Pseudo-Random Sequences
Introduction:
A Pseudo-random Noise (PN) sequence is a sequence of binary numbers, e.g. ±1, which appears to be random; but is in fact perfectly deterministic. The sequence appears to be random in the sense that the binary values and groups or runs of the same binary value occur in the sequence in the same proportion they would if the sequence were being generated based on a fair "coin tossing" experiment. In the experiment, each head could result in one binary value and a tail the other value.
Pseudo-Random Sequence Generator:
- Binary sequences are shifted through the shift registers in response to clock pulses, and the output of the various stages are logically combined and fed back as the input to the first stage.
Figure 12.2 Block diagram of a generalized feedback shift register with m stages. |
PN sequence generator:
- When the feedback logic consists of exclusive-OR gates, the shift register is called a linear PN sequence generator.
- There are exactly 2^{M}-1 nonzero states for an rn-stage feedback shift register, the period of a PN sequence produced by a linear M-stage shift register cannot exceed2^{M}-1 symbols.
- A sequence of period 2^{M}-1 generated by a linear feedback register is called a maximal length (ML) sequence
Figure 12.2 PN Sequence Generators |
A pseudonoise sequence has many characteristics that are similar to those of random binary sequences
- They having a nearly equal number of 0s and 1s.
- They having a very low correlation between shifted versions of the sequence.
- They having a very low crosscorrelation between any two sequences.