In
cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...
, pseudorandom noise (PRN) is a
signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...
similar to
noise
Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference aris ...
which satisfies one or more of the standard tests for
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.
Statistical randomness does ...
. Although it seems to lack any definite
pattern
A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated li ...
, pseudorandom noise consists of a deterministic
sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is calle ...
of
pulses
In medicine, a pulse represents the tactile arterial palpation of the cardiac cycle (heartbeat) by trained fingertips. The pulse may be palpated in any place that allows an artery to be compressed near the surface of the body, such as at the nec ...
that will repeat itself after its period.
In
cryptographic devices, the pseudorandom noise pattern is determined by a
key and the repetition period can be very long, even millions of digits.
Pseudorandom noise is used in some
electronic musical instruments
Electronic may refer to:
*Electronics, the science of how to control electric energy in semiconductor
* ''Electronics'' (magazine), a defunct American trade journal
* Electronic storage, the storage of data using an electronic device
* Electronic ...
, either by itself or as an input to
subtractive synthesis
Subtractive synthesis is a method of sound synthesis in which partials of an audio signal (often one rich in harmonics) are attenuated by a filter to alter the timbre of the sound. While subtractive synthesis can be applied to any source audio ...
, and in many
white noise machines.
In
spread-spectrum
In telecommunication and radio communication, spread-spectrum techniques are methods by which a signal (e.g., an electrical, electromagnetic, or acoustic signal) generated with a particular bandwidth is deliberately spread in the frequency dom ...
systems, the receiver
correlates a locally generated signal with the received
signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...
. 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 narrow band 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
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 ...
system, each bit in the
pseudorandom binary sequence
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 rand ...
is known as a ''
chip Chromatin immunoprecipitation (ChIP) is a type of immunoprecipitation experimental technique used to investigate the interaction between proteins and DNA in the cell. It aims to determine whether specific proteins are associated with specific genom ...
'' and the ''inverse'' of its period as ''
chip rate''; ''compare
bit rate and
symbol rate.''
In a
frequency-hopping spread spectrum
Frequency-hopping spread spectrum (FHSS) is a method of transmitting radio signals by rapidly changing the carrier frequency among many distinct frequencies occupying a large spectral band. The changes are controlled by a code known to both tr ...
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 narrow band frequency-hopping systems.
GPS satellites broadcast data at a rate of 50 data bits per second – each satellite modulates its data with one PN bit stream at 1.023 million
chips per second and the same data with another PN bit stream at 10.23 million chips per second.
GPS
The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...
receivers correlate the received PN bit stream with a local reference to measure distance. GPS is a receive-only system that uses relative timing measurements from several satellites (and the known positions of the satellites) to determine receiver position.
Other
range-finding applications involve two-way transmissions. A local station generates a pseudorandom bit sequence and transmits it to the remote location (using any modulation technique). Some object at the remote location echoes this PN signal back to the location station – either passively, as in some kinds of radar and sonar systems, or using an active transponder at the remote location, as in the Apollo
Unified S-band
The Unified S-band (USB) system is a tracking and communication system developed for the Apollo program by NASA and the Jet Propulsion Laboratory (JPL). It operated in the S band portion of the microwave spectrum, unifying voice communications, ...
system. By correlating a (delayed version of) the transmitted signal with the received signal, a precise round trip time to the remote location can be determined and thus the distance.
PN code
A pseudo-noise code (PN code) or pseudo-random-noise code (PRN code) is one that has a spectrum similar to a
random sequence The concept of a random sequence is essential in probability theory and statistics. The concept generally relies on the notion of a sequence of random variables and many statistical discussions begin with the words "let ''X''1,...,''Xn'' be independ ...
of bits but is
deterministically generated. The most commonly used sequences in
direct-sequence spread spectrum
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 ...
systems are
maximal length sequences,
Gold code
A Gold code, also known as Gold sequence, is a type of binary sequence, used in telecommunication ( CDMA) and satellite navigation ( GPS). Gold codes are named after Robert Gold. Gold codes have bounded small cross-correlations within a set, which ...
s,
Kasami code Kasami may refer to:
* Kasami, Iran, a village in Sistan and Baluchestan Province, Iran
* Pajtim Kasami, a Swiss footballer
* Tadao Kasami, a Japanese information theorist
:* Kasami code, a line code associated with him
{{dab ...
s, and
Barker code
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 sender and receiver.
Explanation
Binary digits ha ...
s.
See also
*
Barker code
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 sender and receiver.
Explanation
Binary digits ha ...
*
Gold Codes
The Gold Codes are the launch codes for nuclear weapons provided to the President of the United States in their role as commander-in-chief of the armed forces. In conjunction with the nuclear football, the Gold Codes allow the president to autho ...
*
Maximum length sequence
A maximum length sequence (MLS) 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 (except th ...
*
Zadoff–Chu sequence
A Zadoff–Chu (ZC) sequence, also referred to as Chu sequence or Frank–Zadoff–Chu (FZC) sequence, is a complex-valued mathematical sequence which, when applied to a signal, gives rise to a new signal of constant amplitude. When cyclically sh ...
*
Pseudorandom number generator
A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generate ...
*
Pseudorandomness
A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process.
Background
The generation of random numbers has many uses, such as for random ...
*
White noise
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines ...
References
{{Cdma
Noise (electronics)
Pseudorandomness