Graphics Programs Reference
In-Depth Information
170
MATLAB Simulations for Radar Systems Design
filter would be the autocorrelation function of the received (or transmitted) sig-
nal. In practice, replicas of the transmitted waveforms are normally computed
and stored in memory for use by the radar signal processor when needed.
3.9. Matched Filter Response to LFM Waveforms
In order to develop a general expression for the matched filter output when
an LFM waveform is utilized, we will consider the case when the radar is
tracking a closing target with velocity
. The transmitted signal is
v
µ
---
t
2
j
2π
f
0
t
+
t
τ'
--
e
s
1
()
Rect
=
(3.101)
The received signal is then given by
s
r
1
()
s
1
=
(
t
∆ ()
)
(3.102)
2
v
c
------
t
∆ ()
t
0
=
(
)
(3.103)
0
where
is the time corresponding to the target initial detection range, and
is
t
0
c
the speed of light. Using Eq. (3.103) we can rewrite Eq. (3.102) as
2
v
c
------
t
0
s
r
1
()
s
1
=
t
+
(
)
=
s
1
(
γ
t
0
(
)
)
(3.104)
0
and
12
v
γ
=
+
--
(3.105)
is the scaling coefficient. Substituting Eq. (3.101) into Eq. (3.104) yields
γ
t
(
)
e
j
πµγ
2
)
2
e
j
2π
f
0
γ
t
0
(
)
(
t
0
0
-------------------
s
r
1
()
Rect
=
(3.106)
τ'
which is the analytical signal representation for
. The complex envelope
s
r
1
()
of the signal
is obtained by multiplying Eq. (3.106) by
.
s
r
1
()
exp
(
j
2π
f
0
t
)
Denote the complex envelope by
; then after some manipulation we get
s
r
()
γ
t
(
)
e
j
πµγ
2
)
2
j
2π
f
0
t
0
e
j
2π
f
0
(
γ
1
)
t
0
(
)
(
t
0
0
-------------------
s
r
()
e
=
Rect
(3.107)
τ'
The Doppler shift due to the target motion is
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