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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.
www.arpnjournals.com
2824
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.
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.
www.arpnjournals.com
2825
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
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.
www.arpnjournals.com
2826
Figure-3. Amplitude distribution with 20 elements for
Triangle pattern.
Figure-4. Phase distribution with 20 elements for
Triangle pattern.
Figure-5. Amplitude distribution with 40 elements for
Triangle pattern.
Figure-6. Phase distribution with 40 elements for
Triangle pattern.
Figure-7. Amplitude distribution with 80 elements for
Triangle attern.
Figure-8. Phase distribution with 80 elements for
Triangle pattern.
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.
www.arpnjournals.com
2827
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.
Figure-11. Amplitude distribution with 20 elements for
stair step pattern.
Figure-12. Phase distribution with 20 elements for stair
step pattern.
Figure-13. Amplitude distribution with 40 elements for
stair step pattern.
Figure-14. Phase distribution with 40 elements for
stairstep pattern.
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.
www.arpnjournals.com
2828
Figure-15. Amplitude distribution with 80 elements for
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
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[3] T. Vidhya Vathi, G.S.N. Raju. 2014. Generation of
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[6] Arunag Sheetal Kalra. 2017. Review of the Teaching
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