A theoretical model of linearly filtered reverberation for pulsed active sonar in shallow water.
This paper presents a statistical model useful for characterizing pulsed active sonar reverberation in shallow water. The model is based on the fundamental assumption that reverberation consists of echoes from point scatterers having random positions, strengths, and Doppler dilations. Receive array beam patterns, simple propagation losses, and planar bistatic geometry are included. The probability distribution of uniformly dense scatterers as a function of echo delay and bearing is explicitly related to the change in the area from which scatterer echoes contribute to the reverberation, and is presented in closed form. The cross Q-function of the transmitted waveform and the linear filter applied to the received signal arises naturally from the development. This function, along with environmental spreading, determines the shape of the reverberation along the Doppler axis. The assumptions and simplifications under which the reverberation decouples into independent spatial (delay and bearing) and Doppler terms are presented.
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John J
JJ
Murray