Near-optimal detection in snapping-shrimp dominated ambient noise

Detection of a known signal in presence of noise is a common requirement in many applications including sonar, ranging, environmental sensing and communications. The optimal detection of signals in noise requires detailed knowledge of the noise statistics. The linear correlator, commonly used in the form of a matched filter, is known to be optimal in the presence of Gaussian noise. However, the performance of the linear correlator is poor in warm shallow waters where snapping shrimp dominate acoustic noise in the range 2-300 kHz. Since snapping shrimp noise consists of a large number of individual transients, its statistics are highly non-Gaussian. In this paper, we show that the ambient noise statistics can be described accurately by the symmetric alphastable family of probability distributions. The knowledge of the probability distribution allows us to design maximum-likelihood and locally optimal detectors, which perform well in such noise. Surprisingly, we found that a simple non-parametric sign correlation detector also performs well in presence of snapping shrimp noise. Although the performance of the sign correlator is slightly inferior to that of the maximum-likelihood detector, it is very simple to implement and does not require detailed knowledge of the noise statistics. This makes it an attractive detector for use in warm shallow waters. Introduction Snapping shrimp (families Alpheus and Synalpheus) produce loud snapping sounds by extremely rapid closure of their snapper claw. The closure produces a high velocity water jet leading to the formation of a cavitation bubble, which collapses rapidly, causing a loud broadband snapping sound [1]. The shrimp are usually found in such large numbers that there is a permanent crackling background noise in warm shallow waters throughout the world. Source levels as high as 190 dB (peak-to-peak) re 1 μPa @ 1 m have been reported [2]. Due to the impulsive nature of the snaps, the sound is broadband. At low frequencies, noise from shipping is significant; from about 2 kHz to well above 200 kHz, snapping shrimp noise is clearly detectable [3]. As ambient snapping shrimp noise is composed of impulsive noise sources, the resulting noise statistics at these frequencies are non-Gaussian [4][5]. The problem of detecting a known signal with unknown amplitude in noise is commonly encountered in areas such as communications, target detection, ranging and environmental sensing. If the noise statistics are known, an optimal detector can be designed based on the maximum-likelihood (ML) criterion. If the noise is Gaussian, the ML detector simplifies to a linear correlator (LC) [6]. Unlike a general ML detector, the LC does not require knowledge of the standard deviation of the Gaussian distribution. In the presence of non-Gaussian noise, the LC is no longer optimal. In spite of this, many signal processing algorithms still use the LC (or equivalently, a matched filter) for signal detection in non-Gaussian noise due to its simple implementation and the lack of detailed statistical information about the noise. Since the LC is not optimal in snapping shrimp dominated ambient noise, a significant potential exists for enhancing the detection performance of signal processing algorithms in these waters. Ambient Noise Statistics Ambient Noise Data Ambient noise recordings have been made in warm shallow waters in and around Singapore throughout the year. We present analysis of the ambient noise statistics from 4 different data sets to demonstrate the ubiquity of the non-Gaussian noise statistics. Data Set 1 was collected using a high frequency data acquisition system (HiDAQ) capable of omni-directional acoustic recordings from 1-180 kHz [7]. The data was collected in Singapore waters with muddy/sandy sea bed, water depths of 15-20 m and water temperature in the range of 25-30°C through out the year. The ambient noise was digitally sampled at 500 kSa/s and pre-whitened using a 64-order finite impulse response (FIR) filter. It was further bandpass filtered with a FIR filter to contain frequencies between 10 and 180 kHz. Data Set 2 was collected using a pop-up ambient noise data acquisition system (PANDA) capable of omni-directional acoustic recordings from 11 Hz – 8.3 kHz [8]. The data was collected in Singapore waters with muddy/sandy sea bed close to a coral reef with water depths of 15-20 m and water temperature in the range of 25-30°C through out the year. The ambient noise was digitally sampled at 20 kSa/s and then bandpass filtered using a digital FIR filter to contain frequencies between 2 and 8 kHz.