Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 257

S/N versus number of incoherent integration
to generate 90% detection

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02468 0 2 4 6 8 0

Number of incoherent integrations
FIGURE 10.19 S / N versus number of summations for 90% detections.

The probability of detection is defined as that the correction initial phase of the
C/A code is obtained within 19 integrations. When the number of integrations is
beyond 19, it is considered that the signal is not detected. When an erroneous
result is obtained within 19 integrations, it is considered as a false alarm. For
example, at C/N 0 = 24 dB, the signal is correctly detected 74 times; a wrong
information is obtained 4 times, and there are 22 runs in which the outputs do not
cross the threshold. It appears that the false alarm is higher than the desired value
of 1 per 100 runs. Since both the methods of determining the threshold and the
probability of detections use very limited data sets because of long calculation
time, the error can be large.
Another way to detect a weak signal is based on the assumption that the signal
is in the input data. Under this condition one can detect the signal by not using
a threshold, but perform noncoherent integration 19 times. After the integration
the highest value will be used as the desired results. This approach yields only
correct and incorrect results. The detection results are listed in Table 10.4. These
results have slightly higher probability of detection (correct results). It takes
more time to process the signal because 19 integrations must be performed in
each operation. In both tables the results are obtained from 100 runs, and they
should not be considered as typical cases.
The worst operating condition is that the frequency of the input signal is
at the center of two frequency bins. After adjacent frequency bin operations
are performed as discussed in Section 10.11, the loss is about 2.8 dB. The worst
digitizing error is 100 ns (half the sampling time of 200 ns) from the initial phase
of the C/A code, and the sensitivity loss is about 0.92 dB. Therefore the overall
degradation should be about 3.72 dB. The overall noncoherent integration gain