The Effect of Multipath on the Envelope Statistics of Bottom Clutter

Active sonar systems operating in shallow-water environments are often faced with high numbers of false alarms, generically referred to as clutter, arising from among other sources bottom scattering that results in heavy tails in the matched filter envelope probability density function compared with the Rayleigh distribution. In this paper, the effect of multipath propagation on the envelope statistics (i.e., the disparity from the Rayleigh distribution) is modeled through the use of the -distribution where the shape and scale parameters are formed from the autocorrelation function of the transmit waveform, the multipath structure, and the strength and spatial density of the bottom scatterers. Use of the -distribution is justified by showing that it is the limiting distribution of the sum of independent but not identically distributed -distributed random variables, which is representative of multipath when the bottom produces -distributed backscatter. The shape parameter, which drives the clutter statistics, is seen to be inversely proportional to bandwidth at bandwidths low enough that the multipath is not resolved and again at bandwidths high enough that all of the paths are resolved. As has been previously reported by LePage [IEEE J. Ocean. Eng., vol. 29, no. 2, pp. 330-346, 2004], multipath is shown to make clutter statistics more Rayleigh-like, which in this analysis equates to an increase in the -distribution shape parameter. The model is used to evaluate the effect on clutter statistics of varying environmental characterizations and system configurations where it is seen that, for a constant sound-speed profile, increasing the vertical aperture of the sonar, the center frequency, or surface roughness can lead to less multipath and, therefore, a reduction in the -distribution shape parameter and an increase in the probability of false alarm.