Graphics Programs Reference
In-Depth Information
166
MATLAB Simulations for Radar Systems Design
cases, sub-optimum filters may be used. Due to this mismatch, degradation in
the output SNR occurs.
Consider a radar system that uses a finite duration energy signal .
Denote the pulsewidth as , and assume that a matched filter receiver is uti-
lized. The main question that we need to answer is: What is the impulse, or fre-
quency, response of the filter that maximizes the instantaneous SNR at the
output of the receiver when a delayed version of the signal
s
i
()
τ'
plus additive
s
i
()
white noise is at the input?
The matched filter input signal can then be represented by
x
()
Cs
i
=
(
t
)
+
n
i
()
(3.76)
1
where is a constant, is an unknown time delay proportional to the target
range, and is input white noise. Since the input noise is white, its corre-
sponding autocorrelation and Power Spectral Density (PSD) functions are
given, respectively, by
C
t
1
n
i
()
N
0
2
------
δ ()
R
n
i
()
=
(3.77)
S
n
i
()
N
0
=
------
(3.78)
2
where is a constant. Denote and as the signal and noise filter
outputs, respectively. More precisely, we can define
N
0
s
o
()
n
o
()
y
()
Cs
o
=
(
t
)
+
n
o
()
(3.79)
1
where
s
o
()
s
i
=
()
h
()
•
(3.80)
n
o
()
n
i
=
()
h
()
•
(3.81)
The operator ( ) indicates convolution, and is the filter impulse
response (the filter is assumed to be linear time invariant).
•
h
()
Let denote the filter autocorrelation function. It follows that the output
noise autocorrelation and PSD functions are
R
h
()
N
0
2
N
0
2
------
δ ()
R
h
------
R
n
o
()
R
n
i
=
()
R
h
•
()
=
•
()
=
R
h
()
(3.82)
N
0
2
S
n
o
()
S
n
i
()
H
()
2
H
()
2
=
=
------
(3.83)
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