Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 236

the carrier frequency. In general, the acquisition method generates two important
parameters: the carrier frequency and the initial phase of the C/A code. From this
information the signal can be tracked. For weak signals the acquisition is also
required to provide the initial position of navigation data. In every 20 ms there
is a data point where a data transition may occur. For a GPS signal of normal
strength the tracking program will find the navigation data transition. Detect-
ing the existence of a data transition for a weak signal, however, is difficult.
To detect the exact location of a data transition in 1 ms is even more difficult.
The acquisition should provide this information by using long data record such
as 1 second. In 1 second there are usually many data transitions separated by
multiple of 20 ms. One can use many data transitions to find the exact location.
This discussion should become clearer when the actual approach is discussed
in Section 10.17. The tracking program must determine whether there is a data
transition at every 20 ms after the acquisition. Once the exact data transition
location is obtained from the acquisition, the tracking program can determine the
existence of a data transition more effectively. This decision on whether there
is a data transition every 20 ms, as discussed in Section 10.3, determines the
receiver sensitivity limit.
Acquisition performed on long data through coherent integration increases
the receiver sensitivity. The calculation, however, is also more complicated and
time-consuming. Recall the circular correlation in frequency domain discussed
in Section 7.7. The number of operations can be treated as proportional to N ×

log 2 N ,where N is the number of data samples. If the data length is increased
from 5000 points (1 ms) to 50,000 (10 ms), the number of operations is increased
by about 12.7 times. Usually the acquisition complexity also limits the total
number of data points.
The acquisition through coherent integration is also limited by the navigation
data phase transition. In any length of data there is the possibility of having one
data transition. If there is a data transition in the input data, the output energy
from coherent integration will be spread into neighboring bins in the frequency
domain. Using two consecutive two 10 ms of data for acquisition, it is guaranteed
that in one set of the 10 ms data there is no data transition. As mentioned in the
previous section, in actual acquisition the noncoherent integration is summing
all the sequential outputs from the coherent integrations rather than summing
the odd and even blocks separately. By this approach the effect of data transi-
tion in the input data is neglected. Akopian ( 12 ) suggests using 16 ms of data for
coherent integration, which is then followed by noncoherent integration. From
limited experiments it was found that the difference from 10 and 16 ms acqui-
sition (combining coherent and noncoherent integrations) was not significant.
The following discussion is based on 10 ms coherent integration followed by
noncoherent integration.
Before discussing the actual acquisition method, the concept of output sam-
pling rate will be presented next because it is used in the acquisition.