Pseudorandom Noise (PN) Sequence Basics and MATLAB Code

PN sequences are widely used in CDMA systems for several key reasons:

• To spread the bandwidth of the baseband modulated signal to a much larger bandwidth before transmission.
• To distinguish between different users by allocating unique PN sequences to them.

Image alt: PN sequence generation

PN sequence stands for Pseudorandom Noise Sequence. Though the name suggests they are random sequences, they are not truly random. PN sequences are deterministic and periodic in nature. The same pattern repeats after a specific duration.

Important Properties of a PN Sequence

• The relative frequencies of ones and zeros are each approximately equal to one half.
• For runs of 1s and 0s, half of all run lengths are of length 1; 1/4 are of length 2; 1/8 are of length 3, and so on.
• If a new sequence is generated by shifting the original sequence by nonzero elements, then an equal number of agreements and disagreements exist between these two sequences.

PN sequences are generated by combining the outputs of feedback shift registers. One such circuit is typically depicted in block diagrams explaining its operation (see linked image for example).

PN Sequence MATLAB Code

Here’s an example of MATLAB code to generate a PN sequence of length 1023:

%%PN Sequence Generator in matlab of length 1023
h = commsrc.pn('GenPoly', [[8 2 0]], 'Mask', [1 0 0 0 0 0 1 0]);
set(h, 'NumBitsOut', 1023);
pnseq = generate(h);
for k=1:length(pnseq)
 if(pnseq(k) == 0)
  pnseq(k) = -1;
 end
end
maxpeak = xcorr(pnseq,pnseq);
plot(maxpeak);