Thinned Concentric Circular Array Antennas Synthesis using Improved Particle Swarm Optimization

ACEEE Int. J. on Communication, Vol. 02, No. 02, July 2011

Thinned Concentric Circular Array Antennas Synthesis
using Improved Particle Swarm Optimization
Durbadal Mandal1, Debanjali Sadhu1 and Sakti Prasad Ghoshal2
1
Department of Electronics and Communication Engineering, National Institute of Technology Durgapur,
West Bengal, India- 713209
Email: durbadal.bittu@gmail.com, debanjali4@gmail.com
2
Department of Electrical Engineering, National Institute of Technology Durgapur,
West Bengal, India- 713209
Email: spghoshalnitdgp@gmail.com

Abstract— Circular antenna array has gained immense Although uniformly excited and equally spaced antenna
popularity in the field of communications nowadays. It has arrays have high directivity at the same time they suffer from
proved to be a better alternative over other types of antenna high side lobe level. Reduction in side-lobe level can be
array configuration due to its all-azimuth scan capability, brought about in either of the following ways, either by
and a beam pattern which can be kept invariant. This paper is keeping excitation amplitudes uniform but changing the
basically concerned with the thinning of a large multiple position of antenna elements or by using equally spaced
concentric circular ring arrays of uniformly excited isotropic array with radially tapered amplitude distribution. These
antennas based on Improved Particle Swarm Optimization
processes are referred to as thinning. Thinning not only
(IPSO) method. In this paper a 9 ringed Concentric Circular
reduces side lobe level but also brings down the cost of
Antenna Array (CCAA) with central element feeding is
considered. The computational results show that the number
manufacturing by decreasing the number of antenna elements
of antenna array elements can be brought down from 279 to [12, 13]. There are various global optimization tools for
147 with simultaneous reduction in Side Lobe Level of about thinning such as Genetic Algorithms (GA) [8], Particle Swarm
20 dB with a fixed half power beamwidth. Optimization (PSO) [14-17] etc. The PSO algorithm has proved
to be a better alternative to other evolutionary algorithms
Keywords- Concentric Circular Antenna Arrays; Particle such as Genetic Algorithms (GA), Ant Colony Optimization
Swarm Optimization; Thinning; Sidelobe Level (ACO) etc. in handling certain kinds of optimization
problems.This paper proposes a method for thinning a large
I. INTRODUCTION multiple concentric circular ring arrays of isotropic antennas
Concentric Circular Antenna Array (CCAA) has several based on PSO. The rest of the paper is organized as follows:
interesting features that make it indispensable in mobile and In section II, the general design equations for the CCAA are
communication applications. CCAA [1-11] has received stated. Then, in section III, a brief introduction for the PSO is
considerable interest for its symmetricity and compactness presented. Computational results are presented in section IV.
in structure. A concentric circular array antenna is an array Finally the paper concludes with a summary of the work in
that consists of many concentric rings of different radii and a section V.
number of elements on its circumference. Since a concentric
circular array does not have edge elements, directional II. DESIGN EQUATION
patterns synthesized with a concentric circular array can be Fig. 1 shows the general configuration of CCAA with M
electronically rotated in the plane of the array without a concentric circular rings, where the mth (m = 1, 2,…, M) ring has
significant change of the beam shape. CCAA provides great a radius rm and the corresponding number of elements is Nm. If
flexibility in array pattern synthesis and design both in narrow all the elements (in all the rings) are assumed to be isotopic
band and broadband applications. It is also favoured in sources, the radiation pattern of this array can be written in
direction of arrival (DOA) applications since it provides almost
terms of its array factor only. Referring to Fig. 1, the far field
invariant azimuth angle coverage. Uniform CCA is the CCA
pattern of a thinned CCAA in x-y plane may be written as
where all the elements in the array are uniformly excited and
[17]:
the inter-element spacing in individual ring is kept almost
half of the wavelength. For larger number of rings with uniform
excitations, the side lobe in the UCCA drops to about 17.5
dB. Lot of research has gone into optimizing antenna
structures such that the radiation pattern has low sidelobe
level. This very fact has driven researchers to optimize the
CCAA design.

