Novel physical interpretations of K-distributed reverberation

Interest in describing and modeling envelope distributions of sea-floor backscatter has increased recently, particularly with regard to high-resolution active sonar systems. Sea-floor scattering that results in heavy-tailed-matched-filter-envelope probability distribution functions (i.e., non-Rayleigh distributions exemplified by the K, Weibull, Rayleigh mixture, or log-normal distributions) is often the limiting factor in the performance of these types of sonar systems and in this context is referred to as reverberation or acoustic clutter analogous to radar clutter. Modeling of reverberation has traditionally entailed fitting various candidate distributions to time samples of the envelope of the scattered sonar (or radar) returns. This type of descriptive analysis and the asymptotic (infinite number of scatterers) analysis defining the K-distribution yield little insight into the environmental mechanisms responsible for heavy-tailed distributions (e.g., distributions and, clustering of discrete scatterers, patchiness in geo-acoustic properties, scattering strength of scatterers, etc.) and do not allow evaluation of the effect of changing sonar system parameters such as bandwidth and beamwidth. In contrast, we derive the envelope distribution for the scattered returns starting from simple physical descriptions of the environment with a finite number of scatterers. It is shown that plausible descriptions of the environment can lead to K-distributed reverberation. This result explains, at least partially, the success of the K-distribution in the modeling of radar clutter and sonar reverberation at a variety of frequencies and scales. The finite-number-of-scatterers model is then used to predict how the shape parameter of the K-distribution will change as the beamwidth of a towed-array receiver is varied. Analysis of reverberation data from a low-frequency (450-700 Hz) active sonar system illustrates that, within our ability to estimate it, the shape parameter of the K-distribution is proportional to the beamwidth of the towed-array receiver, a result important for sonar simulation and performance prediction models. These results should prove useful in developing methods for modeling, predicting and mitigating reverberation on high-resolution sonar systems.