Proceedings CEEM' 2012/Shang 'hai

Design of Concentric Circular and Concentric

Hexagonal Antenna Array Using Hybrid EPSO/DE

Algorithm M A. Mangoud, H M Elragal and M T. Alsharaa,

Department of Electrical and Electronics Engineering University of Bahrain

P. O. Box 32038, lsa Town, Kingdom of Bahrain Abstract- In this paper, the novel hybrid enhanced

particle swarm optimization and differential evolution

(EPSO/DE) optimization technique [1-2] is used in

designing different configurations of concentric circular arrays (CCAA) and concentric hexagonal arrays (CHAA).

Many advantages were achieved by the rearrangement of

the circular arrays (CA) and hexagonal arrays (HA)

elements into CCAA and CHAA multi-ring geometries.

Different configurations with two-rings, three-rings and

four-rings are designed with the same number of elements

and the same main beamwidth of the initial circular and

helical geometries. The objective of this paper is to design

optimum multi-ring antenna arrays that achieve minimum

sidelobe level (SLL), high directivity and reduced mutual

coupling in compare to traditional circular and helical

arrays. Hybrid EPSO/DE algorithm is applied to optimize

the complex weights (amplitude and phase) of the

elements current. The objective is to minimize the SLL of

the concentric configuration arrays while achieving the

highest possible directivity and minimum mutual

coupling.

I. INTRODUCTION

A very low side lobe level radiation pattern of a

lin�ar array could be synthesized with a high gain

mam lobe and narrow beam width in any given

direction for the elevation plane, but it does not work

equally well in the azimuth plane. The two dimensional

antenna arrays have the capability to transmit and receive

data in elevation and azimuth angles as well, thus two

dimensional antenna arrays configurations have been

widely used in the field of 3D beamforming. One of the

best configuration of two dimensional antenna arrays is

the circular antenna array, since its main lobe could be

steered an all azimuth angles without changing its beam

width [3-4], Nevertheless, a circular array is a high

side lobe geometry. If the inter-element distance is

decreased to minimize the sidelobes level, the mutual

coupling effect becomes more severe. For reducing the

high side lobe levels, concentric multi-ring arrays could be used as an alternative design. Furthermore, the hexagonal

array as a special case of multi-ring arrays could

overcome the problem of high side lobes. It is proved that

the hexagonal array has better steerability and higher gain

properties than circular array for both hexagonal and

concentric hexagonal arrays [5]. The circular array has a

high side lobe level pattern so the inter-element distance of array antenna should be small to minimize the SLL. But

the small distance between elements increase the mutual

978-1-4673-0029-2/12/$26.00 ©2011 IEEE 33

coupling effect. To overcome this, the multi-ring antenna arrays [6] with adequate inter-element distance are

utilized in synthesizing radiation pattern with low SLL in

the azimuth plane. The objective of this paper is

redesigning a circular array with fixed number of elements

into different concentric hexagonal and concentric circular

configurations arrays employing hybrid EPSO IDE [2].

Many advantages were achieved by the rearrangement of

the circular array elements like the reduction in the SLL,

increasing in the directivity and increasing in the inter­

element distance which has a direct impact in mitigating

the mutual coupling effect between elements.

The rest of this paper is organized as follows: In section

II, the design of circular array CA and hexagonal array

HA are presented. Section III introduces the design of

concentric circular and concentric hexagonal array. The

complex weights of CCAA and CHAA are optimized in

section V. Finally, some conclusion remarks are noted in Section VI.

II. DESIGN OF CONCENTRIC CIRCULAR AND CONCENTRIC HEXAGONAL ANTENNA ARRAY

If several ring arrays sharing the same center point but

with different radii, then the formed configuration is a

concentric circular/hexagonal array. Recently, the antenna

designers have been exerted a lot time in enhancing the

performance of mobile and wireless communication

systems through increasing channel capacity, customizing

antenna beams and increasing coverage area as possible. However, the unstudied well array synthesis could result

in many problems like the appearance of undesired

radiations which interfere with other communication

systems, beside wastage of the radiated power, which

consider a distressing problem for power-limited battery­

driven wireless devices. Among different types of planar

antenna arrays concentric circular array (CCA) was

studied in [5] gained more popularity in mobile and

wireless communications. These arrays have various advantages like steerablity, high gain and their compact

size compared to the circular arrays. The array factor for

the CCA will be as in the hexagonal array in equation

(4.7), but with angular position tPmn as follow:

m= l ,2, . . . ,M n=1,2, . . . , Nm (1)

