Signal detection and normalization in underwater noises modeled as a Gaussian-Gaussian mixture

Knowledge of the noise probability density function is central in signal detection problems, not only for optimum receiver structures but also for processing procedures such as power normalization. The statistical knowledge must be acquired since the classical assumption of a Gaussian noise PDF is often not valid in underwater acoustics. This report studies statistical modeling by a Gaussian-Gaussian mixture for three different underwater noise samples. One of them can adequately be described by a Gaussian-Gaussian mixture, one is very close to a Gaussian model and is described by a mixture with a very small perturbating term, whereas the third one seems closer to the Middleton class A model but is non-stationary. The first noise is studied with emphasis on the normalization needed in the receiver in order to achieve a constant false alarm probability and also on the optimal receiver structure for the detection of a deterministic signal. It is shown that the classical noise power estimate, calculating the norm L-squared of the observation vector, is a good approximation to the square of the maximum likelihood estimator of the noise amplitude for the Gaussian-Gaussian mixture.