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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 communication channel. This allows several users to share a band of frequencies. To permit this without undue interference between the users, CDMA employs spread spectrum technology and a special coding scheme.
In telecommunications, direct-sequence spread spectrum (DSSS) is a spread-spectrum modulation technique primarily used to reduce overall signal interference. The direct-sequence modulation makes the transmitted signal wider in bandwidth than the information bandwidth. After the despreading or removal of the direct-sequence modulation in the receiver, the information bandwidth is restored, while the unintentional and intentional interference is substantially reduced.
In cryptography, pseudorandom noise (PRN) is a signal similar to noise which satisfies one or more of the standard tests for statistical randomness. Although it seems to lack any definite pattern, pseudorandom noise consists of a deterministic sequence of pulses that will repeat itself after its period.
The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit.
In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state.
DCF77 is a German longwave time signal and standard-frequency radio station. It started service as a standard-frequency station on 1 January 1959. In June 1973 date and time information was added. Its primary and backup transmitter are located at 50°0′56″N9°00′39″E in Mainflingen, about 25 km south-east of Frankfurt am Main, Germany. The transmitter generates a nominal power of 50 kW, of which about 30 to 35 kW can be radiated via a T-antenna.
A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent.
A maximum length sequence (MLS) is a type of pseudorandom binary sequence.
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). As of 2024, four global systems are operational: the United States's Global Positioning System (GPS), Russia's Global Navigation Satellite System (GLONASS), China's BeiDou Navigation Satellite System (BDS), and the European Union's Galileo.
A pseudorandom binary sequence (PRBS), pseudorandom binary code or pseudorandom bitstream is a binary sequence that, while generated with a deterministic algorithm, is difficult to predict and exhibits statistical behavior similar to a truly random sequence. PRBS generators are used in telecommunication, such as in analog-to-information conversion, but also in encryption, simulation, correlation technique and time-of-flight spectroscopy. The most common example is the maximum length sequence generated by a (maximal) linear feedback shift register (LFSR). Other examples are Gold sequences, Kasami sequences and JPL sequences, all based on LFSRs.
Real-time kinematic positioning (RTK) is the application of surveying to correct for common errors in current satellite navigation (GNSS) systems. It uses measurements of the phase of the signal's carrier wave in addition to the information content of the signal and relies on a single reference station or interpolated virtual station to provide real-time corrections, providing up to centimetre-level accuracy. With reference to GPS in particular, the system is commonly referred to as carrier-phase enhancement, or CPGPS. It has applications in land surveying, hydrographic surveying, and in unmanned aerial vehicle navigation.
In a digitally modulated signal or a line code, symbol rate, modulation rate or baud rate is the number of symbol changes, waveform changes, or signaling events across the transmission medium per unit of time. The symbol rate is measured in baud (Bd) or symbols per second. In the case of a line code, the symbol rate is the pulse rate in pulses per second. Each symbol can represent or convey one or several bits of data. The symbol rate is related to the gross bit rate, expressed in bits per second.
In telecommunication technology, a Barker code, or Barker sequence, is a finite sequence of digital values with the ideal autocorrelation property. It is used as a synchronising pattern between the sender and receiver of a stream of bits.
In applied mathematics, complementary sequences (CS) are pairs of sequences with the useful property that their out-of-phase aperiodic autocorrelation coefficients sum to zero. Binary complementary sequences were first introduced by Marcel J. E. Golay in 1949. In 1961–1962 Golay gave several methods for constructing sequences of length 2N and gave examples of complementary sequences of lengths 10 and 26. In 1974 R. J. Turyn gave a method for constructing sequences of length mn from sequences of lengths m and n which allows the construction of sequences of any length of the form 2N10K26M.
Kasami sequences are binary sequences of length 2N−1 where N is an even integer. Kasami sequences have good cross-correlation values approaching the Welch lower bound. There are two classes of Kasami sequences—the small set and the large set.
GPS signals are broadcast by Global Positioning System satellites to enable satellite navigation. Receivers on or near the Earth's surface can determine location, time, and velocity using this information. The GPS satellite constellation is operated by the 2nd Space Operations Squadron (2SOPS) of Space Delta 8, United States Space Force.
Binary offset carrier 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 and is a square sub-carrier modulation, where a signal is multiplied by a rectangular sub-carrier of frequency 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 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.
In the mathematical field of combinatorics, a bent function is a Boolean function that is maximally non-linear; it is as different as possible from the set of all linear and affine functions when measured by Hamming distance between truth tables. Concretely, this means the maximum correlation between the output of the function and a linear function is minimal. In addition, the derivatives of a bent function are balanced Boolean functions, so for any change in the input variables there is a 50 percent chance that the output value will change.
JPL sequences or JPL codes consist of two linear feedback shift registers (LFSRs) whose code sequence lengths La and Lb must be prime. In this case the code sequence length of the generated overall sequence Lc is equal to:
Ultra-wideband impulse radio ranging is a wireless positioning technology based on IEEE 802.15.4z standard, which is a wireless communication protocol introduced by IEEE, for systems operating in unlicensed spectrum, equipped with extremely large bandwidth transceivers. UWB enables very accurate ranging without introducing significant interference with narrowband systems. To achieve these stringent requirements, UWB-IR systems exploit the available bandwidth that they support, which guarantees very accurate timing and robustness against multipath, especially in indoor environments. The available bandwidth also enables UWB systems to spread the signal power over a large spectrum, avoiding narrowband interference.
References
- ↑ George, Maria; Hamid, Mujtaba; Miller, Andy (2001-01-10). "Gold Code Generators in Virtex Devices" (PDF). Virtex Series, Virtex-II Series, and Spartan-II family (Application note). 1.1. Xilinx. XAPP217. Archived from the original (PDF) on 2008-07-05. (9 pages)
- ↑ "Transmitted GPS Signals". The GPS System. kowoma GPS. 2009-04-19. Archived from the original on 2012-08-04.
- ↑ "Robert Gold, BS, MS, Ph.D." Robert Gold Comm Systems. 2011. Archived from the original on 2017-06-24. Retrieved 2008-07-18.
- ↑ Gold, Robert (October 1967). "Optimal binary sequences for spread spectrum multiplexing". IEEE Transactions on Information Theory (Correspondence). IT-13 (4): 619–621. doi:10.1109/TIT.1967.1054048.
- ↑ Holmes, Jack K. (2007-06-30). Spread Spectrum Systems for GNSS and Wireless Communications. GNSS Technology and Applications Series. Vol. 45. Artech House. p. 100. ISBN 978-1-59693-083-4.
