Modeling colored impulsive noise by Markov chains and alpha-stable processes

We present a novel method of modeling ambient noise in warm shallow underwater channels. Due to large snapping shrimp populaces inhabiting these regions, the noise process is known to be impulsive and bursty (colored). Conventionally, researchers have used white noise models to simulate snapping shrimp noise. Though efficient in portraying the amplitude statistics, these models fail to represent the burstiness encountered in practical observations. We offer insights into the dependence between recorded noise samples. Scatter plots of closely spaced observations are shown to have near-elliptical geometries. Using this observation and the fact that stable distributions model outliers very well, we propose a memory model based on stable α-sub-Gaussian distributions. The new model offers a better match to empirical data in comparison to white and colored noise models currently employed in the literature.