Receiver Hardware Considerations - Fundamentals of Global Positioning System Receivers: A Software Approach - page 112

FIGURE 6.2 Relation between sampling rate and C/A code.

synchronized sampling frequency, it is difficult to obtain fine distance resolution.
This phenomenon is illustrated as follows.
Figure 6.2 shows the C/A code chip rate and the sampled data points. Figures
6.2a and 6.2b show the synchronized and the unsynchronized sampling, respec-
tively. In each figure there are two sets of digitizing points. The lower row is a
time-shifted version of the top row.
In Figure 6.2a, the time shift is slightly less than 195.5 ns. These two sets of
digitizing data are exactly the same as shown in this figure. This illustrates that
shifting time by less than 195.5 ns produces the same output data, if the sampling
frequency is synchronized with the C/A code. Since the two digitized data are
the same, one cannot detect the time shift. As a result, one cannot derive finer
time resolution (or distance) better than 195.5 ns through signal processing.
In Figure 6.2b the sampling frequency is lower than 5.115 MHz; therefore, it
is not synchronized with the C/A code. The output data from the time-shifted case
are different from the original data as shown in the figure. Under this condition,
a finer time resolution can be obtained through signal processing to measure the
beginning of the C/A code. This fine time resolution can be converted into finer
distance resolution.
As discussed in Chapter 3, the Doppler frequency on the C/A code is about
± 6 Hz, which includes the speed of a high-speed aircraft. Therefore, the code
frequency should be considered as in the range of 1 . 023 × 10 6 ± 6 Hz. The sam-

pling frequency should not be a multiple of this range of frequencies. In general,
even in the sampling frequency is close to the multiple of this range of frequen-
cies, the time-shifted data can be the same as the original data for a period of
time. Under this condition, in order to generate a fine time resolution, a relatively
long record of data must be used, which is not desirable.