Tracking Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 276

certain ms of data, which is also the beginning of a navigation data. In other
words, the selected initial C/A code is also a navigation data transition point. It
should be noted that the navigation data transition point may or may not have
an actual phase transition. For this reason, the tracking starts at a specific initial
C/A code within the first 20 ms of data, as shown in Figure 11.3. In this figure
the initial C/A codes of two satellites, A and B, are shown. The beginning of
the navigation data of satellite A is in the third ms; thus, the tracking starts from
the third ms. For satellite B the tracking starts from the fifth ms. Once the initial
tracking starts, the tracking will run continuously.
11.5 GENERATION OF C/A CODE
In this section the generation of a digitized C/A will be presented because it
is different from the program listed in the end of Chapter 7. Here the Doppler
frequency and the initial code phase will be included in the code. By including the
Doppler frequency in the C/A code, the peak correlation output will be improved
slightly. First, the Doppler frequency affecting the sampling frequency will be
discussed. Second, the Doppler frequency also affects the initial code phase of
the C/A code generated in 20 ms time intervals.
The Doppler frequency effect was discussed in Section 10.12. However, there
are some differences between the discussion of that section and here. In
Section 10.12, the C/A code was only generated once. The Doppler frequency
was used to adjust the time shifting for noncoherent processing. In this section,
the C/A code is generated every 20 ms to better match the input data by taking
the carrier frequency into consideration. In generating 1 ms C/A code, if the car-
rier frequency is taken into consideration, the output will be slightly different.
For example, two sets of 5000 digitized points are generated from 1 ms of C/A
code of satellite number 1: one set with zero Doppler frequency and one with
a Doppler frequency of 5 kHz. Between the two sets of data there are about 6
points having different values that are dependent on the starting sample point. If
the Doppler frequency is taken into consideration in generating the C/A code, the
number of difference points can be reduced. This operation results in a slightly
higher correlation peak. The following paragraph will derive the relation between
the sampling frequency and the Doppler frequency.
If the Doppler frequency is positive, then the equivalent length of the C/A
code shrinks in time at the receiver, as shown in Figure 11.4. Figure 11.4a
shows the original C/A code and the sampling time. Figure 11.4b shows the
shortened C/A code with the same sampling rate. Another way to express this
effect is to decrease the equivalent sampling frequency but keep the length of
the C/A code at a constant value, which is equivalent to extending the sampling
time, as shown in Figure 11.4c. Note that the digitized values obtained from
Figures 11.4b and 11.4c should be the same.
The decreased sampling frequency is used to digitize the C/A code. The equiv-
alent sampling frequency f se and the corresponding sampling time t se can be