Global Positioning System Reference
In-Depth Information
FIGURE 2.4. Stem plot of an ACF for a Gold sequence. The left stem has correlation value
r
p
(
0
)
=
1; all other correlation values are
63
1023
,or
−
65
−
1
1023
,
1023
. Only the first 50 lags out
of 1023 are shown.
have 10 cells generating sequences of length 1023. The two resulting 1023 chip-
long sequences are modulo-2 added to generate a 1023 chip-long C/A code, only
if the polynomial is able to generate code of maximum length.
Every 1023rd period, the shift registers are reset with all ones, making the code
start over. The
G
1
register always has a feedback configuration with the polyno-
mial
x
3
x
10
f
(
x
)
=
1
+
+
,
(2.6)
meaning that state 3 and state 10 are fed back to the input. In the same way, the
G
2
register has the polynomial
x
2
x
3
x
6
x
8
x
9
x
10
f
(
x
)
=
1
+
+
+
+
+
+
.
(2.7)
To make different C/A codes for the satellites, the output of the two shift reg-
isters are combined in a very special manner. The
G
1
register always supplies its
output, but the
G
2
register supplies two of its states to a modulo-2 adder to gen-
erate its output. The selection of states for the modulo-2 adder is called the phase
selection. Table 2.3 shows the combination of the phase selections for each C/A
code. It also shows the first 10 chips of each code in octal representation.
As the generation of the C/A codes are of immense importance, we outline in
detail the principle of operation of the C/A code generator in the next section.
2.3.3 Gold Sequence Generation—Details
A shift register is a set of one bit storage or memory cells. When a clock pulse
is applied to the register, the content of each cell shifts one bit to the right. The
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