Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 223

σ n . Using
this result, the single trial probability of detection, P d , is computed for the expected
C / N 0 and dwell time, T , using (5.37) and (5.40) with

For example, if it is desired that P fa = 16%, then V t = X σ n = 1.9144615

1 (normalized). Some
examples of the single trial probability of detection are shown in Table 5.10 for var-
ious SNRs.
Figure 5.36, taken from [18], illustrates the structure of search detectors used
for signal acquisition. Referring to Figure 5.36, two types of search detectors used in
GPS receiver designs will be described. A variable dwell time detector makes a “yes”
or “no” decision in a variable interval of time if “maybe” conditions are present. A
fixed dwell time detector makes a “yes” or “no” decision in a fixed interval of time.
The probability of detection and especially the poor false alarm rate from single
dwell time detectors (single trial decisions as shown in Table 5.10) are usually
unsatisfactory for GPS applications. So, single dwell time search detector schemes
are seldom used. All other things being equal, a properly tuned variable dwell time
(sequential) multiple trial detector will search faster than a fixed dwell time multiple
trial detector.

σ n =

5.8.1 Tong Search Detector
The first example of a search algorithm is a sequential variable dwell time search
detector called the Tong detector. Figure 5.37 illustrates the block diagram of the
Tong detector. Search algorithms are typically implemented as a receiver baseband
process. Because of its simplicity, the Tong detector can be implemented as part
of the receiver correlation and preprocessing hardware, with its search parameters
programmed by the baseband process. The Tong detector has a reasonable compu-
tational burden and is excellent for detecting signals with an expected ( C / N 0 ) dB of
25 dB-Hz or higher. If acquisition is to be performed under heavy jamming condi-
tions where the ( C / N 0 ) dB will be less than this, then a hybrid maximum-likelihood
search detector should be used. A pure maximum-likelihood search detector would
require the receiver hardware to produce the results of all of the search dwells in
parallel, which is usually impractical. The Tong detector is a suboptimal search
algorithm that requires an average factor of only 1.58 longer to make a decision
than a maximum-likelihood (optimum) search algorithm [19].

Table 5.10 Single Trial Probability of Detection

C/N P d (C/N 0 ) dB =(C/N) dB 10log 10 T (dB-Hz)

(ratio) (dimensionless) T 1 ms T 2.5 ms T 5 ms T 10 ms

1.0 0.431051970 30.00 26.02 23.01 20.00

2.0 0.638525844 33.01 29.03 26.02 23.01

3.0 0.780846119 34.77 30.79 27.78 24.77

4.0 0.871855378 36.02 32.04 29.03 26.02

5.0 0.927218854 36.99 33.01 30.00 26.99

6.0 0.959645510 37.78 33.80 30.79 27.78

7.0 0.978075147 38.45 34.47 31.46 28.45

8.0 0.988294542 39.03 35.05 32.04 29.03

9.0 0.993845105 39.54 35.56 32.55 29.54