The correlation functions of single elements of the modulating functions of double complex meander noise-like navigation signals (alternative binary offset carrier modulated signals)

Abstract

The correlation characteristics of elements of complex meander pseudo-random sequences (PRSs) are analyzed. These sequences are the basis for forming double complex meander (DCM) noise-like signals (alternative binary offset carrier modulated signals—AltBOC signals) applied in new-generation satellite radio navigation systems (in particular, the European Galileo and Chinese Bei-Dou/Compass systems). Analytical expressions are obtained for the correlation functions (CFs) of single complex meander symbols (MSs) and for the cross CFs (CCFs) of the sine and cosine components of complex MSs. Formulas for the CFs of single elements of the modulating functions (MFs) of an elementary (two-component) AltBOC signal and a four-component AltBOC signal are derived for typical values of multiplicity coefficient Nm (Nm = 2 and 3). Plots of CFs and CCFs are depicted, and the properties of these functions are discussed. The Fourier transform is applied to obtain the energy spectra of single MSs of an elementary AltBOC signal and a complete four-component AltBOC signal. In the examples, the attention is focused on AltBOC signals with the AltBOC (15, 10) modulation and the repetition rate of PRS elements fs = 10 fref = 10.23 MHz, where the reference frequency is fref = 1.023 MHz.