Polynomial Transformation Method for Non-Gaussian Noise Environment

TL;DR

This paper introduces a polynomial transformation method that preprocesses data to approximate non-Gaussian noise as Gaussian, improving signal detection and estimation in challenging noise environments.

Contribution

The paper proposes a novel polynomial transformation approach combined with minimum error-variance criterion for optimal detection in non-Gaussian noise.

Findings

Transforms non-Gaussian noise into near-Gaussian noise using polynomial approximation.

Monte Carlo simulations validate the Gaussian hypothesis via bicoherence analysis.

Histogram and kurtosis tests confirm the effectiveness of the transformation.

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.