PATTERN SYNTHESIS OF NON-UNIFORM AMPLITUDE EQUALLY SPACED MICROSTRIP ARRAY ANTENNA USING GA, PSO AND...

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International Journal of Advanced Research in Engineering and Technology

(IJARET) Volume 7, Issue 2, March-April 2016, pp. 132–147, Article ID: IJARET_07_02_013

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PATTERN SYNTHESIS OF NON-UNIFORM

AMPLITUDE EQUALLY SPACED

MICROSTRIP ARRAY ANTENNA USING

GA, PSO AND DE ALGORITHMS

K. Karuna Kumari

Department of ECE, GITAM University, Visakhapatnam, A.P., India

Prof. P. V. Sridevi

Department of ECE, Andhra University, Visakhapatnam, A.P., India

ABSTACT

In the recent years the development in communication systems requires the

development of low cost, minimal weight, low profile antennas that are

capable of maintaining high performance over a wide spectrum of

frequencies. This technological trend has focused much effort into the design

of a micro strip patch antennas. Nowadays Evolutionary Computation has its

growth to extent. Generally electromagnetic optimization problems generally

involve a large number of parameters. Synthesis of non-uniform linear

antenna arrays is one of the most important electromagnetic optimization

problems of the current interest. This paper is mainly focus on the reduction in

side lobe level of Microstrip linear arrays by using evolutionary

programming-real valued genetic algorithm (EP-GA), particle swarm

optimization algorithm(PSO) and Differential Evolution Algorithm(DE) . The

simulation results of non uniform linear arrays in terms of SLL is calculated.

The Best-Weights for 20 elements array are listed .The Radiation patterns are

presented for different number of elements. All the simulated results are

obtained by using MATLAB software.

Key words: Microstrip antenna Linear array, Real valued-Genetic Algorithm

(GA), Particle Swarm Optimization (PSO) algorithm, Differential Evolution

(DE) algorithm, Side-lobe Level.

Cite this Article: K. Karuna Kumari and Prof. P. V. Sridevi. Pattern Synthesis

of Non-Uniform Amplitude equally Spaced Microstrip Array Antenna Using

GA, PSO and DE Algorithms. International Journal of Advanced Research in

Engineering and Technology, 7(2), 2016, pp. 142–147.

http://www.iaeme.com/IJARET/issues.asp?JType=IJARET&VType=7&IType=2

Pattern Synthesis of Non-Uniform Amplitude equally Spaced Microstrip Array Antenna

Using GA, PSO and DE Algorithms


1. INTRODUCTION

Low side lobe antennas are becoming an increasingly important component of high

performance electronic systems, particularly those operating in heavy clutter and

jamming environments. Practically, the radiation pattern of antenna array has not only

having the main beam but also side lobes .Most of the power is confined in main

beam which provides the coverage in desired portion. Some of the power is also

remained in sidelobe levels that are nothing but wastage of transmitting power [16]. If

the sidelobe levels are very high, large amount of transmitting power is wastage. For

efficient use of transmitting power and desired radiation characteristics can be

achieved by using this five following control methods: 1) The geometrical

configuration of the overall array 2) The relative displacement between the elements

3) The excitation amplitude of the individual elements 4) The excitation phase of

individual elements 5) The relative pattern of the individual elements .Various

analytical and numerical methods have been used to optimize the side lobe levels

relative to the main beam by using above controls.

Several new optimization techniques have been emerged in the past two decades,

that mimic biological evolution, or the way biological entities communicate in nature.

Some of these algorithms have been used successively in many electromagnetic and

antenna problems include Genetic Algorithms (GA) [1], Particle Swarm Optimization

(PSO) [2], and the method of Differential Evolution (DE) Algorithm [3]. In the

electromagnetism research area, mainly the antenna synthesis, the use of these

optimizers is widely and clearly appreciated. To date, different GA, PSO and DE

algorithms have been successfully applied to different problems including antenna

design and the array synthesis.

Many efforts have also been devoted to compare these algorithms to each other.

