Shared Aperture Wideband array...
Transcript of Shared Aperture Wideband array...
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Shared Aperture Wideband array concept
Abdullah Alshammary
KACST, KSA
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Array Antenna
Antenna array Classical antenna
scanning Electronic (fast and maintenance free)
Mechanical (slow and unreliable)
Multiple targets or shaped beam
X
Conformance to surfaces X
Feed network Complex Simple
Bandwidth Requires extra axis Depends on feed element
Mutual coupling X
advantage disadvantage Color code
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Multi-mode array
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bandwidth
Narrowband Wideband
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wideband weight
• True Time Delay TTD
• Digital receiver
Costly & Bulky
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contiguous subarray
R. Mailloux “Phased array antenna handbook”
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contiguous subarray (phase)
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Array Model
nmefSfSnm ),(),( 00
)sinsincossin(2 yxnm dmdnc
f
2
2
2
2
)sincos(2
),(),(N
Nn
M
Mm
dmdnc
fj yx
emnwfH
For even N and M
0orif0
otherwise1
2
2
2
2
)sin)2
1(cos)
2
1((2
where
),(),(
mn
N
Nn
M
Mm
dmdnc
fj
a
emnwfHyx
Odd N and M
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SRV Constrained Pattern Synthesis
Convex Optimization
Array Response
T
MNmnMNMMNMN SSSSSSSfS ],...,,...,,...,...,,...,,[),( 2,2,0,02,22,02),12(2,2
T
MNmnMNMMNMN wwwwwwww ],...,,...,,...,...,,...,,[ 2,2,0,02,22,02),12(2,2
),(),Response( fSwf T
mi
bxf
xf
ii
,...,2,1where
tosubject
minimize 0
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Spatial Response Variation (SRV)
• SRV
• Steering vector
• Constrained SRV
fN
nf
ffN
SRV1
20 ),(response),(response
1)(
ddffSfSfSfSBWB
R
B BWf
H
)],(),([)],(),([11
0
SRVT twRw
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Other Pattern Characteristics
• Sidelobe level
• Gain
• Weights Level
regionsidelobewhere
),(response 0
sl
slsl tf
gtf 1),(response 00
wtw
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Example
name symbol Value description
N 7 Number of elements in x axis
M 13 Number of elements in x axis
dx .05 Spacing along the x axis
dy .05 Spacing along the y axis
Frequency
Band f
[1.9,2.5]
GHz
Frequencies considered in the
analysis
Reference
frequency f0 2.2 GHz
Reference frequency is set at
centre
Field of view Ф
Mainlobe
angle Φ0 15
mainlobe Φm (-5 , 35)
sidelobe Φsl [-90 , -5]U[35 , 90]
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SRV Pattern constraints
Minimize
Subject to
SRV:
SLL:
Gain:
2-norm weight: 10
001.1),(response
regionsidelobe e wher35),(response
00
0
w
f
f
twRw
t
slsl
SRVT
SRV
mainlobe mainlobe sidelobes sidelobes sidelobes sidelobes
SRV constraint region
min max regions
min max region
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SRVCPS Result
-80 -60 -40 -20 0 20 40 60 80-80
-70
-60
-50
-40
-30
-20
-10
0
Angle (degrees)
Arr
ay P
att
ern
(d
B)
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Comparison
pattern Frequency Variance
HPBW FNBW SLR
=20*log10(Linea
r) dB
Processin
g speed
(sec)
SRVCPS 0.0076
18⁰ [-4,35]=39⁰ -35.14 112
IDFT 0.26
18.73⁰ [-3,40]=43⁰ -16.35 2.5
SRVCPS IDFT
QUALITY Optimum pattern given
problem is convex Depends on ref. pattern
COMPUTATION
COMPLEXITY
Complexity increase with
problem size Simple, analytical
GENERALITY Comprehensive Pattern only
FORMULATION Difficult to formulate to
standard form Straight forward
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2D extension
• Extend the 1-D pattern to 2-D by dynamic allocation of optimization constraints.
• Reduced performance due to limited solution space.
• Doesn’t require any additional hardware ( still using scalar weights)
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Circular array example
• Clipped circular array
• 98 elements
• 8-12 GHz
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Results:3D pattern
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Results: Frequency invariance Elevation cut, Azimuth=0 ̊
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THANK YOU
Questions?