Tracking Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 272

in detail here. Before we proceed to the discussion of method, some trade-offs
between performance and calculation speed will be pointed out.

11.2 FREQUENCY OF REGENERATING OF LOCAL C/A CODE

In Section 8.10 we saw that the local C/A code is only generated once in order
to save operation time. Since the signal is sampled at 5 MHz, the corresponding
sampling interval is 200 ns. Under the worst mismatch condition the locally
generated C/A code and the input C/A code can be off by 100 ns, which is half
of the sampling time. Since each chip of the C/A code is 977.5 (10 6 /1023) ns, the
100 ns mismatch can cause approximately a 0.94 dB loss in the peak correlation
output, as was calculated in Section 8.11. If the input signal is relatively strong,
this loss does not greatly affect the operation. Under weak signal conditions it is
desirable to maximize the operation gain. In other words, it is desirable to match
in time the local C/A code and the C/A code of the input signal.
Two factors can cause a mismatch in the C/A codes between the input and the
local signals. One is caused by the sampling frequency, which will be discussed
in Section 11.13. The other cause is related to Doppler frequency, as was briefly
discussed in Section 10.12. The mismatch caused by Doppler frequency shift will
be discussed some more here.
The obvious way to match the C/A code of the input signal is to generate the
local code every ms. For each ms the local code is digitized at a different point
to match the input. The operation is time-consuming but may be applied later
when a faster computer is available. The other approach is to generate the C/A
code every few ms. The frequency of generating the local C/A can be understood
by a brief example. Let us assume that the maximum Doppler frequency is about
± 5 kHz, caused by the satellite motion. The rate change of the Doppler shift
caused by the receiver motion will be neglected because the receiver must be in
a low dynamic environment. As discussed in Section 3.6, it takes about 15.8 ms
(approximated as 16 ms) to shift 100 ns in the C/A code if the Doppler frequency
is at ± 10 kHz. Thus it takes about 31.5 ms to shift 100 ns when the Doppler is
at ± 5kHz.
Based on this time of 31.5 ms and the navigation data length of 20 ms, it
is decided that the C/A code is regenerated every 20 ms because at 20 ms the
initial C/A is shifted less than 100 ns. This means that the local C/A can match
the input C/A code every 20 ms. At the end of 20 ms and under the worst case
condition (at ± 5 kHz Doppler) the mismatch is about 63.5 ns (100 × 20/31.5).
In order to achieve a better match, this mismatch time can be separated into 2
portions, each having 31.75 ns. One portion is placed at the beginning and the
other at the end of the 20 ms. In the 20 ms duration the average mismatch is about
16 ns (half of 31.75 ns). Another reason to separate the mismatch into two equal
portions is to better estimate the fine time. These points will be further discussed
in Section 11.11. A simple estimation of correlation peak loss is about 0.14 dB,
which is obtained from 20 log[(977 . 5 − 16)/977.5]. This can be considered as