Typically, such comparisons have been based on artificial numerical benchmark

problems. The goal of many studies was to verify that one algorithm outperformed

another on a given set of problems. In general, it has been possible to improve a given

standard method within a restricted set of benchmark problems by making minor

modifications to it.Recently, Genetic Algorithms (GA) ,particle swarm optimization

(PSO) and differential evolution (DE) have been introduced and particularly PSO has

received increased interest from the EC community. These techniques have shown

great promise in several real-world applications [4]-[7]. In this paper, we investigated

the performance of GA, DE, PSO for the optimization of SLL.

In the following part of the paper, the theory and formulation of the optimization

problem will be explained. After words, the details of the proposed ensemble based

Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Differential

Evolution (DE) algorithms will be given. Finally, the application of algorithms in the

optimization of SLL will be demonstrated for 20 element antenna array. The

corresponding results of three algorithms will be compared.

2. MICRO STRIP PATCH ANTENNA

Microstrip antennas are used not only as single element but are very popular in arrays.

Arrays are very versatile and are used to synthesize a required pattern that cannot be

achieved with a single element. Arrays increase the directivity, and perform various

other functions which would be difficult with any one single element.

For the microstrip antenna, the x-y plane (π/2, 0 π /2, 3 π /2 2 π) is the principal E-plane. For this plane, the expression for the radiated fields is[8-9]

K. Karuna Kumari and Prof. P. V. Sridevi


cos2

sin

cos2

cos2

sin0

0

0

Lk

hk

hk

E

2. DESIGN OF LINEAR ARRAY ANTENNAS

Consider a Linear array of 2N symmetric array elements uniformly spaced of distance

d between the elements in x-z plane. The array factor for the linear antenna array is

shown below [10].

Where k is the wave number, k=2ᴨ/λ, θ is the angle measured from the axis of the

array, θo is the steering angle, [ , ] is the excitation of the current for the element on either side of the array midpoint to be controlled and d is the spacing

between elements. By the array factor, the fitness function is obtained. Here, the

fitness function is used to obtain the optimum weights and to achieve maximum SLL.

Assuming the linear array is symmetric about its center of the array.

Mathematically, the array factor of a 2N element linear array is given by [10]

)coscos()5.0(cos2 01

dnkeIAF nJN

n N

2k

Where k is the wave number

Fig 1: Geometry of Linear Antenna Array

θ is the angle measured from the axis of the array, θo is the steering

angle,[ , ] is the excitation of the current for the element on either side of the

array midpoint to be controlled and d is the spacing between elements. The fitness

function associated with this array is the maximum SLL of its associated far-field

pattern to be minimized. The general form of the fitness function is given by

)(

))(log20( 10

AFMax

AFMaxFitness

Where |AF(θ)|=|AF(θo)| 0 , θ

d




3. THE GENETIC ALGORITHM (GA)

The Genetic Algorithm (GA) is an optimization and global search technique based on

the mechanics of natural selection and natural genetics. A Genetic Algorithm allows a

population composed of many individuals to involve under specified selection rules to

a state that minimizes the cost function. This optimization algorithm is more powerful

for problems with more number of variables and local minima. GA is very efficient in

exploring the entire search space or the solution space, which is large and complex.

The Genetic algorithm is implemented using computer simulation [9]. Genetic

Algorithm may be represented as shown in Fig.3.

In computer algorithm, a chromosome is an array of genes, a number of

chromosomes make up one population. The chromosomes are generated randomly in

the selected space. Each chromosome has an associated fitness function, assigning a

relative merit to that chromosome. The algorithm begins with a large list of random

chromosomes.

Figure 2 Genetic Algorithm for optimization of side lobe level

yes

yes No

No

New Chromosomes= parents+ new offspring

Select best SLL

Stop SLL≤ SLL_ Max

SLL≤SLL_Max

Cross over and mutation to generate new

chromosome as child

Evaluate SLL for each chromosome

Chromosomes having best SLL as parent

Create initial population



Fitness functions are evaluated for each chromosome. The chromosomes are

ranked from the best-fit to the least-fit, according to their respective fitness functions.

