Non-uniform Concentric Circular Antenna Array Design using IPSO Technique for Side Lobe Reduction

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Procedia Technology 6 (2012) 856 – 863

Non-Uniform Concentric Circular Antenna Array Design Using IPSO Technique for Side Lobe Reduction 1

Durbadal Mandal, 1Md. Asif Iqbal Ansari, 1Rajib Kar, 2S. P. Ghoshal

1

Department of Electronics and Comm. Engineering, 2Department of Electrical Engineering National Institute of Technology Durgapur, West Bengal, India- 713209 Email: [email protected], [email protected]

Abstract In this paper the optimal design for maximum sidelobe level (SLL) reduction of three-ring Concentric Circular Antenna Array (CCAA) is determined using a novel Particle Swarm Optimization (PSO) technique namely Improved Particle Swarm Optimization (IPSO) algorithm. Standard PSO is also adopted for the comparative optimization. The present text assumes non-uniformly excited and non-uniform inter-element spacing array with a design goal of maximizing SLL reduction using the above two evolutionary optimization techniques. It is shown that among all the designs, the three-ring structure containing (N1=4, N2=6, N3=8) elements proves to be the optimal design owing to the highest SLL reduction achieved by each technique. IPSO yields grand minimum SLL (-31.86 dB) for the above optimal set. © 2012 Published by Elsevier Ltd.

© 2012 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Department of Computer Selection and/or peer-review under responsibility of the Department of Computer Science & Engineering, National Science & Engineering, National Institute of Technology Rourkela Open access under CC BY-NC-ND license.

Institute of Technology Rourkela

Keywords: Concentric Circular Antenna Array; Non-uniform Excitation; Sidelobe Level; Particle Swarm Optimization; IPSO

1. Introduction An antenna array consists of multiple stationary antenna elements, which are often fed coherently. Recently, varied applications of antenna array have been suggested to improve the performance of mobile and wireless communication systems through efficient spectrum utilization, increasing channel capacity, extending coverage area, tailoring beam shape etc. [1-3]. However, arbitrary array design may lead to increment in pollution of the electromagnetic environment and more importantly, wastage of precious power, which may prove fatal for power-limited battery-driven wireless devices. This explains the presence of abundant open technical literatures [4-14], bearing a common target - bridging the gap between desired radiation patterns having nil SLL with what is practically achievable. The primary method in all these research works is improvement of array pattern by manipulating the structural

2212-0173 © 2012 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Department of Computer Science & Engineering, National Institute of Technology Rourkela Open access under CC BY-NC-ND license. doi:10.1016/j.protcy.2012.10.104

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geometry to suppress the SLL while preserving the gain of the main beam. The goal in such antenna array geometry synthesis techniques is to determine the physical layout of the array that produces the radiation pattern closest to the desired pattern. As the shape of the desired pattern can vary widely depending on the application, many synthesis methods coexist. Among the different types of antenna arrays CCAA [4-12] have become most popular in mobile and wireless communications. This very fact has inspired the design of CCAA and evaluation of the performance of corresponding antenna arrays. In this paper optimization of CCAA design having a uniform element separation and a non-uniform excitation is performed with the help of evolutionary optimization techniques. Contribution of the paper is two-fold. Firstly, the outcome of non-uniform excitation in various CCAA design structures is examined to find the best possible design structure by two evolutionary techniques, PSO [15-16] and IPSO [17-18]. Secondly, regarding the comparative effectiveness of the techniques, the newly proposed IPSO technique proves to be the best in attaining minimum SLL, reduction of major lobe in the optimization of various CCAA design problems. The rest of the paper is arranged as follows: in section II, the general design equations for the nonuniformly excited CCAA are stated. Then, in section III, brief introductions for the PSO and IPSO are presented. Numerical results are presented in section IV. Finally the paper concludes with a summary of the work in section V. 2. Design Formulation Fig. 1 shows the general configuration of CCAA with M concentric circular rings, where the m th (m = 1, 2, , M) ring has a radius r m and the corresponding number of elements is N m. If all the elements (in all the rings) are assumed to be isotopic sources, the radiation pattern of this array can be written in terms of its array factor only. Referring to Fig. 1, the array factor, AF , I , d mi for the CCAA in x-y plane may be written as [1]: M Nm

