Correlation Functions of Navigational cosGBOC Signals as the Inverse Fourier Transform of the Energy Spectra

Abstract

Abstract—The modulating functions (MFs) of cosGBOC signals (cosine generalized BOC signals) for new-generation satellite radio navigation systems, such as Galileo (EU), GPS (USA), GLONASS (Russia), and BeiDou (China), are considered. Based on inverse Fourier transform (FT) of the energy spectra, analytical expressions are obtained and graphs are constructed for the correlation functions (CFs) of single elements of MFs of cosGBOC signals with a pulse ratio of $${{N}_{{\text{p}}}}$$ = 2 and 4 for different duty cycle values $$\rho $$, where $$\rho $$$$ \in $$ [0, 1]. When calculating the CF, the methodology is based on representing the energy spectrum as the weighted algebraic sum of the cosines of angles determined from the characteristic points of the cosine symbol of the MFs (CF kinks) of cosGBOC signals. In some cases, calculating the CFs of cosGBOC signals by inverse FT of the energy spectra is more preferable (in particular, in terms of labor intensiveness) compared to the method of obtaining the CF based on its general definition.