pseudorandom noise (PRN), PN code, maximum-length sequence

pseudonoise, pseudorandom noise (PRN)

• PRN is a signal which is similar to noise

although it seems to lack any definite pattern, PRN consists of a deterministic sequence of pulses that will repeat itself after its period.

pseudonoise code (PN 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.

maximum length sequence^{[각주:1] [각주:2]}

• one of the simplest and most effective devices for generating deterministic sequences of pseudorandom Ones and Zeros is the shift register.

shift register of degree n is a device consisting of n consecutive binary storage positions, which shifts the contents of each position to the next position down the line at the rate set by a timing device, or clock. 

• a shift register can be converted into a pseudorandom sequence generator (more specific, maximum length sequence) by including a feedback loop, which computes a new term for the first stage based on the previous n terms.

from fig. 3, in the case of n=4, and feedback from stages 3 and 4 is modulo-2 added and returned to stage 1. if the initial state of the shift register is 1 0 0 0, then the output (from position 4) at each state would be 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 . this would continue repeating itself with a period of 15 states.

it may be ovserved that, while this looks like a random sequence, it is deterministic and has a finite periodicity.

 

• given any linear shift register of degree n, the ouput sequence is always ultimately periodic, with a period  at most. any output sequence achieving a period of  is called a maximum length sequence.

 

• correlation function and its power spectra of maximum length sequence
• correlation function

(FYI) for general signal,

for binary sequence auto-correlation,

 

based on above formula, general auto-correlation function for maximum length sequence looks like,

 

• power spectrum of correlation function

 

1. 자료는 'spread spectrum - principles and possible application to spectrum utilization and allocation, IEEE communication magazine 9 1978' 에서 발췌하였다. [본문으로]
2. 추가. 자료는 'theory of spread-spectrum communications - a tutorial [IEEE transactions on communications May 1982]' 에서 발췌하였다. [본문으로]