The Utility of Higher-Order Statistics in Gaussian Noise Suppression

The properties of higher-order statistics are becoming more and more thoroughly studied in the field of signal processing. One property of great interest is the fact that the cumulants of Gaussian signals disappear entirely at higher orders. Because many noise and interference signals have Gaussian distributions, this property offers the possibility that higher-order statistics may be useful in signal recovery or interference mitigation, which would be of great advantage in military communications, intelligence, or surveillance systems. This thesis examines some of the theory behind higher-order statistics, and discusses the estimation of third-order cumulant values for several random variable distributions. After a minimum sample size has been determined, the study progresses to the frequency domain for an examination of the bispectra of the distributions. The thesis then explores the bispectra of non-Gaussian signals in the presence of Gaussian noise, and concludes with recommendations for implementing signal processing systems which utilize higher-order statistics. The original document contains color images.