Application of Bio-Inspired Optimization Technique for Finding the Optimal set of Concentric Circular Antenna Array with Central Element Feeding

ACEEE Int. J. on Information Technology, Vol. 02, No. 02, April 2012

Application of Bio-Inspired Optimization Technique
for Finding the Optimal set of Concentric Circular
Antenna Array with Central Element Feeding
Durbadal Mandal1, Bipul Goswami1, Rajib Kar1, Sakti Prasad Ghoshal2 and Anup Kr. Bhattacharjee1
1
Department of Electronics and Communication Engineering.
2
Department of Electrical Engineering.
National Institute of Technology Durgapur
West Bengal, India- 713209
Email: {durbadal.bittu, goswamibipul, rajibkarece, spghoshalnitdgp}@gmail.com, akbece12@yahoo.com

Abstract- In this paper the maximum sidelobe level (SLL) re- of array pattern by manipulating the structural geometry to
ductions of three-ring concentric circular antenna arrays suppress the sidelobe level (SLL) while preserving the gain of
(CCAA) without and with central element feeding are exam- the main beam. The goal in such antenna array geometry syn-
ined using two different classes of evolutionary optimization thesis techniques is to determine the physical layout of the
techniques to finally determine the global optimal three-ring
array that produces the radiation pattern closest to the de-
CCAA design. Apart from physical construction of a CCAA,
one may broadly classify its design into two major categories: sired pattern. As the shape of the desired pattern can vary
uniformly excited arrays and non-uniformly excited arrays. widely depending on the application, many synthesis meth-
The present paper assumes non-uniform excitations and uni- ods coexist.
form spacing of excitation elements in each three-ring CCAA Among the different types of antenna arrays CCAA [8,
design and a design goal of maximizing SLL reduction associ- 9, 11] have become most popular in mobile and wireless
ated with optimal beam patterns and beam widths. The design communications. This very fact has inspired the design of
problem is modeled as an optimization problem for each CCAA CCAA and evaluation of the performance of corresponding
design. Binary coded Genetic Algorithm (BGA) and Bacteria antenna arrays. In this paper optimization of CCAA design
Foraging Optimization (BFO) are used to determine an opti-
having uniform inter-element separations and non-uniform
mum set of normalized excitation weights for CCAA elements,
which, when incorporated, results in a radiation pattern with excitations (to be optimized) is performed with the help of a
optimal (maximum) SLL reduction. Among the various CCAA novel Bio-inspired optimization technique (BFO) [13-15] and
designs the three-ring CCAA containing (N 1=4, N 2= 6, N 3=8) BGA [10, 15]. The array factors due to optimal non-uniform
elements along with central element feeding proves to be glo- excitations in various CCAA design structures are examined
bal optimal design. BFO yields global minimum SLL (-34.18 to find the best possible design structure. Regarding the
dB) and global minimum BWFN (81.50) for the optimal design. comparative effectiveness of the techniques, the newly
proposed BFO technique proves to be better in attaining
Index Terms- Bacteria Foraging Optimization (BFO); Binary minimum SLL, reduction of major lobe beamwidth and hence
coded Genetic Algorithm (BGA); Concentric Circular Antenna
minimum “Misfitness” objective function values in the
Array (CCAA); First null beamwidth (BWFN); Non-uniform
Excitation; Sidelobe Level (SLL).
optimization of various CCAA designs.
The paper is arranged as follows: In section II, the general
I. INTRODUCTION design equations for the non-uniformly excited CCAA are
stated. Then, in section III, brief introductions for the BGA
An antenna array consists of multiple stationary antenna and BFO are presented. Numerical results are presented in
elements, which are often fed coherently. Recently, varied section IV. Finally the paper concludes with a summary of the
applications of antenna array have been suggested to im- work in section V.
prove the performance of mobile and wireless communica-
tion systems through efficient spectrum utilization, increas- II.DESIGN EQUATION
ing channel capacity, extending coverage area, tailoring beam
shape etc. However, arbitrary array design may lead to incre- Geometrical configuration is a key factor in the design
ment in pollution of the electromagnetic environment and process of an antenna array. The geometry controls radia-
tion pattern and almost all other important factors of array
more importantly, wastage of precious power, which may prove
antenna. For CCAA, the elements are arranged in such a way
fatal for power-limited battery-driven wireless devices. This
that all antenna elements are placed in multiple concentric
explains the presence of abundant open technical literatures
circular rings, which differ in radii and in number of
[1-12], bearing a common target - bridging the gap between
elements.Fig. 1 shows the general configuration of CCAA
desired radiation pattern with what is practically achievable.The
with M concentric circular rings, where the mth (m = 1, 2,…, M)
primary method in all these research works is betterment