Corresponding author: Durbadal Mandal
Email: durbadal.bittu@gmail.com
21
© 2011 ACEEE
DOI: 01.IJCOM.02.02.163


angle where the maximum sidelobe  AF  msl 2 , I mi  is attained
in the upper band. WF 1 and WF 2 are so chosen that optimiza-
tion of SLL remains more dominant than optimization of
FNBWcomputed and CF never becomes negative. In (4) the
two beamwidths, FNBWcomputed and FNBW  I mi  1 basically
refer to the computed first null beamwidths in radian for the
non-uniform excitation case and for uniform excitation case
respectively. Minimization of CF means maximum reductions
of SLL both in lower and upper sidebands and lesser
FNBWcomputed as compared to FNBW  I mi  1 . The evolution-
ary optimization techniques employed for optimizing the cur-
rent excitation weights resulting in the minimization of CF
and hence reductions in both SLL and FNBW are described in
Figure 1. Concentric circular antenna array (CCAA). the next section. In this case, I mi is 1 if the mi-th element is
turned “on” and 0 if it is “off.” All the elements have same
excitation phase of zero degree.
where I mi denotes current excitation of the ith element of the mth
An array taper efficiency can be calculated from
ring, k  2 /  ;  being the signal wave-length. If the elevation
number of elements in the array turned on
angle,  = constant, then (1) may be written as a periodic function  ar 
total number of elements in the array
of  with a period of 2π radian i.e. the radiation pattern will be a
broadside array pattern. The azimuth angle to the ith element of III. EVOLUTIONARY TECHNIQUES E MPLOYED
the mth ring is mi . The elements in each ring are assumed to be
A. Particle Swarm Optimization (PSO)
uniformly distributed. mi and  mi are also obtained from [13]
PSO is a flexible, robust population-based stochastic search/
as:
optimization technique with implicit parallelism, which can easily
mi  2 i  1 / N m  (2) handle with non-differential objective functions, unlike
 mi   Krm sin  0 cos   mi  (3) traditional optimization methods. PSO is less susceptible to
getting trapped on local optima unlike GA, Simulated Annealing,
 0 is the value of  where peak of the main lobe is obtained. etc. Eberhart and Shi [14] developed PSO concept similar to the
After defining the array factor, the next step in the design process behavior of a swarm of birds. PSO is developed through
is to formulate the objective function which is to be minimized. simulation of bird flocking in multidimensional space. Bird
The objective function “Cost Function” CF  may be written flocking optimizes a certain objective function. Each particle
knows its best value so far (pbest). This information corresponds
as (4):
to personal experiences of each particle. Moreover, each particle
knows the best value so far in the group (gbest) among pbests.
Namely, each particle tries to modify its position using the
following information:
• The distance between the current position and pbest.
• The distance between the current position and gbest.
Mathematically, velocities of the particles are modified
FNBW is an abbreviated form of first null beamwidth, or, in according to the following equation [15, 16]:
simple terms, angular width between the first nulls on either
side of the main beam. CF is computed only if
FNBWcomputed  FNBW I mi  1 and corresponding solution
of current excitation weights is retained in the active popula-
tion otherwise not retained. WF 1 (unitless) and where Vi k is the velocity of ith particle at kth iteration; w is the
weighting function; Cj is the weighting factor; randi is the
WF 2 ( radian 1 ) are the weighting factors.  0 is the angle
random number between 0 and 1; S ik is the current position
where the highest maximum of central lobe is attained in
of particle i at iteration k; pbesti is the personal best of par-
    ,   .  msl1 is the angle where the maximum sidelobe ticle i; gbest is the group best among all pbests for the group.
AF  msl 1 , I mi  is attained in the lower band and  msl 2 is the The searching point in the solution space can be modified by
the following equation:
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© 2011 ACEEE
DOI: 01.IJCOM.02.02.163


