Hyperbolic tangent cyclic correlation and its application to the joint estimation of time delay and doppler shift

Abstract

Gaussian distribution is a classic model for additive background noise in scientific research. By assuming and applying Gaussian noise, scholars in different fields can apply themselves to fundamental research and propose many innovative theories based upon Gaussianity. As the scope of engineering applications continues to expand, a single model of background noise cannot meet the more stringent conditions, and the errors caused by inappropriate noise models cannot be ignored. In this paper, alpha-stable distribution is utilized to model additive background noise because of the generality of this distribution. Correspondingly, a novel similarity measurement named hyperbolic tangent correlation (HTC) is proposed to replace the conventional correlation. Then, hyperbolic tangent cyclic correlation (HTCC) used in cyclostationary signal processing is proposed and thoroughly studied. HTC and HTCC emphasize preserving the signal of interest (SOI) rather than suppressing the noise, as traditionally practiced. In particular, they effectively process both the amplitude and phase information in the SOI. To demonstrate the superiority of HTCC in processing amplitude and phase information against background noise, a representative application in time-frequency analysis is presented, and the resulting performance is compared to that of the existing methods. Considering the beneficial mathematical properties of the hyperbolic tangent function, we hope that HTC and HTCC will have more applications in signal processing.