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Broadside Radiation Synthesis of Concentric

Antenna Array Using Improved Particle Swarm

Optimization

Durbadal Mandal

Rajib KarDibbendu Roy

Sakti Prasad Ghoshal

National Institute of Technology Durgapur

India

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ANTENNA

An antenna is a metallic device (a rod or wire) for radiating or

receiving radio waves.

A transmission Line (a waveguide, coaxial line etc.) is used to

transport electromagnetic energy from transmitter to antenna

or from antenna to receiver.

In addition to receiving and transmitting energy, an antenna in

an advanced wireless system is usually required to optimize the

radiation energy in some direction and suppress it in others.

Varying current with space and time produces the radiation

according to Maxwells Equations.

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RADIATION PATTERN

This is a graphical representation of the radiation properties

of the antenna as a function of spatial coordinates.

For practical applications a few plots pattern as a function of

polar angle (angle off z axis) for some particular azimuth

angle , plus a few plots as a function of for someparticular , provide the needed information.

Fig 1. 3-D radiation pattern

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The main beam is the region around the direction of maximum radiation (usually the region that is within 3 dB

of the peak of the main beam). The main beam in Figure 2 is centered at 90 degrees.

The sidelobes are smaller beams that are away from the main beam. These sidelobes are usually radiation in

undesired directions which can never be completely eliminated. The sidelobes in Figure 2 occur at roughly 45

and 135 degrees.

The Half Power Beamwidth (HPBW) is the angular separation in which the magnitude of the radiation pattern

decrease by 50% (or -3 dB) from the peak of the main beam. From Figure 2, the pattern decreases to -3 dB at77.7 and 102.3 degrees. Hence the HPBW is 102.3-77.7 = 24.6 degrees.

Another commonly quoted beamwidth is the Null to Null Beamwidth. This is the angular separation from

which the magnitude of the radiation pattern decreases to zero (negative infinity dB) away from the main beam.

From Figure 2, the pattern goes to zero (or minus infinity) at 60 degrees and 120 degrees. Hence, the Null-Null

Beamwidth is 120-60=60 degrees.

Finally, the Sidelobe Level is another important parameter used to characterize radiation patterns. The sidelobe

level is the maximum value of the sidelobes (away from the main beam). From Figure 2, the Sidelobe Level(SLL) is -14.5 dB.

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ARRAYS Directivity: This is a measure of how directional a radiation

pattern is. Hence we get the idea of maximum radiated

power in a particular direction.

Usually the radiation pattern of single antenna is relatively

wide with low directivity. To increase directivity, electrical

size of antenna should be increased.

Without increasing the size (physical dimension) the

directivity problem can be solved by forming an assembly of

radiating elements in an electrical and geometrical

configuration, called ARRAY.

Total field of array is determined by vector addition. In

required direction they should add constructively &

destructively otherwise.

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ARRAY FACTOR

Let, , . , represent the output from antennas 1 through N respectively.The output from these are often multiplied by a set of N weights - , , , -and added together. The output of an antenna array can be written as:

=

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Consider set of N identical antennas each with radiation pattern (,). Output of antenna will vary based on the angle of arrival. The output Y

is a function of (,).

Y= R (,) . R (,) . R (,)..

This can be written as R (,) .= .

We define the term .= as ARRAY FACTOR (AF).

Hence Y= R (,) AF. (pattern multiplication rule)

AF can be compactly written as: AF = (). The Array Factor is a function of the positions of the antennas in the

array and the weights used. By altering these parameters the antenna

array's performance may be optimized to achieve desirable properties.

ARRAY FACTOR

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Broadside Radiation and Concentric Circular

Antenna Arrays

Broadside radiation refers to maximum radiation directed

normal to axis of array ( ) . This is used in manyapplications.

Concentric Circular Antenna Arrays (CCAA) is very popular

in mobile and wireless communications. Fig 4. shows a generalCCAA with M concentric circular rings.

Its array factor in x-y plane is given by

, [(

== ] is current excitation of the element of the ring, /; being the signal wave-length. If elevation angle =constant then the AF can be expressed as a function of

with

period 2 (broadside pattern).

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The azimuth angle to the element of the ring is . Theelements in each ring are assumed to be uniformly distributed and are obtained as : ( ), ( )is the value of where peak of the main lobe is obtained.

