Optimal and Near-Optimal Detection in Bursty Impulsive Noise

In many practical scenarios, the ambient noise process is known to be impulsive. To combat this, several robust measures have been proposed in the literature. Most of them assume white noise processes, i.e., the noise samples are independent and identically distributed heavy-tailed random variables. However, noise is seldom white in practice and therefore exhibits memory. For impulsive noise, dependency among samples results in outliers clustering together. The process is thus impulsive and bursty. In our work, we employ stationary <inline-formula><tex-math notation="LaTeX"> $\alpha$</tex-math></inline-formula>-sub-Gaussian noise with memory order <inline-formula><tex-math notation="LaTeX"> $m$</tex-math></inline-formula> (<inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>SGN( <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula>)) to model bursty impulsive noise. The model is based on the multivariate <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> -sub-Gaussian (<inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>SG) distribution family and statistically characterizes adjacent samples from elliptical distributions. The latter assumption holds well for snapping shrimp noise found in warm shallow underwater channels. We investigate the performance of conventional robust detectors in <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>SGN(<inline-formula> <tex-math notation="LaTeX">$m$</tex-math></inline-formula>) and also propose novel near-optimal detectors. The Neyman–Pearson (NP) approach for binary hypothesis testing is considered and extensive simulation results for the aforementioned detectors are offered. For all instances, we employ an <inline-formula><tex-math notation="LaTeX"> $\alpha$</tex-math></inline-formula>SGN(<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula>) process whose parameters are tuned to snapping shrimp noise data sets. By incorporating good signal design rules, it is shown that there is a large performance gap between the new and conventional detectors in various impulsive regimes. Moreover, it is possible to derive a near-optimal detector if one only has information of the temporal statistics of the noise process.