Graphics Programs Reference
In-Depth Information
Rectangular Arrays
DFTSQM operation and signal processing for 2-D arrays can be described as
follows. Consider an rectangular array. All elements are fired
sequentially, one at a time. After each firing, all the array elements
receive in parallel. Thus, samples of the quadrature components are col-
lected after each firing, and a total of
samples will be collected. How-
ever, in the far field operation, there are only distinct
equiphase returns. Therefore, the collected data can be added coherently to
form a 2-D information array of size . The two-way
radiation pattern is computed as the modulus of the 2-D amplitude spectrum of
the information array. The processing includes 2-D windowing, 2-D Discrete
Fourier Transformation, antenna gain, and range attenuation compensation.
The field of view of the 2-D array is determined by the 3 dB pattern of a single
element. All the scatterers within this field will be detected simultaneously as
peaks in the amplitude spectrum.
N
x
×
N
y
N
x
N
y
N
x
N
y
N
x
N
y
(
N
x
N
y
)
2
(
2
N
x
1
)
×
(
2
N
y
1
)
(
2
N
x
1
)
×
(
2
N
y
1
)
Consider a rectangular array of size
NN
×
, with uniform element spacing
d
x
==
d
y
d
, and wavelength
λ
. The coordinates of the
n
th
element, in
d
-
units, are
N
2
1
x
n
=
-------------
+
n
;
=
0 …
N
,
1
(12.60)
N
2
1
y
n
=
-------------
+
n
;
=
0 …
N
,
1
(12.61)
Assume a far field point defined by the azimuth and elevation angles
. In this case, the one-way geometric phase for an element is
P
(
αβ
,
)
2π
λ
------
ϕ'
xy
(
,
)
=
[
x
βα
sin
cos
+
y
βα
sin
sin
]
(12.62)
Therefore, the two-way geometric phase between the
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
ele-
ments is
2π
λ
ϕ
x
1
(
,
y
1
,
x
2
,
y
2
)
=
------
sin
β
[
(
x
1
+
x
2
)
cos
α
+
(
y
1
+
y
2
)
sin
α
]
(12.63)
The two-way electric field for the
l
th
scatterer at
(
α
l
β
l
,
)
is
----
4
G
2
β()
R
0
Ex
1
(
,
x
2
,
y
1
,
y
2
α
l
β
l
;
,
)
=
σ
l
exp j
ϕ
x
1
[
(
(
,
y
1
,
x
2
,
y
2
)
)
]
(12.64)
R
Assuming multiple scatterers within the arrayÓs FOV, then the cumulative elec-
tric field for the two-way path
(
x
1
,
y
1
)
⇒
(
x
2
,
y
2
)
is given by
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