ring. The limits of the radius of a particular ring of CCAA are
S i k 1  S ik  Vi  k 1 (6)
decided by the product of number of elements in the ring and
The first term of (5) is the previous velocity of the particle. The the inequality constraint for the inter-element spacing, d,
second and third terms are used to change the velocity of the
particle. Without the second and third terms, the particle will d   2 ,   . For all the cases,  0 = 00 is considered so that
keep on ‘‘flying’’ in the same direction until it hits the boundary. the peak of the main lobe starts from the origin. Since PSO
Namely, it corresponds to a kind of inertia and tries to explore techniques are sometimes quite sensitive to certain parameters,
new areas. The values of w , C1 and C2 are given in the next the simulation parameters should be carefully chosen. Best
section. chosen maximum population pool size= 120, maximum iteration
cycles for optimization= 50, and C1 = C2 = 1.5.
B. Improved Particle Swarm Optimization (IPSO) Fig. 2 is a diagram of a 279 element concentric ring array. Nine
The global search ability of traditional PSO is very much rings (N1, N2, ……., N9) are considered for synthesis having (6,
enhanced with the help of the following modifications. This 12, 18, 25, 31, 37, 43, 50, 56) elements with central element feeding.
modified PSO is termed as IPSO [15, 16]. i) The two random
parameters rand1 and rand2 of (5) are independent. If both 
For this case rm  m  and inter-element spacing in each
are large, both the personal and social experiences are over 2
used and the particle is driven too far away from the local
optimum. If both are small, both the personal and social 
rings are d m  . The number of equally spaced elements in
experiences are not used fully and the convergence speed of 2
the technique is reduced. So, instead of taking independent ring m is given by
rand1 and rand2, one single random number r1 is chosen so
2rm
that when is large, is small and vice versa. Moreover, to Nm   2m
control the balance of global and local searches, another dm (9)
random parameter is introduced. For birds flocking for food, Since the number of elements must be an integer, the value in (9)
there could be some rare cases that after the position of the
particle is changed according to (6), a bird may not, due to 
must be rounded up or down. To keep d m  , the digits to
inertia, fly toward a region at which it thinks is the most 2
promising for food. Instead, it may be leading toward a region the right of the decimal point are dropped. Table I. lists the ring
which is in the opposite direction of what it should fly in spacing and number of elements in each ring for a uniform
order to reach the expected promising regions. So, in the step concentric ring array with nine rings as shown in Figure 2.
that follows, the direction of the bird’s velocity should be The IPSO generates a set of optimal uniform current excitation
reversed in order for it to fly back into the promising region.
is introduced for this purpose. Both cognitive and social weights for each synthesis set of CCAA. I mi is 1 if the mi-th
parts are modified accordingly. Finally, the modified velocity element is turned “on” and 0 if it is “off”. The optimal results are
of jth component of ith particle is expressed as follows: shown in Tables II- III.

Vi k 1  r2  signr3  Vi k  1  r2   C1  r1  pbestik  S k
i  A. Analysis of Radiation Patterns of CCAA

 1  r2   C2  1  r1   gbest  S
k k
i  (7) Fig. 3 depicts the substantial reductions in SLL with optimal
current excitation weights after thinning, as compared to the
where r1 , r2 and r3 are the random numbers between 0 and 1; case of uniform current excitation weights and of fully populated
array (considering fixed inter-element spacing, dH”λ/2).
S ik is the current position of particle i at iteration k; pbestik is
As seen from Table III and Fig. 3, the SLL reduces to H”20 dB for
the personal best of ith particle at kth iteration; gbest k is the the given Set, with respect to -17.4 dB for uniform excitation and
group best among all pbests for the group at kth iteration. The dH”λ/2. Further, the above improvement is achieved for an array
searching point in the solution space can be modified by the of H”53% elements turned off.
following equation (6). The above results reveal that the thinned 9 rings CCAA set with
central element feeding yield reductions in SLL as compared to
signr3  is a function defined as:
the fully populated same array.
signr3   1 when d” 0.05,
B. Convergence Profile of IPSO
= 1 when > 0.05. (8)
The minimum CF values are plotted against the number of
iteration cycles to get the convergence profiles as shown in Fig.
IV. COMPUTATIONAL RESULTS 4. The IPSO technique yield convergence to the minimum SLL in
less than 25 iterations. All computations were done in MATLAB
This section gives the computational results for the CCAA 7.5 on core (TM) 2 duo processor, 3.00 GHz with 2 GB RAM.
synthesis obtained by IPSO technique. Each CCAA maintains a
fixed optimal inter-element spacing between the elements in each

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© 2011 ACEEE
DOI: 01.IJCOM.02.02.163


Figure 2. Concentric ring array with nine rings spaced l / 2 apart Figure 3. Array pattern found by IPSO for 9 rings CCAA set with
and dmH”l/2. central element feeding.

T ABLE I.
RING RADIUS AND NUMBER OF ELEMENTS PER RING FOR A 9-RING CONCENTRIC CIRCULAR
ANTENNA ARRAY.

TABLE II.
EXCITATION AMPLITUDE DISTRIBUTION (IMN) USING IPSO

Figure 4. Convergence profile for IPSO in case thinned CCAA

V. CONCLUSIONS
This paper illustrates a PSO based technique for thinning
of large Concentric Circular Antenna Array of isotropic
elements. The ultimate objective of the technique is to design
an array with a reduction of around 53% of the total elements
used in case of a fully populated array with a simultaneous
reduction in side lobe level to around 20 dB. The IPSO
algorithm can efficiently handle the thinning of a large multiple
concentric circular ring arrays of uniformly excited isotropic
antennas. The Half Power Beamwidth (HPBW) of the
synthesized array pattern with fixed inter-element spacing is
remain same to that of a fully populated array of same shape
TABLE III. THINNED AND FULLY POPULATED ARRAY RESULTS
and size, moreover has a better side lobe level.

