A Hybrid Optimization Algorithm for Low RCS Antenna Design
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RADIOENGINEERING, VOL. 21, NO. 4, DECEMBER 2012 1007
A Hybrid Optimization Algorithm
for Low RCS Antenna Design
Wei SHAO, Xinyue ZHU
School of Physical Electronics, University of Electronic Science and Technology of China, 610054 Chengdu, China
weishao@uestc.edu.cn, zhuxinyue888@163.com
Abstract. In this article, a simple and efficient method is antennas. Due to the basic radiation requirement of patch
presented to design low radar cross section (RCS) patch antennas, the shaping method becomes one of the most
antennas. This method consists of a hybrid optimization effective methods for the antenna RCS reduction. In [8],
algorithm, which combines a genetic algorithm (GA) with circle and rectangular slots on the antenna patch are intro-
tabu search algorithm (TSA), and electromagnetic field duced to cut off surface currents of high-order modes.
solver. The TSA, embedded into the GA frame, defines the Techniques of ground-cut slots are applied to the design of
acceptable neighborhood region of parameters and a patch antenna which achieves the RCS reduction [9]. [10]
screens out the poor-scoring individuals. Thus, the repeats introduces some types of fractal slots on an antenna patch
of search are avoided and the amount of time-consuming to obtain the low backscattering. Frequency selective sur-
electromagnetic simulations is largely reduced. Moreover, face (FSS) structures are also presented to reduce RCS of
the whole design procedure is auto-controlled by program- reflect-array antennas [11].
ming the VBScript language. A slot patch antenna example
In general, a low RCS antenna is difficult to design
is provided to verify the accuracy and efficiency of the
due to the simultaneous consideration on antenna radiation
proposed method.
and scattering. This design often relies on an optimization
procedure with a number of EM simulations, which are
very time consuming. [12] uses a differential evolution
Keywords algorithm (DEA) to optimize geometric parameters of
a low RCS antenna. Based on the separate DEA for the
Genetic algorithm, RCS, slot antenna, tabu search radiation and scattering modules, the individuals of bad
algorithm. radiation performance avoid the unnecessary RCS simula-
tion of the method of moment (MoM). However, the fit-
ness calculations for each generation involve both of the
1. Introduction radiation and scattering factors, which maybe lead to
an inefficient solution. In [13], combined with the high fre-
An antenna is often a main contributor to the overall quency simulation software (HFSS), a genetic algorithm
radar cross section (RCS) of an aircraft platform. The (GA) is proposed to design two low RCS slot antennas.
antenna RCS reduction has been a hot topic for the current Some strategies, such as separation of radiation and scatter-
stealth technologies in electromagnetic (EM) engineering ing models, elitist selection and two-point crossover, are
[1]-[2]. used to speed up the convergence of the GA.
In the past few decades, patch antennas have been Although the GA is robust and widely used in EM
widely used due to their conformability and simplicity of optimization, it needs to call the time-consuming EM
design. By creating a resonance with an appropriate load simulation solver hundreds of times to converge to a global
impedance, the RCS of a patch antenna can be substantially extremum. Therefore, how to reduce the amount of calls of
reduced at a specific frequency [3]-[4]. For a circular patch the EM solver is a key issue to improve the optimization
antenna, scattering and radiation responses are tuned by efficiency. To possess quicker convergence and obtain
controlling the bias voltage across a varactor diode to re- global optimum in the most probability, a tabu search algo-
duce the antenna RCS at some threat frequencies [5]. The rithm (TSA) is embedded into GA for multilayer optical
RCS of a rectangular patch antenna in a lossy substrate- coating optimization and yard cranes scheduling [14]-[15].
superstrate configuration is reduced at the cost of lowering The TSA, as a local search procedure, is a very efficient
the radiation efficiency [6]. The RCS peaks of a patch optimization algorithm whose tabu list avoids the repeats
antenna printed on a ferrite substrate can be shifted by of search. In this article, more exact optimized solutions
changing the magnetic bias field [7]. can be obtained through controlling the searching
Above methods for RCS reduction of patch antennas neighborhood region from the parameter sweeping. For the
are at the cost of worsening the gain and bandwidth of the proposed hybrid algorithm, the GA is applied as the main
1008 W. SHAO, X. ZHU, A HYBRID OPTIMIZATION ALGORITHM FOR LOW RCS ANTENNA DESIGN
frame due to its global ability and the improved TSA is information, which has important effect on the radiation
embedded into the GA to overcome the disadvantages of performance of antennas, is evaluated by the tabu list. Each
slow convergency of GA. individual gets a score determined by a criterion to judge
its quality. If the score is low, which means that this indi-
vidual is not similar to the feature of bad individuals, it will
2. Hybrid Optimization Algorithm be sent to HFSS simulation. If the score is high, parameters
of the individual incorporate more bad features and it will
Presently, GA has been widely applied to the optimi- not take time in conducting the simulation in HFSS for it.
