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
+
2
1
2πψ 2
-------------
f n I
(
,
n Q
)
=
exp
–
-----------------
(2.4)
) 2
) 2
1
2πψ 2
(
r
cos
ϕ
–
A
+
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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