Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 265

Six hundred ms of data through coherent processing can provide about
27.78 dB (10 × log(600)) of gain. In combining with the squaring operation of
1 ms, the overall S / N is about 9.78 dB (27 . 78 − 18). For the 2 ms summation,
the coherent gain is 24.77 dB (10 log(600/2)) because only 300 data blocks can

be processed coherently. The overall S / N is about 11.1 dB (24 . 77 − 13 . 67). For
the 4 ms summation, the coherent gain is about 21.76 dB (10 × log(600/4)), and
the overall S / N is 12.21 dB (21 . 76

×

−

9 . 55). From this simple example, one can
see that by increasing the number of ms of data summed, a higher overall S / N
can be achieved. However, longer ms of data summed can increase the chance
of including a navigation data transition, which is undesirable. For example, if
1 ms is used for squaring, the navigation has no effect. If 2 ms is summed,
the possibility exists that in every 10 blocks there is one with navigation data.
If 4 ms is summed, the possibility exists that in every 5 blocks there is one
with navigation data. The blocks with navigation data will reduce the coherent
processing gain. Of course, there is also the 50% chance that the navigation date
transition has no effect on the 2 ms data summation and 25% chance on the
4 ms summation.
The actual processing is as follows: The input frequency is down-converted to
a baseband of less than 1 kHz, such as near 100 Hz, because the input fre-
quency can be determined about ± 25 Hz through the acquisition. After the
down-conversion, the C/A code is stripped off, and every millisecond of data is
averaged into one data point. This averaging is equivalent to sampling at 1 kHz.
Thus, the total frequency coverage is 1 kHz because the outputs are complex.
If 200 ms of data are used, the achievable frequency resolution is 5 Hz. Since
the frequency is doubled, the frequency resolution is 2.5 Hz and the frequency
accuracy can be ± 1.25 Hz.
Simulated data are used to test this method for signals with C/N 0 near 24 dB.
In these simulations, the number of ms data summed is 1, 2, and 4. This input
signal has a Doppler frequency of 55 Hz, which is arbitrarily chosen, but worse
than the frequency accuracy of

±

25 Hz obtained from acquisition. It is also cho-
sen that the measured frequency must be within ± 2 Hz of the Doppler frequency;
otherwise, it is considered to be a failure. Since the tracking method for weak
signal can achieve frequency accuracy of ± 0.5 Hz, ± 2 Hz is arbitrarily selected
as the acquisition requirement. This test runs 100 times with different sequences
of noise, and the number of successful results is recorded. In the tests, the actual
data length is from 240 to 600 ms. The results are shown in Table 10.5.
In this table 600 simulated ms data are generated. The first 240 ms of data are
used for the 240-ms test. Similar approaches are used for the 360- and 480-ms
tests. From these results one can see that longer data and a larger number of ms
summed combined will improve the frequency reading. For this special criterion
of 2 Hz, from 240 to 360 ms the improvement is significant, but from 360 to

600 ms little improvement is realized. In these simulations the navigation data
are not included. In using real data, if there is a navigation phase transition in
the summed data, the final results from the 2-ms and 4-ms summations will be

±