10

# signal which has been buried under noise. Ideally, a pseudorandom sequence should have an

autocorrelation function with the property that for ϕ(n) = 0 and ϕ(j) = 0 for 1 ≤ j ≤ n-1. For m-

=

=0

−1

(1 ≤ ≤ − 1)

sequences the autocorrelation function is written as:

(2)

# For large m-sequences, the size of the off-peak values of the autocorrelation are relative to the

peak value

/

0

= -1/n , which becomes small and irrelevant. Therefore, m-sequences are

almost ideal when viewed in terms of autocorrelation function [12].

# In anti-jamming applications of PN spread spectrum signals, the period of the sequence

must be large in order to prevent the jammer from learning the feedback connections of the PN

generator. However, this requirement is impractical in most cases because the jammer can

determine the feedback connections by observing only 2n-1 chips from the PN sequence. This

vulnerability of the PN sequence is due to the linearity property of the generator. To solve this,

output sequences from several stages of the shift register or outputs from several distinct m-

sequences are combined in a non-linear way to produce a non-linear sequence that is

considerably more difficult for the jammer to learn.

# The periodic autocorrelations functions for most of the Gold sequences are not as good as

the periodic autocorrelations functions for m-sequences. Also, Gold sequences of period 2^{n}-1

can be generated by linear feedback shift registers with 2n storage elements, and so their periods

are approximately the square root of the maximum periods for linear sequences generated with