Unacceptable chromosomes are discarded, leaving a superior species-subset of an

original list, which is the process of selection. Genes that survive become parents, by

crossing over some of their genetic material to produce two new offspring. The

parents reproduce enough to offset the discarded chromosomes. Thus, the total

number of chromosomes remains constant after every iteration. Mutations cause small

random changes in a chromosome. Fitness functions are evaluated for the offspring

and mutated chromosome, and the process is repeated. The algorithm stops after a set

number of iterations, or when an acceptable solution is obtained.

In the genetic algorithm, initial chromosomes are combination of random

chromosome and amplitude excitations of linear array instead of all random

chromosomes. The halves of the chromosome are discarded and new half of

chromosomes are generated from parents chromosome which are best fits to fitness

function. The cost function is the maximum side lobe level for the antenna pattern.

4. PRACTICAL SWARM OPTIMIZATION ALGORITHM

Practical swarm optimization (PSO) is a population-based self-adaptive search

optimization technique first introduced by Kennedy and Eberhart [11]. The PSO

method is becoming very popular due to its simplicity of implementation and ability

to quickly converge to a reasonably good solution. In the practical swarm algorithm,

the trajectory of each individual in the search space is adjusted by dynamically

altering the velocity of each particle, according to its own flying particles in the D-

dimensional search space can be represented as and respectively.




Fig 3.PSO Algorithm for optimization of side lobe level

DE ALGORITHM

To update the velocity matrix at each iteration K, every particle should now its

personal best and global best position vectors in addition to the neighbor best position.

The personal best position vector defines the position at which each particle attained

its best fitness value up to the present iteration. The personal best position of the

particle is represented as the global best position vector defines the position in the solution space at which the best fitness

value was achieved by all particles, and is defined by

[12]

Initialize particles with random position&

Velocity Vectors

Calculate fitness values for each particle

Is current fitness value

better than pBest

Assign current fitness as new pBest Keep previous pBest

Use each particle’s velocity value to update

its data values

Calculate velocity for each particle

Assign best particle’s p Best value to g Best

Target or maximum

epochs reached

NO YES

NO YES

sss

Ss

ss

St

ar

t

END

Start



The particles are manipulated according to the following equations:

(2)

(3)

In 1995, Price and Storn commenced the Differential Evolution (DE) algorithm

[10] which is based upon differential mutation operator. Practically there are many

problems with different types of objective functions such as non-linear, noisy, flat,

non-differentiable, non-continuous, and multi-dimensional or have many local

minima which are difficult to solve analytically. DE is a robust statistical method for

cost function minimization which does not make use of a single nominal parameter

vector but instead it uses a population of equally important vectors and is very

advantageous to find the most approximate solution to any type of problems.

Differential evolution is a simple, efficient and robust evolutionary algorithm, and

is usually mark as DE/x/y/z, where x denotes how the differential mutation base is

chosen , y denotes the number of vectors differences added to the base vector and z

indicates the crossover method. It has been successfully applied to the array synthesis

problems, electromagnetic inverse problems and many other scientific and

engineering problems. Although it has been reported that differential evolution

performs better than many other algorithms, it is still a dream for differential

evolution users to have a strategy perfectly balancing exploration and exploitation, or

equivalently, reliability and efficiency.

It has been well known that the critical idea behind the success of Differential

Evolution is the creative invention of differential mutation [13-15]. Different

differential mutation strategies balance exploration and exploitation differently. For

example, DE/Best/*/* generally converges faster due to the guidance by the best

individual but may be locally trapped because of loss of directivity, while

DE/Rand/*/* gains directivity at the cost of efficiency. In order to simultaneously,

provide both diversity and guidance so that exploration and exploitation can be more

efficiently balanced. Synthesis capability, reliability and efficiency of DE/Rand/*/*

are tested. The simulation results show that DE/Rand/*/* is able to achieve lower

peak side lobe levels and converge reliably and efficiently.

