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Design of Microstrip ReflectarrayAntenna Using a Genetic Algorithm BasedOptimization MethodYu Chen a , Xing Chen a & Kama Huang aa College of Electronics and Information Engineering, SichuanUniversity , Chengdu , ChinaPublished online: 31 Jan 2012.

To cite this article: Yu Chen , Xing Chen & Kama Huang (2012) Design of Microstrip ReflectarrayAntenna Using a Genetic Algorithm Based Optimization Method, Electromagnetics, 32:2, 77-85, DOI:10.1080/02726343.2012.645423

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Electromagnetics, 32:77–85, 2012

Copyright © Taylor & Francis Group, LLC

ISSN: 0272-6343 print/1532-527X online

DOI: 10.1080/02726343.2012.645423

Design of Microstrip Reflectarray Antenna Using aGenetic Algorithm Based Optimization Method

YU CHEN,1 XING CHEN,1 and KAMA HUANG 1

1College of Electronics and Information Engineering, Sichuan University,

Chengdu, China

Abstract The design of the microstrip reflectarray antenna is commonly based on the

reflection phase curve, but this is not an accurate method, as many parameters havebeen neglected in the design procedure. This work explores the genetic algorithm in

conjunction with full-wave simulation and the cluster parallel computation to designa microstrip reflectarray antenna. A microstrip reflectarray antenna, which consists

of a 7 � 7 rectangular-patch/ring-combination reflection elements and is illuminatedby a patch antenna, is designed for high gain. Results demonstrate that in comparison

with the design method based on the reflection phase curve, the proposed optimizationmethod is able to design a microstrip reflectarray antenna with better performances;

e.g., the gain has been considerably improved (from 18.1 dBi to 19.5 dBi) at thedesign frequency of 5.8 GHz.

Keywords microstrip reflectarray antenna, high gain, genetic algorithm, full-wavesimulation, parallel computation

1. Introduction

Since it was proposed by Malagisi (1978), the microstrip reflectarray antenna has attracted

significant interest and been studied by many researchers because it combines salient

features of both the flat reflector and the array antenna (Pozar et al., 1997). It provides

an attractive alternative to conventional directive antennas, such as the parabolic reflector

antenna, and has been widely applied in many fields, e.g., space applications, wireless

communication applications, etc. (Encinar, 2007; Li et al., 2011).

A microstrip reflectarray antenna usually consists of a feed source and a reflector.

The reflector is an array of microstrip patches and/or slots etched on a grounded dielectric

substrate. The feed source is placed at a particular distance from the reflector. The

microwave is illuminated from the feed source and scattered by the reflector. Elements

in the reflector are designed to generate proper phase compensations associated with

the path lengths from the feed source, so that a planar phase surface is formed in front

of the aperture of the antenna. Various element types have been proposed to vary the

reflection phase: patches of variable size (Venneri et al., 2002; Chaharmir et al., 2006),

patches loaded with variable-length phase delay lines (Javor et al., 1995), and patches with

Received 15 June 2011; accepted 29 September 2011.Address correspondence to Xing Chen, College of Electronics and Information Engineering,

Sichuan University, Chengdu, 610064, China. E-mail: xingcsc@yahoo.com.cn

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78 Y. Chen et al.

different angular rotation (Huang & Pogorzelski, 1998). Elements may be rectangular or

circular patches, loops, dipoles, rings, or double square rings, etc.

Up to now, the design of the microstrip reflectarray is mostly based on the reflection

phase curve, which describes the one-to-one correspondence between the phases and

the geometry parameters that control element reflection phase. Several methods (Tsai &

Bialkowski, 2002; Encinar, 2001) can be utilized to create a reflection phase curve.

However, a microstrip reflectarray designed by these methods may not be optimum

and accurate because the reflection phase curve is obtained under the assumption of

a normal incidence (Tsai & Bialkowski, 2002); when the path length is calculated for

the determination of the phase compensation, the feed source and reflection elements are

essentially considered as sizeless points (Huang & Encinar, 2008); the coupling effects

between reflection elements may not be negligible when the distance between patch edges

is small (e.g., less than a quarter wavelength) (Javor et al., 1995; Huang & Encinar, 2008);

and the field diffracted by the edges are not taken into account (Zich et al., 2002). Those

approximations may bring forth errors in the design and subsequently deteriorate the

performances of the designed antennas.

