Detection of random signals in Gaussian mixture noise

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Abstract
A locally optimal detection algorithm for random signals in dependent noise is derived and applied to independent identically distributed complex-valued Gaussian mixture noise. The resulting detector is essentially a weighted sum of power detectors-the power detector is the locally optimal detector for random signals in Gaussian noise. The weighting functions are modified to enhance the detection performance for small sample sizes. An implementation of the mixture detector, using the expectation-maximization algorithm, is described. Moments of these detectors are calculated from piecewise-polynomial approximations of the weighting functions. The sum of sufficiently many independent identically distributed detector outputs is then approximated by a normal distribution. Probability distributions are also derived for the power detector in Gaussian mixture noise. For a particular set of noise parameters, the theoretical distributions are compared with those obtained from Monte Carlo simulation and seen to be quite close. The theoretical distributions are then used to compare the performance of the mixture and power detectors in Gaussian mixture noise over a range of parameters and to assess the impact of parameter error on detection performance. In this study, the signal gain of the mixture detectors varies from 15 to 38 dB, and the degradation of the probability of detection due to parameter estimation error is relatively minor

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