Fig 4. CCCA

(Concentric Circular

Antenna Array)

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COST FUNCTION

This is the objective function to be optimized to produce minimum SLL.

| , + , || , | ( )

FNBW is an abbreviated form of first null beamwidth. CF is computed only if

< and corresponding solution of current excitationweight is retained in the active population otherwise discarded. (unitless) and (1) are the weighting factors. is the angle where the

highest maximum of central lobe is attained in [,]. is the angle where themaximum sidelobe is attained in the lower band and is the angle where themaximum sidelobe ( , ) is attained in the upper band. 1 and 2 are sochosen that optimization of SLL remains more dominant than optimization of and CF never becomes negative.

The two beamwidths, and basically refer to thecomputed first null beamwidths in radian for the non-uniform excitation case and for

uniform excitation case respectively. Minimization ofCF means maximum reductions

of SLL both in lower and upper sidebands and lesser

as compared to

.

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PARTICLE SWARM OPTIMIZATION (PSO)

It was developed in 1995 by Russell Eberhart & James Kennedy

PSO is a robust stochastic optimization technique based on the movement and

intelligence of swarms with implicit parallelism, which can easily handle with non-

differential objective functions, unlike traditional optimization methods

The system is initialized with a population of random solutions.

Also each solution is assigned a randomized velocity & the potential solutions

calledparticles areflown through the problem space.

Each particle keeps track of its coordinate in the problem space which is associated

with the best solution (fitness) it achieved so far calledpbest.

Another best value is tracked by global version of the optimizer is the overall

best value, & its location obtained so far by any particle in the population called

gbest.

In each step velocity of each is particle is changed (accelerated) towards itspbest &

gbest locations. Acceleration is weighed by random terms.

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IMPROVED PSO (IPSO)

Global search ability is enhanced with help of modifications.

If both

and

(independent) are large, both personal and social

experiences are over used and particle is driven away from local solutions.

If both and are small, both personal and social experiences are notfully used and convergence speed of technique is reduced.

Hence instead of taking independent and one single random number is chosen so that when is large (1-) is small. To control global and local searches another parameter is introduced.

In some rare cases after changing position and velocity of particle (according to

general PSO algorithm) a bird may not fly to the most promising position due to itsinertia.

Instead it may lead to a region in opposite direction to the most promising position.

Hence the birds position should be reversed in order to fly it back into promising

region.

The modified velocity update equation is established by introducing .

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IPSO EQUATION

+ ( ) ( ) . (3) 1st term is the inertial component. prevents flying in opposite direction,

where . 5

> .

2nd term is the cognitive component dependent onpbest of the particle. This models

the memory of the bird about itspbest position.

3rd term is the social component which models the memory of the bird about itsgbest

position.

and maintains the overuse and underuse of cognitive and socialexperiences.

and controls between inertia and social and cognitive terms.

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ASSUMPTIONS

For each optimization 8, 3-ring (M=3) CCAA structures

are assumed.

Each CCAA maintains a fixed optimum inter elemental

spacing. Limits of radius of a particular ring is decided by

the product of number of elements in ring and inequalityconstraint for inter element spacing, d, ( [ , ]).

For all experiments :

. . .

. This assumption is considered so thatpeak of main lobe starts from origin.

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PSO Parameters and Results

Best chosen maximum population pool size=120, maximum

iteration cycles for optimization=40, . .

The IPSO generates a set of non-uniform current excitation

weights and optimal radii for each synthesis set of CCAA.

Sets of 3-ring CCAA (, , ) synthesis considered are:(3,5,7); (4,6,8); (5,7,9); (6,8,10); (7,9,11); (8,10,12); (9,11,13);(10, 12, 14).

The SLL, FNBW values have been tabulated in Table I(uniform excitation =1), Table II and Table III (non-uniform excitation) for:

Case (a): Without Central element feeding.

Case (b): With Central element feeding.

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Set

No.

