Compound variance gamma distribution for modeling randomly scattered signals and detection at two sensors

Decision metrics for automated target recognition and classification rely upon statistical distributions for the signal of interest and the background noise. This paper describes distribution models for situations in which an acoustic, RF, optical, or seismic signal is randomly scattered by the environment and received at one or two sensors, with the scattering strength varying randomly in space and time. A new distribution, called the compound variance gamma, is introduced, which applies to partially correlated data between two sensors with random scattering strength. This distribution reduces to several previously known scattering distributions as special cases. Calculation of receiver operating characteristic (ROC) curves using the new distribution is also discussed. A second new distribution, involving a product of modified Bessel functions, is also introduced to describe the magnitude of the cross product between a pair of sensors as needed to calculate the ROC curves. It is shown that the randomized scattering strength and correlation between the two sensors significantly impact signal detection.