empirical antenna array optimization · zsynthesis of “on-the-vehicle” performance optimization...

Copyright © 2004-2005 Hutt Systems, Inc.

Optimization of the Onboard Performance of

Antenna Arrays Using

The Empirical Optimization Algorithm as Implemented

in the EmpOp™ Program

Stephen Jon BlankMichael F. Hutt

Hutt Systems, Inc.


Empirical Optimization of Antenna Arrays, The EmpOp™ Program

Iterative ‘on-the-vehicle’ performance optimization that accounts for electromagnetic coupling and scattering. Based on ‘in-situ’ measured or computed element pattern data.

Synthesis of optimum element excitations and spacings, including conformal and thinned array configurations.

Numerical optimum search to minimize normed difference between actual pattern and specified desired pattern. Applicable to:

• Minimization of max sidelobe• Minimization of sidelobe power• Shaped beam synthesis• Maximization of scan angle/bandwidth product• Optimization of Sum/Difference patterns

Applicable to adaptive array systems and maximization of SNR.


Antenna Configuration

φ

θ

ap

rp

Antenna Element

Far-Field

φ' = (θ,φ)

r (φ')


The Antenna Array Problem

Array field pattern:

a = (a1, a2,… aN) = vector of element excitationsr = (r1, r2,… rN) = vector of element locationsh = (h1, h2,… hN) = vector of element ‘in-situ’ field patternsΦ’ = observation angle (θ,Φ)Φ’s = scan angle (θs,Φs)

E φ' a, r,( )1

N

n

hn φ' r,( ) an⋅ ej

2 π⋅

λ⋅ r n⋅ u φ'( ) u φ' s( )−( )

⋅∑=

:=


The Antenna Array Problem...

Normalized array power patternP(Φ’,a,r) = E(Φ’,a,r) Ẽ(Φ’,a,r)/ E(Φ0’,a,r) Ẽ(Φ0’,a,r)

Performance OptimizationFind min || P(Φ’,v) - PD(Φ’) ||

v

v = (v1, v2 … vN) = vector of variable element excitations and/or element locations.


Array Performance Optimization

Find min || P(Φ’,v) - PD(Φ’) || → v*vv = (v1, v2 … vN) = vector of variable element excitations and/or element locations.

PD(Φ’) = desired array power pattern.

v* = optimum vector of element excitations and/or element locations.


Performance Function Optimization

Find min || P(Φ’,v) - PD(Φ’) || v

The choice of function norm depends on the specific array performance desired.

For minimization of the maximum array pattern sidelobe, the max norm is used, i.e.,

Find min max P(Φ’,v) v Φ’1 < Φ’ < Φ’2

where Φ’1 < Φ’ < Φ’2 defines the sidelobe region in angular space, and PD(Φ’)=0.


Minimize Max Sidelobe

0 60 120 18030

20

10

0

P φ( )

φ 57.3⋅

SLmax=-12.7 dB at φ=66 degrees


Minimize Sidelobe Power

To minimize the power in the sidelobe region:

Find min ∑ P(Φ’,v) v Φ’1 < Φ’ < Φ’2

0 60 120 1800

0.33

0.67

1

E φ'( )

E φt( )

φ' 57.3⋅ φt 57.3⋅,

SLpower=Σ P(fi)


Shaped Beam Synthesis

For min-max shaped beam synthesis, the criterion statement would be:

Find min max | P(Φ’,v) - PD(Φ’) | v Φ’1 < Φ’ < Φ’2

where Φ’1 < Φ’ < Φ’2 defines the region in angular space where it is desired to synthesize the pattern PD(Φ’).

1 0.33 0.33 10

0.33

0.67

11

0

E u( )

csc2 u( )

11− u


Finding Element Excitation From Given Array Pattern Data

0 20 40 60 80 100 120 140 160 18040

36

32

28

24

20

16

12

8

4

00

40−

empopInitial 1⟨ ⟩

empopFinal 1⟨ ⟩

desiredPattern 1⟨ ⟩

1800 empopInitial 0⟨ ⟩


Example 1


Example 2


Example 3


Example 4


Example 5


Sum/Difference Pattern Optimization

Application to monopulse radar performance optimization.

Performance objective example:Determine the optimum array parameters that will ensure that the difference pattern sidelobe level not exceed the sum pattern sidelobe level, as the pattern is scanned ±45°.


Monopulse Array System Block Diagram

. . . . . .

36 Radiating Elements

36 Element-to-Phase Shifter Cables

36 Phase Shifters

36 Phase Shifter-to-Power Divider Cables

18-Way Power Divider 18-Way Power Divider

180° Hybrid Junction

2 Power Divider-to-Hybrid Junction Cables

Sum Port Difference Port


Array Sum and Difference Patterns

100 80 60 40 20 0 20 40 60 80 10040

30

20

10

00

40−

P sum θ( ) P sum θ s( )−

P diff θ( ) P sum θ s( )−

9090−θ

180

π⋅

100 80 60 40 20 0 20 40 60 80 10040

30

20

10

07.105− 10 14−×

40−

P' sum θ( ) P' sum θ s( )−

P' diff θ( ) P' sum θ s( )−

9090−θ

180

π⋅

100 80 60 40 20 0 20 40 60 80 10020

10

0

10

20

30

40

5045.032

20−

R θ( )

R' θ( )

9090−θ

180

π⋅

OptimizedInitial

Ratio


Applications of EmpOp™

Synthesis of “on-the-vehicle” performance optimization of antenna arrays using EmpOp™ in conjunction with NEC to account for scattering and coupling between the array elements and the nearby structure.

Determination of array excitations from measured pattern data.

Optimization of array performance over a range of scan angles and frequency bandwidth.

Synthesis of optimum element excitations and spacings, including conformal and thinned array configurations.

empirical antenna array optimization · zsynthesis of “on-the-vehicle” performance optimization...

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