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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?