Pseudorandom noise

In cryptography, pseudorandom noise (PRN^[1][2]) 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.^[3]

In cryptographic devices, 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 machines.

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

• 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 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.

PN Code

A pseudonoise code (PN code) is one that has a spectrum similar to a random sequence of bits but is deterministically generated. The most commonly used sequences in direct-sequence spread spectrum systems are maximal length sequences, Gold codes, Kasami codes, and Barker codes.^[4]

See also

• Maximum length sequence
• Pseudorandom number generator
• Pseudorandomness
• White noise

References

1. ^ "Change Topic: Pseudorandom Noise (PRN) Expansion". GPS.GOV. http://www.gps.gov/technical/icwg/meetings/2011/09/13/WAS-IS-FINAL_PRN_Expansion_4May2011.pdf. Retrieved 13 July 2011. 
2. ^ "Pseudorandom Noise (PRN) Code Assignments". Los Angeles Air Force Base. http://www.losangeles.af.mil/library/factsheets/factsheet.asp?id=8618. Retrieved 13 July 2011. 
3. ^  This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C" (in support of MIL-STD-188).
4. ^ [1]