Array Modeling of Active Sonar Clutter

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. It is known that the clutter probability density function, and therefore the probability of false alarm (P_falpha), depends on the scattering sources, propagation conditions, sonar system and signal processing. In this paper the effect of sonar array processing on clutter statistics is evaluated through approximation by the K distribution where the shape parameter (alpha tilde) provides an inverse relationship to P_falpha with decreases in alpha tilde representing an increase in P_falpha. When the transmit waveform bandwidth is narrowband with respect to the array processing and propagation is restricted to the direct path, a was found to be separable into the product of an array-processing effect, a transmit-waveform effect, and a clutter-source scattering effect. The array effect was found to coarsely follow the array beamwidth, although precise evaluation is straightforward given the array beampattern and, for an equi-spaced line array, an asymptotic approximation was seen to be quite accurate for even moderate array sizes. As might be expected, array design or processing that tends to increase the beamwidth (e.g., reducing the size of an array or transmit waveform frequency, steering away from broadside to a line array, or shading an array to reduce sidelobes) was found to increase alpha tilde. Uniform shading was found to provide a practical, though not exact, lower bound on alpha tilde for common array shading functions.