Design and Optimization of a Single Element Dual [621844]

Design and Optimization of a Single Element Dual
Band Microstrip Patch Antenna for Long Term
Evolution (LTE) Using Genetic Algorithm

Mohammad Hossain Pappu1, Moben Ur Rashid1, Dr. Md. Fokhrul Islam2, and Md. Mostafa Amir Faisal3*
1Department of ETE, International Islamic University Chittagong, Bangladesh
2Assistant Professor, Department of EEE, Islamic University of Technology, Bangladesh
3Lecturer, Department of ETE, International Islamic University Chittagong, Bangladesh
* E-mail: oranta68@yahoo.c om

Abstract— Antennas are inseparable part of modern wireless
communication industry as they make it possible to convert
electrical signals into electromagnetic wave. Different types of
antennas have attracted the designers from time to time based on
their performance and size. Micro -strip antennas have been very
appealing since commencement because of their light weight and
compatibility with PCBs and MMICs. Long Term Evolution
(LTE), which is currently in use in many countries, uses multiple
frequency bands for its operation. It necessitates designing a
compact single element Multiband antenna for Long Term
Evolution (LTE) that covers as many frequency bands as possible.
Design and simulation of a dual -band mi crostrip antenna covering
1.8 GHz and 2.6 GHz bands of LTE is proposed in this paper. This
will allow roaming facilities with LTE compatible devices in large
areas like Asia, Europe, Australia, New Zealand etc. without
enlarging the device size. Genetic al gorithm is used to optimize the
s11 parameter of the proposed antenna due to its efficiency.
Designed antenna is simulated by IE3D (ZELAND) software due
to its accuracy for regular shapes.
Keywords — Microsrip antenna, Long Term Evolution (LTE),
Multiband, Roaming, Gain, Optimization, Genetic Algorithm.
I. INTRODUCTION
Microstrip patch antennas are popular for their low profile
and easy of fabrication by using modern printed circuit
technology [1]. These are easy to use in mobile, radio and
wireless communicat ion devices because of their lightweight
[1]. Long term Evolution (LTE) is one of the most popular
advancements in modern communication technology. It is an
advanced technology that offers high speed packet access and
capacity. The conventional microstrip antenna are limited
because of their poor gain, low bandwidth and polarization
purity [3].
Due to diversity of usage of frequencies in different regions
in this technology, roaming with the same device becomes
difficult as antenna used in the devices does not always support
frequency bands in the roaming places [5]. So, to overcome the
problem, incorporating more antennas in a device is necessary
to resonate at different frequencies, which make the device size
bigger. Research is going on to incorporate more frequency bands in a single antenna so that it takes lesser space and help
make the devic e smaller.
One of the most popular ways to incorporate more
frequency bands in a single element has been to cut slots of
different shapes on a fundamental geometry. An antenna is to
cover 750 -960 MHz and 1700 -2700 MHz is proposed in [6].
Multiband MIMO ant enna for LTE operation to operate at LTE
band 13 and LTE band 7 was designed in [7]. Another antenna
to operate at bands 0.5 -0.75, 1.1 -2.7, 3.3 -3.9 GHz was designed
in [8]. Similarly many more researches incorporating many
bands in a single geometry has be en going on recently [9] [10]
[11].
A compact single element triple band antenna covering LTE
FDD bands 2 and LTE TDD band 38 and 41 has been proposed
in this work. These frequencies are in action in different regions
of the world which would allow designe rs to make the devices
compatible with LTE to roam in those resigns without making
the device size bigger.
With the fortunate, fast and rapid development of
wireless communications, the microstrip patch antennas must
meet more requirements, which make the configuration and
design process much more complicated. Thus the antenna
design problems (so to say) involve a large number of
parameters which have great effect on performance of the
antenna. These parameters must be taken as a whole into
account. The traditional optimization techniques are not
efficient in solving such problems. Genetic Algorithm (GA) is
a class of search techniques that use the mechanisms of
natural selection and genetics to c onduct a global search of
the solution space [2] and this method can handle the
common characteristics of electromagnetics [4]. So genetic
algorithm is utilized in the design process [12, 13]. In this
paper, genetic algorithm is adopte d to optimize the S11
parameter of the microstrip patch antenna. The electrical
properties of the antenna are computed using IE3D (Zeland)
software. For practical use, gain with respect to return loss of –
7dB is acceptable. As this work is based on si mulation, return
loss of 10dB, which corresponds to VSWR of 2, is taken to be
minimum.