No. of elements in

each rings

(1, 2, 3)

Case(a): Without Central

element Excitation

Case(b): With Central

element Excitation

SLL (dB) FNBW (deg) SLL (dB) FNBW (deg)

I 3,5,7 -20.8 129.1 -32.69 152.6

II 4,6,8 -12.96 99.88 -15.90 108.0

III 5,7,9 -11.2 83.84 -13.20 88.4

IV 6,8,10 -10.5 71.8 -12.16 75.2

V 7,9,11 -9.94 63.2 -11.34 65.5

VI 8,10,12 -9.57 56.9 -10.78 58.6

VII 9,11,13 -9.28 51.18 -10.34 52.9

VIII 10,12,14 -9.07 46.6 -10.00 47.7

TABLE I. SLL AND FNBW FOR UNIFORMLY EXCITED ( )BROADSIDE CCAA SETS

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TABLE II. CURRENT EXCITATION WEIGHT DISTRIBUTION, CF, SLL AND FNBW FOR SOME SETS

OF NON-UNIFORMLY EXCITED BROADSIDE CCAA WITH-OUT CENTRAL ELEMENT FEEDING

(CASE (a)) USING IPSO

Set

No

(11, 12, . );(, ) in

CF SLL (dB) FNBW

(deg)

II 0.7662 1.0000 0.6328 0.83320.3229 1.0000 1.0000 0.7217

0.9451 0.9809 0.5622 0.5305

0.9778 0.4445 0.7093 0.1928

0.1135 0.3613;

0.3741 0.6292 1.0068

0.21 -49.72 103.6

IV 0.9047 1.0000 1.0000 0

1.0000 1.0000 0 0.95591.0000 1.0000 0.0990 0.3344

1.0000 0 0.0278 1.0000

0.0035 0 0.0260 0.2197

0.9247 1.0000 0.8123 0.6786;

0.5996 0.7896 1.2135

0.78 -36.23 75.92

VI 0.7065 0.2071 1.0000 0

0.3784 0.2286 0.6107 00.1004 0.1504 1.0000 1.0000

1.0000 0.6976 0.4606 0.4111

1.0000 0.6624 0.3335 0.3210

0.0907 0.8748 1.0000 0.3506

1.0000 0.3181 0.3835 0.5025

0 0.8244;

0.7564 0.8658 1.4111

1.25 -30.48 58.00

A C C A O G S O C S A O SO S S

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TABLE III. CURRENT EXCITATION WEIGHT DISTRIBUTION, CF, SLL AND FNBW FOR SOME SETS

OF NON-UNIFORMLY EXCITED BROADSIDE CCAA WITH CENTRAL ELEMENT FEEDING (CASE

(b)) USING IPSO

Set

No

(11, 12, . );(, ) in

CF SLL (dB) FNBW

(deg)

II 0.7192 0.5145 0.8201 0.64150.2463 0.8098 0.5252 0

0.7331 0 0.5339 0.3632

0.4696 0.0898 0.4292 0.2132

0.1329 0.1660 0.2300;

0.3717 0.5584 1.1343

0.058 -55.86 102.27

IV 0.6940 0.9632 0.7949 0.8928

0 0.8959 0.5918 0.39330.9306 0.5128 0.4056 0.7495

0.5819 0.7357 0 0.7292

0.1780 0.5344 0.1795 0.4973

0.3567 0.0793 0.0941 0

0.8365;

0.5104 0.7396 1.2719

0.45 -41.58 76.94

VI 0.8063 0.7962 0.4154 0.54140.6327 0 0.6989 0.6108

0 0.0599 0.1179 0

0.1723 0.2743 0.0889 0.4535

0.4204 0.3062 0.5164 0

0.6354 0.0005 0.3686 0

0.0066 0.6152 0 0.1541

0.2962 0.6027 0.0015;

0.7702 1.0828 1.3724

1.07 -32.12 59.76

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Analysis of Radiation pattern of Optimal CCCA

Figs. 5-6 depict the substantial reductions in SLL with optimal non-uniform current

excitation weights and radii, as compared to the case of uniform current excitation

weights and radii (considering fixed inter-element spacing, d=/2).

As seen from Table II, the SLL reduces to -49.72 dB for Set II, -36.23 dB for Set IV,

and -30.48 dB for Set VI with respect to -12.96 dB, -10.50 dB and -9.57 dB for

uniform excitation and d= /2 respectively for Case (a).

