Polynomial Transformation Method for Non-Gaussian Noise Environment

Abstract: Signal processing in non-Gaussian noise environment is addressed in this paper. For many real-life situations, the additive noise process present in the system is found to be dominantly non-Gaussian. The problem of detection and estimation of signals corrupted with non-Gaussian noise is difficult to track mathematically. In this paper, we present a novel approach for optimal detection and estimation of signals in non-Gaussian noise. It is demonstrated that preprocessing of data by the orthogonal polynomial approximation together with the minimum error-variance criterion converts an additive non-Gaussian noise process into an approximation-error process which is close to Gaussian. The Monte Carlo simulations are presented to test the Gaussian hypothesis based on the bicoherence of a sequence. The histogram test and the kurtosis test are carried out to verify the Gaussian hypothesis.