International Journal of Engineering Trends and Technology (IJETT) – Volume23 Number 3- May 2015
“Pattern Synthesis of Linear Antenna Array Using Multiple
Optimizaion Techiques for Wi-Max Technology”
Videep Patkar
Prof. Sunil Kumar Singh
Research Scholar, Department of Electronics & Communication Engineering,
Jabalpur Engineering College, Jabalpur -482011, (M.P), India.
Assistant Professor, Department of Electronics & Communication Engineering,
Jabalpur Engineering College, Jabalpur -482011, (M.P), India.
Abstract
Antenna arrays with high directivity, low side
lobe levels and radiated power need to be
designed for enhancement theefficiency of
WI-MAX in communication systems. A new
optimization algorithm REAL CODED
GENETIC
ALGORITHM
(RCGA),isproposed for the synthesis of linear
antenna arrays. The RCGA is a high
performance computational methodcapable of
solving linear and non-linear optimization
problems. RCGA is applied to optimize the
antennaelement positions for suppressing side
lobe levels and for achieving nulls in desired
directions. This paper presents the
comparison
of
different
optimization
techniques. Simulation result shows that
RCGA give best result as compare to Particle
swarm optimization (PSO)and Big Bang
Crunchtechniquesfor synthesis of broadside
and end-firelinear antenna array in WI-MAX
technology.
Keywords
Linear antenna array, Array factor, RCGA,
PSO, BBC, Cost function, Fitness function
WI-MAX.
I. INTRODUCTION
Antenna arrays [1, 2] are being widely used in
wireless,
satellite,mobile
and
radar
communications systems. They help in
improving the system performance by
enhancing
directivity,
improvingsignal
quality, extending system coverage and
increasing
spectrumefficiency.
The
performance of the communication system
greatlydepends on the efficient design of the
antenna arrays. Systems withnarrow first null
beam width (FNBW) are desired for obtaining
highdirectivity. On the other hand, systems
need to maintain low sidelobe level (SLL) to
avoid interference with other systems
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operating in same frequency band. The above
mentioned requirements ofSLL and FNBW
are in contrast to each other as arrays with
narrowbeam width generally do not produce
lower side lobe levels andvice versa, i.e., the
performance
cannot
be
improved
significantlyfor one aspect without degrading
the other. In many applicationsit becomes
necessary to sacrifice gain and beam width in
order toachieve lower side lobe level. Also
the increasing EM pollution hasprompted the
placing of nulls in undesired directions. So it
is necessary to design the antenna array with
low side lobe levels whilemaintaining fixed
beam width and placing of nulls in
undesireddirections.The radiationpattern of
the antenna array depends on the structure of
the array, distance between the elements and
amplitude andphase excitation of individual
elements. For the linear array geometry,
suppressing side lobe levels and placing of
nulls in desireddirections can be achieved in
two ways either by optimizing thespacing’s
between the element positions while
maintaining uniform excitations, or by
employing non uniform excitations of
theelements while using periodic placement
of antenna elements. Linear antenna array
synthesis has been extensively studied from
thepast 5 decades. In order to optimize this
type
of
electromagneticdesign
problems,evolutionary algorithms such as
Real
coded
genetic
algorithm
(RCGA),particle swarmoptimization (PSO)
[3], have been successfullyapplied. In this
paper, a new optimization algorithm, REAL
CODED
GENETIC
ALGORITHM(RCGA)[4-5] is proposed for
synthesis of linear antennaarrays. RCGA is a
high performance computational method.
However, this is the first time that RCGAis
being proposed for WI-MAX applications. In
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International Journal of Engineering Trends and Technology (IJETT) – Volume23 Number 3- May 2015
this paper, RCGA is used to optimize the
spacing between the elements ofthe linear
antenna array in order to produce a radiation
pattern with minimum side lobe levels with
nulls placed in desireddirections.
II.THEORY
A. Linear antenna array
The geometry of uniform linear antenna array
with 2N elementsplaced symmetrically along
x axis is considered and shown in Fig. 1
Figure 1: Geometry of the symmetrically placed linear array
The array factor (AF) in the azimuth plane is
(1)
Here k =2π/λis the wave number,θ is the
azimuth angle and In, ψn and xnare the
excitation amplitude, phase and position of
element respectively.Let us assume uniform
amplitude and phase excitation for all
elements, i.eIn= 1 and ψn = 0.
(2)
The main aim is that to find the optimized
positions ofx1, x2 ...... xnof the corresponding
elements to achieve desiredradiation pattern
with minimum side lobe levels and nulls
atdesired directions. In antenna arrays, proper
placement of antennaelements is essential.