© 2012 ACEEE 6
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ring has a radius rm and the corresponding number of ele- BWFN is an abbreviated form of first null beamwidth, or, in
ments is Nm. If all the elements (in all the rings) are assumed to simple terms, angular width between the first nulls on either
be isotopic sources, then the radiation pattern of this array side of the main beam. MF is computed only if
can be written in terms of its array factor only. BWFN computed  BWFN I mi  1 and corresponding solution
Referring to Fig.1, the array factor, AF  , I  for the CCAA in of current excitation weights is retained in the active popula-
x-y plane is expressed as (1) [8]:
tion otherwise not retained. WF 1 and WF 2 are the weighting
factors. 0 is the angle where the highest maximum of central
lobe is attained in     ,   . msl1 is the angle where the
maximum sidelobe  AF msl1 , I mi  is attained in the lower
band and msl 2 is the angle where the maximum sidelobe
AF msl 2 , I mi  is attained in the upper band. are so chosen
that optimization of SLL remains more dominant than optimi-
zation of and never becomes negative.
After experimentation, best proven values of are fixed as
18 and 1 respectively. In (4) the two beamwidths, and basi-
cally refer to the computed first null beamwidth in radian for
the non-uniform excitation case and for uniform excitation
case respectively. Minimization of means maximum reduc-
Figure 1. Concentric circular antenna array (CCAA). tions of SLL both in lower and upper bands and lesser as
Nm
compared to . The evolutionary optimization techniques em-
M
AF  , I    I mi exp j krm sin  cos   mi    mi  (1) ployed for optimizing the current excitation weights result-
m 1 i 1 ing in the minimization of and hence reductions in both SLL
where, I mi denotes current excitation of the ith element of and BWFN are described in the next section.
the mth ring, k  2 /  ;  being the signal wave-length, and
III. EVOLUTIONARY TECHNIQUES EMPLOYED
 and  symbolize the zenith angle from the positive z axis
and the azimuth angle from the positive x axis to the orthogo- A. BINARY CODED GENETIC ALGORITHM (BGA)
nal projection of the observation point respectively. It may GA is mainly a probabilistic search technique, based on the
be noted that if the elevation angle is assumed to be 90 de- principles and concept of natural selection and evolution. At
grees i.e.  = 900 then (1) may be written as a periodic func- each generation it maintains a population of individuals where
each individual is a coded form of a possible solution of the
tion of  with a period of 2π radians. The angle mi is ele-
problem at hand and called chromosome. Chromosomes are
ment to element angular separation measured from the posi- constructed over some particular alphabet, e.g., the binary
tive x axis. As the elements in each ring are assumed to be alphabet [0, 1], so that chromosomes’ values are uniquely mapped
uniformly distributed, mi may be written as: onto the decision variable domain. Each chromosome is evaluated
by a function known as fitness function, which is usually the
 i 1
mi  2  cost function or the objective function of the corresponding
 N  ; m  1,....., M ; i  1,....., N m
 (3)
 m  optimization problem. Steps of BGA as implemented for
optimization of current excitation weights are adopted from
where 0 is the value of  where the peak of the main [15].
lobe is obtained.
B. BACTERIA FORAGING OPTIMIZATION (BFO):
After defining the array factor, the next step in the design
process is to formulate the objective function which is to be Steps of BFO as implemented for optimization of current
minimized. As it is a minimization problem, so fitness function excitation weights are adopted from [15].
may be considered as the “Misfitness” MF  objective IV. EXPERIMENTAL RESULTS
function, which may be written as:
This section gives the experimental results for various
AF  msl 1 , I mi   AF  msl 2 , I mi  CCAA designs obtained by BGA and BFO techniques. For
MF  WF 1  each optimization technique ten three-ring (M=3) CCAA struc-
AF 0 , I mi 
tures are assumed. Each CCAA maintains a fixed spacing be-

 WF 2  BWFN computed  BWFN I mi  1  (4) tween the elements in each ring (inter-element spacing being

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0.55ë, 0.61ë and 0.75ë for the first ring, the second ring and the 75.80 (BFO) for Case (a), 78.30 (BGA) and 81.50 (BFO) for Case
third ring respectively). These spacings are the means of the (b) against 90.3 0 (Case (a)), 95.4 0 (Case (b)) for the
values determined for the ten structures for non-uniform inter- corresponding uniformly excited CCAA having the same
element spacing and non-uniform excitations in each ring number of elements. So, these techniques yield maximum
using 25 trial generalized optimization runs for each structure. reductions of BWFN also for this optimal CCAA.
For all sets of experiments, the number of elements for the From Tables II-V, it is observed that as compared to BGA,
inner most ring is N1, for outermost ring is N3, whereas the BFO always yields higher SLL reductions for all the CCAA
middle ring consists of N2 number of elements. For all the sets.
cases, 0 = 00 is considered so that the centre of the main In Figures 4-5, the minimum MF values are plotted against
lobe in radiation patterns of CCAA starts from the origin. the number of iteration cycles to get the convergence curves
The following best proven parameters are for BGA and BFO respectively. Table VI as well as Figures 4-
(a) for BGA: 5 show BFO yields optimal (least) values consistently in all
i) Initial population, np = 120 chromosomes ii) Maximum cases. With a view to the above facts, it may finally be inferred
number of genetic cycles = 3000, iii) Selection probability, that BFO yields better optimization than BGA. All
Crossover (dual point) ratio and mutation probability = 0.3, computations were done in MATLAB 7.5 on core (TM) 2
0.8 and 0.004 respectively, and duo processor, 3.00 GHz with 2 GB RAM
(b) for BFO: TABLE I. SLL AND BWFN FOR UNIFORMLY EXCITED ( I mi =1) CCAA
i) max reprod  90 , ii) maxchemo  120 , iii) maxdispersal  2 , iv) SETS

