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Concept
Pseudorandom noise
Summary
In cryptography, pseudorandom noise (PRN) 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.
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, 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 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 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 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 receivers correlate the received PN bit stream with a local reference to measure distance.
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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 random sequence. PRBS generators are used in telecommunication, such as in analog-to-information conversion, but also in encryption, simulation, correlation technique and time-of-flight spectroscopy. The most common example is the maximum length sequence generated by a (maximal) linear feedback shift register (LFSR).
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 the information bandwidth. After the despreading or removal of the direct-sequence modulation in the receiver, the information bandwidth is restored, while the unintentional and intentional interference is substantially reduced.
Linear-feedback shift register
In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function of single bits is exclusive-or (XOR). Thus, an LFSR is most often a shift register whose input bit is driven by the XOR of some bits of the overall shift register value. The initial value of the LFSR is called the seed, and because the operation of the register is deterministic, the stream of values produced by the register is completely determined by its current (or previous) state.
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