Graphics Programs Reference
In-Depth Information
From antenna
and lo
w nois
e
r
()
Band Pass
Filter (IF)
Envelope
Detector
Low Pass
Filter
Threshold
Detector
Amp.
v
()
to display
devices
Threshold V
T
Figure 2.1. Simplified block diagram of an envelope detector and threshold
receiver.
The case when the noise subtracts from the signal (while a target is present) to
make smaller than the threshold is called a miss. Radar designers seek to
maximize the probability of detection for a given probability of false alarm.
r
()
The IF filter output is a complex random variable that is composed of either
noise alone or noise plus target return signal (sine wave of amplitude
A
). The
quadrature components corresponding to the first case are
v
I
()
n
I
()
v
Q
()
n
Q
()
=
=
(2.2)
and for the second case,
v
I
()
An
I
=
+
()
=
r
() ϕ()
cos
⇒
n
I
()
=
r
() ϕ()
cos
A
(2.3)
v
Q
()
n
Q
=
()
r
() ϕ()
=
sin
where the noise quadrature components
n
I
()
and
n
Q
()
ψ
2
n
I
are uncorrelated zero
mean low pass Gaussian noise with equal variances,
. The joint Probability
Density Function (
pdf)
of the two random variables
;
n
Q
is
n
I
2
n
2
+
2ψ
2
1
2πψ
2
-------------
f n
I
(
,
n
Q
)
=
exp
-----------------
(2.4)
)
2
)
2
1
2πψ
2
(
r
cos
ϕ
A
+
2ψ
2
(
r
sin
ϕ
=
-------------
exp
-----------------------------------------------------------
The
pdfs
of the random variables
r
()
and
ϕ ()
, respectively, represent the
modulus and phase of
v
()
. The joint
pdf
for the two random variables
r
()ϕ()
;
is given by
f r
ϕ
(
,
)
=
fn
I
n
Q
(
,
)
J
(2.5)
where
[]
is a matrix of derivatives defined by
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