Average Rating:     In this post we are going to see the most important pseudo-noise sequences that are used in DSSS (direct-sequence spread-spectrum). As it was mentioned in previous post, these are deterministically generated, therefore, the time waveform generated from the PN also looks like random noise for an undesired receiver.

The first type of PN sequences are the m-sequences (binary maximal length shift-register sequence): as their name indicates, they are generated by using linear feeadback shift-registers and exclusive OR-gates. These circuits are configured to form an specific generator polynomial: when the coefficient is 1, the circuit switch is closed, otherwise it's open: There are some intesting properties about m-sequences:

- A cyclic shift of a m-sequence gives another valid m-sequence.

- All m-sequences have to satisty the recurrence condition: - Any m-sequence contains 2m-1 1's and 2m-1 -1 0's.

- The addition of two m-sequences is also a m-sequence. Even if one them is shifted of itselft (mod2).

- The normalized periodic autocorrelation function of an n-sequence is 1 at 0 and -1/N for the rest of the values: These are the most important proterties, thought there are some other concepts like the periodic and non-periodic autocorrelation functions, that I will post if I receive any request Gold sequences is the next type of PN sequences used in DSSS. Actually, they are constructed from a preferred-pair...and what is preferred pair?  It's just a pair of m-sequences with the same period N. They are related by some function y=x[q], where q is an odd number. It can be shown that preferred pairs don't exist for m=4,8,12,16 and q= 2k +1 or q= 22k - 2k + 1. Therefore, a set of Gold sequences includes a prefered-pair x and y, and the mod2 additions of x and cyclic shifts of y. The next image is an exmaple of Gold sequence for m=5: There are more PN sequences derived from the m-sequences, as the Kasami sequences which are obtained by decimating a m-sequence and performing mod2 sum on cyclically shifted sequences. Another type of PN sequences are orthogonal codes, and the most popular are the Walsh and Hadamard sequences, highly used in CDMA. These sequences have zero crosscorrelation (they are orthogonal). Comments and feedback will be welcomed! 