Global Positioning System Reference
In-Depth Information
chip-by-chip sum of a maximal-length register sequence and any shift of itself is
the same sequence except for a shift). The delayed version of the
G
2
sequence is
binary-added to the output of
G
1
. That becomes the C/A code. The
G
1
and
G
2
shift registers are set to the all-ones state in synchronism with the epoch of the
X
1
code used in the generation of the P code (see ahead). The various alternative
pairs of
G
2
taps (delays) are used to generate the complete set of 36 unique PRN
C/A codes. These are Gold codes, Gold (1967), Dixon (1984), and any two have
a very low cross correlation (are nearly orthogonal).
There are actually 37 PRN C/A codes, but two of them (34 and 37) are identical.
A subset of the first 32 codes are assigned to (nominally 24) satellites and recycled
when old satellites die and new satellites are launched. Codes 33 through 37 are
reserved for other uses, including ground transmitters.
The P code generation follows the same principles as the C/A code, except that
4 shift registers with 12 cells are used. Two registers are combined to produce the
X
1
code, which is 15,345,000 chips long and repeats every 1.5 seconds; and two
registers are combined to produce the
X
2
code, which is 15,345,037 chips long.
The
X
1
and
X
2
codes can be combined with 37 different delays on the
X
2
code
to produce 37 different one-week segments of the P code. Each of the first 32
segments is associated with a different satellite.
2.3.4 Correlation Properties
The Gold codes are selected as spreading sequences for the GPS signals because
of their characteristics. The most important characteristics of the C/A codes are
their correlation properties. These properties are described now.
The two important correlation properties of the C/A codes can be stated as
follows:
Nearly no cross correlation
All the C/A codes are nearly uncorrelated with each
other. That is, for two codes
C
i
and
C
k
for satellites
i
and
k
, the cross
correlation can be written as
1022
C
i
C
k
r
ik
(
m
)
=
(
l
)
(
l
+
m
)
≈
0
for all
m
.
(2.8)
l
=
0
Nearly no correlation except for zero lag
All C/A are nearly uncorrelated with
themselves, except for zero lag. This property makes it easy to find out
when two similar codes are perfectly aligned. The autocorrelation property
for satellite
k
can be written as
1022
C
k
C
k
r
kk
(
)
=
(
)
(
+
)
≈
|
|≥
.
m
l
l
m
0
for
m
1
(2.9)
l
=
0
Figure 2.6 shows an example of the auto- and cross-correlation properties of the
C/A code. As expected, the figure shows high correlation at lag 0 when correlating
with the same C/A code, and low correlation when correlating with another C/A
code.
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