Graphics Programs Reference
In-Depth Information
coherently. In this manner the information sequence
{
b
()
m
;
=
02
N
,
1
}
is
computed, where
b
2
N
(
1
)
is set to zero. At the same time one forms the
sequence
{
c
()
m
;
=
0 …2
N
,
2
}
which keeps track of the number of
returns that have the same
(
x
n
1
+
x
n
2
)
sum. More precisely, for
m
1
=
+
n
2
;
(
n
1
n
2
,
) 0
N
=
,
1
b
()
b
()
Ex
n
1
=
+
(
,
x
n
2
)
(12.55)
c
()
c
()1
=
+
(12.56)
It follows that
m
+
1
;
m
=
0 …
N
,
2
{
c
()
m
;
=
0 …2
N
,
2
}
=
Nm
;
=
N
1
(12.57)
2
N
1
mm
=
N
…2
N
,
2
which is a triangular shape sequence.
The processing of the sequence is performed as follows: (1) the
weighting takes the sequence into account; (2) the complex sequence
is extended to size , a power integer of two, by zero padding; (3)
the DFT of the extended sequence
{
b
()
}
{
c
()
}
{
b
()
}
N
F
{
b
' ();
=
0
N
F
,
1
}
is computed,
N
F
∑
1
j
2π
qm
N
F
;
--------------
B
()
=
b
' ()
exp
⋅
=
0 …
N
F
,
1
(12.58)
m
=
0
and, (4) after compensation for antenna gain and range attenuation, scatterers
are detected as peaks in the amplitude spectrum
B
()
. Note that step (4) is
true only when
λ
q
2
Nd
sin
β
q
=
---------- ;
=
0 …2
N
,
1
(12.59)
where
sin
β
q
denotes the direction-sine of the
q
th
scatterer, and
N
F
=
2
N
is
implied in Eq. (12.59).
The classical approach to multiple target detection is to use a phased array
antenna with phase shifting and tapering hardware. The array beamwidth is
proportional to , and the first sidelobe is at about -13 dB. On the other
hand, multiple target detection using DFTSQM provides a beamwidth propor-
tional to as indicated by (Eq. (12.59), which has the effect of dou-
bling the arrayÓs resolution. The first sidelobe is at about -27 dB due to the
triangular sequence . Additionally, no phase shifting hardware is
required for detection of targets within a single elementÓs field of view.
(
λ
Nd
⁄
)
(
λ 2
Nd
⁄
)
{
c
()
}
Search WWH ::
Custom Search