Global Positioning System Reference
In-Depth Information
Table 4.4
GPS Code Generator Polynomials and Initial States
Register
Polynomial
Initial State
C/A code G1
X
3
X
10
1111111111
1
+
+
C/A code G2
X
2
X
3
X
6
X
8
X
9
X
10
1111111111
1
+
+
+
+
+
+
X
6
X
8
X
11
X
12
P code X1A
1
+
+
+
+
001001001000
P code X1B
1
+
X
1
+
X
2
+
X
5
+
X
8
+
X
9
+
X
10
+
X
11
+
X
12
010101010100
P code X2A
1
+
X
1
+
X
3
+
X
4
+
X
5
+
X
7
+
X
8
+
X
9
+
X
10
+
X
11
+
X
12
100100100101
P code X2B
1
+
X
2
+
X
3
+
X
4
+
X
8
+
X
9
+
X
12
010101010100
There is also a phase precession between the X2A/X2B shift registers with respect
to the X1A/X1B shift registers. This is manifested as a phase precession of 37 chips
per X1 period between the X2 epochs (shown in Figure 4.11 as the output of the
divide by 37 counter) and the X1 epochs. This is caused by adjusting the X2 period to
be 37 chips longer than the X1 period. The details of this phase precession are as fol-
lows. The X1 epoch is defined as 3,750 X1A cycles. When X1A has cycled through
3,750 of these cycles, or 3,750
15,345,000 chips, a 1.5-second X1 epoch
occurs. When X1B has cycled through 3,749 cycles of 4,093 chips per cycle, or
15,344,657 chips, it is kept stationary for an additional 343 chips to align it to X1A
by halting its clock control until the 1.5-second X1 epoch resumes it. Therefore, the
X1 registers have a combined period of 15,345,000 chips. X2A and X2B are con-
trolled in the same way as X1A and X1B, respectively, but with one difference: when
15,345,000 chips have completed in exactly 1.5 seconds, both X2A and X2B are kept
stationary for an additional 37 chips by halting their clock controls until the X2
epoch or the start of the week resumes it. Therefore, the X2 registers have a combined
period of 15,345,037 chips, which is 37 chips longer than the X1 registers.
Note that if the P code were generated by X1
×
4,092
=
X2, and if it were not reset at the
end of the week, it would have the potential sequence length of 15,345,000
⊕
×
15,345,037
10
6
, this sequence
has a period of 266.41 days or 38.058 weeks. However, since the sequence is trun-
cated at the end of the week, each SV uses only one week of the sequence, and 38
unique one-week PRN sequences are available. The sequence length of each P code,
with the truncation to a 7-day period, is 6.1871
=
2.3547
×
10
14
chips. With a chipping rate of 10.23
×
10
12
chips. As in the case of C/A
code, the first 32 PRN sequences are reserved for the space segment and PRN 33
through 37 are reserved for other uses (e.g., pseudolites). The PRN 38 P code is
sometimes used as a test code in P(Y) code GPS receivers, as well as to generate a ref-
erence noise level (since, by definition, it cannot correlate with any used SV PRN sig-
nals). The unique P code for each SV is the result of the different delay in the X2
output sequence. Table 4.3 shows this delay in P code chips for each SV PRN num-
ber. The P code delays (in P code chips) are identical to their respective PRN num-
bers for the SVs, but the C/A code delays (in C/A code chips) are different from their
PRN numbers. The C/A code delays are typically much longer than their PRN num-
bers. The replica C/A codes for a conventional GPS receiver are usually synthesized
by programming the tap selections on the G2 shift register.
Table 4.3 also shows the first 10 C/A code chips and the first 12 P code chips in
octal format, starting from the beginning of the week. For example, the binary
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