Graphics Programs Reference
In-Depth Information
sufficient. In practice, high sidelobe levels are not preferable because noise
and/or jammers located at the sidelobes may interfere with target returns in the
main lobe.
Weighting functions (windows) can be used on the compressed pulse spec-
trum in order to reduce the sidelobe levels. The cost associated with such an
approach is a loss in the main lobe resolution, and a reduction in the peak value
(i.e., loss in the SNR). Weighting the time domain transmitted or received sig-
nal instead of the compressed pulse spectrum will theoretically achieve the
same goal. However, this approach is rarely used, since amplitude modulating
the transmitted waveform introduces extra burdens on the transmitter.
Consider a radar system that utilizes a correlation processor receiver (i.e.,
matched filter). The receive window in meters is defined by
R
rec
=
R
max
R
min
(5.12)
where and , respectively, define the maximum and minimum range
over which the radar performs detection. Typically is limited to the extent
of the target complex. The normalized complex transmitted signal has the form
R
max
R
min
R
rec
µ
---
t
2
s
()
=
exp
j
2π
f
0
t
+
0
≤≤
t
τ′
(5.13)
τ′
is the pulsewidth,
µ
=
B
τ′
⁄
, and
B
is the bandwidth.
The radar echo signal is similar to the transmitted one with the exception of a
time delay and an amplitude change that correspond to the target RCS. Con-
sider a target at range
R
1
. The echo received by the radar from this target is
µ
---
t
)
2
s
r
()
a
1
=
exp
j
2π
f
0
(
t
τ
1
)
+
(
τ
1
(5.14)
where is proportional to target RCS, antenna gain, and range attenuation.
The time delay
a
1
τ
1
is given by
τ
1
=
2
R
1
⁄
c
(5.15)
The first step of the processing consists of removing the frequency
f
0
. This
is accomplished by mixing
s
r
()
with a reference signal whose phase is
2π
f
0
t
.
The phase of the resultant signal, after low pass filtering, is then given by
µ
---
t
)
2
ψ () 2π
=
0
τ
1
+
(
τ
1
(5.16)
and the instantaneous frequency is
2
R
1
c
1
2π
d
ψ () µ
t
B
τ′
f
i
()
=
------
=
(
τ
1
)
=
----
t
---------
(5.17)
d
t
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