stair step pattern and triangle pattern synthesis …r. krishna chaitanya 1, p. mallikarjuna rao and...

VOL. 14, NO. 16, AUGUST2019 ISSN 1819-6608

ARPN Journal of Engineering and Applied Sciences ©2006-2019 Asian Research Publishing Network (ARPN). All rights reserved.

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STAIR STEP PATTERN AND TRIANGLE PATTERN SYNTHESIS

USING TLBO ALGORITHM

R. Krishna Chaitanya

1, P. Mallikarjuna Rao

1 and K. V. S. N Raju

2

1Department of Electronics and Communication Engineering, SRKR Engineering College, Bhimavaram, India 2Department of Electronics and Communication Engineering, Andhra University, Visakhapatnam, India

E-Mail: [email protected]

ABSTRACT

Optimization methods have played a vital role in the design of Array antenna. Array antennas have wide range of

varying parameters which cannot be predicted by traditional methods. Large random values are involved in the design of

Antenna parameters. Random optimization methods are used in linear array antennas not only for beam shaping methods

but also for side lobe reduction and beam width optimization. Stair step and triangle shape pattern are generated using

TLBO algorithm. Stair step is used for communicate to different entities at different levels. Triangle pattern is used for

communication to a particular entity in particular direction. An error plot based on number of iterations has been used to

evaluate the error minimum value in order to generate stair step and triangle pattern for linear array antennas and the same

are presented in this paper.

Keywords: stair step pattern, triangle pattern, TLBO algorithm, linear array antenna.

INTRODUCTION

In Linear array antennas there are N number of

elements with amplitude and phase inputs, to generate the

radiation pattern. To generate the shaped beam patterns

these amplitude and phase values are utilised using

optimization algorithms. Traditional methods like Fourier

transform method and woodward lawson method are used

to generate the shaped beams. In Fourier transform

method, amplitude distribution and phase distribution

values are determined using traditional mathematical

techniques. In woodward lawson method, a combination

of sinc functions are used to generate the shaped beam.

Traditional methods have their own limitations. If the

numbers of elements are more, it is very difficult to realise

amplitude distribution and phase distribution. In

woodward lawson method typical shapes like triangle

cosecant pattern is not possible to generate due to more

number of side lobes in the non-shaped region. Based on

all these drawbacks, optimization methods are used to

generate shaped beams as there are N numbers of

elements, where N is very large. Optimization methods [1-

5] GA, PSO, and Firefly algorithm has been used to

generate shaped beams like stair step, triangle, M pattern,

multiple beams. Also multiple flat beams can be generated

using these optimization methods. TLBO [6-9] is used to

solve constraint optimization, unconstraint optimization,

and complex constraint optimization in engineering

problems. In TLBO, there are different variants based on

initialisation techniques, adaptive parameters, different

learning strategies, and hybridization methods for

optimization of maximization and minimization function.

TLBO with initialization techniques can be used to

determine good starting point to optimize the fitness

constraints. In adaptive TLBO technique searching can be

done in different manner at both starting stage and ending

stage. In TLBO-GA the calculation of search moves are

modified based on genetic algorithm for exploring new

results. In self-learning TLBO (SLTLBO) precision and

convergence are improved with the utilization of different

self-examination and Gaussian search techniques.

This paper is described in the following ways

section II describes about the array factor expression for

linear arrays. Section III describes about the Teaching

Learning Based Optimization algorithm to synthesis the

shaped beams. Section IV describes about the results

obtained for generation of shaped beams for different

array configurations. Section V discusses about

conclusions obtained for TLBO algorithm to generate

shaped beam.

Array factor for linear array antennas

In Linear array antenna, the radiation pattern is

given by the array factor [10] presented in equation 1.

M

i

psxskj

im

Mi

psxskj

im eAeArArrayFacto1

)(1

)( 1111)( (1)

Mifori

s

iMfori

s

k

x

122

)12(

122

)12(

/2

cos

1

1

1

ps

= phase fed to the antenna elements.

= Observation angle.

miA = excitation amplitude that is fed to the elements.

1s =distance between the antenna elements.




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IMPLEMENTATION In this technique, the difference between the

acquired sample value and the desired sample value is

minimized. The fitness function used is mean square value

between the acquired sample and desired sample.

Fitness function=

s

i

i

x

xCN 1

2)(

1

(2)

)()()( 21 xAxAxC

)(1 xA =acquired sample value

)(2 xA =Desired sample value

xN = total sample points in the region

.

