General distributions for one- and two-point scattered signal statistics, including incomplete saturation and...

Scattering by turbulence and other phenomena causes the intensity of sound waves to vary randomly. Due to the importance of random scattering effects in a variety of applications involving detection, communication, and beamforming of signals, extensive research has gone into formulating appropriate statistical models. This article presents a unified family of models intended for broad application across a variety of scattering scenarios and propagation environments. The formulation is based on extensions to the ordinary gamma distribution under the premise that there are three primary properties to be incorporated into a general model: saturation (relative importance of scattered and unscattered signal intensity), intermittence (variations in the scattering environment), and decorrelation (as occurs when two sensors are increasingly separated in space and time). The ultimate result is a distribution incorporating all three of these properties simultaneously, called the noncentral compound variance gamma. This distribution is presented as a series expansion in terms of the Rice factor, which represents the ratio of unscattered to scattered signal intensity. Most commonly used statistical models for random signals are special cases or closely approximated by the family of distributions presented here.