Modeling of underwater non-Gaussian noise based on alpha-stable distribution

The copious pulse signals in the ocean disrupt the adherence of underwater noise to the conventional Gaussian probability distribution function. Addressing the non-Gaussian nature of underwater noise, the Alpha-stable distribution model is incorporated into the statistical modeling of noise. Initially presenting the mathematical empirical model of the Alpha-stable distribution, the underwater noise data samples are then simulated based on this model. The model accuracy is validated through parameter estimation, and a comparative analysis is conducted between the modeling efficacy of the Alpha-stable distribution and the normal distribution for real underwater noise data. The research findings indicate that, for Gaussian noise samples, the modeling effectiveness of the Alpha-stable distribution is comparable to that of the normal distribution. Conversely, for non-Gaussian noise, the normal distribution gradually becomes ineffective as the characteristic index $\alpha$ decreases, whereas the Alpha-stable distribution consistently accurately captures the features of the noise samples.