Correlation functions of complete AltBOC signals with a constant envelope

Abstract

The structure of the modulating function (MF) of a complete alternative binary offset carrier modulated signal (AltBOC signal) with a constant envelope (eight-component complete AltBOC signal) is considered. Analytical expressions for the correlation functions (CFs) of single elements of the MFs of complete AltBOC signals with a constant envelope are derived at typical values of multiplicity coefficient Nm of meander pulses (Nm = 2 and 3). Plots of the CFs of single elements of the MFs of complete AltBOC signals with a constant envelope are obtained for Nm = 2 and 3. The properties of these CFs are discussed. With the help of the Fourier transform applied to the CFs, the energy spectra (spectral power densities) of single elements of the MFs of complete AltBOC signals with a constant envelope are calculated at Nm = 2 and 3. In illustrating examples, most attention is focused on complete AltBOC signals with a constant envelope at the carrier frequency fcar = 1191.795 MHz for the AltBOC (15, 10) modulation and the repetition rate of the elements of ranging-code pseudorandom sequences fs = 10fref = 10.23 MHz, where the reference (base) frequency is fref = 1.023 MHz. These signals are applied in the Galileo European satellite radio navigation system (SRNS) and, as is supposed, in the Chinese BeiDou-2/Compass SRNS.