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© 2011 ACEEE
DOI: 01.IJCOM.02.02.163


REFERENCES [11] K. -K. Yan and Y. Lu, “Sidelobe Reduction in Array-Pattern
Synthesis Using Genetic Algorithm,” IEEE Trans. Antennas
[1] C. Stearns and A. Stewart, “An investigation of concentric ring
Propag., vol. 45(7), pp. 1117-1122, July 1997.
antennas with low sidelobes,” IEEE Trans. Antennas Propag., vol.
[12] R. L. Haupt, “Thinned concentric ring arrays,” Antennas and
13(6), pp. 856–863, Nov. 1965.
Propagation Society International Symposium, 2008. AP-S 2008.
[2] R. Das, “Concentric ring array,” IEEE Trans. Antennas Propag.,
IEEE , pp.1-4, 5-11 July 2008.
vol. 14(3), pp. 398–400, May 1966.
[13] R. L. Haupt, “Thinned interleaved linear arrays,” Wireless
[3] N. Goto and D. K. Cheng, “On the synthesis of concentric-ring
Communications and Applied Computational Electromagnetics,
arrays,” IEEE Proc., vol. 58(5), pp. 839–840, May 1970.
2005. IEEE/ACES International Conference on , pp. 241- 244, 3-7
[4] L. Biller and G. Friedman, “Optimization of radiation patterns
April 2005
for an array of concentric ring sources,” IEEE Trans. Audio
[14] R. C. Eberhart and Y.Shi, “Particle swarm optimization:
Electroacoust., vol. 21(1), pp. 57–61, Feb. 1973.
developments, applications and resources, evolutionary
[5] M D. A. Huebner, “Design and optimization of small concentric
computation,” Proceedings of the 2001 Congress on Evolutionary
ring arrays,” In Proc. IEEE AP-S Symp., 1978, pp. 455–458.
Computation, vol. 1 pp. 81–86, 2001.
[6] M. G. Holtrup, A. Margulnaud, and J. Citerns, “Synthesis of
[15] D. Mandal, S. P. Ghoshal, and A. K. Bhattacharjee, “Improved
electronically steerable antenna arrays with element on concentric
Swarm Intelligence Based Optimal Designof Concentric Circular
rings with reduced sidelobes,” In Proc. IEEE AP-S Symp., 2001,
Antenna Array.” In: IEEE Applied Electromagnetics Conference
pp. 800–803.
AEMC’09, Dec. 14-16, Kolkata, pp. 1-4, 2009.
[7] R. L. Haupt, “Optimized element spacing for low sidelobe
[16] D. Mandal, S. P. Ghoshal, and A. K. Bhattacharjee, “Swarm
concentric ring arrays,” IEEE Trans. Antennas Propag., vol. 56(1),
Intelligence Based Optimal Design of Concentric Circular Antenna
pp. 266–268, Jan. 2008.
Array,” Journal of Electrical Engineering, vol. 10, no. 3, pp. 30–
[8] R. L. Haupt, and D. H. Werner, Genetic Algorithms in
39, 2010.
Electromagnetics, IEEE Press Wiley-Interscience, 2007.
[17] D. Mandal, S. P. Ghoshal, and A. K. Bhattacharjee, “Design
[9] M. Dessouky, H. Sharshar, and Y. Albagory, “Efficient sidelobe
of Concentric Circular Antenna Array With Central Element Feeding
reduction technique for small-sized concentric circular arrays,”
Using Particle Swarm Optimization With Constriction Factor and
Progress In Electromagnetics Research, vol. PIER 65, pp. 187–
Inertia Weight Approach and Evolutionary Programing Technique,”
200, 2006.
Journal of Infrared Milli Terahz Waves, vol. 31 (6), pp. 667–680,
[10] M. A. Panduro, A. L. Mendez, R. Dominguez and G. Romero,
2010.
“Design of non-uniform circular antenna arrays for side lobe
reduction using the method of genetic algorithms,” Int. J. Electron.
Commun. (AEÜ) vol. 60 pp. 713 – 717, 2006.

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Thinned Concentric Circular Array Antennas Synthesis using Improved Particle Swarm Optimization

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