Acquisition of GPS C/A Code Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 150

consideration, the 2 π /5 threshold can be extended slightly, such as using 2 . 3 π /5,
which means the difference must be equal to or less than this value. If the final
value of the adjusted phase difference is still greater than this threshold, it means
that there is a phase shift between the two milliseconds of data and π should be
subtracted from the result. Of course, the final angle should also be adjusted by
adding or subtracting 2 π to obtain the final result of less than the threshold.
From the above discussion, the following steps are required to find the begin-
ning of the C/A code and the carrier frequency of a certain satellite:

1. Perform circular correlation on 1 ms of data; the starting point of a certain
C/A code can be found in these data and the carrier frequency can be found
in 1 kHz resolution.
2. From the highest-frequency component X ( k ), perform two DFT operations
on the same 1 ms of data: one is 400 kHz lower and the other one is
400 kHz higher than k in X ( k ). The highest output from the three outputs
[ X(k − 1 ) , X(k) , X(k + 1 ) ] will be designated to be the new X ( k )and
used as the DFT component to find the fine frequency.
3. Arbitrarily choose five milliseconds of consecutive data starting from the
beginning of the C/A code. Multiply these data with 5 consecutive C/A
codes; the result should be a cw signal of 5 ms long. However, it might
contain one π phase shift between any of the 1 ms of data.
4. Find X n ( k ) on all the input data, where n = 1 , 2 , 3 , 4, and 5. Then find the

phase angle from Equation (7.20). The difference angle can be defined as

θ = θ n + 1 − θ n ( 7 . 23 )

5. The absolute value of the difference angle must be less than the threshold
(2 . 3 π /5). If this condition is not fulfilled, 2 π can be added or subtracted
from θ . If the result is still above the threshold, π can be added or
subtracted from θ to adjust for the π phase shift. This result will also be
tested against the 2 . 3 π /5 threshold. If the angle is higher than the threshold,
2 π can be added or subtracted to obtain the desired result. After these
adjustments, the final angle is the desired value.
6. Equation (7.22) can be used to find the fine frequency. Since there are 5 ms
of data, there will be 4 sets of fine frequencies. The average value of these
four fine frequencies will be used as the desired fine frequency value to
improve accuracy.

Program (p7 1) listed at the end of this chapter can be used to find the
initial point of the C/A code as well as the fine frequency. This program calls
the digitizg.m, which generates digitized C/A code. The digitizg.m in turn calls
codegen.m, which is a modified version of program (p5 2), and generates the
C/A code of the satellites. These programs just provide the basic idea. They can
be modified to solve certain problems. For example, one can add a threshold