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 adv ...

, 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 called ...

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 co ...

, 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 machine A white noise machine is a device that produces a noise that calms the listener, which in many cases sounds like a rushing waterfall or wind blowing through trees, and other serene or nature-like sounds. Often such devices do not produce actual wh ...

s. 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 do ...

systems, the receiver correlates a locally generated signal with the received

. 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 In digital communications, a chip is a pulse of a direct-sequence spread spectrum (DSSS) code, such as a pseudo-random noise (PN) code sequence used in direct-sequence code-division multiple access (CDMA) channel access techniques. In a binary di ...

''; ''compare

bit rate In telecommunications and computing, bit rate (bitrate or as a variable ''R'') is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction ...

and

symbol rate 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 ' ...

.'' 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 ''CHiPs'' is an American crime drama television series created by Rick Rosner and originally aired on NBC from September 15, 1977, to May 1, 1983. It follows the lives of two motorcycle officers of the California Highway Patrol (CHP). The ser ...

and the same data with another PN bit stream at 10.23 million chips per second. GPS 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 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 of bits but is deterministically generated. The most commonly used sequences in

systems are maximal length sequences, Gold codes, Kasami codes, and Barker codes.

References

{{Cdma Noise (electronics) Pseudorandomness

PN code

See also

References