Because, if the adjacent elements are
placedcloser, then it leads to mutual coupling
effects or if they are placedtoo far, then it
leads to grating lobes. Therefore, while
solving thisoptimization problem, the
following conditions must be satisfied in
order to overcome the disadvantages
mentioned above.
|xi−xj|>0.25(3)
min{xi}>0.125_i=1,2.......N.i/=j (4)
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III. OPTIMIZATION TECHNIQUES
With the current development in antenna
technology, optimization techniques have
been as popular as a method of improving the
recent standards in various parameters. In this
paper we have used the particle swarm a
optimization method. The increased level of
side lobes can significantly degrade the
system performance as well as antenna power
efficiency. Though it is confirmed that Side
lobe reduction is the basic way to achieve
power efficiency and signal losses during
transmission, yet it has to be followed with
certain processes that results in side lobe
reduction. Below are the processes through
which the fact can be achieved.
1) Amplitude Only Control
2) Phase Only Control
3) Position Only Control
4) Complex Weights (Includes amplitude and
phase control).
3.1 GENETIC ALGORITHM
Genetic algorithmis a part of evolutionary
computing, which is a rapidly growing area of
artificial intelligence. Genetic algorithms find
application in bioinformatics, phylogenetics,
computational
science,
engineering,
economics,
chemistry,
manufacturing,
mathematics, physics and other field.
A typical genetic algorithm requires:
1. A genetic representation of the solution
domain,
2. A fitness function to evaluate the solution
domain.
A standard representation of the solution is as
an array of bits. Arrays of other types and
structures can be used in essentially the same
way. The main property that makes these
genetic representations convenient is that
their parts are easily aligned due to their fixed
size, which facilitates simple crossover
operations. Variable length representations
may also be used, but crossover
implementation is more complex in this case.
Tree-like representations are explored in
genetic programming and graph-form
representations are explored in evolutionary
programming; a mix of both linear
chromosomes and trees is explored in gene
expression programming.
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International Journal of Engineering Trends and Technology (IJETT) – Volume23 Number 3- May 2015
The fitness function is defined over the
genetic representation and measures the
quality of the represented solution. The
fitness function is always problem dependent.
For instance, in the knapsack problem one
wants to maximize the total value of objects
that can be put in a knapsack of some fixed
capacity. A representation of a solution might
be an array of bits, where each bit represents a
different object, and the value of the bit (0 or
1) represents whether or not the object is in
the knapsack. Not every such representation
is valid, as the size of objects may exceed the
capacity of the knapsack. The fitness of the
solution is the sum of values of all objects in
the knapsack if the representation is valid or 0
otherwise. In some problems, it is hard or
even impossible to define the fitness
expression; in these cases, a simulation may
be used to determine the fitness function
value of a phenotype (e.g., computational
fluid dynamics is used to determine the air
resistance of a vehicle whose shape is
encoded as the phenotype), or even
interactive genetic algorithms are used. Once
the genetic representation and the fitness
function are defined, a GA proceeds to
initialize a population of solutions (usually
randomly) and then (usually) to improve it
through repetitive application of the mutation,
crossover, inversion and selection operators.
A path through the components of the GA is
shown as a flowchart in Figure.2 and
described below:
Define cost function and cost
For each problem there is a cost function. For
example, maximum of a 3D surface with
peaks and valleys when displayed in variable
space, Cost, a value for fitness, is assigned to
each solution.
Chromosomes and genes
A gene is a number between 0 to n-1. A
chromosome is an array of these genes. It
could be an answer. Population in each
generation has determined the number of
chromosomes.
Create a random initial population
An initial population is created from a
random selection of chromosomes. The
number
of
generations
needed
for
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convergence depends on the random initial
population.
Decode the chromosome and find the cost
To find the assigned cost for each
chromosome a cost function is defined. The
result of the cost function called is called cost
value. Finally, the average of cost values of
each generation converges to the desired
answer.
Mating and next generation
Those chromosomes with a higher fitness
(lesser cost) value are used to produce the
next generation. The offspring is a product of
the father and the mother, whose composition
consists of a combination of genes from them
(this process is known as "crossing over"). If
the new generation contains a chromosome
that produces an output that is close enough
or equal to the desired answer then the
problem has been solved. If this is not the
case, then the new generation will go through
the same process as their parents did. This
will continue until a solution is reached.
Figure 2. A path through the components of the GA
3.2 PARTICLE SWRAM OPTIMIZATION
Particle swarm optimisation can has been
used across a wide range of applications.