zation of various EM problems [16]. It has a particular
In the classical TSA, the search progresses by itera-
parallel mechanism that guarantees the diversity of solution
tively moving from the current solution to an improved
to a certain degree. But its converging speed will become
solution in the neighborhood. Instead, the proposed TSA
slow when the solution approaches the optimum. For our
mainly aims at picking out the individuals with unaccept-
proposed hybrid algorithm, GA is applied as the main
able radiation performances, which will not be sent to be
frame because the global information can be clearly re-
simulated in HFSS. The tabu list with the effect of parame-
flected with the strong ability of general search. A simpli-
ters is established by pre-determination from parameter
fied TSA is embedded in GA to overcome the disadvan-
sweeping in HFSS. Through the use of the memory struc-
tages of GA. For the low RCS patch antenna design, the
ture, the amount of time-consuming simulations will be
flowchart which consists of the optimization module and
largely reduced. The score for each individual is given by
simulation module is shown in Fig. 1. The optimization
module obtains optimized individuals of next generation Score ai | xi Ti |, i 1, 2, 3,... (1)
and controls HFSS with VBScript. With the VBScript, i
HFSS returns its results to the optimization algorithm for where ai is the empirical scale factor which stands for the
calculating the fitnesses after finishing a simulation of the influence of an optimized parameter, xi is the optimized
present generation. The two processes are being run alter- parameter, and Ti is the corresponding threshold value that
nately until the program is terminated or an optimal solu- determines an acceptable neighborhood of each solution in
tion is got. | xi Ti | , where | | is a norm.
2.2 Optimization for Low RCS Antennas
The initialized population in Fig. 1 is made up of the
randomly created chromosomes. Each chromosome coded
by a binary number represents an individual prototype of
an antenna structure. In the binary coding, the parameters xi
are each represented by a finite length binary string. The
combination of all the encoded parameters is a string of
ones and zeros.
Firstly, each individual in a new population generated
by the GA will be evaluated by the tabu list. If the score is
higher than a given value, which means the individual in a
poor-scoring area, its fitness value is set to a large number
a and it will not be sent to HFSS with simulation. The
acceptable individuals with small scores will be sent to be
simulated in HFSS through the VBScript. Secondly, ac-
cording to their geometry parameters, the antenna radiation
Fig. 1. Flowchart for the low RCS antenna design.
models are established and calculated in HFSS. Thirdly, if
the individuals meet the radiation requirements, such as S11
2.1 A Simplified TSA and gain conditions, their corresponding scattering models
are established and fitness values are calculated. Other-
TSA enhances the search performance by using a tabu wise, the fitness value is set to the large number a and the
list that describes the visited solutions or user-provided sets scattering simulation is skipped. Thus, a waste of time to
of rules. If a potential solution has been previously visited simulate scattering models of the worse individuals is
within a certain short-term period or if it has violated avoided. Last, the fitness of each individual of the current
a rule, the algorithm does not consider its possibility re- generation is transferred to GA and the parameters of indi-
peatedly. The most important feature of the simplified TSA vidual are optimized to produce a new population. The
in this article is to prevent the revisiting of local minima in fitness function is defined as follows:
the parameter space. The tabu list is adopted to depict the N
1 M
features of acceptable individuals and judge the candidates fitness A RCS( i ) (2)
to be simulated or not for the next step. Some parameter j 1 M i 1 
RADIOENGINEERING, VOL. 21, NO. 4, DECEMBER 2012 1009
where M is the number of the RCS sample point versus the slope of each curve, and Ti is appropriately the value
frequencies, ARCS is the RCS value of an individual corresponding to 2.2 GHz for each curve, respectively. For
antenna, and N represents for the different incident angles. example, the value of 12 mm can be extract from the inter-
section of the dot line and circle line, which stands for the
According to the results of fitness evaluation, indi-
threshold value of lP1. Because the slope of lP3 curve is
viduals are selected by the proportionate selection strategy.