If the amplitude excitation are taken to be lrun = I run + Nrn/2

then,

Proceedings

M N,.12

AF(¢) = 2 L L Imn cos {krm cos(¢ - ¢"",) + amn} (2) nFl n=1

To direct the peak of the main beam in the 90 direction,

the phase excitation of the mnth element can be chosen to

be:

a"", = - amrri-N m = -krm cos(¢o - ¢",d (3)

The array factor for the concentric hexagonal array

(CHAA) will be the same as in equation (4.9). Similarly to

[5], the radii and the angular positions of the CHAA

elements will be calculated according to the assumed

geometry.

Design example: 36 elements, uniform amplitude, equally spaced CA and HA

It is assumed here for comparison purpose, a uniform

amplitude (i.e. In = 1) equally spaced circular array (UCA)

and uniform amplitude equally spaced hexagonal array (UHA) with 36 isotropic elements for each. The elements

spaced with do = 0.25)" therefore the radius r will be

1.43A for the circular and 1.5A as maximum radius rj for

the hexagonal array. The radiation pattern of both

geometries in the x-y azimuth plane (9=90°) is depicted in

Fig. I. From this figure it is clear that both patterns almost have the same beam width, with slight reduction in SLL

for the hexagonal array by -0.25 dB. The values of

beamwidths and SLL for the hexagonal and circular array

are summarized in table I.

o Phi (Oeg)

• Uniform Hexagonal -- Uniform Circular

Fig. 1 Radiation pattern of uniform HA and CA with 36

elements and 0.25"- inter-element spacing at 8=90°.

Table I

The SLL and Beam width for both 36 elements Geometries.

C:onClguratloli

Hexagonal Array

C ircular Array

Dca D:l '\vtd tb [De,,]

32

31

51..1.. [dB]

-8.1 S

-7.9

B. Design Examples: 36 Isotropic Elements, Uniform Amplitude Concentric Circular and Concentric Hexagonal Antenna Array

CA and RA arrays obtained SLL=-8.15dB as low result in

previous section with 36 element equally spaced with

0.25A. This section presents a comparative study of

different types of multi-rings arrays. The uniform

concentric circular arrays (UCCA), and uniform

concentric hexagonal arrays (UCHA) , are designed with

978-1-4673-0029-2/12/$26.00 ©2011 IEEE

34

CEEM' 2012/Shang 'hai

fixed number of elements (36 elements). The UCCAs and

UCHAs are designed with uniform inter-element distance

0.5A at least in the same ring. The resulted radiation

pattern of each case will be compared to the other, from

the aspects of side lobe level SLL and main lobe beam

width BW. Starting with 36 isotopic elements that are

needed to be arranged in two-rings, three-rings and four­

rings, many configurations can be assumed according to the number of elements in each ring. One ring at least

should have 0.5A inter-element spacing in the array. This

depends on the configuration and the number of ring's

elements Nm. Two cases in each configuration for UCCA

and UCHA are chosen. Fig. 2 shows the geometries of

UCCA and UCRA with different configurations for the

four rings arrays.

(a) (b) �axjs y-axis

Fig. 2 The geometries with rotated outer rings with respect to

the inner ring x-axis, for the: (a) UCCA and (b) UCHA.

Table II depicted the definition of these configurations.

The table also shows the number of elements Nm, the

inter-element distance dom and the radius of circular ring

or the maximum radius r m of hexagonal ring.

Table II

The configurations details: number of elements and the dimensions of

each ring for UCCA and UCHA In R..ing

Configuration do,

Config.2.1 UCCA L43 0.5

{ l B. IS} UCHA 1.5 0.5

Config.2.2 UCHA 0.95 0.5

{12. 24} UCHA 1.0 0.5

Config3.1 UCHA 0.48 0.5

{6. 6. 24} UCHA 0.5 0.5

C onfig3 _2 UCHA OA8 0.5

{6. 12. IS) UCHA 0.5 0.5

ConfigA_ l UCHA OA8 0.5

{6.6 . 12.12} UCHA 0.5 0.5

Config_4_2 UCHA OA8 0.5

{6. 6. 6. IS} UCHA 0.5 0.5

2nd Ring

do> L 9 1 0.67

0.67

1.91 0.5

0.5

0.95

0.95 0.5

0.5

0.95

0.95

3M R.ing 4th Ring

1.91 0.5

2 0.5

l A3 0.5

1.5 0.5

1.43 0.75 1.91

1.5 0.75

1.43 1.5 1.91 0.67

1.5 1.5 0.67

The radiation pattern's characteristics of the designed

configurations are shown in table III. It is obvious that the

beamwidths of these configurations are close to the

beamwidths of the uniform circular and hexagonal array

illustrated in table 1 earlier. The SLL of most configurations are better than the SLL of the uniform

