresnel zones can be large and yet where Rayleigh parameters can also be quite high. Using a simple Fresnel corrected geometric optics model for the surface-scatter channel, it is possible to explain the unusually high deggee of dispersive scattering observed. The Scattering function for the channel is derived and its shape shown to be range dependent for wide beam excitation. Under certain not unreasonable assumptions about the surface statistics this function is, in fact, shown to exhibit a narrow parabolic ridge with a "hollow" interior.