This work explores employing the genetic algorithm (GA) (David & Goldberg, 1989;

Zbigniew, 1996) in conjunction with the full-wave simulation and the cluster parallel

computation to design a microstrip reflectarray antenna. This optimization-based design

method has already been estimated by many researchers (Ares-Pena et al., 1999; Rattan

et al., 2008; Gandelli et al., 2005) to be a powerful and effective tool for the antenna

design. Moreover, the full-wave simulation provides an accurate approach for the design

of the microstrip reflectarray antenna because it allows taking all involved effects into

account without the above-mentioned approximations. Therefore, one can expect that a

microstrip reflectarray antenna could achieve better performances by the optimization

algorithm in conjunction with the full-wave simulation rather than the reflection phase

curve.

However, for a microstrip reflectarray antenna, the proposed method confronts two

problems. The first is the large quantity of unknown parameters due to various ele-

ments in the reflector lead; the second is the heavy computational burden connected

with the full-wave simulation, which requires hundreds or even thousands of simu-

lations in an optimization procedure. Hence, to the best knowledge of the authors,

very little research has employed an optimization algorithm to design a microstrip

reflectarray antenna, and none utilized the full-wave simulation. For example, a GA

(Zich et al., 2002; Mussetta et al., 2004) and a hybrid algorithm combining the GA and

the swarm algorithm (Gandelli et al., 2005) was utilized to optimize geometry features

of reflectarray antennas, but all of them adopted an approximate method to evaluate

antennas’ performances, which analyzes the reflection elements through their equivalent

circuits and obtains the total radiated field by summing up the radiated field from single

elements.

In this work, prior to the implementation of the GA, some techniques are adopted to

decrease the quantity of unknown parameters and an initial antenna structure is designed

by using the reflection phase curve to determine roughly the value range of those unknown

parameters. Meanwhile, in the optimization procedure, the cluster parallel computation

is employed for tackling the heavy computational burden.

Section 2 introduces the configuration of the proposed antenna. The method of the

antenna optimization is introduced in Section 3. The simulated and measured character-

izations of the optimized antenna are presented in Section 4. A conclusion is stated in

Section 5.

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Design of Microstrip Reflectarray Antenna 79

2. Antenna Configuration

Figure 1 depicts the configuration of the microstrip reflectarray antenna in this work. A

rectangular patch (see Figure 1(b)) is used as the feed source and placed at a distance of

h1 from the reflector. The reflector includes a printed circuit board (PCB) with relative

permittivity "r D 4:4, thickness h2 D 3 mm, and a metal ground. Between the PCB and

the metal ground is an air layer with thickness h3. This antenna adopts variable-sized

patches (Li et al., 2009), which is a preferable choice in many designs due to its simplicity

(Tsai & Bialkowski, 2002), to achieve the phase compensation. Reflection elements are

etched on the PCB, as illustrated in Figure 1(d). Each includes a square patch with length

L1, as well as a square ring with length L2 and width W , and occupies a square area

with length L.

3. GA Optimization

3.1. Techniques to Reduce the Quantity of Unknown Parameters

In this work, a microstrip reflectarray antenna comprising 7 � 7 elements on the reflector

operated at 5.8 GHz will be designed by the GA in conjunction with the full-wave

simulation for high gain.

Figure 1. Configuration of reflectarray: (a) side view of the reflectarray antenna, (b) top view of

the patch antenna, (c) top view of the reflector, and (d) an element in the reflector.

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80 Y. Chen et al.

Figure 2. Reflection phase versus the square ring length L2.

Considering the geometrical symmetry of the elements in the reflector, it is easy to

observe that there are ten types of elements with different sizes, which are indexed from

one to ten, as shown in Figure 1(c). Hence, 42 unknown parameters in total need to be

optimized by the GA, i.e., h1, h3, L1.i/, L2.i/, L.i/, and W.i/, where i D 1; : : : ; 10.

Obviously, the quantity of unknown parameters is too large for the GA optimization

and will lead to great difficulty for the GA in obtaining an optimum result. Hence,

the following techniques are adopted to reduce the unknown parameters prior to the

implementation of the GA.

First, the square areas containing reflection elements are fixed to an identical size,

i.e., L.i/ D L. In this work, L is set to be 0:6� (31 mm, where � is the wavelength of

the working frequency 5.8 GHz in free space), which is helpful to avoid the appearance

of grating lobes to a certain extent (Huang & Encinar, 2008).

Then, for a reflectarray antenna, the distance h1 between the feed source and the

reflector is required to be large enough so that the incident wave to the reflection elements

is the approximate plane wave (Targonski & Pozar, 1994; Pozar & Metzler, 1993), but

h1 cannot be very large to ensure that the reflector covers at least the main-lobe of the

feed source. As a compromise, h1 is set to be 75 mm in this work.

