Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 229

False alarm time of phase transition

60

50

40

30

20

10

0 22

22.5 23 23.5

Input C/N 0 in dB

24 24.5 25

FIGURE 10.2 False alarm time of phase transition.

about 13 seconds false alarm time. Under this condition the input signal strength is
at − 150 dBm. Because the nominal signal strength of a GPS signal is − 130 dBm,
an additional 20 dB improvement in processing gain is required above normal
processing. The simulated data show that a signal with C / N 0 = 23 dB can still
be tracked for about at least 20 seconds ( 8 ) . By the aided approach introduced in
Section 10.1, C / N 0 = 16 dB can be achieved ( 9 ) .

10.4 PROBABILITY OF DETECTION AND FALSE ALARM RATE ( 1-3 )

The probability of detection P d and the probability of false alarm P fa are impor-
tant parameters for acquisition. They are functions of input S / N and threshold.
For a fixed input S / N , a lower threshold produces a higher probability of detec-
tion and a higher false alarm rate. A higher threshold produces a lower probability
of detection and a lower false alarm. Depending on the threshold setting, there
are numerous combinations of P d and P fa . A commonly used S / N in radar
detection of a single pulse is about 14 dB. Under this condition, two sets of P d
and P fa will be given as an example. The probability of detection can be 90%
( P d 10 − 7 ) ( 1 , 2 ) . With

the same S / N a different threshold can provide approximately P d

= 0 . 9) with a probability of false alarm about 10 − 7 ( P fa =

= 0 . 5 with