Graphics Programs Reference
In-Depth Information
reference
cells
guard
cells
guard
reference
cells
CUT
cells
…
…
non-coherent
integrator
M
⁄
2
M
⁄
2
…
Σ
Σ
square law
detector
Σ
input
Y
1
Z
K
1
Z
K
1
comparator
threshold
output
Figure 2.19. Conventional CA-CFAR with non-coherent integration.
Eq. (2.107) implies that one must first find the joint
pdf
for the ratio .
However, this can be avoided if is first computed for a fixed threshold
value , then averaged over all possible values of the threshold. Therefore,
let the conditional probability of false alarm when
Y
1
⁄
Z
P
fa
V
T
y
=
be
P
fa
(
V
T
=
y
)
. It
T
follows that the unconditional false alarm probability is given by
∞
∫
P
fa
=
P
fa
(
V
T
=
y
)
f
()
d
(2.108)
0
where is the
pdf
of the threshold. In view of this, the probability density
function describing the random variable
f
()
K
1
Z
is given by
2
K
0
ψ
2
(
y
⁄
)
)
Mn
P
1
(
yK
1
⁄
e
f
()
=
---------------------------------------------------------
;
y
≥
0
(2.109)
)
Mn
P
K
1
2ψ
2
(
Γ
Mn
P
(
)
It can be shown that in this case the probability of false alarm is independent
of the noise power and is given by
n
P
∑
1
----
Γ
Mn
P
(
+
k
)
K
1
k
1
1
k
!
----------------------------
-----------------------------
---------------
P
fa
=
(2.110)
)
Mn
P
Γ
Mn
P
(
)
1
+
K
1
(
1
+
K
1
k
=
0
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