numBact  120 , v) d attract  1.0 , vi) wattract  0.1 , vii)
d repelent  1.0 , viii) wrepelent  0.1 , ix) s r  0.3 , x) Ped  0.3 , xi)
c max  0.1, xii) c min  0.01 , xiii) d1  0.01 , xiv) d 2  0.01 , xv)
max swim  4 .
Each BGA and BFO generates a set of normalized non-
uniform current excitation weights for each set of CCAA.
I mi =1 corresponds to uniform current excitation. Sets of three-
ring CCAA (N1, N2, N3) designs considered for both without
and with central element feeding are (2,4,6), (3,5,7), (4,6,8),
(5,7,9), (6,8,10), (7,9,11), (8,10,12), (9,11,13), (10,12,13) and
(11,13,15). Some of the optimal results for BGA and BFO are
shown in Tables II-V. Table I depicts SLL values and BWFN TABLE II. C URRENT EXCITATION WEIGHTS , SLL AND BWFN FOR NON-
values for all corresponding CCAA structures but uniformly UNIFORMLY EXCITED CCAA SETS (CASE (A)) USING BGA
excited (=1).
A. ANALYSIS OF R ADIATION PATTERNS OF CCAA
Figs. 2-3 depict the substantial reductions in SLL with
non-uniform optimal current excitations as compared to the
case of uniform non-optimal current excitations. All 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)). As seen from Tables II-V,
SLL reduces to -26.14 dB (BGA), -29.96 dB (BFO) for Case (a)
and -29.06 dB (BGA), -34.18 dB (grand highest SLL reduction
as determined by BFO for Case (b), shown as a shaded row
in Table V) for the CCAA having N1=4, N2=6, N3=8 elements
(Set No. III). This optimal set along with central element feeding
yields grand maximum SLL reductions for both techniques
among all the sets.
BWFN values become less for non-uniform optimal current
excitations as compared to the case of uniform non-optimal
excitations for all design sets in both the cases. For the same
optimal CCAA set, the BWFN values are 73.60 (BGA) and

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TABLE III. CURRENT EXCITATION WEIGHTS, SLL AND BWFN FOR NON- TABLE V. CURRENT EXCITATION WEIGHTS , SLL AND BWFN FOR NON-
UNIFORMLY EXCITED CCAA SETS (CASE (B)) USING BGA UNIFORMLY EXCITED CCAA SETS (CASE (B)) USING BFO

TABLE IV. C URRENT EXCITATION WEIGHTS , SLL AND BWFN FOR NON-
UNIFORMLY EXCITED CCAA SETS (CASE (A)) USING BFO TABLE VI. MINIMUM VALUES BGA AND BFO
MF OF

0
Normalized array factor (dB)

-10

-20

-30

-40

-50

-60 Uniform Excitation (without central element feeding)
Uniform Excitation (with central element feeding)
-70 BFO (without central element feeding)
BFO (with central element feeding)
-80
-150 -100 -50 0 50 100 150
Angle of Arival (Degrees)

Figure 3. Radiation patterns for a uniformly excited CCAA and
corresponding BFO based non- uniformly excited CCAA Set III.
3.5
0
Normalized array factor (dB)

-10 3

-20
2.5
Misfitness

-30

-40 2

-50
1.5
-60 Uniform Excitation (without ce ntral e leme nt feeding)
Uniform Excitation (with central element feeding)
1
-70 BGA (without central element feeding) 0 500 1000 1500 2000 2500 3000
BGA (with ce ntra l element fee ding) Iteration Cycle
-80
-150 -100 -50 0 50 100 150
Angle of Arival (De gre es)
Figure 4. Convergence curve for BGA in case of non-uniformly
excited CCAA Set III with central element feeding.
Figure 2. Radiation patterns for a uniformly excited CCAA and
corresponding BGA based non- uniformly excited CCAA Set III.

© 2012 ACEEE 9
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Application of Bio-Inspired Optimization Technique for Finding the Optimal set of Concentric Circular Antenna Array with Central Element Feeding

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