Theory And Application Of Gini Correlation For Detecting Known Signals In Colored Noise

Since the origin and development of correlation analysis in the 1880 s,it has become a research topic to explore the relationship between two random variables.The general metric used is the correlation coefficient.Correlation analysis has important research significance in statistical signal processing,which is an important research direction of signal processing.In the present literature and research materials,in addition to the spearman correlation coefficient,Pearson product moment correlation coefficient and Kendall correlation coefficient,which are widely used the their research and relatively perfect,scholars are also broadening the research field of the correlation coefficient,the concept of Gini correlation coefficient is proposed.In signal processing,the correlation analysis of the actual application of scene tend to be complex and changeable,in addition to gaussian white noise,signal mixed noise often has pulse noise,and sometime the noise may also have correlation between data sequence,which called the colored noise.The classical correlation coefficient called Pearson product moment correlation coefficient already no longer applicable in this situation,It does not have robustness when the signal has the impulse noise or the data with nonlinear transformation.Therefore,based on colored noise,this paper studies the detection of known signals by Gini correlation.In the process of theoretical analysis,this paper has completed the following work.Firstly,in order to facilitate research Gini correlation coefficient performance under colored noise,this article uses the gaussian mixture model to simulate the samples in colored noise with pulse scenes,and the expectation and variance of mathematical expressions of Gini correlation coefficient in this model is deduced,and through the monte carlo simulation experiments,we can verify the accuracy of the theoretical expression.Secondly,based on the expectation and variance mathematical expression of Gini correlation coefficient,we has managed the monte carlo simulation in efficiency to compare Gini correlation coefficient with The matched filter detcetor(MFD),The sign correlator(SC),Spearman 's rho(SR)and Kendall' s tau(KT)under the gaussian mixture model.It is verified that the validity of the Gini correlation is more practical under this model.Thirdly,under the monte carlo simulation experiments,we compared performance of Gini correlation coefficient with the locally optimal detector(LOD),MFD,SC,SR and KT on the ROC and the detection probability.Althought the LOD is optimal in theory,because distribution of noise is hard to know in actual application,so it is difficult to let LOD applied to the actual situations,so throught the result of the experiment,we also proved that Gini correlation coefficient has more excellent performance in this scenario.As the technology of correlation analysis becomes more and more mature in signal processing,our analysis of the characteristics of Gini correlation under colored noise will be of great significance for the selection of correlator in the subsequent practical application scenarios of signal detection.