Locally Optimal Inspired Detection in Snapping Shrimp Noise

In this paper, we address the problem of detecting a known signal in snapping shrimp noise. The latter dominates the ambient soundscape at medium-to-high frequencies in warm shallow waters. The noise process is impulsive, exhibits memory and is modeled effectively by 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>)), which is essentially an impulsive Markov process. Robust detectors have long been used to mitigate the impact of impulsive noise on the performance of digital systems. However, conventional notions of robustness do not assume memory within the noise process. The <inline-formula> <tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>SGN(<inline-formula><tex-math notation="LaTeX">$m$ </tex-math></inline-formula>) model offers a mathematical model to develop robust detectors that also exploit the mutual information between noise samples. Recent works in this area highlight substantial improvement in detection performance over traditional robust methods in snapping shrimp noise. However, implementing such detectors is a challenge as they are parametric and computationally taxing. To achieve more realizable detectors, we derive the locally optimal detector for <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>SGN( <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula>). From it, we introduce the generalized memory-based sign correlator and its variants, all of which offer near-optimal performance in <inline-formula> <tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>SGN(<inline-formula><tex-math notation="LaTeX">$m$ </tex-math></inline-formula>). The proposed detectors offer excellent performance in snapping shrimp noise and low computational complexity. These properties make them attractive for use in underwater acoustical systems operating in snapping shrimp noise.

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