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Binary offset carrier modulation (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 Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( , , ) or mononymously as Galileo, was an Italian astronomer, physicist and engineer, sometimes described as a poly ...
and is a square sub-carrier
modulation Signal modulation is the process of varying one or more properties of a periodic waveform in electronics and telecommunication for the purpose of transmitting information. The process encodes information in form of the modulation or message ...
, where a signal is multiplied by a rectangular sub-carrier of frequency f_\text equal to or greater than the chip rate. Following this sub-carrier
multiplication Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division (mathematics), division. The result of a multiplication operation is called a ''Product (mathem ...
, the
spectrum A spectrum (: spectra or spectrums) is a set of related ideas, objects, or properties whose features overlap such that they blend to form a continuum. The word ''spectrum'' was first used scientifically in optics to describe the rainbow of co ...
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 set up, 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.


Design

The main idea behind BOC modulation is to reduce the interference with BPSK-modulated signals, which have a
sinc function In mathematics, physics and engineering, the sinc function ( ), denoted by , has two forms, normalized and unnormalized.. In mathematics, the historical unnormalized sinc function is defined for by \operatorname(x) = \frac. Alternatively, ...
shaped spectrum. Therefore, BPSK-modulated signals such as C/A GPS codes have most of their spectral energy concentrated around the
carrier frequency In telecommunications, a carrier wave, carrier signal, or just carrier, is a periodic waveform (usually sinusoidal) that conveys information through a process called ''modulation''. One or more of the wave's properties, such as amplitude or fre ...
, while BOC-modulated signals (used in Galileo system) have low energy around the carrier frequency and two main spectral lobes further away from the carrier (thus the name of split-spectrum). BOC modulation has several variants: sine BOC (sinBOC), cosine BOC (cosBOC), alternative BOC (altBOC), multiplexed BOC (MBOC), double BOC (DBOC) etc. and some of them have been currently selected for Galileo
GNSS A satellite navigation or satnav system is a system that uses satellites to provide autonomous geopositioning. A satellite navigation system with global coverage is termed global navigation satellite system (GNSS). , four global systems are op ...
signals. A BOC waveform is typically denoted via BOC(m, n) or BOC(f_\text,\; f_\text), where f_\text is the sub-carrier frequency, f_\text is the chip frequency, m = f_\text/f_\text, n = f_\text/f_\text, and f_\text = 1.023Mcps is the reference chip frequency of C/A GPS signal. A sine BOC(1, 1) modulation is similar to
Manchester code In telecommunications and data storage, Manchester code (also known as phase encoding, or PE) is a line code in which the encoding of each data bit is either low then high, or high then low, for equal time. It is a self-clocking signal with no ...
; that is, in the digital domain, a '+1' is encoded as a '+1 −1' sequence, and a '0' is encoded as a '−1 +1' sequence. For an arbitrary N_\text = 2m/n modulation order, in sine BOC(''m'', ''n'') case, a '+1' is encoded as an alternating sequence of '+1 −1 +1 −1 +1 ...', having N_\text elements, and a '0' (or '−1') is encoded as an alternating '−1 +1 ...' sequence, also having N_\text elements. BOC modulation is typically applied on
CDMA Code-division multiple access (CDMA) is a channel access method used by various radio communication technologies. CDMA is an example of multiple access, where several transmitters can send information simultaneously over a single communicatio ...
signals, where each chip of the
pseudorandom A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process. Pseudorandom number generators are often used in computer programming, as tradi ...
code is split into BOC sub-intervals, as explained above (i.e., there are N_\text BOC intervals per chip). The
power spectral density In signal processing, the power spectrum S_(f) of a continuous time signal x(t) describes the distribution of power into frequency components f composing that signal. According to Fourier analysis, any physical signal can be decomposed into ...
of a BOC-modulated signal depends on the BOC modulation order N_\text = 2\frac = 2\frac. BOC-modulated signals, by difference with BPSK signals, create the so-called ambiguities in the correlation function. The BOC-modulated signals in GNSS can be processed either with a Full BOC receiver or via various unambiguous approaches.


See also

* Multiplexed binary offset carrier


References

{{DEFAULTSORT:Binary Offset Carrier Quantized radio modulation modes