Reverberation envelope statistics and their dependence on sonar bandwidth and scattering patch size

Increasing transmit waveform bandwidth in an active sonar-system results in an increase in the signal-to-reverberation power ratio in reverberation-limited environments, but also changes the probability density function of the reverberation envelope. A recent model that relates a description of the sonar system and environment to the parameters of the K-distribution predicts that the shape parameter (α) is proportional to range, beamwidth, and the density of scattering patches on the sea floor and is inversely proportional to bandwidth. In this paper, the bandwidth relationship is examined with real data from a low-frequency active sonar system with a towed array receiver. The inverse proportionality is observed at low bandwidths as a trend away from a Rayleigh-distributed envelope (decreasing α) as bandwidth increases. However, a trend back toward Rayleigh reverberation (increasing α) is observed as bandwidth continues to increase. Hypothesizing that the increase in α arises from over-resolving scattering patches in range and not in angle, the model of is extended to account for patch size relative to that of the sonar-resolution cell. The shape parameter of a moment-matched K-distribution derived from the extended model is then seen to provide a good fit to that estimated from the data.