Acquisition of GPS C/A Code Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 132

no transition. In reality, there is a good probability that a data record more than
10 ms long does not contain a data transition.
The second limit of data length is from the Doppler effect on the C/A code.
If a perfect correlation peak is 1, the correlation peak decreases to 0.5 when a
C/A code is off by half a chip. This corresponds to 6 dB decrease in ampli-
tude. Assume that the maximum allowed C/A code misalignment is half a chip
(0.489 us) for effective correlation. The chip frequency is 1.023 MHz and the
maximum Doppler shift expected on the C/A code is 6.4 Hz as discussed in
Section 3.6. It takes about 78 ms (1/(2 6 . 4)) for two frequencies different

by 6.4 Hz to change by half a chip. This data length limit is much longer
than the 10 ms; therefore, 10 ms of data should be considered as the longest
data used for acquisition, in this topic, although other researchers used longer
data.

×

7.4 FREQUENCY STEPS IN ACQUISITION

Another factor to be considered is the carrier frequency separation needed in
the acquisition. As discussed in Section 3.6, the Doppler frequency range that
needs to be searched is ± 10 kHz. It is important to determine the frequency
steps needed to cover this 20 kHz range. The frequency step is closely related
to the length of the data used in the acquisition. When the input signal and
the locally generated complex signal are off by 1 cycle there is no correlation.
When the two signals are off less than 1 cycle there is partial correlation. It is
arbitrarily chosen that the maximum frequency separation allowed between the
two signals is 0.5 cycle. If the data record is 1 ms, a 1 kHz signal will change
1 cycle in the 1 ms. In order to keep the maximum frequency separation at 0.5
cycle in 1 ms, the frequency step should be 1 kHz. Under this condition, the
furthest frequency separation between the input signal and the correlating signal
is 500 Hz or 0.5 Hz/ms and the input signal is just between two frequency bins.
If the data record is 10 ms, a searching frequency step of 100 Hz will fulfill
this requirement. A simpler way to look at this problem is that the frequency
separation is the inverse of the data length, which is the same as a conventional
FFT result.
The above discussion can be concluded as follows. When the input data used
for acquisition is 1 ms long, the frequency step is 1 kHz. If the data is 10 ms
long, the frequency is 100 Hz. From this simple discussion, it is obvious that
the number of operations in the acquisition is not linearly proportional to the
total number of data points. When the data length is increased from 1 ms to
10 ms, the number of operations required in the acquisition is increased more
than 10 times. The length of data is increased 10 times and the number of
frequency bins is also increased 10 times. Therefore, if the speed of acquisition
is important, the length of data should be kept at a minimum. The increase in
operation depends on the actual acquisition methods, which are discussed in the
following sections.