larger than those of lP1 and lP2, the empirical scale factor a
The selected individuals act as parents for a two-point
corresponding to lP3 is chosen larger than the two others.
crossover to rearrange the genes for producing better com-
Similarly, ai and Ti corresponding to the locations Pi of the
binations of genes. Therefore, a new generation will have
patch slot can be obtained through the parameter sweeping.
more fit individuals than the former one. In order to speed
Thus, a tabu list can be established from Fig. 3, as shown
up the convergence of GA, a certain amount of best indi-
in Tab. 1. Here, only the positions and lengths of patch
viduals are saved and inserted into the new generation
slots are involved because the effect of ground slots on
directly in the elitist strategy. Moreover, the TSA reduces
radiation performance is relatively weak. Through the use
the consuming time of EM simulations, too. In order to
of tabu list, about one fifth of the individuals in a popula-
avoid sticking at local optima, the mutation occurs with
tion avoid the unnecessary radiation simulation in HFSS in
a low probability, of a value of 0.01 in this article. After
this design.
the GA produces a new generation, the individuals in the
new population are evaluated by the tabu list and sent to
2.7
HFSS for simulation again. The simulation and optimiza-
tion are run alternatively until the termination condition is 2.6
lp1
Resonant frequency(GHz)
satisfied. 2.5
lp2
2.4 lp3
3. A Low RCS Slot Antenna Example 2.3
2.2
As an example, a slot patch antenna, shown in Fig. 2,
is studied. The substrate is 2 mm thick RT5880 with a 2.1 Operating frequency
relative permittivity of 2.2. The coaxial feed probe is 2.0
3.3 mm beneath the center of the patch. The width of each 5 6 7 8 9 10 11 12 13 14 15 16
Length of patch slot (mm)
rectangular slot on the patch and ground is 2 mm. The
parameters to be optimized are the slot location Pi (i=1, 2, Fig. 3. Parameter sweeping for the lengths of patch slots.
3) on patch and Gj (j=1, 2, 3, 4) on ground, and slot length
lPi (i=1, 2, 3) and lGj (j=1, 2, 3, 4). A rectangular patch P1 P2 P3 lP1 lP2 lP3
a 1 2.5 2 3 3 5
antenna without slots is used as a reference antenna, with
T(mm) (-10,-3) (-5,3) (7,2.5) 12 11 15
a patch of 41.6×32 mm2 on a ground of 80×70 mm2.
Tab. 1. Information of the tabu list.
A population incorporates 40 individuals and the ma-
ximal iteration of generation is 10. The acceptable radia-
tion performance is set as S11 < -15 dB and gain > 7dB,
respectively. Besides, the best 10% individuals of
population have been considered as the elitists. The
optimization results are listed in Tab. 2.
Patch slots
Location (x, y) lP
P1 (-10.4,-0.65) 14.3
P2 (-2.9,2.85) 10.5
P3 (8.6, 1.6) 16.8
Ground slots
Location (x, y) lG
G1 (17.6, 16.7) 14.8
G2 (24.2, -16.15) 16.9
Fig. 2. Geometric structure of the optimized slot antenna. G3 (-27.6, 14.35) 14.3
G4 (-27.8, -17) 13.4
Sweeping each optimized parameter in HFSS before
Tab. 2. Geometry of the optimized slot antenna (unit: mm)
the whole optimization process is needed to determine ai
and Ti in (1). As mentioned above, the tabu list is obtained Fig. 4 shows the convergence for RCS reduction of
with the radiation requirement, and the operating frequency the hybrid GA, non-elitist GA and elitist GA programs,
of 2.2 GHz is considered here. Taking the length lPi of the which consist of the minimum values of average RCS of
three patch slots for example, Fig. 3 plots the results of different incident angles for each generation. From Fig. 4,
parameter sweeping. So, ai is appropriately determined by the convergency speed of the hybrid GA, which involves
1010 W. SHAO, X. ZHU, A HYBRID OPTIMIZATION ALGORITHM FOR LOW RCS ANTENNA DESIGN
the parameter sweeping in HFSS before optimization proc- The photographs of the reference and slot antennas
ess, is higher than that of the Non-elitist GA and elitist GA. are shown in Fig. 5. Fig. 6 depicts the simulated and meas-
ured return losses of the two antennas. Both their resonant
-20
frequencies are about 2.17 GHz. The simulated xoz-plane
Average RCS of incident angles (dBsm)
-22
and yoz-plane radiation patterns of the antennas at
Elitist GA 2.17 GHz are shown in Fig. 7. The slot antenna has normal
-24 Non-elitist GA radiation performance compared with that of the reference
Hybrid GA antenna.
