BOC power spectrum densities

Abstract : The GPS and GALILEO systems will take advantage of new signal modulations such as Binary Offset Carrier (BOC) that uses a square wave sub-carrier to create separate spectra on each side of the transmitted carrier. That signal could share the existing frequency bands with each other while reserving the spectrum, it provides spectral isolation and leads to significant improvements in terms of tracking, interference and multipath mitigation. As this BOC modulation, along with a modified version called alternate BOC (ALTBOC), is a serious candidate for GALILEO and GPS, it is important to understand all characteristics of this signal, in order to conduct several studies like payload design, receiver implementation, performance and robustness evaluation. One of the aspects of this signal is the power spectrum density that impacts all characteristics presented above. The aim of this paper is, in a first part, to review the currently admitted BOC power spectrum density theoretical expressions, and to discuss a deviation of the assumptions necessary for the derivation of these classical theoretical expressions w.r.t to the reality of these signals. Then, a second objective is to present theoretical expressions of ALTBOC and constant envelope ALTBOC power spectrum densities. First the paper recalls the formal expressions of the different possible offset carrier modulations: BOC, ALTBOC and constant envelop ALTBOC signals in the time domain. Then, the assumptions for the development of the classical power spectrum density calculation are clearly laid down. Next, it is shown that in the case of odd ratio (2*fs/fc) BOC signals, these assumptions, and particularly the fact that the BOC square sub-carrier can be incorporated in the chip waveform, are not met. Then, we show that, for these calculation assumptions to be met in that case of odd ratio BOC, it is equivalent to modify the code sequence. Finally, with this view, the obtained power spectrum density is the same as the one obtained with the classical theory, due to the negligible effect of the code sequence correlation values. Finally, we present the theoretical expressions of the ALTBOC and constant envelope ALTBOC power spectrum densities.
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Emilie Rebeyrol, Christophe Macabiau, Laurent Lestarquit, Lionel Ries, Jean-Luc Issler, et al.. BOC power spectrum densities. ION NTM 2005, National Technical Meeting of The Institute of Navigation, Jan 2005, San Diego, United States. pp 769 - 778. ⟨hal-01021737⟩

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