Novel Robust Normality Measure for Sparse Data and its Application for Weak Signal Detection

Abstract

In this paper, an important statistical signal processing characteristic, namely Gaussianity or normality, is studied. In contrast to the existing Gaussianity measures, we propose a novel measure, which is based on Kullback-Leibler divergence (KLD) between the Gaussian probability density function (PDF) and the generalized Gaussian PDF incorporated with the skewness for the normality test. In our studies, conventional normality tests may often not be robust when they are employed for the non-Gaussian processes with symmetric PDFs. We call this new test as the KGGS test. Our proposed KGGS test is heuristically justified to be more robust than conventional tests for different PDFs, especially symmetric PDFs. A popular application of the normality test for QPSK signal detections is also presented to verify the effectiveness of our proposed technique and the simulation results demonstrate that our new KGGS test would outperform all others even for sparse data samples.