-26
0
-28
-30 -5
-32 -10
0 2 4 6 8 10
S11(dB)
Generation number
-15
Fig. 4. Convergence for RCS reduction of three GAs. Ref. antenna (simulated)
-20 Slot antenna (simulated)
Tab. 3 shows the calculation time of the three GAs. Ref. antenna (measured)
Slot antenna (measured)
Because the simulation time in HFSS is much more than
-25
the GA operation time in Matlab, only the CPU time of 1.0 1.5 2.0 2.5 3.0 3.5 4.0
HFSS simulation is given in Tab. 3. All calculations are Frequency (GHz)
performed on an AMD X6 2.8-GHz and 4G RAM ma-
Fig. 6. S11 of the reference and slot antennas.
chine. Although more CPU time is required for parameter
sweeping in the hybrid GA, more than 20% of individuals 0
in a population are not sent to HFSS for radiation simula- 10 330 30
tion with the tabu list, which leads to an efficient solution. 5
0
300 60
-5
Elitist GA Non-elitist GA Hybrid GA -10
Parameter sweeping --- --- 4617 -15
Radiation simulation 27640 28462 21376 -20 270 90
-15
Scattering simulation 16552 17068 11945 -10
Total time 44192 45530 37938 -5 Ref. antenna
240 120
0 Slot antenna
Tab. 3. Calculation time for three GAs (unit: sec). 5
10 210 150
180
(a) xoz-plane
0
10 330 30
5
0
-5 300 60
-10
-15
-20
-25
270 90
-25
-20
-15
(a) Reference antenna -10
-5 240 Ref. antenna 120
0 Slot antenna
5
10 210 150
180
(b) yoz-plane
Fig. 7. Simulated radiation patterns of the reference and slot
antennas at 2.17 GHz.
The comparisons of simulated RCS versus frequency
between the slot and reference antennas for different inci-
dent angles are shown in Fig. 8. The incident plane wave is
with the θ polarization. As shown in Fig. 8, the monostatic
RCS of the optimized slot antenna is reduced in the fre-
(b) Slot antenna quency range of 2-8 GHz compared to that of the reference
Fig. 5. Photographs of the antennas with top and back views. antenna.RADIOENGINEERING, VOL. 21, NO. 4, DECEMBER 2012 1011
-15
-20
Acknowledgements
-25
This work was supported in part by the NCET Foun-
-30
dation (11-0065), the Natural Science Foundation of China
RCS (dBsm)
-35
(60901023) and the Fundamental Research Funds for the
-40 Central Universities (ZYGX2010J043).
-45
-50 Ref. antenna
Slot antenna
-55
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The results show that the optimized slot antenna achieves
[15] MAK, K. L., SUN, D. A new hybrid genetic algorithm and tabu
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tains good radiation performances. don (UK), 2009, p. 526-531.1012 W. SHAO, X. ZHU, A HYBRID OPTIMIZATION ALGORITHM FOR LOW RCS ANTENNA DESIGN
[16] RAHMAT-SAMII, Y., MICHIELSSEN, E. Electromagnetic respectively. He joined the UESTC and is now an associate
Optimization by Genetic Algorithms. New York: John Wiley &
professor. He has been a visiting scholar in the Electro-
Sons, 1999.
magnetic Communication Laboratory, Pennsylvania State
University in 2010. His research interests include the com-
putational electromagnetics and antenna technique.
About Authors ... Xinyue ZHU was born in Henan, China in 1985. He re-
ceived the B. E. degree in Henan Polytechnic University,
Wei SHAO was born in Chengdu, China in 1975. He re- Jiaozuo, China, in 2009. From 2009 to now, he is pursuing
ceived the M. Sc. and Ph. D. degrees in Radio Physics the M. Sc. degree in the Institute of Applied Physics at
from the University of Electronic Science and Technology UESTC, Chengdu, China. His current research interests
of China (UESTC), Chengdu, China, in 2004 and 2006, include the antenna design and optimization method.You can also read