Furthermore, L1.i/ D k1 � L2.i/ and w.i/ D k2 � L2.i/ are ordered, which means

that for a reflection element, only L2.i/ is an independent parameter. To determine k1,

k2, and h3, many full-wave EM simulations were conducted, and it was discovered that

a linear and smooth reflection phase curve (see Figure 2) can be derived when k1 D 0:4,

k2 D 0:15, and h3 D 7 mm.

Now, the quantity of unknown parameters needed to be optimized by the GA is

sharply reduced from 42 to 10, i.e., L2.i/, where i D 1; : : : ; 10.

3.2. An Initial Antenna Design Using the Reflection Phase Curve

In an optimization procedure, the determination of unknown parameters value range is

very important, because it has a major impact on the optimization efficiency and results.

The value range of unknown parameters should be a good tradeoff between ensuring the

optimum to be included in the solution space and minimizing the solution space to alle-

viate the optimization difficulty. In this work, the value range of the unknown parameters

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Design of Microstrip Reflectarray Antenna 81

is roughly determined by designing an initial antenna design using the reflection phase

curve.

The required reflection phase �i for element i can be calculated (Pozar & Metzler,

1993) by

�i D k�

Ri � Eri � Er0

�

; (1)

where k is the propagation constant in vacuum, equal to 2�=�; Ri is the distance from

the phase center of the feed source to the element; Eri is the vector from the center of the

reflectarray to the element; and Er0 is the unit vector in the main beam direction.

In this work, the main beam of the feed antenna is along the z-axis, so the included

angle between Eri and Er0 is 90ı; thus, the part Eri � Er0 will be zero, which simplifies Eq. (1)

to �i D kRi . As a consequence, the values of required reflection phase �i for each

element in the reflector are (unit: degrees): �1 D �198, �2 D �155:2, �3 D �475:4,

�4 D �402:7, �5 D �369:2, �6 D �276:9, �7 D �248:5, �8 D �220:9, �9 D �143:2,

and �10 D �386:2. By referring to the reflection phase curve in Figure 2, the square ring

length L2.i/ can be determined as follows (unit: mm): L2.1/ D 12:5, L2.2/ D 10:8,

L2.3/ D 23:4, L2.4/ D 19:7, L2.5/ D 18:5, L2.6/ D 15:5, L2.7/ D 14:5, L2.8/ D 13:4,

L2.9/ D 10:4, and L2.10/ D 19:1.

3.3. GA Optimization

After given a considerable margin for the GA-based optimization, the parameters L2.i/

are confined to be (unit: mm): 10–15, 9–13, 20–28, 18–22, 16–21, 13–18, 12–18, 11–17,

8–13, and 17–21, respectively.

In this work, the popular commercial software CST Microwave Studio (MWS; Com-

puter Simulation Technology, Darmstadt, Germany) is employed to simulate radiation

properties of the proposed microstrip reflectarray antenna. The computation of the GA-

based antenna optimization is parallelized in a master–slave model and implemented on

a Beowulf cluster system (Chen et al., 2005; Chen et al., 2007). The Beowulf cluster

system is composed of 32 processors interconnected by a fast 1,000 Mb/s Ethernet. One

processor, named the master processor, carries out the GA optimization, while other

processors, called slave processors, execute full-wave EM simulations.

The goal of the GA optimization is to achieve a high gain and good impedance

match at the working frequency of 5.8 GHz. Hence, the fitness function, which represents

the desired performance requirements and guides the direction of GA optimization, is

defined as

Fitness D C1 � Max Gain C C2 � Max S11; (2)

where Fitness represents the value of the fitness function; Max Gain refers to the radiation

gain at the working frequency of 5.8 GHz; Max S11 denotes the maximum jS11j over a

preset frequency band ranging from 5.7 to 5.9 GHz; values of the gain and jS11j are in dB;

C1 and C2 are weight coefficients, whose values should emphasize relative importance

of each term in the design requirements, but no specific rule exists for determining their

values. In this work, they are determined by experience and are set to be 0.03 and �0.02,

respectively.

A GA-based optimization is executed. In the optimization, the GA employs tour-

nament selection with an elitist, single-point crossover with probability Pc D 0:5 and a

jump mutation with probability Pm D 0:2, and it uses 50 generations and 100 individuals

in a population.

