Editing Pseudorandom noise (section)

{{Short description|Pseudo-random signal with characteristics similar to noise}}
{{Use American English|date = March 2019}}
{{Use mdy dates|date = March 2019}}

In [[cryptography]], '''pseudorandom noise''' ('''PRN'''<ref>{{cite web |url=http://www.gps.gov/technical/icwg/meetings/2011/09/13/WAS-IS-FINAL_PRN_Expansion_4May2011.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.gps.gov/technical/icwg/meetings/2011/09/13/WAS-IS-FINAL_PRN_Expansion_4May2011.pdf |archive-date=2022-10-09 |url-status=live |title=Change Topic: Pseudorandom Noise (PRN) Expansion |publisher=GPS.GOV |access-date=13 July 2011 }}</ref>) is a [[signal]] similar to [[noise (physics)|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 [[Pulse (signal processing)|pulses]] that will repeat itself after its period.<ref>{{FS1037C MS188}}</ref>

In [[cryptography|cryptographic device]]s, the pseudorandom noise pattern is determined by a [[key (cryptography)|key]] and the repetition period can be very long, even millions of digits.

Pseudorandom noise is used in some [[synthesizer|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 [[correlation|correlates]] a locally generated signal with the received [[signal (information theory)|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 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]] system, each bit in the [[pseudorandom binary sequence]] is known as a ''[[Chip (CDMA)|chip]]'' and the ''inverse'' of its period as ''[[chip rate]]''; ''compare [[bit rate]] and [[symbol rate]].''

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&nbsp;Hz hop rate for narrow band frequency-hopping systems.

GPS satellites broadcast data at a rate of 50 data bits per second &ndash; 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]] 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 &ndash; 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.<ref>[http://www.ab9il.net/aviation/apollo-s-band.html "The Apollo Unified S Band System"]
</ref> 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.