Impulsive noise model based on stable $\alpha$-sub-Gaussian distribution

Noise modeling is crucial for underwater acoustic signal identification, separation and localization. The traditional Gaussian noise model is unable to fit the heavy-tailed distribution characteristics of non-Gaussian noise field. In the past, the Alpha stable distribution model was used to simulate the non-Gaussian noise. Although the Alpha stable distribution model can fit the amplitude statistics of the impulse noise well, it cannot establish the dependence between the noise samples. A stable
$\alpha$
sub-Gaussian distribution model
$(\mathrm{S}\alpha \text{SG})$
is proposed to address the sample dependence of underwater non-Gaussian impulse noise. Based on the DeepShip real underwater ship noise, the modeling effects of the Alpha stable distribution model and the
$\mathrm{S}\alpha \text{SG}$
model are compared. The results show that both the Alpha stable distribution model and the
$\mathrm{S}\alpha \text{SG}$
model can fit the empirical amplitude distribution of the impulse noise well, but the Alpha stable distribution can only provide four-tailed shaped scatter plots; while the
$\mathrm{S}\alpha \text{SG}$
model can provide elliptical shaped scatter plots, which is consistent with the performance of real underwater noise samples.