In DE algorithm the objective function is sampled by a set of initial points which

are chosen randomly from the entire search space. Then in the next step the algorithm

adds the weighted difference between the two randomly selected population vectors to

the third random population vector to generate a new parameter vector. This process

of generating the new parameter vector is called mutation. Now this parameter vector

is further mixed with the predefined parameters to produce the trial vector and this

process is called crossover. Then in the last step, called selection in which trial vector

is replaced by the target vector if the trial vector reduces the values of the cost

function then that obtained due to the target vector.

To realize the algorithm let the problem is function of D number of independent

parameters. In this work for N element array, the number of independent parameters

is 2N in which the first N parameters are the normalized amplitude coefficient of the

N array elements and remaining N parameters are to represent the static phase of each

element. Hence, if NP be the population size then the parameter vectors are

represented as




The target vector compared with the trial vector and the minimum value is

admitted to the next generation. The above steps are continued until the predefined

number of generations reached or the desired value of the cost function is obtained.

The entire process of DE for solving problem is shown in flowchart in Fig 4.

Fig4: DE Algorithm for optimization of SLL

C

R

O

S

S

O

V

E

R

S

E

L

E

C

T

I

O

N

M

U

T

A

T

I

O

N

Yes

Yes

No

Yes

No

No

Start Set G=0 and randomly initiate

Compute

i=1

Save the result and stop

+F( )

f (

G

f(

i=i+1

i=NP

G=G+1



6. RESUITS AND DISCUSSIONS

In this paper, the Non-Uniform linear antenna array is synthesized using global

optimizing techniques called GA, PSO and DE algorithms. The Non-Uniform array is

symmetric array of 2N elements towards the center of the array. The array having

progressive phase and uniform spacing between the elements is 0.5λ.The radiation

pattern of linear antenna array with N=20 elements at scan angles and deg are

given for GA, PSO and DE. In this paper, the array factor is the objective function for

optimizing the fitness /cost function called SLL. By using this evaluation techniques

the est weights are obtained for linear antenna arrays to reduce the SLL.

Figure 5 Radiation pattern of 20 element microstrip array antenna using GA

Figure 6 Cost function graph for 500 iterations

-1.5 -1 -0.5 0 0.5 1 1.5-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Theta in (Radians)

Norm

aliz

ed A

mplit

ude(d

B)

Optimized Radiation pattern of microstrip array using GA

0 50 100 150 200 250 300 350 400 450 500-24

-23

-22

-21

-20

-19

-18

-17

-16

-15

No.of generation

cost

fun

ctio

n






-1.5 -1 -0.5 0 0.5 1 1.5-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Theta in (Radians)

Norm

aliz

ed A

mplit

ude(d

B)

Optimized Radiation pattern of microstrip array using PSO

0 50 100 150 200 250 300 350 400 450 500-21

-20.5

-20

-19.5

-19

-18.5

-18

No.generation

Cost

function





-1.5 -1 -0.5 0 0.5 1 1.5-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Theta in (Radians)

Norm

aliz

ed A

mplit

ude(d

B)

Optimized Radiation pattern of microstrip array using DE

0 50 100 150 200 250 300 350 400 450 500-34

-32

-30

-28

-26

-24

-22

-20

-18

-16

No.of generations

cost

function




Figure 11 Radiation Pattern of Linear antenna array of 20 elements using GA, PSO and DE at

θ= (deg)

Figure 13 Radiation Pattern of Linear antenna array of 20 elements using GA, PSO and DE at

θ= (deg)

-1.5 -1 -0.5 0 0.5 1 1.5-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Theta in (Radians)

Norm

aliz

ed A

mplit

ude(d

B)

Optimized Radiation pattern of microstrip array using GA,PSO,DE

GA

PSO

DE

-1.5 -1 -0.5 0 0.5 1 1.5-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Theta in Radians

Norm

aliz

ed A

mplit

ude(d

B)

Optimized Radiation pattern of microstrip array using GA,PSO,DE

GA

PSO

DE



Table 1 Best weights for GA, PSO and DE Algorithms with 200 iterations

Table 2 SLL for GA, PSO and DE Algorithms with 200 iterations

S.No

Optimized weights

using

GA(N=20)

