Binary offset carrier

# Binary offset carrier

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Encyclopedia
Binary Offset Carrier modulation currently used in Galileo  is a square sub-carrier modulation
Modulation
In electronics and telecommunications, modulation is the process of varying one or more properties of a high-frequency periodic waveform, called the carrier signal, with a modulating signal which typically contains information to be transmitted...

, where a signal is multiplied by a rectangular sub-carrier of frequency equal or higher to the chip (CDMA)
Chip (CDMA)
In digital communications, a chip is a pulse of a direct-sequence spread spectrum code, such as a pseudo-noise code sequence used in direct-sequence code division multiple access channel access techniques....

rate. Following this sub-carrier multiplication
Multiplication
Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic ....

, the spectrum
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...

of the signal is divided into two parts, therefore BOC modulation is also known as a split-spectrum modulation.

The main idea behind BOC modulation is to reduce the interference with BPSK-modulated signal, which has a sinc function shaped spectrum. Therefore, BPSK-modulated signals such as C/A GPS codes have most of their spectral energy concentrated around the carrier frequency, 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
MBOC
Multiplexed binary offset carrier modulation is a modulation proposed for Galileo and modernized GPS signals, which combines a sine binary offset carrier SinBOC signal with a SinBOC signal, either via weighted sum/difference or via time-multiplexing...

), Double BOC (DBOC) etc. and some of them have been currently selected for Galileo GNSS signals.

A BOC waveform is typically denoted via BOC(m,n) or BOC, where is the sub-carrier frequency, is the chip frequency, , , and Mcps is the reference chip frequency of C/A GPS signal.

A sine BOC(1,1) modulation is similar to Manchester code
Manchester code
In telecommunication and data storage, Manchester code is a line code in which the encoding of each data bit has at least one transition and occupies the same time...

, that is, in digital domain, a '+1' is encoded as a '+1 −1' sequence, and a '0' is encoded as a '−1 +1' sequence.
For an arbitrary modulation order, in sine BOC(m,n) case, a '+1' is encoded as an alternating sequence of '+1 −1 +1 −1 +1 ...', having elements, and a '0' (or '−1') is encoded as an alternating '−1 +1 ...' sequence, also having elements.

BOC modulation is typically applied on CDMA signals, where each chip of the pseudorandom code is split into BOC sub-intervals, as explained above (i.e., there are BOC intervals per chip).

The power spectral density
Spectral density
In statistical signal processing and physics, the spectral density, power spectral density , or energy spectral density , is a positive real function of a frequency variable associated with a stationary stochastic process, or a deterministic function of time, which has dimensions of power per hertz...

of a BOC-modulated signal depends on the BOC modulation order and its derivation can be found, for example, in