Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 258

TABLE 10.4 Signal Detection at C / N 0 around 24 dB

without Threshold

C/N 0 (dB) 25 24 23

Correct results 94 78 61

Incorrect results 6 22 39

required is 13.72 dB instead of 10 dB, which is the most favorable condition. In
order to obtain 13.72 dB of gain, the noncoherent integration must be summed
about 72 times. As mentioned previously when every other 10 ms of data is
added together to accommodate the navigation data, a total of 1440 ms of data
will be processed. From the discussion above, it is clear that to acquire a signal at
C/N 0 = 24 dB, a fair amount of processing is needed. For simplicity, however,
it is assumed that with 19 summations a C/N 0 = 24 dB can be achieved. The
last point in Figure 10.19 is based on this assumption.

10.15 THRESHOLD DETERMINATION FROM REAL DATA

Weak GPS signals have been collected to evaluate the acquisition method dis-
cussed in the previous sections. Data were collected inside a building, also
collected outdoor under a shelter, and under trees. There were 16 data sets and the
correct detection, false alarms, and missed signals were recorded. Some results
show that a signal at times can be clearly observed from the visual output dis-
play but not detected. To understand this problem, the acquisition results (from
20 noncoherent summations of 10 ms coherent integration) were studied. The
purpose was to find the noise distribution and the threshold. In order to find
the noise distribution, a certain signal that was not in the input data had to be
acquired. In other words, the acquisition was performed on a specific satellite
(i.e., satellite 6), but this satellite was not in the input data. Such acquisition
results can be considered as the noise floor, and they are shown in Figure 10.20.
The results are displayed in the time domain as well as in a histogram, and they
are from different data sets. After 20 summations the results should be close to
a Gaussian distribution, as discussed in Section 10.13 and Figure 10.15.
The results in Figure 10.20 were generated from 2048 point FFT operation as
discussed in Section 10.10. Figure 10.20a shows the distribution to be close to a
Gaussian distribution. The distributions - Figures 10.20b and 10.20c are not close
to Gaussian. In Figures 10.20d through 10.20f the noise floors have amplitude vari-
ations. The reason for these deviations is not clear, since the data were not collected
under controlled environments. However, from the different distributions it is clear
that a fixed threshold based on a Gaussian distribution will not be the optimum
selection, especially for the distributions of Figures 10.20d through 10.20f.
A different approach was tried to detect the signals. In this method, the coher-
ent integration uses 10 ms of data. After every noncoherent integration, the result
is obtained in the time domain shown in Figure 10.20. From this result two