Global Positioning System Reference
In-Depth Information
advanced to the next cell. The determination of
A
must be by simulation. Its
selection is a tradeoff between search speed and probability of detection, but
a typical range is
A
8 for high expected
C
/
N
0
. Note that it is possible for the Tong detector to get trapped into an
extended dwell in the same cell under certain poor signal conditions. For this
reason, a
mush
counter should be used that counts every test within the same
cell then declares the signal not present when the mush count exceeds
A
by
some reasonable amount.
=
12 for low expected
C
/
N
0
to
A
=
The mean number of dwell times to dismiss a cell containing noise only is deter-
mined as follows:
1
12
N
=
(5.44)
n
−
P
fa
Since most of the time is spent searching cells that contain only noise, the Tong
detector search speed can be estimated from:
(
)
d
12
−
P
d
NT
fa
(
)
R
=
=
chips/s
(5.45)
S
T
n
where
d
chips per cell (typically 1/2 chip per cell)
For example, for
P
fa
=
=
16%, a dwell time of 5 ms, and 1/2 chip per cell, the code
search rate is
68 chips/s. Note that the search speed increases when the probability
of false alarm decreases.
The overall probability of false alarm for the Tong detector is [19]:
=
B
1
−
P
fa
−
1
P
fa
P
=
(5.46)
FA
AB
+−
1
1
−
P
fa
−
1
P
fa
The overall probability of detection for the Tong detector is [19]:
B
1
−
P
d
−
1
P
d
P
=
(5.47)
D
AB
+−
1
1
−
P
d
−
1
P
d
Figure 5.38 is a plot of (5.47) as a function of the Tong detector input SNR,
(
C
/
N
)
dB
,
1 and
A
as a running
parameter ranging from 2 to 12, and with the overall probability of false alarm set
equal to 1
=
10log
10
(
C
/
N
) expressed in units of decibels, with
B
=
10
−6
for every case [17]. Figure 5.38 illustrates the excellent search detec-
tor performance of the Tong detector and the increased sensitivity of the detector
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