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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