circular and hexagonal array, except the case of config.4.1

{6, 6, 12, 12} UCHA which gave -7 dB. The best case

was for config.3.2 {6, 12, 18} UCHA with SLL= -14.3

dB, by a reduction of -6.15 dB than the uniform

Proceedings

hexagonal array with 4" degrees wider beamwidth. It can

be seen that the UCHA configurations are better in SLL

than the UCCA configurations according to these results

on the mentioned table. It could be said that, for the same

number of elements (36 elements) with 0.5A at least as

inter-element distance, many configurations UCCA and

UCHA have lower SLL than the uniform circular and

hexagonal array with 0.25A inter-element distance and

almost have the same beamwidth. The 0.5A have been

chosen to be the minimum distance between any two

adjacent elements in the UCCA and UCHA , to mitigate

the effects of the mutual coupling between elements,

which will be severe in the case of 0.25A inter-element

distance in the uniform circular and hexagonal array. Fig. 3 illustrates the radiation pattern of Config.3.2 {6, 12, IS}

UCHA and UCCA in the azimuth plane at 8=90°.

m � l.L «

Table III The BW and SLL of different configurations

Configul':iltion Bealll ,"Vidth SLL

Config.2.1 UCCA

{18, 18} DCliA

Config.2.2 DCCA

{12, 24} DCliA

COllfig.3 . 1 UCCA

{6, 6, 24} DCliA

eonfig.3 .2 DCCA

{6, 12, 18} DCliA

Config .. 4.1 UCCA

{6,6,12,12 } DCliA

Config.4.2 DCCA

{6, 6, 6, 18} DCliA

-20

-30

-40

-&0

..,0

-70 - - - -� -------

-80

-- - -� - ------ � - -- - - � , , , , , , , ,

(neg) [dB)

27

28

29

30

31

32

35

36

31

32

30

30

-8.5

-10.1

-10

-9.5

-11.5

-9.5

-11.8

-14.3

-10.9

-7

-7.9

-9.3

, , , ("" -----,... ------- T --, , , , , ,

-90

-- - -:- - ------� - -- - ---�- - - -- - -:--- -- Concentric H exagonaJ : : : : -- Concentric Ci rcula. r

-

100

L-""'_1 �

50:-------:-'�OO::----&�

0�---,lO---''===:'

50:======' OO�===' �

50===!..l

Phi (Degree)

-

Fig. 3 Radiation pattern of Config.3.2 {6, 12, IS} UCHA

and UCCA in the azimuth plane at 8=90°.

IV. OPTIMIZING OF COMPLEX WEIGHTS IN

HEXAGONAL, CONCENTRIC CIRCULAR AND

CONCENTRIC HEXAGONAL ANTENNA ARRAYS

In this section the complex weights (Amplitude and

Phase) of the elements in the hexagonal, concentric

circular antenna array (CCAA) and concentric hexagonal

antenna array (CHAA) will be optimized. For the case of

CCAA and CHAA, the effect of adding a central feeding

element to the array will be studied. At the same time we

will compare the resulted radiation patterns with

chebyshev-like radiation pattern of a circular array [4],

which used the same number (36 elements) of the

isotropic elements, from aspects of the SLL, beam width

978-1-4673-0029-2/12/$26.00 ©2011 IEEE

35

CEEM' 2012/Shang 'hai

and directivity. The configurations to be optimized are

Config.2.2 {12, 24} , Config.3.2 {6, 12, IS} and

ConfigA.1 {6,6, 12, 12} , since they achieved the lowest

SLL in the two-ring, three-ring and four-ring of rotated

CCAA and CHAA configurations as in table V. In this

section the excitation amplitude of the array's elements

will not be uniform any more, as well as the excitation

phase of the elements. This complex weight of the array's

elements will be optimized with three algorithms DE,

EPSO and Hybrid EPSO/DE, to get the lowest SLL with

acceptable change in main lobe beam width compared to

the reference pattern in [4], which use the same number of

elements with 0.25A inter-element distance.