AF , I , d mi

I mi exp j krm sin cos

mi

mi

(1)

m 1i 1

where

Nm

krm

d mi

i 1

d mi is inter-element spacing between the elements. I mi denotes current excitation of the ith element of the mth ring, k 2 / ; being the signal wave-length. If the elevation angle, = 900 then (1) may be written as a periodic function of is the element to element mi angular separation measured from the positive x-axis. The elements in each ring are assumed to be nonuniformly distributed. mi and mi are also obtained from [13] as: Nm

2

i 1 mi

N i 1

mi

d mi (2)

d mi

Krm cos

0

mi

(3)

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where peak of the main lobe is obtained. After defining the array factor, the next 0 is the value of step in the design process is to formulate the objective function which is to be minimized. The objective MF may be written as (4):

MF

WF 1

AF

msl 1

, I mi AF

AF 0

msl 2

, I mi

, I mi

WF 2

BWFN computed

BWFN I mi

1

(4)

BWFN is the angular width between the first nulls on either side of the main beam. MF is computed only if BWFNcomputed BWFN I mi 1 and the corresponding solution of current excitation weights is retained in the active population otherwise not retained. WF 1 and WF 2 are the weighting factors. Minimization of

MF means maximum reductions of SLL both in lower and upper bands and lesser BWFNcomputed as compared to BWFN I mi 1 . The evolutionary techniques employed for optimizing the current excitation weights resulting in the minimization of MF and hence reductions in both SLL and BWFN are described below.

Figure 1. Concentric circular antenna array (CCAA).

3. Evolutionary Techniques Employed PSO and IPSO as implemented for the optimization of current excitation weights and radii of the rings of the CCAA are given in [17-18]. So, the steps of PSO and IPSO are not described due to limitation in space. 4. Simulation Results This section gives the experimental results for various CCAA designs obtained by PSO and IPSO techniques. For each optimization technique ten three-ring (M=3) CCAA structures are assumed, each maintaining a non-uniform excitation and non-uniform inter-element spacing with a design goal of maximizing SLL reduction. For obtaining the best non-uniform spacing and non-uniform excitations sets in each ring, 50 trial generalized optimization runs are used for each structure. For all sets of experiments, the number of elements of the inner most circle is N1, for outermost circle is N3, whereas the middle circle consist of N2 number of elements. For all the cases, 0 = 00 is considered so that the centre of the main

Durbadal Mandal et al. / Procedia Technology 6 (2012) 856 – 863

lobe in radiation patterns of CCAA starts from the origin. After experimentation, best proven values of WF 1 and WF 2 are fixed as 18 and 1 respectively. Since PSO techniques are sometimes quite sensitive to certain parameters, the simulation parameters should be carefully chosen. Best chosen maximum population pool size, np =120, maximum iteration cycles for optimization, Nm = 100. Lesser number of cycles is found to be sufficient for the convergences PSO and IPSO with C1 = C2 = 1.5 is experimentally found to be very effective. The predefined probability of craziness is introduced to maintain the diversity of the particles. Results obtained with this technique prove to be the better compared to other technique considered. This novel technique has very rapidly converged to the correct optimal solution unlike PSO. PSO and IPSO with C1 = C2 = 1.5 is experimentally found to be very effective. The predefined probability of craziness is introduced to maintain the diversity of the particles. Results obtained with this technique prove to be the better compared to other technique considered. This novel technique has very rapidly converged to the correct optimal solution unlike PSO. TABLE I.

