Novel Nonlinear Functions used for Optimal Detection in Gaussian Mixture Noise based on Maximum Entropy Densities

Non-Gaussian noise poses a challenge to conventional detector techniques. In such a case it is possible to design a nonlinear detector that performs better than the optimal linear detectors. Locally optimal detector is one that has good performance when the signal is weak and the probability density function (PDF) of noise is known precisely. This paper deals with a new nonlinear detector for binary signal detection in Gaussian mixture noise. This detector is optimal without any constraints on signal strength, and it is convenient for non-Gaussian even symmetric PDF's. Furthermore, it does not require the knowledge of the exact noise PDF. We use maximum likelihood (ML) and maximum entropy, that are two optimal criteria, in obtaining this new detector. The proposed detector consists of new nonlinear functions followed by an accumulator and threshold comparator. These new nonlinear functions are polynomials consisting of odd power terms. Simulation results confirm the superiority of the new detector with respect to the previously proposed methods