Graphics Programs Reference
In-Depth Information
only on range bins containing significant scatterer returns. The difference
between the two images is used as an indication of target height. Computer
simulation shows that this technique is accurate and virtually impulse invari-
ant.
12.9.2. DFTSQM Operation and Signal Processing
Linear Arrays
Consider a linear array of size , uniform element spacing , and wave-
length . Assume a far field scatterer located at direction-sine .
DFTSQM operation for this array can be described as follows. The elements
are fired sequentially, one at a time, while all elements receive in parallel. The
echoes are collected and integrated coherently on the basis of equal phase to
compute a complex information sequence
N
d
λ
P
sin
β
l
{
b
();
=
02
N
,
1
}
. The x-
coordinates, in
d
-units, of the
x
th
element with respect to the center of the
array is
N
2
1
;
x
n
=
-------------
+
n
=
0 …
N
,
1
(12.50)
x
th
x
th
The electric field received by the
element due to the firing of the
, and
l
th
reflection by the
far field scatterer
P
, is
s
()
R
0
4
----
Ex
1
(
,
x
2
;
s
l
)
=
G
2
σ
l
exp j
φ
x
1
(
(
,
x
2
;
s
l
)
)
(12.51)
R
2π
λ
------
φ
x
1
(
,
x
2
;
s
l
)
=
(
x
1
+
x
2
)
s
()
(12.52)
s
l
=
sin
β
l
(12.53)
G
2
where is the target cross section, is the two-way element gain, and
is the range attenuation with respect to reference range . The scat-
terer phase is assumed to be zero; however it could be easily included. Assum-
ing multiple scatterers in the arrayÓs FOV, the cumulative electric field in the
path
σ
l
s
()
)
4
(
R
0
⁄
R
R
0
x
1
⇒
x
2
due to reflections from all scatterers is
∑
Ex
1
(
,
x
2
)
=
[
E
I
(
x
1
,
x
2
;
s
l
)
+
jE
Q
(
x
1
,
x
2
;
s
l
)
]
(12.54)
all l
where the subscripts denote the quadrature components. Note that the
variable part of the phase given in Eq. (12.52) is proportional to the integers
resulting from the sums
(
IQ
,
)
{
(
x
n
1
+
x
n
2
);
(
n
1
n
2
,
)
=
0 …
N
,
1
}
. In the far field
operation there are a total of
(
2
N
1
)
distinct
(
x
n
1
+
x
n
2
)
sums. Therefore,
the electric fields with paths of the same
(
x
n
1
+
x
n
2
)
sums can be collected
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