Array Modeling of Active Sonar Clutter

Abstract

Active sonar systems operating in shallow-water environments often deal with excessive false alarms, generically referred to as clutter, that are more numerous than expected for Rayleigh-distributed reverberation. The clutter probability density function, and therefore the probability of false alarm ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fa</sub> ), depends on the scattering sources, propagation conditions, sonar system, and signal processing. Clutter statistics are often approximated by the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -distribution where the shape parameter (alpha macr) provides an inverse relationship to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fa</sub> with decreases in alpha macr representing an increase in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fa</sub> . In this paper, the effect of sonar array processing on clutter statistics is evaluated by first modeling clutter at the hydrophone level and then analyzing the resulting <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -distribution shape parameter after conventional beamforming. When the transmit-waveform bandwidth is narrowband with respect to the array processing and propagation consists primarily of low-angle paths, alpha macr was found to be separable into the product of a clutter-source scattering effect, an array processing effect, and a coupled transmit-waveform and propagation effect. The array effect was found to coarsely follow the array beamwidth, although precise evaluation is straightforward given the array beampattern. As might be expected, array design or processing that tends to increase the beamwidth was found to increase alpha macr. Uniform shading was seen to provide a practical, though not exact, lower bound on alpha macr for common array shading functions. For circular arrays with unaliased spatial sampling, an asymptotic beampattern was found to provide a very accurate approximation to alpha macr. These results should be useful in predicting the performance of sonar systems in clutter dominated areas, in the design of arrays and array processing, in the inversion of clutter data for clutter-source scattering parameters, or to improve signal processing algorithms aiming to reduce or control clutter-related false alarms.