SLL AND BWFN FOR UNIFORMLY EXCITED ( I mi =1) Set No. I II III IV V VI VII VIII IX X

No. of elements in each rings (N1,N2,N3) 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, 14 11, 13, 15

CCAA SETS

SLL (dB) -12.56 -13.8 -11.23 -11.2 -10.34 -10.0 -9.6 -9.28 -9.06 -8.90

BWFN (deg) 128.4 107.2 90.3 78.2 68.4 61.0 54.8 50.0 46.0 42.0

Each of PSO and IPSO techniques generates a set of normalized non-uniform current excitation weights and non-uniform spacing for all sets of CCAA. I mi =1 corresponds to uniform current excitation. Sets of three-ring CCAA (N1, N2, N3) designs considered 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), (11,13,15). Partial results for PSO and IPSO are shown in Tables II-III. Table I depicts SLL values and BWFN values for all corresponding CCAA structures but uniformly excited. 4.1. Analysis of Radiation Patterns of CCAA Sets and Optimal CCAA Figures 2-4 show the radiation patterns for a uniformly excited CCAA having different number of elements, with fixed spacing of 2 between elements and for non-uniformly and optimally excited and spaced CCAA, using PSO and IPSO optimization techniques respectively. From the figures it is clearly visible that the SLL reduction is marginal for the uniformly excited set, although the number of elements is the same.

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TABLE II. EXCITATION DISTRIBUTION AND THE UNIFORM CCAA USING STANDARD PSO

Set No. III

V

Side lobe level relative to the main beam (dB)

VII

( I11 , I12

RESULTING ELEMENT DISTRIBUTIONS FOR NON-

I mi );

(d11, d12, d13 . . . , dmi) 0.5572 0.7268 0.6060 0.5076 1.0000 0.5662 0.5834 0.2887; 0.5086 0.5000 0.5000 0.5900 0.5900 0.7622 0.7742 0.7568

0.7445 0.7886

0.5270 0.4340

0.5956 0.2433

0.9808 0.4454

0.6423 0.8517

0.5086 0.7677

0.5900 0.5929 0.5958 0.5911 0.7671 0.6900 0.7772 0.7572

0.8693 0.7976 0.9947 0.8808 0.5867 1.0000 0.8466 0.3807 0.9300 0.9216 0.6276 0.0015 0.4578 0.6694 0.2640 0.8604 0.6485 0.5356 0.5156 0.6770 0.7949 0.6356 0.4987 0.2937; 0.5500 0.5500 0.5500 0.5500 0.5500 0.5330 0.6352 0.6400 0.6400 0.6345 0.6196 0.6400 0.6349 0.6311 0.7576 0.7547 0.7559 0.7550 0.7537 0.7271 0.7583 0.7913 0.7474 0.7450 0.8445 0.5636 0.9108 1.0000 0.8779 0.2927 0.8471 1.0000 0.8072 0.1211 0.2562 1.0000 0.7438 0.5414 0.3100 0 0.8407 0.3603 0.4866 0.6057 1.0000 1.0000 0.3517 0.6302 0.5448 0.4099 0.9977 0.4998 0.6545 0.7746; 0.5555 0.5555 0.5555 0.5555 0.5555 0.5555 0.5555 0.5555 0.6100 0.6100 0.6084 0.6100 0.6100 0.6100 0.6100 0.5968 0.6100 0.6100 0.7555 0.7555 0.7555 0.7555 0.7555 0.7555 0.7555 0.7555 0.7555 0.7555 0.7555 0.7555

SLL (dB)

BWFN (deg)

-28.62

76.68

-21.8

58.5

-23.0

47.88

0 Uniform PSO IPSO

-10

Figure 2. Radiation patterns for a uniformly excited CCAA and corresponding standard PSO and IPSO based nonuniformly excited CCAA for N1=4, N2=6, N3=8 elements.

-20

-30

-40

-50

-60

-150

-100

-50 0 50 Angle of arival (degrees)

100

150

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Side lobe level relative to the main beam (dB)

0 Uniform PSO IPSO

-10

Figure 3.Radiation patterns for a uniformly excited CCAA and corresponding PSO and IPSO based non-uniformly excited CCAA for N1=6, N2=8, N3=10 elements

-20

-30

-40

-50

Side lobe level relative to the main beam (dB)

-60

-150

-100

-50 0 50 Angle of arival (degrees)

100

150

0 Uniform PSO IPSO

-10

Figure 4.Radiation patterns for a uniformly excited CCAA and corresponding PSO and IPSO based non-uniformly excited CCAA for N1=8, N2=10, N3=12 elements

-20

-30

-40

-50

-60

-150

-100

-50 0 50 Angle of arival (degrees)

