Cyclostationary correntropy: Definition and applications

Information extraction is a frequent and relevant problem in digital signal processing. In the past few years, different methods have been utilized for the parameterization of signals and the achievement of efficient descriptors. When the signals possess statistical cyclostationary properties, the Cyclic Autocorrelation Function (CAF) and the Spectral Cyclic Density (SCD) can be used to extract second-order cyclostationary information. However,second-order statistics tightly depends on the assumption of gaussianity, as the cyclostationary analysis in this case should comprise higher-order statistical information. This paper proposes a new mathematical formulation for the higher-order cyclostationary analysis based on the correntropy function. The cyclostationary analysis is revisited focusing on the information theory, while the Cyclic Correntropy Function (CCF) and Cyclic Correntropy Spectral Density (CCSD) are also presented. The CCF has different properties compared with CAF that can be very useful in non-gaussian signal processing, especially in the impulsive noise environment which implies in the expansion of the class of problems addressed by the second-order cyclostationary analysis. In particular, we prove that the CCF contains information regarding second- and higher-order cyclostationary moments, being a generalization of the CAF. The performance of the aforementioned functions in the extraction of higher-order cyclostationary characteristics is analyzed in a wireless communication system in which non-gaussian noise is present. The results demonstrate the advantages of the proposed method over the second-order cyclostationary.