A. Objective Function Formulation o/the Design Problem.

To optimize the complex weights of the array's elements,

the optimized parameters will be the Amplitude Imn and

the Phase amn of the array's elements. It is needed to solve

the mini-max of the optimization problem under one

constraint, according to the following objective function

of the problem:

min ImnlXmn E c �a'{;;;A;BW IAF(¢Jmn. amn) l} (6) Subject to .5BW:::: £.

Where AF (<1>, Imn, u,nn) is the array factor of the multi-ring

array. Imw amn are the excitation amplitude and phase of

the mn1h element, C is the set of all vectors, �<1>BW and

cSBW are main lobe beam width and the change in the

main lobe beam width respectively. Finally E: is the

maximum allowable change in the main lobe beam width.

This problem is optimized using the three algorithms

EPSO, DE and the Hybrid EPSO/DE techniques

according to the following fitness function:

�=ISO f = L: , WJ.!wew(¢).AF«(1l)I +W2.,u(¢o) ��ISO

p( rAJ ) = IAF(¢o) - max{ AF(¢)} 12

(7)

(S)

WI, W2 are weighting factors in the fitness function, WRW

will be the same as in equation 4.14. The directivity will

be calculated according to following equation:

IE (Bo , ¢0) 12 D = 1 2Jl H 2 (9) - J JIE(B. ¢>I .sin B.dB.d¢

4n 0 0

B. Analysis and numerical results.

It is desired to optimize the complex weights of the arrays

with different configurations, to suppress the side lobe of

the radiation pattern according to the previous fitness

function. First the hexagonal array will be optimized using

the three algorithms, and compare it to an optimized

circular array [4], from aspects of SLL, beam width (BW)

and directivity. It is found by trial and error concept, that

the best value of wl=O.land W2=1. The boundaries of the

optimized parameters are: the amplitude Imn = {0.1-1} , for the phase amn = {-1I - 1I}, and E: =1.

For the four-ring array, configA.l {6, 6, 12, 12} CCAA

and CHAA are chosen to be optimized using the three

Proceedings

algorithms. Table V summarized the results of optimizing

these configurations. Similar to the CCAA configurations

of two-ring and three-ring, the CCAA in the four-ring

array couldn't reach the SLL of the reference pattern.

However, it was the closer to it with SLL= -29.9 dB,

optimized with the Hybrid algorithm in the case of adding

central element. For the case of configo4.1 {6, 6, 12, 12}

CHAA, the obtained SLL = -3304 dB optimized with the

Hybrid algorithm. This low SLL achieved with a little

increase in the BW with 8BW= 1.6 compared to the

reference BW. Obviously the directivity = 10.2 dBi is

high with respect to the reference's directivity. Fig. 6

depict the radiation pattern of optimized configo4.1 {6, 6,

12, 12} CHAA without additional central element, using

the three optimization algorithms versus the reference

pattern. While Fig. 7 shows the values of the complex

weights of the array elements, using the hybrid algorithm,

for this configuration. Configo4.1 {6, 6, 12, 12} CHAA

with central element, obtained SLL= -34 dB in the case of

using the Hybrid algorithm. With decrease of -2.6 dB

compared to the reference pattern and directivity =9.8

dBi. The dynamic range ratio Imd1min=6, is lower than the

ratio of the same configuration.

C. Conclusion o{Optimizing Complex weights in hexagonal, Concentric Circular and Concentric Hexagonal Antenna Arrays

It can be conclude that, for certain radiation pattern

synthesized by a circular array with certain number of

elements, spaced with uniform O.2SA inter-element

distance, this radiation pattern could be synthesized with

better features using reconfigurable arrays. These different

configuration arrays utilized the same number of elements

with O.SA inter-element distance at least, to mitigate the effect of mutual coupling between elements. The

presented concentric hexagonal antenna array CHAA for

the three-ring and four-ring succeeded to synthesize lower

SLL pattern, than the circular reference pattern. The

synthesized patterns have higher directivity up to 10.2 dBi

with minor change in the BW. The Hybrid algorithm in

this optimization gave the best result in the SLL of the

radiation pattern.

Table V. Comparison between Config.4.1 (6, 6, 12, 12} CCAA and

CHAA with and without central element in SLL, BW and Directivity.