100

150

4.2. Comparative effectiveness and convergence profiles of PSO and IPSO

5.5

10

5

9

4.5

8 7

4

Misfitness

Misfitness

The minimum MF values against number of iteration cycles are recorded to get the convergence profile of each technique. Figures 5-6 portray the convergence profiles of minimum MF of PSO and IPSO respectively. From these figures it is clear that PSO yields suboptimal higher values of MF . IPSO yields near optimal (least) MF consistently in all cases. With a view to the above facts, it may finally be inferred that IPSO yields true optimization. The programming has been written in Matlab language using MATLAB 7.5 on core (TM) 2 duo processor, 3.00 GHz with 2 GB RAM.

3.5 3

6 5 4

2.5

3 2 1.5

2 0

10

20

30

40 50 60 Iteration Cycle

70

80

90

100

Figure 5. Convergence curve for standard PSO in case of non-uniformly excited CCAA (N1=4, N2=6, N3=8 elements).

1

0

50

100

150

Iteration Cycle

Figure 6. Convergence curve for IPSO in case of nonuniformly excited CCAA (N1=4, N2=6, N3=8 elements).

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TABLE III. EXCITATION DISTRIBUTION AND THE UNIFORM CCAA USING IPSO

Set No. III

V

VII

( I11 , I12

RESULTING ELEMENT DISTRIBUTIONS FOR NON-

I mi );

(d11, d12, d13 . . . , dmi) 0.5572 0.7268 0.6060 0.5076 1.0000 0.5662 0.5834 0.2887; 0.5086 0.5000 0.5000 0.5900 0.5900 0.7622 0.7742 0.7568 0.3107 0.1900 0.4461 0.4790 0.3936 0.3870 0.3523 0.1783 0.0536 0.5455 0.5455 0.5455 0.6093 0.5981 0.5955 0.7455 0.7521 0.7457 0.4964 0.3733 0.2693 0.7246 0.0018 0.0890 0.5038 0.5296 0.1794 0.3723 0.1790 0.6382 0.5000 0.5000 0.5000 0.5900 0.5947 0.5900 0.5900 0.6009 0.6900 0.6900 0.6900 0.6924

0.7445 0.7886

0.5270 0.4340

0.5956 0.2433

0.9808 0.4454

0.6423 0.8517

0.5086 0.7677

0.5900 0.7671

0.5929 0.5958 0.5911 0.6900 0.7772 0.7572

0.3801 0.2343 0.2509 0.1973 0.0035 0 0.3764 0.2952 0.1125 0.2165 0.1427 0.3026 0.3899 0.0999 0.1169; 0.5459 0.5515 0.5517 0.5955 0.6100 0.6042 0.6023 0.5955 0.7475 0.7460 0.7464 0.7455 0.7455 0.7478 0.7487 0.5156 0.3195 0.3734 0.6420 0.5964 0.4677 0.7623 0.7153 0.0738 0 0.3549 0.4246 0.0413 0.3642 0.2225 0.2429 0.3597 0.1038; 0.5000 0.5000 0.5000 0.5033 0.5000 0.5900 0.6061 0.5936 0.5900 0.5900 0.7034 0.7332 0.6900 0.6900 0.7022 0.6913 0.7614 0.6900

SLL (dB)

BWFN (deg)

-31.86

76.5

-24.44

59.58

-28.56

59.76

5. Conclusions In this paper, the design of a non-uniformly excited concentric circular antenna array with non-uniform spacing between the elements has been described using the techniques of PSO and IPSO. Comparing with the other techniques reported in the work, IPSO technique gives near global minimum values of SLL for all sets of CCAA designs. Experimental results reveal that non-uniform CCAA offers a considerable SLL reduction along with the reduction of BWFN with respect to corresponding uniform CCAA. Contribution of the paper is twofold: first, for two techniques the CCAA having N 1=4, N2=6, N3=8, gives grand maximum SLL reduction compared to all other sets, which one is the optimal set among three-ring structures, and second, comparing the performance of both techniques IPSO shows the better optimization performance compared to PSO. References [1] [2] [3] [4] [5] [6]

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