Graphics Programs Reference
In-Depth Information
A Solution:
From the function Ðmarcumsq.mÑ the SNR corresponding to and
is approximately 12dB. By using a similar analysis to that which
led to Eq. (2.98), we can express the SNR at any range
P
D
=
0.5
7
P
fa
=
10
R
as
10
R
(
SNR
)
R
=
(
SNR
)
10
+
40
log
------
=
52
40
log
R
By using the function Ðmarcumsq.mÑ we can construct the following table:
P
D
R
Km
(SNR) dB
2
39.09
0.999
4
27.9
0.999
6
20.9
0.999
8
15.9
0.999
9
13.8
0.9
10
12.0
0.5
11
10.3
0.25
12
8.8
0.07
14
6.1
0.01
16
3.8
ε
20
0.01
ε
where
ε
is very small. A sketch of
P
D
versus normalized range is shown in
The cumulative probability of detection is given in Eq. (2.95), where the proba-
bility of detection of the first frame is selected to be very small. Thus, we can
arbitrarily choose frame 1 to be at . Note that selecting a different
starting point for frame 1 would have a negligible effect on the cumulative
probability (we only need to be very small). Below is a range listing for
frames 1 through 9, where frame 9 corresponds to
R
=
16
Km
P
D
1
R
=
8
Km
. The cumulative
frame
1
2
3
4
5
6
7
8
9
range in Km
16
15
14
13
12
11
10
9
8
probability of detection at 8 Km is then
P
C
9
=
1
(
1
0.999
) 10.9
(
) 10.5
(
) 1 . 5
(
) 1 . 7
(
)
)
2
(
1 . 1
) 1
(
ε
≈
0.9998
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