Detection of Gaussian bandpass transients under impulsive noise: a wavelet transform approach

In underwater acoustics, the modeling of impulsive noise ambients by symmetric-α-stable laws is motivated by the generalized central limit theorem. However, detection of stochastic signals under such additive noise is a difficult task to implement, due to the lack of a closed-form expression of the a-posteriori probability density function. We present a suboptimal detector for Gaussian bandpass transients in impulsive noise that uses a nonlinear, memoryless prefilter followed by a discrete wavelet transform. The resulting signals present a Gaussian-like behavior and the decision is achieved by the comparison of a quadratic likelihood ratio with a threshold. The tuning of the nonlinearity parameter is performed either by looking at the receiver operating characteristic or using the Chernoff distance, that, although resulting in an approximate solution, is easier to compute. Simulation results are presented by Monte-Carlo simulation