Simulating underwater acoustic data using random variable transformations

Abstract

Recent advances in underwater acoustics have shown the non-gaussian nature of acoustic signals in a random ocean. These advances have also demonstrated that the probability distribution of the amplitude of an acoustic signal is modeled quite well by the generalized gamma density function. This model is further developed in this study to include a phase distribution. This non-gaussian nature makes it difficult to simulate data needed to develop new signal processing methods for source localization. However, with the knowledge of these two first order statistics, a method for simulating a random ocean based purely on its statistical properties and using random variable transformations is presented. Although an accurate model for both the phase distribution and the amplitude distribution can be obtained, because of the non-gaussian nature of the acoustic signals, it is a more difficult problem to find the joint probability distribution of the two components. In the author's model for the phase distribution, referred to as the ricean model in communication literature, there is an inherent model for the amplitude distribution as well. This model also provides a convenient expression for the joint probability density function of the amplitude and phase. Hence, by using this model, random data can be created which have a known amplitude, phase and joint distribution. However, this amplitude distribution does not describe what is observed in practice. To overcome this problem, the idea of transforming random variables is used. In this idea, the generalized gamma amplitude distribution is obtained by passing the author's amplitude distribution model through a non-linearity while the phase is left unperturbed. The resulting amplitude and phase distributions match what is observed in practice for the single point statistics of a random ocean. Furthermore, by using the ricean model, a dependence between the amplitude and phase has been introduced, albeit somewhat modified by the non-linearity. Although it is difficult to solve for this transformation in closed form, numerically it is quite simple. This process does not give much insight into the resulting joint phase and amplitude distribution, but it does provide an excellent means to simulate data of a random ocean based only on its statistical properties. Furthermore, by correlating the data in some manner one can simulate the stochastic nature observed at a vertical array of hydrophones.<>