Optimized weights

using

PSO (N=20)

Optimized weights

using

DE (N=20)

1 0.12379 1 0.1795

2 0.27239 1 0.2314

3 0.58451 0.71775 0.2507

4 0.36378 -0 0.2329

5 0.29836 1 0.3088

6 0.50807 1 0.3644

7 0.40648 -0 0.3992

8 0.6828 -0 0.6065

9 0.63655 1 0.5111

10 0.63238 0.27016 0.6688

11 0.66836 1 0.7699

12 0.50739 1 0.7218

13 0.86033 0.33163 0.7597

14 0.58251 1 0.7547

15 0.94851 1 1.0864

16 0.91995 1 0.8410

17 0.98516 1 0.9401

18 0.71477 1 1.0661

19 0.986 1 0.9943

20 0.92949 1 1.0953

GENETIC ALGORITHM

PARTICLE SWARM

ALGORITHM

DIFFERENTIAL

EVOLUTION

ALGORITHM

No.of

element

s

Side lobe

level(dB)

Converging

time (sec)

Side lobe

level(dB)

Converging

time (sec)

Side lobe

level(dB)

Converging

time (sec)

10 -27.99 37.62441 -27.808 29.252831 -38.8 14.43

20 -23.97 65.20003 -20.745 51.378521 -32.58 23.99

30 -22.70 93.89461 -20.726 74.199701 -28.12 32.49

40 -21.06 123.4181 -20.708 97.361576 -27.76 42.35

50 20.733 154.0718 -20.658 121.027607 -27.35 51.16

60 -20.645 187.3938 -20.574 144.979070 -27.06 59.89

70 -20.681 216.5338 -20.550 170.463793 -27.168 71.30

80 -20.68 248.7792 -20.393 195.657447 -25.198 83.39

90 -20.6 281.5972 -20.307 220.838639 -24.514 97.67

100 -20.572 281.5972 -20.214 247.091233 -23.625 114.02




Figure 14 Maximum Side lobe level with the number of elements

Figure 15 No. of elements verse Elapse time

10 20 30 40 50 60 70 80 90 100-40

-38

-36

-34

-32

-30

-28

-26

-24

-22

-20

No.of Elements(N)

Norm

alis

ed A

mplit

ude(d

B)

No.of elements verse Normalised Amplitude(dB)

GA

PSO

DE

10 20 30 40 50 60 70 80 90 1000

50

100

150

200

250

300

350

No.of Elements(N)

Ela

pse T

ime(s

econds)

No.of elements verse Elapse Time(seconds)

GA

PSO

DE



In three algorithms N=20 elements are used. The radiation pattern of Linear

antenna array of 20 elements using GA, PSO algorithm and DE algorithm at

θ= (deg) and at θ= (deg) are represented. The radiation pattern of Linear antenna

array of 20 elements using GA, PSO and DE algorithms at θ= (deg) ,the SLL is -

23.97 dB , -20.45dB and -32.58 dB obtained respectively. The cost functions of

GA,PSO and DE algorithms of 200 iterations are represented. All the three algorithms

produced best results than normal linear antenna array having -13.6dB and

comparatively DE Algorithm produces maximum SLL than PSO and GA. All the

simulation results are obtained using MATLAB software

7. CONCLUSION

In this paper the optimization of 20 elements linear arrays in terms of side level using

genetic algorithm ,particle swarm optimization algorithm ,Differential Evaluations are

given. The side level for GA is -23.97 dB, PSO is - -20.45 dB and for DE is -32.58 for

20 element arrays. All three optimization techniques gives the good results for given

problem, however the elapsed time or converging time for genetic algorithm is more

when compared with PSO algorithm and DE algorithm. The number of generations

/iterations required to get best fitness value for DE is more compared with GA and

PSO.

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PATTERN SYNTHESIS OF NON-UNIFORM AMPLITUDE EQUALLY SPACED MICROSTRIP ARRAY ANTENNA USING GA, PSO AND...

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