PseudoNoise

PseudoNoise, often abbreviated as PN, refers to a type of digital signal or sequence that exhibits properties similar to random noise but is generated by a deterministic algorithm. This means that while the sequence appears random and unpredictable to an observer without knowledge of the generating algorithm, it is entirely reproducible if the starting point, often called a seed, and the algorithm are known.

The primary characteristic of pseudo-noise sequences is their correlation properties. When a PN sequence is compared with a time-shifted version of itself, the correlation is very low, except when the shifts are multiples of the sequence length, at which point the correlation is maximal. This property makes them useful in various applications where distinguishing between signals and noise or synchronizing signals is important.

Pseudo-noise sequences are generated using mathematical operations, most commonly linear feedback shift registers (LFSRs). An LFSR is a shift register whose input bit is a linear function of its previous state. By choosing the appropriate taps for the feedback, LFSRs can generate maximal-length sequences (m-sequences), which are a common type of PN sequence. The length of the sequence is determined by the number of stages in the shift register.

Applications of pseudo-noise sequences are diverse. They are employed in spread spectrum communication systems, such as Direct Sequence Spread Spectrum (DSSS), to spread a narrow-band signal over a wider frequency band, improving resistance to interference and jamming. They are also used in cryptography for generating random keys and in testing digital systems due to their statistical randomness properties. In satellite navigation systems like GPS, PN sequences are used for ranging and code division multiple access (CDMA).