Abstract
A general theoretical formulation is developed for echo statistics associated with a finite number of scatterers and patches of scatterers, each being randomly located in a directional sonar beam. This is the case of a direct-path sonar where there are no echoes from the seafloor and sea surface. The formulation is derived by combining the equations of Ehrenberg and colleagues (single scatterer randomly located in sonar beam) and Barakat (sum of finite number of random variables). Each scatterer or patch of scatterers is independent and can have its own echo probability density function (PDF) (before beampattern effects). Examples show that the PDF of the echo (as received by the sonar) is strongly non-Rayleigh due to beampattern effects and finite number of scatterers or patches. Numerical simulations are made for validation. [Work supported by ONR.]
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