STAIR STEP PATTERN AND TRIANGLE PATTERN SYNTHESIS
USING TLBO ALGORITHM
R. Krishna Chaitanya
1, P. Mallikarjuna Rao
1and K. V. S. N Raju
21
Department 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 ps x s k j i m M i ps x s k j ime A e
A r ArrayFacto 1 ) ( 1 )
(11 11
) (
(1)M
i
for
i
s
i
M
for
i
s
k
x
1
2
2
)
1
2
(
1
2
2
)
1
2
(
/
2
cos
1 1 1
ps
= phase fed to the antenna elements.
= Observation angle.mi
A
= excitation amplitude that is fed to the elements.
1
s
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 xx
C
N
1 2)
(
1
(2))
(
)
(
)
(
x
A
1x
A
2x
C
)
(
1
x
A
=acquired sample value
)
(
2
x
A
=Desired sample value
x
N
= 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:
)
*
(
*
teacherj factor jrand j
j
new
X
X
X
X
M
X
(3)
factor
X
is teaching factor ranges between 1 and 2.
j
M
is the mean state of the classThe interaction between students is given as
otherwise
X
X
X
X
X
X
X
X
X
X
X
j a j b rand j a j b j a j b j a rand j a j Newa)
(
*
)
(
(4) RESULTSTriangle 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.
cos
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-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-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
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arrays. 2nd Asian-Pacific Conference 08 January 2010.
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[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.
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