Teaching Learning Based Optimization algorithm

Teaching learning based optimization algorithm

is an algorithm designed based on the activity that takes

place in the class between teacher and the students. There

will be only one teacher in the class who delivers the

subject to the students. Each teacher has different

delivering style based on which student understands the

subject in different ways taught by the teacher. Each

student has their own way of understanding capability

based on which each student understand the subject

differently. Some student like the subject when it is taught

more in visual style. Some student like the subject when is

taught connector style. Some understand the subject well

when it is taught with storytelling style. The different

delivery style of the teacher is represented by teaching

factor. The expression for the interaction between the

teacher and student in the class is given by:

)*(* j

factor

j

teacherrand

jj

new MXXXXX (3)

factorX is teaching factor ranges between 1 and 2.

jM is the mean state of the class

The interaction between students is given as

otherwise

XXXX

XX

XXXX

Xj

a

j

brand

j

a

j

b

j

a

j

b

j

arand

j

a

j

Newa

)(*

)(

(4)

RESULTS

Triangle pattern generated using TLBO algorithm

for 20, 40, 80 element linear array shown in Figure-1. The

error value minimised between the desired and obtained

sample value by TLBO algorithm for 20, 40, 80 elements

is 0.009919, 0.003359, 0.001457 shown in Figure-2. The

amplitude and phase distribution for the three

configurations of the arrays has been presented in Figures

3-8. Stair step pattern generated using TLBO algorithm for

20, 40, 80 element linear array shown in Figure-9. The

error value minimised between the desired and obtained

sample value by TLBO algorithm is 0.001921, 0.0009542,

0.0006402 as shown in Figure-10. The amplitude and

phase distributions for the three configurations of the

arrays have been presented in Figures 11-16.

Figure-1. Triangle pattern Comparison for different

antenna elements for 20, 40, 80 element array using

TLBO algorithm.

Figure-2. Tringle pattern error minimum value

Comparison for different antenna elements for 20, 40, 80

element array using TLBO algorithm.

cosx




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Figure-3. Amplitude distribution with 20 elements for

Triangle pattern.

Figure-4. Phase distribution with 20 elements for

Triangle pattern.


Triangle pattern.


Triangle pattern.


Triangle attern.


Triangle pattern.




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Figure-9. Stair step pattern Comparison for different

antenna elements for 20, 40, 80 element array using

TLBO algorithm.

Figure-10. Stair step pattern error minimum value

Comparison for different antenna elements for 20,

40, 80 element array using TLBO algorithm.


stair step pattern.

Figure-12. Phase distribution with 20 elements for stair

step pattern.


stair step pattern.


stairstep pattern.




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stair step pattern.

Figure-16. Phase distribution with 80 elements for stair

step pattern.

5. CONCLUSIONS It is observed from the results that TLBO has

better performance in terms of shaped beam for stair step

and triangle patterns. In TLBO as there are no standard

assumptions for parameters, it is much simple to

implement the algorithm. For more number of elements

the algorithm has different performance in terms of error

reduction. The error value is better minimized for stair

step pattern than for triangle pattern. The error is

minimized for more number of elements compared with

less number of elements for both stair step and triangle

patterns.

REFERENCES

[1] Mao X.-L, Zheng H.-L and Fan X.-H. 2009. An

optimization algorithm in shaped-beam antenna

arrays. 2nd Asian-Pacific Conference 08 January

2010.

[2] Gopi Ram, Durbadal Mandal, Rajib Kar, Sakti Prasad

Ghoshal. 2014. Design of Non-uniform Circular

Antenna Arrays Using Firefly Algorithm for Side

Lobe Level Reduction. International Journal of

Computer and Information Engineering. 8(1).

[3] T. Vidhya Vathi, G.S.N. Raju. 2014. Generation of

Ramp Pattern using Modified Differential Evolution

algorithm. IOSR Journal of Electronics and

Communication Engineering. 9(6): 01-12.

[4] Sabareeswar Gowri Shankar. 2015. Antenna Arrays

and Optimization Techniques. International Journal of

Advancements in Research & Technology. 4(8).

[5] VVSSS Chakravarthy, P. Mallikarjuna Rao. 2015.

Circular Array Antenna Optimization with Scanned

and Unscanned Beams using Novel Particle Swarm

Optimization. Indian Journal of Applied Research.

5(4).

[6] Arunag Sheetal Kalra. 2017. Review of the Teaching

Learning Based Optimization Algorithm. Indian

Journal of Computer Science and Engineering. 8(3).

[7] Zou F., Chen D. and Xu, Q. 2018. A Survey of

Teaching - Learning - Based Optimization.

Neurocomputing. 335: 366-383.

[8] Venkata Rao, R. 2016. Review of applications of

TLBO algorithm and a tutorial for beginners to solve

the unconstrained and constrained optimization

problems. Decision Science Letters. 5(1): 1-30 ·

[9] Santosh J. Chauhan and Vishal V. Rodrigues. 2016.

Teaching Learning Based Optimization (TLBO) for

Optimal Placement of Piezo-Patches Indian Journal of

Science and Technology. 9(34).

[10] C. A. Balanis, 2005. Antenna theory analysis and

design, 3rd

ed. Wiley-Interscience: New Jersey. pp.

385-424.

stair step pattern and triangle pattern synthesis …r. krishna chaitanya 1, p. mallikarjuna rao and...

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