We will present two approaches used to generate PN code sequences: namely, the Fibonacci and
Galois approaches. The relationship between these two approaches will be provided in order to gain
insight into the PN codes [4].
General shift register implementations of PN sequences are given by . The first
approach is called the Fibonacci approach and is given in Fig. 7.22.
The polynomial for this implementation is given as (where x represents a shift in time)
(7.32) p(x) 1 C1x C2x2 c Cn1xn1 xn
Ci GF(2)
3G WIDEBAND CDMA 359
FIGURE 7.21 Chip-level RAKE receiver.
RF
Section
ADC
X
*
Time
Deskew
&
Combine
X
*
RAKE
Output
...
hN(t)
h1(t)
C1(t)
X
Matched Filter
PG
. Tc
dt
0
??«
360 CHAPTER SEVEN
FIGURE 7.22 Fibonacci-type PN generator.
Tc
X C1
Tc Tc Tc
+
X
+
C2 X
+
Cn??“2 X
+
Cn??“1
. . .
xn??“1 x2 x xn
. . .
FIGURE 7.23 Galois-type PN generator.
Tc
X C1
Tc Tc Tc +
X
+
C2 X
+
Cn??“2 X
+
Cn??“1
. . .
xn??“1 xn
x2 x
. . .
The second approach is called the Galois approach and is given in Fig. 7.23.
The polynomial for this implementation is given as (where x represents a shift in time)
(7.33)
where the following relationship holds true between the two approaches: The value of n is used to represent
the maximum number of shift registers used in the generation of the PN code.
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