ConC".g.4.1 Algorithm

SLL oBW Directivity I_.,/I .... {6, 6, 12, 121 [dB] [O.g.] [dBI]

Chebyshev_like [35] -31.4 79

DE -19.2 -12_2 10.95 3.3 CCAA

'Without central EPSO -235 -4.2 10.77 6 6 element

HYBRID -27.8 -2.4 10.48 7.9

DE -22.2 -3.7 10.7 4.9 CCAA

with cent ... al EPSO -25.8 -2.8 10.52 element

HYBRID -29.9 10.34 4.4

DE -22 -9.1 10.87 CHAA

without centml EPSO -27_4 -1_2 10_38 78 element

HYBRID -33_4 1.6 10_2 6.5

DE -21.3 -2 10.12 8.4 CHAA

with central EPSO -28_3 -4.5 1059 9 4 element

HYBRID -34 3 3 9_81

978-1-4673-0029-2/12/$26.00 ©2011 IEEE

36

. --10

-20

-30

iii' -40

2- -50 i..L. « -60

-70

-80

I ,:, " " \

Ij� ( " ' filII II ,

� r I , ,

. -90

-100 -150 -100

CEEM' 2012/Shang 'hai

I � , , , ..

..

, /' :., ,..'\ i',I' '\ ill Ii .f 'il.tlt. ,..

I I

. :[ 'I, I

I I· I

I I: f I . ' ..

.

-50 0 50 Phi (Degree)

. Hybrid -EPSO

--DE --- Chebyshev-like

100 150

Fig. 6 The radiation pattern of Config.4. 1 {6, 6, 12, 12} CHAA

without central element using the 3 optimization algorithms

compared to chebyshev-like pattern.

IV. CONCLUSION

Using high number of elements in circular and hexagonal arrays

to achieve narrow beamwidth and high directivity leads to high

mutual coupling due to the reduced inter-element spacing

between array elements. Designing CCAA and CHAA with the

same radiation pattern properties and reduced mutual coupling

is desirable. Therefore, this paper provides the procedures of

designing and optimization of concentric circular arrays

(CCAA) and concentric hexagonal arrays (CHAA). Numerical

results show that concentric circular and concentric hexagonal

arrays with 36 elements spaced with 0.5A spacing between

elements are designed to mitigate the effect of mutual coupling

as alternatives to circular and hexagonal arrays with 36 elements

spaced with 0.25A. The UCHA proved to give lower SLL in the

azimuth plane, than the UCCA, the circular and the hexagonal

arrays after rotating the outer ring(s) of the arrays. After

optimizing the complex weights of these concentric arrays, a

pattern with SLL= -35 dB and directivity =8.85 dBi was

achieved with slight change in BW compared to a circular

reference pattern [4] used the same number of elements arranged

in circular array. Also this paper proves that the Hybrid

ESPOIDE technique is found to be very promising evolutionary

optimization technique for the global optimization of any

antenna array problem.

REFERENCES

[1] M. A.-A. Mangoud and H. M. Elragal "Antenna Array Pattern

Synthesis and Wide Null Control Using Enhanced Particle Swarm

Optimization," Progress In Electromagnetics Research B, PIERB 17, 1-

14, 2009.

[2] Elragal H., Mangoud M., Alsharaa M. "Hybrid differential evolution

and enhanced particle swarm optimization technique for design of

reconnfigurable phased antenna arrays" lET Microw., Antennas Propag.

Vol. 5, Issue 11, p. 1280-1287, Aug. 2011.

[3] loannides, P. and C. A. Balanis, "Uniform circular arrays for smart

antennas," IEEE Antennas and Propagation Mag., Vol. 47,No. 4, 192-

206, August 2005. [4] N Goto and Y. Tsunoda "Side lobe Reduction of Circular Anay with

a constant Excitation Amplitude," IEEE Trans. Antennas Propag., vol. 25, No. 6, pp. 896-898, Nov. 1977.

[5] Mahmoud K. R.,M. EI-AdawY,and S. M. M. Ibrahem,"A

comparison between circular and hexagonal geometries for smart antenna systems using particle swarm optimization algorithm,"

Progress In Electromagnetics Research, PIER 72, 75-90, 2007.

[6] Mandai D., S.P. Ghoshal, A. K. Bhattacharjee "Concentric Circular

Antenna Anay Synthesis Using Particle Swarm Optimization with

Constriction Factor Approach," A workshop on advanced antenna technology, 2010 Indian antenna week pp. 1-4, June 2010.