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In recent years, underwater acoustic wireless sensor networks have been used in many areas. There have been many field trials of acoustic propagation models and statistics for shallow water conditions. However, field trials are limited environmentally and, hence, not widely accepted. Simulations of the impulse response of a shallow underwater acoustic channel allows less expensive system tests that are reproducable. This paper presents a shallow water acoustic channel model based on the actual acoustic propagation characteristics with path attenuation, ambient noise, multiple paths, and Doppler effects. The second-order statistical characteristics of the simulation model are verified with the autocorrelations and crosscorrelations of the quadrature components and the complex envelopes of channel impulse responses. The channel model is implemented in Matlab with the results showing that the absorption coefficient and path losses are both dependent on the frequencies and propagation distances and that the path gain can be improved with Light of Sight (LOS) and short range acoustic propagation. Analysis of the channel impulse response and the frequency response that the zero-order Bessel function of first kind can be used to describe the correlation functions for the impulse response. The shallow underwater acoustic channel is time-varying and can not be modeled as a wide-sense stationary-uncorrelated scattering channel.