Basic formulation for the simulation of underwater reverberation

Abstract

A basic equation to simulate underwater reverberation for monostatic sonar is obtained. The derivation is based on these simple assumptions: The phase shift caused by scatterers has a uniform distribution, the scatterers are independent of each other, the reverberation is approximated as a quasistationary Gaussian process, the bandwidth of the transmit signal is narrow, and the sound propagation speed is constant. Using these assumptions, the stochastic property of a modified DDM (Doppler density matrix) is examined, which is an extension to the original DDM of REVGEN [D. W. Princehouse, tr7511, Appl. Phys. Lab., Univ. of Washington (1975)]. The correlation of the modified DDM has a simple form. Using the modified DDM, the reverberation is expressed as an overlapped summation of the randomly modulated convolution of the transmit signal and white noise of finite duration. The modulation is related to the Doppler shift caused by the motion of the sonar platform and the scatterers. Using the formulation, an extension to the many beams case is also examined.