Pseudorandom noise

In <a href="/facts/Cryptography/e94PEVau">cryptography</a>, pseudorandom noise (PRN) is a <a href="/facts/Signal/41YqUJ8c">signal</a> similar to <a href="/facts/Noise_(physics)/Izbv38Rr">noise</a> which satisfies one or more of the standard tests for <a href="/facts/Statistical_randomness/Ns0bkleV">statistical randomness</a>. Although it seems to lack any definite <a href="/facts/Pattern/mzD7uLQa">pattern</a>, pseudorandom noise consists of a deterministic <a href="/facts/Sequence/gV2S4uqp">sequence</a> of <a href="/facts/Pulse_(signal_processing)/2v5sWtyB">pulses</a> that will repeat itself after its period.
In <a href="/facts/Cryptography/e94PEVau">cryptographic devices</a>, the pseudorandom noise pattern is determined by a <a href="/facts/Key_(cryptography)/5W5PAmT4">key</a> and the repetition period can be very long, even millions of digits.
Pseudorandom noise is used in some <a href="/facts/Synthesizer/NrmdVrPa">electronic musical instruments</a>, either by itself or as an input to <a href="/facts/Subtractive_synthesis/2Kk3TqUE">subtractive synthesis</a>, and in many <a href="/facts/White_noise_machine/0fARlw5j">white noise machines</a>.
In <a href="/facts/Spread-spectrum/0NKdJX1S">spread-spectrum</a> systems, the receiver <a href="/facts/Correlation/egkluAEm">correlates</a> a locally generated signal with the received <a href="/facts/Signal_(information_theory)/41YqUJ8c">signal</a>. Such spread-spectrum systems require a set of one or more "codes" or "sequences" such that

<ul><li>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.</li>
<li>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.</li></ul>
In a <a href="/facts/Direct-sequence_spread_spectrum/l3u1HVTd">direct-sequence spread spectrum</a> system, each bit in the <a href="/facts/Pseudorandom_binary_sequence/fFSVtEE4">pseudorandom binary sequence</a> is known as a <a href="/facts/Chip_(CDMA)/SzuKoSWg">chip</a> and the inverse of its period as <a href="/facts/Chip_rate/SzuKoSWg">chip rate</a>; compare <a href="/facts/Bit_rate/ppUNMmVd">bit rate</a> and <a href="/facts/Symbol_rate/YlQ3JHVr">symbol rate</a>.
In a <a href="/facts/Frequency-hopping_spread_spectrum/hJS6o3xy">frequency-hopping spread spectrum</a> sequence, each value in the pseudorandom sequence is known as a channel number and the inverse of its period as the hop rate. <a href="/facts/FCC_Part_15/Dv80r4R3">FCC Part 15</a> 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 <a href="/facts/Chips_per_second/SzuKoSWg">chips per second</a> and the same data with another PN bit stream at 10.23 million chips per second.
<a href="/facts/GPS/DKVLnzF3">GPS</a> 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 <a href="/facts/Range-finding/ACNYnqPa">range-finding</a> 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 <a href="/facts/Unified_S-band/Q52AILHG">Unified S-band</a> 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.

Pseudorandom noise open-in-new

Pseudorandom noise