Modeling sonar signal peak to average intensity ratio

The peak envelope or intensity of a sonar signal is an important quantity in many applications (e.g., object detection, fish density estimation, and quantifying risk to marine mammals). However, modeling, prediction, and analysis is often limited to second-order statistics (e.g., sonar equation, transmission loss). Standard techniques from order-statistics are applied to approximate sonar signal peak statistics where both signal statistics and non-stationarity are captured through the use of heavy-tailed probability distributions. Analysis of real data from an echo-repeater sonar signal over six bandwidths and varying signal-to-noise ratio showed a good fit of the model for the expected peak to average intensity ratio. Predictions of spread overestimated the observed spread for small bandwidth-time (WT) products but improved in accuracy as WT increased.