Further, from Table III, the SLL reduces to -55.86 dB for Set II, -41.58 dB for Set IV,

and -32.12 dB for Set VI with respect to -15.90 dB, -12.16 dB and -10.78 dB for

uniform excitation and d= /2 respectively for Case (b).

The above results reveal that all the CCAA sets having central element feeding (Case

(b)) yield much more reductions in SLL as compared to the same not having central

element feeding (Case (a)).

The CCAA Set No. II along with central element feeding yields grand minimum SLL

among all the sets. So, this is the optimal CCAA set for broadside radiation.

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Fig 5:Radiation pattern for a uniformly excited CCAA and corresponding IPSO based non-uniformly excited CCAA Set No. II

Fig 6:Radiation pattern for a uniformly excited Broadside CCAA and corresponding IPSO based non-uniformly excited CCAA Set No. IV

-150 -100 -50 0 50 100 150-80

-70

-60

-50

-40

-30

-20

-10

0

Uniform Excitation (without central element feeding)

Uniform Excitation (with central element feeding)

IPSO (without central element feeding)

IPSO (with central element feeding)

-150 -100 -50 0 50 100 150-80

-70

-60

-50

-40

-30

-20

-10

0

Uniform Excitation (without central element feeding)

Uniform Excitation (with central element feeding)

IPSO (without central element feeding)

IPSO (with central element feeding)

Normlizedarrayfactor(dB)

Normlizedarra

yfactor(dB)

Angle of Arrival

Angle of Arrival

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Fig 7. Convergence profile for IPSO in case of non-uniformly excited CCAA Set No. II Case (b)

Fig 8. Convergence profile for IPSO in case of non-uniformly excited broadside CCAA Set No. IV Case (b)

0 5 10 15 20 25 30 35 400

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30 35 400

0.5

1

1.5

2

2.5

3

3.5

CF

C

F

Iteration Cycle

Iteration Cycle

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CONCLUSIONS

1. The optimization technique yields better radiation pattern

for optimally excited CCAA with optimal radii than thoseobtained for uniformly excited CCAA with d=/2 inter-

element spacing in each ring.

2. In the CCAA, the central element plays a very important

role to improve the performance of the radiation pattern.

3. The CCAA set No. II, with central element feeding gives thegrand maximum SLL reduction (-55.86 dB) as compared to

all other sets, obtained by IPSO; which one is thus the

optimal set among all the three-ring structures.

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REFERENCES

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[7] R. L. Haupt, Optimized element spacing for low sidelobe concentric ring arrays, IEEE Trans. AntennasPropag., vol. 56(1), pp. 266268, Jan. 2008.[8] R. L. Haupt, and D. H. Werner, Genetic Algorithms in Electromagnetics, IEEE Press Wiley-Interscience, 2007.[9] M. Dessouky, H. Sharshar, and Y. Albagory, Efficient sidelobe reduction technique for small-sized concentriccircular arrays,Progress In Electromagnetics Research, vol. PIER 65, pp. 187200, 2006.[10] M. A. Panduro, A. L. Mendez, R. Dominguez and G. Romero, Design of non-uniform circular antenna arraysfor side lobe reduction using the method of genetic algorithms, Int. J. Electron. Commun. (AE) vol. 60 pp. 713717, 2006.

[11] K. -K. Yan and Y. Lu, Sidelobe Reduction in Array-PatternSynthesis Using Genetic Algorithm, IEEE Trans. Antennas Propag., vol. 45(7), pp. 1117-1122, July 1997.[12] D. Mandal, S. P. Ghoshal, and A. K. Bhattacharjee, Improved Swarm Intelligence Based Optimal DesignofConcentric Circular Antenna Array. In: IEEE Applied Electromagnetics Conference AEMC09, Dec. 14-16, Kolkata,pp. 1-4, 2009.[13] D. Mandal, S. P. Ghoshal, and A. K. Bhattacharjee, Design of Concentric Circular Antenna Array With CentralElement Feeding Using Particle Swarm Optimization With Constriction Factor and Inertia Weight Approach andEvolutionary Programing Technique, Journal of Infrared Milli Terahz Waves, vol. 31 (6), pp. 667680, 2010.[14] R.C. Eberhart and Y.Shi, Particle swarm optimization: developments, applications and resources, evolutionary

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