Let N1
denote the number of times ???1??? occurs in a single period, and let N0 be the number of times ???0???
occurs in one period. Then we have the relationship N1 N0 1.
2. Shift and Add: If the m-sequence is added to its time-shifted version, the result is the same
m-sequence with a new shift.
3. Correlations: A measure of similarity or dissimilarity between the m-sequences of interest.
A goal of WCDMA system design is to find a set of spreading codes such that as many users as
possible can utilize the same bandwidth with as little multiple access interference (MAI). In order to
achieve such a goal, we are forced to study the autocorrelation and cross-correlation properties of PN
sequences.
Consider the following autocorrelation of the m-sequence:
(7.44) Rcc(k) aN
n1
Ckn # Cn eN; k 0
1; k 2 0
Similarly, the cross-correlation of the m-sequence is
(7.45)
In Fig. 7.29, we plot the results of the autocorrelation and cross-correlation for a few chosen
m-sequences. The sequences used a primitive polynomial of degree L5. From this particular example,
it is clear that the autocorrelation function has values that vary and depend on the lag of interest.
Rc1c2
(k) aN
n1
C(1)
kn # C(2)
n
3G WIDEBAND CDMA 365
FIGURE 7.
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