Binary offset carrier

Binary Offset Carrier (BOC) is a special coding method for frequency spreading with application areas in digital communications technology with so-called code division multiplex . A number of user data sequences to be transmitted are distinguished by different pseudo-random code sequences (PRN). BOC is a special form of digital modulation technology that is also part of current research.

motivation

Conventional CDMA methods modulate the chips, as the individual discrete state values at the output of a pseudo-random data generator (PRN) are called, in most applications by means of analog phase shift keying of the RF carrier signal ( BPSK ) for data transmission, as it can be a radio channel. In the case of BOC, a further, discrete link is inserted between the chips of the PRN and the analog modulation of the RF carrier signal, which, depending on the parameters of the BOC method, leads to an additional bandwidth spread.

The aim is to minimize the mutual interference of different codes that are used in the context of different code division multiplexing methods in a shared medium such as a radio channel. This is particularly important if different code classes come together by means of code division multiplexing and the mutual interference between these different code classes is to be minimal. As an example, BOC enables a higher mutual immunity to interference while using special PRN generators such as gold sequences with different generator polynomials.

BOC does not change the properties on which the respective PRN generators are based, such as the respective generator polynomials, start values ​​or code phase shifts. BOC represents a kind of "intermediate layer" between different code generators for the purpose of improved code multiplexing over different code classes.

Procedure

To represent the function of BOC and its parameters, it is easiest to start from the so-called chip rate. This rate indicates the number of chips that the PRN generator delivers per second. The basic frequency f _{0 of} the BOC system is derived from this chip rate . The factor by which the fundamental frequency f _{0 is} lower than the chip rate is usually referred to in the literature as m :

${\displaystyle f_{0}={\frac {\text{Chip-Rate}}{m}}}$

The binary subcarrier, engl. Binary Offset Carrier , from which the name of this method is derived, represents a binary sequence {1, -1} with a fixed frequency f _s . This frequency is a multiple of the basic frequency f ₀ ; the factor in between is usually referred to in the literature as n :

${\displaystyle f_{s}=n\cdot f_{0}}$

The output signal is formed by a logical XOR link between the intermediate carrier and the chip sequence. The classification of the BOC method is derived from the factors n and m presented above ; In the literature this is usually written in the form BOC ( n , m ). n and m can be any real values ​​greater than or equal to 1.

In the spectral range , the two parameters n and m can be interpreted equally and more clearly:

• The parameter n indicates the factor by which, multiplied by the chip rate, the center frequency of the transmission spectrum is offset. For example, if n is 1 and the chip rate is 1 Mchip per second, then the transmission spectrum of the code sequence is spectrally offset by 1 MHz. Both sidebands occur, i.e. H. the BOC spectrum is mirrored symmetrically around the carrier center frequency. This spectral offset enables several different codes to be accommodated on the same transmission frequency by means of BOC by means of frequency division multiplexing.

• The parameter m specifies the factor by which the transmission spectrum of the output sequence is expanded. If m is 1, the spectrum of the BOC sequence is not expanded, is m equal to 5, the transmission spectrum is 5 times as wide as the original code sequence. In addition to the chip sequence, this factor represents a further band spreading and spectral expansion. The additional spreading facilitates the code multiplexing of different code sequences which do not necessarily have to be orthogonal to one another in the code space, i.e. with minimal cross-correlation of the code sequences to one another. Without BOC as a kind of intermediate coding layer, the PRN codes would therefore have a greater degree of mutual interference.

Examples

• BOC (1, 1) as the simplest form means that the fundamental frequency of the subcarrier is equal to the chip code rate. Exactly one chip is transmitted per period of the intermediate carrier. This clearly means that in the chronological sequence, each chip is inverted in half the transmission time. This additional inversion doubles the bit rate at the output of the BOC and thus achieves a spectral offset around the center frequency, similar to the Manchester coding. The spectrum of the BOC sequence at the output is only spectrally shifted by the chip rate at the input, but not expanded additionally.
• BOC (5, 3): The fundamental frequency of this system is 1/3 of the chip rate. Exactly 3 chip bits are transmitted per period of the basic frequency f ₀ . The carrier frequency with which the PRN chip sequence is XORed is exactly five times the basic frequency. Due to the non-integer divisibility from 5 to 3, chip changes within the period of the fundamental frequency result in spectral frequency multiples which cause the complex band spreading. The spectrum of the BOC sequence at the output is offset by 5 times the chip rate symmetrically around the center frequency and spectrally expanded 3 times as much as the chip sequence at the input.
• With BOC, the chip rate does not have to be an integer multiple of the basic frequency. Methods such as BOC (15, 2.5), where 2.5 chips are transmitted per period of the basic frequency, are also possible. However, these special coding methods are currently rarely used in practice and are still the subject of corresponding research.

Applications

BOC is used in digital code division multiplex transmissions such as those used in the newer generation of satellite navigation. This scheme was specified for the European GALILEO system for the first time for satellite-based navigation. This was z. Taken over for the American NAVSTAR. The new satellites of the GPS system use BOC-based transmission techniques in combination with the older and previously common transmission techniques with C / A code or P / Y code .

Multiplexed binary offset carrier

Various BOC methods can be multiplexed in order to achieve a further redistribution of the spectral signal power. For Galileo and the newer GPS L1C signal, a combination of a BOC (1,1) and a BOC (6,1) signal is being discussed. The BOC (1,1) signal receives 10/11 of the total signal energy with the following spectral power density Φ:

${\displaystyle \Phi (f)={\frac {10}{11}}BOC(1,1)+{\frac {1}{11}}BOC(6,1)}$

For the L1C signal, however, a time division multiplex procedure (TMBOC) is being used. The BOC (1,1) modulated signal is sent for 30 symbols at full power and the BOC (6,1) modulated signal for 3 symbols at full power. The spectrum is the same in both cases. However, if only short symbol sequences are analyzed, the behavior is not identical. The technical implementation for coding and decoding is also different.

The advantage of the MBOC method compared to the conventional method is, on the one hand, a targeted possible spectral deformation in order to avoid interference from other signals, and, on the other hand, the ability to select the individual signal components. So z. B. With Galileo a receiver that only supports BOC (1,1) signals can also decode MBOC signals.

Individual evidence

1. ↑ GPS-Galileo Recommendations on Ll OS / LIC Optimization ( Memento from July 25, 2011 in the Internet Archive ) (English; PDF; 103 kB)

Web links

• BOC generator function for the Matlab program package .