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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.
Copyright © 2004-2005 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.
Copyright © 2004-2005 Hutt Systems, Inc.
Antenna Configuration
φ
θ
ap
rp
Antenna Element
Far-Field
φ' = (θ,φ)
r (φ')
Copyright © 2004-2005 Hutt Systems, Inc.
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( )−( )
⋅∑=
:=
Copyright © 2004-2005 Hutt Systems, Inc.
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.
Copyright © 2004-2005 Hutt Systems, Inc.
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.
Copyright © 2004-2005 Hutt Systems, Inc.
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.
Copyright © 2004-2005 Hutt Systems, Inc.
Minimize Max Sidelobe
0 60 120 18030
20
10
0
P φ( )
φ 57.3⋅
SLmax=-12.7 dB at φ=66 degrees
Copyright © 2004-2005 Hutt Systems, Inc.
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)
Copyright © 2004-2005 Hutt Systems, Inc.
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
Copyright © 2004-2005 Hutt Systems, Inc.
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⟨ ⟩
Copyright © 2004-2005 Hutt Systems, Inc.
Example 1
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Example 2
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Example 3
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Example 4
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Example 5
Copyright © 2004-2005 Hutt Systems, Inc.
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°.
Copyright © 2004-2005 Hutt Systems, Inc.
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
Copyright © 2004-2005 Hutt Systems, Inc.
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
Copyright © 2004-2005 Hutt Systems, Inc.
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.
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