29 Auto- and cross-correlation plots for an m-sequence of degree 5.
Auto- and Cross-Correlations of an m-sequence
??“10
??“5
0
5
10
15
20
25
30
35
24 20 16 12 8 40 2832
Lag Number
Value
Autocorrelation
Cross-Correlation
7.5.2 Gold Codes
In this section, we will discuss Gold codes (1967) and their properties [12]. Gold codes obey the following
theorem: Sequences generated by combining binary m-sequences, a(x) and b(x), give crosscorrelation
peaks that are not greater than the minimum possible cross-correlation peaks between any
pair of maximal length sequences. This is a tremendous property to have since having a low crosscorrelation
function can directly relate to having low MAI as new users begin to use the available
spectrum. A general block diagram showing the method used to generate Gold codes is provided in
Fig. 7.30.
FIGURE 7.30 General Gold sequence generator block diagram.
PN Generator
#1
a(x)
b(x)
Gold Sequence
PN Generator
#2
+
In Fig 7.30, the binary m-sequences are sometimes referred to as ???preferred pairs.??? Gold
sequences are not maximal sequences. Hence, the autocorrelation function is not two valued; it is
three valued.
Given a(x) is an m-sequence of length N 2L 1, b(x) can be either an m-sequence or decimated
version from a(x), say a(rx).
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