Study On Signal Correlation Analysis Under Gaussian Mixture Model

The study on correlation analysis was started from the foundation of statistics, and it became one of the important branches of statistics. Even now topics about correlation analysis are still the hot spots in many subjects, including statistical signal processing. When we are dealing with signal detection and parameter estimation in radar and communication systems, it is frequently needed to figure out the correlation between the transmitted signal and the received signal. Correlation coefficient is the effective tool to quantify the strength of this correlation. Among the members of correlation coefficients, Pearson's correlation coefficient is always the most popular one because of the excellent performance in linear case, the completed proof and the simple and efficient algorithm. According to practical experience, researchers recognize that Spearman's correlation coefficient and Kendall's correlation coefficient do a good job on some nonlinear cases. In addition to these three classical correlation coefficients, researchers have proposed some other correlation coefficients, such as Gini Correlation and Pearson's rank-variate correlation coefficient. Nowadays, the theoretical study on Pearson's correlation coefficient, Spearman's correlation coefficient and Kendall's correlation coefficient is just on the base of the idealized bivariate-normal-model. The asymptotic properties of Gini Correlation under bivariate-normal-model has been published in recent years. The study work on Pearson's rank-variate correlation coefficient has been sluggish for a very long time. In spite of the widely use of correlation coefficient, some gaps are needed to be filled on the theoretical study on correlation coefficient.Except the general problems in correlation analysis, there are some particular fators when we focus on the cases about correlation analysis between transmitted signal and received signal. Correlation analysis between two signals is one of the techniques in signal processing, which are used to extract interesting information from noise. Then the character of noise is an essential factor for the performance of correlation analysis. Untill now, most of the studies about signal processing are based on addictive Gaussian white noise. But it has been verified that addictive Gaussian white noise can not simulate some common noise any more, because particular assumptions are needed to be met for the utility of addictive Gaussian white noise, and it does not in the real word. Caused by the disequilibrium among noise sources, impulsive noise appears. Then it is in need to study the signal correlation analysis under impulsive noise.For this purpose, we discuss some topics about signal correlation analysis under impulsive noise in this dissertation:1. Establish the model of impulsive noise. Refering to Middleton's Class A model, we use two-term Gaussian mixture model to simulate impulsive noise, and establish contaminated Gaussian Model as the system model to illustrate the relationship between transmitted signal and received signal;2. Study the properties of all correlation coefficients mentioned above under CGM. At first, we explore the properties of three classical correlation coefficients under CGM. Based on the results from the previous step, we reveal the properties of Gini Correlation and Pearson's rank-variate correlation coefficient under CGM in order to find out the best one to deal with impulsive noise;3. Rewrite the definition expressions of Gini Correlation and Pearson's rank-variate correlation coefficient and propose the parallel computation frameworks for these two correlation coefficients;4. Based on the theoretical results and experimental data, we peopose a signal detection scheme under CGM.According to the main Contents in this dissertation, there are two kinds of contribution. In terms of theoretical contribution, some gaps of the study on correlation coefficients under CGM are filled. It sets the baseline for follow-up research and provide guidance for the application of correlation coefficients. For application, we propose a signal detection scheme based on Gini Correlation and the parallel computation frameworks for Gini Correlation and Pearson's rank-variate correlation coefficient. It is helpful for the application of correlation coefficients.