II. GENETIC ALGORITHM
Genetic Algorithms (GAs) are adaptive heuristic search
algorithm based on the evolutionary ideas of natural selection
and genetics. As such they repr esent an intelligent exploitation
of a random search used to solve optimization problems.
Although randomized, GAs are by no means random, instead
they exploit historical information to direct the search into the
region of better performance within the sea rch space. The basic
techniques of the GAs are designed to simulate processes in
natural systems necessary for evolution. A solution generated
by genetic algorithm is called a chromosome, while collection
of chromosome is referred as a population. A chromo some is
composed from genes and its value can be either numerical,
binary, symbols or characters depending on the problem want
to be solved. These chromosomes will undergo a process called
fitness function to measure the suitability of solution generated
by GA with problem. Some chromosomes in population will
mate through process called crossover thus producing new
chromosomes named offspring which its genes composition are
the combination of their parent. In a generation, a few
chromosomes will also mutati on in their gene. The number of
chromosomes which will undergo crossover and mutation is
controlled by crossover rate and mutation rate value. The
chromosome which has higher fitness value will have greater
probability of being selected again in the next g eneration. After
several generations, the chromosome value will converges to a
certain value which is the best solution for the problem.
III. ANTENNA CONFIGURATIO N
A. Configuration of Antenna
The first design step is to choose a suitable dielectric
substrate of appropriate thickness (h). Three most common
substrate materials used are rexolite (εr=2.6), RT Duroid
(εr=2.2) and Alumina (εr=9.8). Here as per the manufacturer
(roger corporation) dat asheet RT duroid with εr= 2.2 having
thickness (h) =1.575mm is chosen as the substrate material for
the patch antenna. First the dimensions of the patch and feed
line are to be determined and the feed line is to be placed
properly to resonate at 1.8 GHz. T hen the modifications of
antenna structure is studied and simulated to create multiple
resonances. For efficient radiation, patch width is given by [14]:
𝑊𝐶
2𝑓𝑟 √ɛ𝑟+1
2
c=velocity of light=3×1011 mm/sec. Effective dielectric
constant is given by [1]:
ɛ𝑟𝑒𝑓𝑓=
( 1
√1+12ℎ
𝑤) (ɛ𝑟−1
2)+(ɛ𝑟+1
2)

Where,
εreff=Effective dielectric constant
εr=Dielectric constant of substrate
h =Height of dielectric substrate
W =Width of the patch For a given resonance frequency fr, the effective length is
given by [1]:
𝐿𝑒𝑓𝑓=𝐶
2𝑓𝑟√ɛ𝑟𝑒𝑓𝑓
The actual length of patch is given by [1]:

𝐿=𝐿𝑒𝑓𝑓−2∆𝐿
Where,
∆𝐿=0.412(ɛ𝑟𝑒𝑓𝑓+0.3)(𝑤
ℎ+0.264)
(ɛ𝑟𝑒𝑓𝑓−0.258)(𝑤
ℎ+0.8)
By using transmission line model analysis the input resistance
due to the two identical slots at the edges of patc h which are
separated by distance 2 / λ is given by [1]:
𝑅𝑖𝑛=1
2(𝐺1±𝐺12)
Where,
G1=Conductance
G12=Mutual conductance
1
120𝜋2∫[sin(𝑘𝑜𝑤
2cos𝜃)
cos𝜃]2
𝑠𝑖𝑛3𝜃𝑑𝜃𝜋
0
And
1
20𝜋2∫[sin(𝑘𝑜𝑤
2cos𝜃)
cos𝜃]𝐽𝑜(𝑘𝑜Lsin𝜃)𝑠𝑖𝑛3𝜃𝑑𝜃𝜋
0

k0=wave number = 2𝜋𝑓𝑟
𝜆
The characteristic impedance of any line is a function of the
geometry of the line and the dielectric constant. For a
transmission line, its characteristic impedance is defined as the
ratio of voltage and current of the travellin g wave. Hence, the
characteristic impedance of a microstrip line of width WF is
governed by the following two equations [1]:

𝑍𝑐=60
√ɛ𝑟𝑒𝑓𝑓ln(8ℎ
𝑊𝐹+𝑊𝐹
4ℎ) 𝐹𝑜𝑟𝑊𝐹ℎ⁄>1
𝑍𝑐=120𝜋
ɛ𝑟𝑒𝑓𝑓
𝑊𝐹
ℎ+0.667ln(𝑊𝐹
ℎ+1.444)+1.393 𝐹𝑜𝑟𝑊𝐹ℎ⁄≤1

The length of inset cut (y0) is calculated by the formula [1]:
𝑅𝑖𝑛𝑜(𝑦=𝑦𝑜)=1
2(𝐺1±𝐺21)𝑐𝑜𝑠2(𝜋
2𝑦𝑜)
𝑦𝑜=𝐿
𝜋cos−1√𝑅𝑖𝑛
𝑅𝑖𝑛𝑜

Table 1

Fig 1 Geometry of an equation based rectangular patch
antenna

B. Optimization Strategy

To optimize the S11 parameter, genetic algorithm has been
adopted in this paper. The optimized method has two phases.
The first one is initiation and the last one is reproduction and
generation replacement. Initiation consists of an initial
population with a predetermined number which is filling of
randomly created chromosomes. Each of these chromosomes
represents an individual or an individual prototype s olution.
The set of individuals is called the current generation. For each
individual in population is assigned a fitness value by
evaluating the fitness function. Reproduction phase produces a
new generation from the curre nt generation. Higher fitness
value is used to fill the new generation by selecting with a
preference for the individuals. Then crossover and mutation
are applied to the individuals for new generation. The
selection, crossover, and mutation operations are repeated un til
the optimal solution is found.
C. Optimization Procedure

The selection strategy is straight and simple, its
proportionate selection. Elitist strategy is adopted to
accelerate the convergence rate.

Fig 2 A block diagram of genetic algorithm function used in
this design

The block diagram of genetic algorithm function in this design
is shown in Fig 2. The optimization procedure in this design is
summarized as follow:

Step 1: From the microstrip patch antenna (MPA) design
parameter, design the equation based antenna.
Step 2: To choose a coding of the parameters into genes. In this
case, a binary -string coding will be used.
Step 3: Create the initial population randomly.
Step 4: Create and solve models in IE3D. Create models
according to the decoded parameters, set solv ing conditions and
solve models in IE3D. Then calculated S11 parameters to main
function automatically. The returned S11 parameters will be
called by fitness function. Parameters for equation based microstrip patch antenna dimensions
Name Parameter
Substrate thickness(h) 1.575 mm
Dielectric Constant( ɛr) 2.2
Length(L) 55.45 mm
Width(W) 65.88 mm
Depth(yo) 19.46 mm
Fed line length(Fd) 28 mm
Fed line width(W f=Td) 4.85 mm
From the MPA de sign
parameters design the
equation based antenna
Initialize Population
Modeling in IE3D
Solving models in
IE3D
Return results in GA
main function
Evaluate Fitness
function
Selection Crossover
rate and Mutation rate
Construct the
geometry of the new
Simulate the design in
IE3D
Me
et
Cri
teri
a?
Desig
ned
optim
ized
N
o
Y
e
d
W
S
1
S
1
O
R
Y

Step 5: The fitness value for each individual is calculated
using the returned S11 parameters from IE3D and the
fitness function (1). Successive generations are produced
by the application of crossover and mutation operators,
until the optimal solution is found.

