Digital Signal Processing Reference
In-Depth Information
Maps. Hence, for a particular range cell (the region within the two successive iso-
range contours of Fig.
3.2
) the radar knows the specific paths, through which the tar-
get information reaches the radar receiver, in terms of its direction-of-arrival (DOA)
unit-vectors (
u
p
,p
1
,
2
,...,P
). Under this scenario, our goal here is to decide
whether a target is present or not in the range cell under test.
In the following, we first develop a parametric OFDM-measurement model that
includes the effects of multipath reflections in between the radar and target. Then,
we discuss our statistical assumptions on the clutter and noise.
=
3.2.1 OFDM Signal Model
We consider a wideband OFDM signaling system with
L
active subcarriers, a band-
width of
B
Hz, and pulse width of
T
p
seconds. Let
a
T
represent
the complex weights transmitted over the
L
subcarriers, and satisfy
L
−
1
=[
a
0
,a
1
,...,a
L
−
1
]
2
1.
Then, the complex envelope of the transmitted signal in a single pulse can be repre-
sented as
l
=
0
|
a
l
|
=
L
−
1
a
l
e
j
2
πlΔft
,
for 0
s(t)
=
≤
t
≤
T
p
,
(3.1)
l
=
0
where the subcarrier spacing is denoted by
Δf
=
B/(L
+
1
/T
p
.Let
f
c
be the
carrier frequency of operation; then a coherent burst of
N
transmitted pulses is given
by
1
)
=
2Re
N
−
1
nT)e
j
2
πf
c
t
,
s(t)
=
s(t
−
(3.2)
n
=
0
where
T
is the pulse repetition interval (PRI). We point out here that in Sect.
3.4
while designing the adaptive waveform we choose the spectral-parameters of the
OFDM waveform,
a
l
s, in order to improve the system performance.
3.2.2 Measurement Model
{
a
l
e
j
2
πf
l
t
For a single-pulse, single-carrier transmitted signal
s
l
(t)
=
2Re
}
, where
f
l
=
lΔf
is the
l
th subcarrier frequency, the received signal along the
p
th path
(represented by the DOA unit-vector
u
p
) and at the same carrier-frequency
f
l
can
be written as
f
c
+
s
l
γ
p
(t
τ
p
)
+
y
lp
(t)
=
x
lp
−
e
lp
(t),
(3.3)
where
x
lp
is a complex quantity representing the scattering coefficient of the target
along the
l
th subchannel and
p
th path;
γ
p
=
1
+
β
p
where
β
p
=
2
v
,
u
p
/c
is the
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