Towards a unified distribution model for randomly scattered sound

Due to turbulent scattering in the atmosphere, sound levels from sonic booms arriving at a receiver vary randomly. Random scattering is also important in a variety of other problems involving detection, communication, beamforming, and remote sensing. This presentation describes progress toward formulating a general (or “unified”) statistical distribution for randomly scattered signals that applies to essentially any propagation geometry and atmospheric condition, with many existing, commonly used statistical models being special cases. The premise upon which this development is based is that there are three primary properties to be incorporated into a general model: saturation (the relative dominance of random over deterministic signal power), intermittence (the extent to which scattering strength varies in space and time), and decorrelation between separated sensors. These three properties can be modeled, individually, using the noncentral gamma, compound gamma, and variance gamma distributions. So far, we have found analytical solutions combining saturation and intermittence (the noncentral compound gamma), and intermittence and decorrelation (the compound variance gamma), but are still seeking a result combining saturation and decorrelation, as well as all three properties together.