Cyclic correntropy: Properties and the application in symbol rate estimation under alpha-stable distributed noise

Abstract

Over the past decades, cyclostationary signal processing has been considered one of the most critical theories in the field of nonstationary signal processing. Moreover, it has been widely adopted to handle practical problems, including signal parameter estimation, weak signal detection and pattern recognition. To improve the robustness of conventional methods under non-Gaussian noise, cyclic correntropy was recently proposed as the extension of correntropy in the cycle frequency domain. Due to the advantages inherited from both cyclostationary statistics and correntropy, cyclic correntropy has been employed in various applications involving co-channel interference and impulsive noise, such as carrier frequency estimation, direction of arrival (DOA) estimation, time difference of arrival (TDOA) estimation, automatic modulation classification and bearing fault diagnosis. Although cyclic correntropy has gained much attention, the related theoretical study is still insufficient, prohibiting further applications in other areas. To complete the theoretical framework, the existence condition of cyclic correntropy is first discussed in detail. Then, the relations among the cyclic correntropy spectrum, the symbol rate and the carrier frequency are addressed and proved mathematically. Besides, other properties of cyclic correntropy are also studied, involving symmetry, conjugation and time-shifting. These properties are studied for the first time and they fulfill the void of cyclic correntropy theory. Furthermore, a novel method is proposed for symbol rate estimation under non-Gaussian noise. Simulations are executed to validate the proposed method's superior robustness compared with other methods based on different cyclic spectra under the framework of cyclostationary signal processing. This method contributes to the application of cyclic correntropy, further highlighting the significance of the properties mentioned above.