Ingeneral we can say that areas where PSO
has shown particular promise include
multimodal problems and problems for which
there is no specialised method available or all
specialised
methodsgive
unsatisfactory
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International Journal of Engineering Trends and Technology (IJETT) – Volume23 Number 3- May 2015
results. However, it is hard to be much more
specific that that. PSO applications are so
numerous and diverse that a whole book
would be necessary just to review themost
paradigmatic ones, assuming someone could
identify them among the many hundreds
ofapplications reported in the literature: a
really enormous task.
Particle swarm optimization works in the
same way as the swarm behavior of insects,
animals herding, birds flocking, and fish
schooling where these swarms search for food
in a collaborative manner. This is a new
stochastic
evolutionary
computation
technique, based on the movement and
intelligence of the swarm, which they learn
from their own experience as well as from
other member’s experiences also. These
swarms
behavior
are
studied
and
mathematical models are constructed this
leads to the construction of PSO algorithm. In
PSO, a member in the swarm, called a
particle, represents a potential solution, which
is a point in the search space of Ddimensions. The global optimum is regarded
as the location of food. Each particle has a
fitness value and a velocity to adjust its flying
direction according to the best experiences of
the swarm to search for the global optimum in
the D-dimensional solution space.
Step 1 Form an initial generation of
Ncandidates in a random manner. Respect the
limitsof the search space.
Step 2 Calculate the fitness function values of
allthe candidate solutions.
Step 3 Find the center of mass according to
(10).Best fitness individual can be chosen as
the centerof mass.
Step 4 Calculate new candidates around the
centerof mass by adding or subtracting a
normal randomnumber whose value decreases
as the iterationselapse of using (11).
Step 5 Return to Step 2 until stopping criteria
hasbeen met.
Figure3: Flow chart of BBC
3.3 BIG BANG CRUNCH (BBC)
The Big Bang–Big Crunch (BB–BC)
optimization algorithm is a new optimization
method that relies on theBig Bang and Big
Crunch theory, one of the theories of the
evolution of the universe. In this paper, a
BigBang–Big Crunch algorithm is presented
for solving optimal power flow (OPF)
problems with valve-pointeffects. The
proposed algorithm has been tested with the
IEEE 30-bus system with different fuel
costcharacteristics, quadratic cost curve
model, and quadratic cost curve with valvepoint effects model. Numerical result
demonstrate the efficiency of the BB–BC
algorithm
compared
to
other
heuristicalgorithms.The BB–BC approach
takes the following steps[11]:
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TABLE 1. PARAMETERS FORMULTIPLE
OPTIMIZATION TECHNIQUES
Value
S.NO
PARAMETER
2
Frequency
of 3.3Ghz
operation
Spacing between 4.5 cm
elements d
3
Phase
between 0 Radian
two elements
1
No. Of elements
4
output parameter
SLL,Directivity,
Beam width
4
5
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International Journal of Engineering Trends and Technology (IJETT) – Volume23 Number 3- May 2015
SIMULATION RESULTS
To illustrate the technique described above,
spacing between elements is 4.5cm,
frequency of operation 3.3 GHz, phase
between two elements is 0 Radian, and 4
elements are considered. With the help of
BBC algorithm SLL, directivity and beamwidth are determined.
S.
N
O
1
2
3
4
Parameter
Withoutoptimization
Side Lobe -11.3035
Level
(in dB)
Directivity 11.3597
(in dB)
Beam
10.83
Width
(in degree)
Convergen
ce time
(in sec)
RCGA
PSO
BBC
-40.82
-35.79
-40.22
10.4611
10.41
10.52
41.00
34.87
40.22
17.094
sec
4.581
sec
18.95
sec
TABLE 2: COPARISON RESULTS OF MULTIPLE
OPTIMIZATION ALGORITHM
Conclusion
Figure4: Unoptimized Radiation Pattern
Figure5: Optiized Radiation Patternwith reduce side
lobelevel -40.823dB for N=4 element
In this paper multiple optimization algorithms
is successfully introduced in linear antenna
array synthesis for WI-MAX. RCGA is
applied to calculate the optimized value of
currents is achieved which minimize side lobe
levels. The reduction in radiated power
increases the directivity of radiation pattern.
These results are compared with other
optimizing techniques such as BBC and PSO
which shows that RCGA exhibits good
performance in terms of accuracy and
convergence time. Hence RCGA provides
better result than other optimizing techniques
in WI-MAX.
References
Figure 6: optimized Radiation pattern with reduce side
lobe level -35.791dB for N=4 elements
Figure7: optimized Radiation pattern with reduce side
lobe level -40.22dB for N=4 elements
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