Graphics Programs Reference
In-Depth Information
γ i
=
γ i
–
A i
;
i
>
0
(2.86)
–
1
V T
(
1
+
(
SNR
)
2
)
A i
=
-----------------------------------------------
A i
;
i
>
1
(2.87)
–
1
n P
+
i
–
1
) n P
(
V T
(
1
+
(
SNR
)
2
)
A 1
=
----------------------------------------------------------------------
(2.88)
n P !
exp
(
V T
(
1
+
(
SNR
)
2
)
)
V T
-------------------------------------
γ 0
=
Γ I
,
n P
(2.89)
(
1
+
(
SNR
)
2
)
For the case when , the Gram-Charlier series and Eq. (2.69) can be
used to calculate the probability of detection. In this case,
n P
50
C 2
2
3
1
–
1
-------------
----------------------------
C 3
=
;
C 6
=
------
(2.90)
) 1.5
3
n P
2
(
–
1
4
1
4 n P
–
1
---------
-------------------------
C 4
=
(2.91)
) 2
2
(
–
1
2
ϖ
=
n P
(
–
1
)
(2.92)
SNR
2
β
=
1
+
-----------
(2.93)
MATLAB Function Ðpd_swerling4.mÑ
The function Ðpd_swerling4.mÑ calculates for Swerling IV type targets.
It is given in Listing 2.23 in Section 2.11. The syntax is as follows:
P D
[pd] = pd_swerling4 (nfa, np, snr)
where
Symbol
Description
Units
Status
nfa
MarcumÓs false alarm number
none
input
np
number of integrated pulses
none
input
snr
dB
input
SNR
pd
probability of detection
none
output
Figure 2.14 shows a plot of the probability of detection as a function of SNR
for , where . This figure can be reproduced
using MATLAB program Ðfig2_14.mÑ given in Listing 2.24.
–
9
n P
=
11050100
,
,
,
P fa
=
10
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