A non-fluctuating target model for McDaniel's reverberation

Active sonar reverberation has often been observed to have probability tails heavier than the traditionally assumed Rayleigh distribution. Many other physics-based and phenomenological statistical models have been proposed to represent such observed reverberation, a few of which have natural target models. One that has shown promise in having a minimal parameterization yet a broad enough scope to adequately represent a wide variety of observed non-Rayleigh reverberation is McDaniel's (1990) model. In this paper a statistical model is developed for a non-fluctuating target in McDaniel's reverberation exploiting the non-central gamma distribution. The probability density function and cumulative distribution function are derived and used to determine likelihood ratio and locally optimal detector non-linearities and also theoretical receiver operating characteristic curves.