Detection of random signals in Gaussian mixture noise

A locally optimal detection algorithm for random signals in dependent noise is derived and applied to complex valved Gaussian mixture noise (GMN). The algorithm is modified so that it will detect signals that are not vanishingly small. 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 performance of the power detector and the locally optimal detector in GMN are compared using simulated and theoretical ROC curves. Additionally, the signal gain of the mixture detector relative to the power detector is calculated, for a fixed false alarm rate, as a function of the mixture parameters. The probability of detection of the mixture detector is also calculated, for fixed parameters and a fixed false alarm rate, as a function of the parameter estimation error