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4. Results and Analysis

The structural parameters of the proposed microstrip reflectarray antenna generated by

the GA-based optimization are as follow (unit: mm): L2.1/ D 13:1, L2.2/ D 11:7,

L2.3/ D 27:4, L2.4/ D 21:1, L2.5/ D 19:4, L2.6/ D 17:4, L2.7/ D 17:4, L2.8/ D16, L2.9/ D 12:2, and L2.10/ D 20:4. The GA-based antenna optimization procedure

takes about 43 hr on the proposed cluster system. Because one full-wave simulation in

this case takes approximately 15 min on a computer (a Quad Core Q6600 at 2.66 GHz

and 4 GB RAM, Lenovo, Beijing, China) of the cluster, the optimization procedure will

cost more time (more than 1,200 hr) without the parallel computation. Therefore, the

parallel computation is quite necessary for the antenna optimization.

A prototype antenna, shown in Figure 3, has been fabricated. Its length and width

are 217 mm and 217 mm, respectively. A microstrip patch antenna is propped by four

polytetrafluoroethylene (PTFE) blocks. To illustrate its dimensions in the figure, a ruler

is placed in front of it as a contrast.

The reflection coefficient of the prototype antenna is measured with an Agilent

E8362B (Santa Clara, California, USA) vector network analyzer. The measured and

simulated jS11j curves are compared in Figure 4, which shows that they are in good

agreement. The S11 < �10 dB impedance bandwidth of 8.3% has been achieved.

Radiation patterns of the proposed antenna are measured in an anechoic chamber.

As an illustration, Figure 5 shows the measured and simulated radiation patterns on the

XZ-plane and YZ-plane, respectively, at 5.8 GHz, and one can observe that they also

agree very well. The measured side-lobes are about 15.8 dB below the main-lobe, and the

measured cross-polarization levels are less than 20 dB in both the XZ- and YZ-planes.

In Section 3.2, an initial antenna has been designed by using the reflection phase

curve. Figure 6 compares the simulated radiation gains against frequencies of two anten-

nas designed by the reflection phase curve and the GA-based optimization, respectively.

It is easy to observe that, in comparison with the commonly adopted design method

using the reflection phase curve, the GA-based optimization method has considerably

Figure 3. Prototype of the fabricated antenna.

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Design of Microstrip Reflectarray Antenna 83

Figure 4. Measured and simulated jS11j.

Figure 5. Measured and simulated radiation patterns on the XZ-plane and YZ-plane: (a) XZ-

plane and (b) YZ-plane. (color figure available online)

improved the gain of the microstrip reflectarray antenna over the frequency band from

5.6 GHz to 6.0 GHz, and it improves the gain over 1.4 dB (from 18.1 dBi to 19.5 dBi)

at the working frequency of 5.8 GHz.

5. Conclusions

The microstrip reflectarray antenna provides an attractive alternative to conventional

directive antennas in that it is conformal, inexpensive, and easy to install and manufacture.

Most microstrip reflectarrays are designed so far by entailing the use of a phase design

curve, which may not be an optimum design because it neglects some effects, such as

the mutual coupling between reflection elements. This work explores employing the GA

in conjunction with full-wave simulation and the cluster parallel computation to design

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Figure 6. Gain comparison with frequency varying from 5.6 GHz to 6.0 GHz.

a microstrip reflectarray antenna. A microstrip reflectarray antenna, which consists of

7 � 7 reflection elements etched on a PCB and illuminated by a patch antenna, has been

optimized for high gain by the GA. A prototype antenna is fabricated and tested. The

measured results agree well with the simulated data and show that the optimized antenna

achieves a high gain of 19.5 dBi, an S11 < �10 dB impedance bandwidth of 8.3%, a

�15.8-dB side-lobe level, and a cross-polarization level of �20 dB.

It is worth noting that a considerable gain improvement of 1.4 dB (from 18.1 dBi to

19.5 dBi) has been obtained by employing the optimization algorithm and the full-wave

simulation. The achievement is valuable for an antenna. The results in this work also

indicate that, for a microstrip reflectarray antenna, the commonly adopted design method

based on the reflection phase curve is far from perfect, and the antenna design should

take into account such items as the sizes of the feed source and reflection elements, the

mutual coupling between reflection elements, and so on, which are neglected by most

designers. Of course, the relatively large computation time (about 43 hr in this work,

even after employing the parallel computation technology) will adversely affect the wide

application of the proposed optimization-based method, especially for the design of a

large-scale microstrip reflectarray. In the future, more research is needed in order to

propose an accurate and effective design method for the microstrip reflectarray antenna.

Acknowledgment

This work was supported by the New Century Excellent Talent Program in China (grant

NCET-08-0369), the National Natural Science Foundation of China (no. 10876020), and

the Key Laboratory of Cognitive Radio (GUET), Ministry of Education, China.

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