D. Parameters for the GA

Optimization object: S11 parameter
Size of population: 23
Crossover rate: 0.7
Mutation rate: 0.15
Number of generations: 550
Fitness function:
𝑃(𝑥)1
𝑁∑𝑄(𝑓𝑖)…………………………………………. (1)𝑁
𝑖=1

Where N is the number of sampling points, fi is sampling
frequency: f1 =1.790GHz, f2=1.795GHz, f 3 =1.800GHz, f 4
=1.805GHz After the optimization the new optimize geometry
parameters are shown in table 2

Table 2

Fig 3 Optimized geometry of the single band patch antenna

Table 3

The first point to note in the design process is the effect of slot
separation on the patch design. With reference to the value of
slot separation, simulation resu lts have shown that placing the
slots close to the radiating & non -radiating edges of patch
increase the effect of slot length on resonant frequency. This
gives greater freedom to tune the resonant frequency of the
TMoδ mode. Increasing the slot width prod uces an increase in
input impedance of the TM01 mode.
The configuration parameters of the proposed antenna are as
follow:

Fig 4 Geometry of the proposed antenna for dual band Parameters of optimized single band microstrip patch antenna
dimensions
Name Parameter
Length (L) 55.202 mm
Width (W) 65.90 mm
Depth (yo) 19.654 mm Parameters for proposed dual band microstrip patch antenna
dimensions
Name Parameter
Length (L) 52.202 mm
Width (W) 65.9 mm
Depth (yo) 19.654 mm
Fed line width (Wf) 4.85 mm
Slot length (LS1) 15.2 mm
Slot width (WS1 ) 1 mm Q(𝑓𝑖){15 𝑆11<−15
|𝑆11(𝑓𝑖) | 𝑆11≥−15 …………. ……… (2)
W
L
F

t
L
L
P
y
Y
L
W
PO

IV. RESULTS AND SIMULATION
Calculation is carried out to demonstrate the performance of the
proposed antenna. The IE3D software based on Moment of
method (MoM) is used for analysis. The S11 parameter of an
equation based ordinary rectangular patch antenna is shown
in Fig. 5 for comparison.
Fig 5 Return loss plot of the equations based antenna
Fig 6 Return loss plot comparison between equations based
and optimized single band antenna
From fig 6 we can see that the comparison between an equation
based and op timized single antenna, where the S11 parameter
of the optimized antenna is exact desire frequency from the
equation based antenna. Here in the fig 6 the pink one is the
equation based antenna and another one is optimized single
band antenna .
Fig 7 Return loss plot of the proposed antenna for Dual band It can be observed from the fig 7 that the return loss on the
two frequency points (1.8GHz and 2.6GHz) mentioned above
is lower than -10dB. From the return loss plot we can easily
antenna understand t hat our proposed antenna is much better
S11. The total simulations results shown in table 4.
Table 4

Parameter Band Frequency
1.8 GHz 2.6 GHz
S11 (return loss in dB) -30 -28.43
VSWR(at frequency point) 1.06 1.09
Gain (dB) 6.99 5.80
Directivity (dB) 7.53 7.69
Antenna Efficiency (%) 88.33 64.70
Radiation Efficiency (%) 88.42 64.78
Bandwidth (MHz) 18 9.68

The simulated patch antenna gave a resonant frequency of
1.8 GHz. The simulated return loss is found to be – 27dB from
the curve shown in fig. 5 . It is shown in fig. 7 useful return loss
peaks of the dual band patch antenna at 1.8GHz and 2.6 GHz
are – 30 dB and -28.43 dB respectively. The radiation pattern at
both frequenc y in polar from shown in fig 8.
Fig 8 Radiation pattern for Dual band antenna

CONCLUSION
The use of MoM based simulation software (IE3D) is
demonstrated to design a Dual -band rectangular microstrip
patch antenna for LTE applications. In this paper a multi -slot
patch antenna is proposed for Dual frequency app lications. The
simulation shows operation at 1.8 GHz and 2.6 GHz with
consistency in radiation patterns. The reflection co -efficient is
below −10dB from 1.794 to 1.812GHz for 1.8GHz and 2.595 to

2.605 for 2.6GHz. The concept can be simply adapted to desig n
and optimize other antennas operating at different frequency
band.
ACKNOWLEDGMENT
All praises to Almighty Allah, Whose enormous blessings
have given us strength and made us able to complete this paper.
We would like to express our gratitude to our kind supervisor
Mostafa Amir Faisal for his guidance, support and
encouragement. Working with him has been a true privilege and
great experience for us. His guidance and advice has been a
great source of inspiration for us throughout the paper work.
And also th anks Dr. Md. Fokhrul Islam sir. Finally, all blessings
upon our beloved parents, families and friends whose prayers
and moral support always motivates us to complete our studies.
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