Binary offset carrier modulation

Binary offset carrier modulation^[1][2] (BOC modulation) was developed by John Betz in order to allow interoperability of satellite navigation systems. It is currently used in the US GPS system, Indian IRNSS system and in Galileo^[3] and is a square sub-carrier modulation, where a signal is multiplied by a rectangular sub-carrier of frequency ${\displaystyle f_{\text{sc}}}$ equal to or greater than the chip rate. Following this sub-carrier multiplication, the spectrum of the signal is divided into two parts, therefore BOC modulation is also known as a split-spectrum modulation. Their major advantages are, that one can shape the spectrum to allow inter-system-compatibility and better theoretically achievable tracking capabilities, due to higher frequencies if downmixed to the complex baseband. On the other hand, a huge variety of different implementations or instantiations was setup, making it difficult to get the whole picture. Early (and sometimes recent) publications dealing with that topic usually do not include matched filters for pulse shaping as well as the concept of complex Gaussian noise - which is very often not treated correctly - to yield a mathematically consistent baseband description, that although complicated looking, models the physics correctly. I.e. if these standards are not treated correctly, theoretical results are not reliable. This is independent of the media and the peer-review and the person, who published it.