Pseudorandom noise
Encyclopedia
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.
In cryptographic device
s, the pseudorandom noise pattern is determined by a key
and the repetition period can be very long, even millions of years.
Pseudorandom noise is used in some electronic musical instruments
, either by itself or as an input to subtractive synthesis
, and in many white noise machine
s.
In spread-spectrum systems, the receiver correlates
a locally generated signal with the received signal.
Such spread-spectrum systems require a set of one or more "codes" or "sequences" such that
In a direct-sequence spread spectrum system, each bit in the pseudorandom binary sequence is known as a chip and the inverse of its period as chip rate. Compare bit rate
and baud
.
In a frequency-hopping spread spectrum sequence, each value in the pseudorandom sequence is known as a channel number and the inverse of its period as the hop rate. FCC Part 15 mandates at least 50 different channels and at least a 2.5 Hz hop rate for narrowband frequency-hopping systems.
sequence of bits but is deterministically generated. The most commonly used sequences in direct-sequence spread spectrum
systems are maximal length sequences, Gold code
s, Kasami code
s, and Barker codes.
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
, pseudorandom noise (PRN) is a signal similar to noise which satisfies one or more of the standard tests for statistical randomness
Statistical randomness
A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal dice roll, or the digits of π exhibit statistical randomness....
.
Although it seems to lack any definite pattern
Pattern
A pattern, from the French patron, is a type of theme of recurring events or objects, sometimes referred to as elements of a set of objects.These elements repeat in a predictable manner...
, pseudorandom noise consists of a deterministic sequence
Sequence
In mathematics, a sequence is an ordered list of objects . Like a set, it contains members , and the number of terms is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence...
of pulses
Pulse (signal processing)
In signal processing, the term pulse has the following meanings:#A rapid, transient change in the amplitude of a signal from a baseline value to a higher or lower value, followed by a rapid return to the baseline value....
that will repeat itself after its period.
In cryptographic device
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
s, the pseudorandom noise pattern is determined by a key
Key (cryptography)
In cryptography, a key is a piece of information that determines the functional output of a cryptographic algorithm or cipher. Without a key, the algorithm would produce no useful result. In encryption, a key specifies the particular transformation of plaintext into ciphertext, or vice versa...
and the repetition period can be very long, even millions of years.
Pseudorandom noise is used in some electronic musical instruments
Synthesizer
A synthesizer is an electronic instrument capable of producing sounds by generating electrical signals of different frequencies. These electrical signals are played through a loudspeaker or set of headphones...
, either by itself or as an input to subtractive synthesis
Subtractive synthesis
Subtractive synthesis is a method of sound synthesis in which partials of an audio signal are attenuated by a filter to alter the timbre of the sound...
, and in many white noise machine
White noise machine
A white noise machine is a device that produces a sound that is random in character, which sounds like a rushing waterfall or wind blowing through trees...
s.
In spread-spectrum systems, the receiver correlates
Correlation
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....
a locally generated signal with the received signal.
Such spread-spectrum systems require a set of one or more "codes" or "sequences" such that
- Like random noise, the local sequence has a very low correlation with any other sequence in the set, or with the same sequence at a significantly different time offset, or with narrowband interference, or with thermal noise.
- Unlike random noise, it must be easy to generate exactly the same sequence at both the transmitter and the receiver, so the receiver's locally generated sequence has a very high correlation with the transmitted sequence.
In a direct-sequence spread spectrum system, each bit in the pseudorandom binary sequence is known as a chip and the inverse of its period as chip rate. Compare bit rate
Bit rate
In telecommunications and computing, bit rate is the number of bits that are conveyed or processed per unit of time....
and baud
Baud
In telecommunications and electronics, baud is synonymous to symbols per second or pulses per second. It is the unit of symbol rate, also known as baud rate or modulation rate; the number of distinct symbol changes made to the transmission medium per second in a digitally modulated signal or a...
.
In a frequency-hopping spread spectrum sequence, each value in the pseudorandom sequence is known as a channel number and the inverse of its period as the hop rate. FCC Part 15 mandates at least 50 different channels and at least a 2.5 Hz hop rate for narrowband frequency-hopping systems.
PN Code
A pseudonoise code (PN code) is one that has a spectrum similar to a randomRandom number
Random number may refer to:* A number generated for or part of a set exhibiting statistical randomness.* A random sequence obtained from a stochastic process.* An algorithmically random sequence in algorithmic information theory....
sequence of bits but is deterministically generated. The most commonly used sequences in direct-sequence spread spectrum
Direct-sequence spread spectrum
In telecommunications, direct-sequence spread spectrum is a modulation technique. As with other spread spectrum technologies, the transmitted signal takes up more bandwidth than the information signal that is being modulated. The name 'spread spectrum' comes from the fact that the carrier signals...
systems are maximal length sequences, Gold code
Gold code
A Gold code, also known as Gold sequence, is a type of binary sequence, used in telecommunication and satellite navigation . Gold codes are named after Robert Gold. Gold codes have bounded small cross-correlations within a set, which is useful when multiple devices are broadcasting in the same range...
s, Kasami code
Kasami code
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....
s, and Barker codes.
See also
- Maximum length sequenceMaximum length sequenceA maximum length sequence is a type of pseudorandom binary sequence.They are bit sequences generated using maximal linear feedback shift registers and are so called because they are periodic and reproduce every binary sequence that can be reproduced by the shift registers...
- Pseudorandom number generatorPseudorandom number generatorA pseudorandom number generator , also known as a deterministic random bit generator , is an algorithm for generating a sequence of numbers that approximates the properties of random numbers...
- PseudorandomnessPseudorandomnessA pseudorandom process is a process that appears to be random but is not. Pseudorandom sequences typically exhibit statistical randomness while being generated by an entirely deterministic causal process...
- White noiseWhite noiseWhite noise is a random signal with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency...