Developing an actual very high frequency antenna using genetic algorithms

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 04 Issue: 11 | Nov-2015, Available @ http://www.ijret.org 40
DEVELOPING AN ACTUAL VERY HIGH FREQUENCY ANTENNA
USING GENETIC ALGORITHMS
Aatish Gandotra1
, Tejaswi Singh2
1
Student, Electronics and Communication Engineering, Guru Tegh Bahadur Institute of Technology, Delhi, India
2
Student,Computer Science Engineering, Guru Tegh Bahadur Institute of Technology, Delhi, India
Abstract
Antenna for the 88-108MHz Very high frequency (VHF) broadcast audio frequency-modulation (FM) band. The antenna is intended
tofit in the flat area inside the head-band of an over ear hearing-protector headset. The space for the antenna is limited by an
existing head-band design, where the unused internal area is the space studied in this thesis.
A genetic algorithm is described for the multiple objective optimization of the antenna matching and radiation pattern optimization.
The results of multiple genetic algorithm evaluations are described, and possible further improvements outlined. Progress is made
on the development of the antenna. The antenna radiation pattern is evolved in desirable way, but a difficulty in solving the antenna
matching problem is identified. Research for resolving the antenna matching problem is described in this paper
Keywords: Antenna, Modulation, Genetic Algorithm, Frequency, Head-Band, Very High Frequency Broadcast.
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1. INTRODUCTION
currently there is an increasing trend in the electronics
industry to move from products with functional
protrusions, such as antennas and wires, to integrated designs
which hide or remove these protrusions. This can most clearly
be seen in the mobile handset industry, but the same move
can be seen in otherfields, such as hand-held transceivers,
headset products and hearing protectors. For instance, a
typical mobile handset may previously have featured a
protruding antenna, protruding buttons and wires for
connecting a headset. In the recent years these parts have
been replaced with fully integrated antennas, at touchscreens
and wireless headsets. The main advantages of this are
improved device reliability for the end user and increased
design freedom during the device design phase. The move to
integrated, protrusion-less devices provide many new and
unique design challenges for these internal parts: internal
antennas must still be able to transmit and receive, despite
the new volume restrictions. Button functions must still be
available and mechanically reliable. Headsets must be able to
function despite the lack of wires, etc.
The antenna described in the present work was conceived as a
potential way for a generic FM-radio hearing protector to
move to such an integrated, conformal antenna. Initially, the
free volume between the head-band wires was identified
as the most promising volume to house an antenna. A
flexible printed circuit board was selected as a suitable
manufacturing method for such an integrated antenna, being
compatible with the mechanical stresses of product usage
and promising low unit cost. The obvious design challenge
posed is the shape and small volume of the available volume,
in addition to the nearby metallic head-band wires. These
limitations largely prohibit the use of traditional antenna
designs and design methods.
In order to realize the antenna, an iterative method of antenna
design using the genetic algorithm was identified as the best
candidate for success. This paper aims at describing the
work carried out in order to simulate this antenna, and to
document the results. The antennas described were simulated
using Numerical Electromagnetics Code 2 (NEC2). No
hardware has been built to verify the simulations.
2. BACKGROUND
The primary motivation for this study is that existing antenna
solutions, based on helical or wire whip designs, constitute a
mechanical protrusion from the otherwise smooth features of
a headset. This protrusion is a major source of mechanical
fatigue problems. It is also an annoyance for the end user due
to its ability to get tangled in foreign objects and as a source
of conducted mechanical noises when it makes mechanical
contact with foreign objects.
Figure 2.1: A typical headset of the type studied in this thesis
The type of headset targeted in this study, as shown in figure
2.1, is typically used in an industrial or semi-industrial

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setting, while the end user is carrying out normal work. This
implies that a cylindrical radiation pattern is desired, as the
received signal strength should be stable while working
facing different directions. It also places high demands on
antenna efficiency and radio receiver sensitivity, as he use in
industrial or semi-industrial settings commonly involve
severe multiple-path fading situations.
2.1 VHF Broadcast FM Radio
The international VHF broadcast FM radio band of interest
covers the frequencies 88 – 108 MHz’s This is the frequency
band used by the majority of nations, with the exception
of Japan and some former Soviet republics[11]. Most of the
former Soviet republics have, or are in the process of
converting to the international VHF broadcast band. Table
2.1 outlines the basic parameters of the VHF FM broadcast
system.
Frequency range 88-108 MHz
Polarization Vertical
Channel allocation raster 50 kHz
Channel bandwidth 200 kHz
Modulation limit +/-75 kHz
Pre-emphasis 75/50 µs
2.2 Existing Antenna Solutions
Antennas on existing headsets are usually of the shortened
helical or whip type, with the headset printed circuit boards
forming the ground plane. A typical design has an antenna
which is approximately 18cm in length, and use a 5x5cm
ground plane. At the frequencies of interest, it is expected
that the size limitations of the ground plane pose a major
limitation for total antenna efficiency. At the center
frequency100MHz, the 5x5cm ground plane is approximately
0, 016λ (λ denotes wave-length). While a larger ground plane
would be technically desirable, it is not practical for a real-
life application. The ground plane overall size is limited by
the cup size, which is ultimately determined by the size of
human heads.
2.3 Possible Flexible Antenna
The mechanical opportunity for an antenna was identified as
the space inside the head-band of the headset, from a practical
point of view; an etched flexible printed circuit board (PCB)
antenna hidden inside the head-band appears feasible.
While other antenna types could be considered, for example a
conformal antenna embedded in the ear-cup surface, the
flexible-PCB proves several advantages over other types.
These include a higher dimensional accuracy, ability to
implement any conceivable two-dimensional structure, good
mechanical flexibility and low cost. Since the final antenna
design is unknown at the onset of work, it was decided that
the flexible printed circuit antenna should be the type studied
in this thesis.
The choice of a flexible printed-circuit defines the surface of
the simulation output-space as the surface which may be
covered by the flexible-PCB. It should be noted that in order
to simplify the simulation, the carrier substrate for the
flexible-PCB is not included in this simulations. Since the
carrier substrate consists of a very thin layer of non-
conductive dielectric it is believed that this is an acceptable
simplification.
The flexible-PCB considered consists of essentially two
layers omitting surface treatments, binders etc: an upper
copper layer and a flexible carrier substrate material made of
polyamide plastic. The copper is approximately 0.04mm
thick, while the thickness of the base substrate is
approximately 0.3mm [12]. A typical exible PCB is shown in
figure 2.2. During theproduction process of a flexible PCB,
the top layer is etched away using a photo-lithographic
process, leaving a conductive copper pattern matching that of
the designed artwork. Since the copper layer is very thin, and
the polyamide is exible, the resulting PCB ishighly flexible.
A bend radius down to 5mm can typically be accepted
without severing the copper, even in extended fatiguetesting
situations [12].
This type of flexible-pcb therefore lends itself well to our
planned antenna. The exibility allows for easy
installationduring headset production, is possible to hide
within existing structures, and allows for flexing of the entire
antenna when the user isfitting the headset.
Figure 2.2: A typical flexible-pcb
2.4 Existing headband
The existing head-band studied in this thesis is based on
two stainless steel metal spring wires which constitute the
front and back main members of the head-band. The central
part between the two wires are traditionally separated by
non-conductive plastic, and constitute the space where the
antenna elements may be placed. Due to the close
proximity to the existing antenna - approximately 5cm or 0,
016λ - the wires are expected to form a part of the existing
radiating structure. Due to their placement, they are expected
to primarily impair the radiation pattern symmetry, although
this has not been verified by measurements. See
Figure 2.1 and figure 4.2

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2.5 Radiation Pattern
The antenna in this application is head-worn and used during
normal work functions without regard to the placement or
direction of the transmitter. It therefore follows that the
primary requirement for the antenna radiation pattern is that it
should be circular or close to circular in azimuth plane.
Practical experience shows that a small deviation from the
ideal circular pattern may be tolerated. Deep notches in the
radiation pattern are highly undesirable, as the end user is
prone to notice and experience and be annoyed by these
regularly during the work day. The elevation pattern
component variation is less critical, since a typical user tend
to keep their heads nominally horizontal for most of the
day. A dipole antenna radiation pattern, circular in azimuth
and with deep notches only in the nadir and zenith
location is therefore very suitable in this application.
2.6 Antenna feed
As the antenna is connected to the receiver circuit placed in
the right hand cup of the headset, it is desirable to have the
antenna feed point as close to this as possible. The preferred
method to connect the antenna to the receiver circuit is by
soldering a short coaxial cable directly to the feed point on
the antenna. For cost reasons, the antenna feed coax should be
kept as short as possible.
2.7 Design Target
Given the above details, the following design goals are
identified 2.2
Frequency range 88 - 108 MHz
Omnidirectional gain > 2 dB
Directionality tolerance 0.3 dB
VSWR <5
Polarization vertical, nominal
Antenna feed system Soldered coax cable on right extreme of
antenna. Manufacturing method Etched exible printed circuit
board.
3. THEORY
3.1 Relevant Antenna Theory
A short summary of the relevant fields of antenna theory is
provided below.
3.1.1 Far Field Theory
In the very simplest, theoretical antenna cases, the far field
radiation pattern can be calculated analytically [13]. This can
then be used for evaluating the performance of the antenna
directly, which is useful for explaining the relevant antenna
far field theory. The description below follows the outline
provided by Cheng [13].
A simple Herzian dipole consists of a short conductive wire
terminated with two small conductive wires. Assume a
sinusoidal current flows in the wire:
i(t) = I cos(ωt) (3.1)
Since the current diminishes at the end of the wire, charges
must build up there, and we canwrite the relation between
charge and current as
i(t) = ±dq(t)/d(t)
Using the magnetic vector potential A, from B = ∇ × A, it can
be shown that
A = az
(µ0Idℓ)/ 4π ( e−jβR R
) (3.2)
From the above equations, it is possible to identify some
basic properties of the results in the far field, for a bound
source:
1. Eθ and Hθare in space quadrature and in phase
2. The ratio |Eθ|/|Hθ| = η0 is constant. This constant
corresponds to the impedance of the medium
3. The magnitude varies inversely proportional with the
distance to the antenna. The phase of Eθ and Hθ is a periodic
function of the distance with a period that is the wavelength,
λ =c/f
Also it is possible to plot the radiation pattern of this antenna.
The far field radiation pattern describes the relative far field
strength as a function of direction, on a fixed direction from
the antenna. The radiation pattern plot is shown in figure
below.
In order to relate this result to the generic case, it is necessary
to consider the case of a real, linear dipole. Relating the result
to a real, finite dipole, presents a mathematical challenge.
While the problem is largely the same, the determination of
the exact current distribution on the antenna is a di-cult
boundary-value problem. An obvious observation is that the
current must be zero at the ends of the antenna ends, and
finite in the feed point, but this unfortunately does not
provide any major breakthrough in solving the current
distribution.
An analytical equation still leads to an integral equation
where the current distribution is unknown under the integral.
3.1.2 Polarization
The polarization of a uniform planar wave, for example
emanating from a dipole antenna, describes the time-varying

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behavior of electric field intensity of a vector at any point in
space. When the E vector of a plane wave, is fixed in the x-
direction the wave is said to be linearly polarized in the x-
direction. Similarly a plane wave may be linearly polarized
along the other unit axes and said to exhibit the corresponding
linear polarization. In cases where the direction of the E
vector of a plane wave changes with time, the plane wave is
said to exhibit nonlinear polarization, either elliptical or
circular.
It can be shown that this case, the plane wave may be
described by a superposition of two linear polarized plane
waves, one linearly polarized along the x-direction and one
linearly polarized along the y-direction. In the case where the
x-direction and y-direction polarized plane waves have the
same linear magnitude, and are in phase quadrature, the
composite field is said to exhibit circular polarization. If this
is not the case, the plane wave is said to exhibit elliptic
polarization. It can be shown that if the transmitting and
receiving antenna does not share the same polarization, path
losses will increase by a factor depending on the angle of
mismatch between the two antennas [13].
This factor, known as Polarization Loss Factor, is defined as
P LF = cos2
ϕ (3.3)
Where PLF is the linear loss factor due to the polarization
mismatch, and ϕ is the misalignment angle. Studying
equation 3.12, it can be shown that a small misalignment has
little effect, but if the polarization misalignment is 90, no
power at all is transmitted between the two antennas.
The VHF FM broadcast radio system employs a linear
vertical polarization. Historically, this was chosen because
vertical polarization provides the minimal propagation
attenuation in most terrestrial line-of-sight or near-line-of-
sight situations at these frequencies [14], and because it
usually simplifies antenna installations when using simple
dipole or ground-plane antennas.
Studies of real-world propagation effects show that a clean
polarization may degrade into a set of superimposed polarized
fields, due to reflections on nearby metal objects. A study
carried out by Shrauger and Taylor have shown that, in a real
terrestrial situation, in our band of interest the nominal
received polarization often greatly differ from the nominal
vertical transmitted polarization[14]. This is the primary
reason for considering the polarization a Secondary property
of this antenna
3.1.3 Impedance
The input impedance of an antenna is defined as the ratio of
voltage to current Z =U/I, as presented to the antenna feed
structure. The antenna impedance will depend on many
parameters of the antenna, primarily mechanical design and
measured frequency [13]. Antenna impedance is - in this case
- important primarily in order to be able transfer the
maximum of the received energy to the radio receiver circuit,
as described in the matching section below. Antennas for
VHF broadcast receivers are traditionally designed to have a
50 or 75 Ohm. In order to be able to compareand ultimately
measure different antenna systems, it is therefore desirable to
adhere to this convention
3.1.4 Radiation Resistance
A measure of the amount of power radiated by an antenna is
the antenna radiation resistance; Rr. is theoretical resistance
that would dissipate power equal to the radiated power when
the current in the resistance is equal to the maximum current
along the antenna. It is therefore desirable for an antenna to
have a high radiation resistance.
3.1.5 Antenna Matching
Antenna matching is the measure of how well the impedance
of the antenna matches the impedance of the load circuit.
When these impedances are equal, the maximum power can
be transferred from load to antenna and vice versa. In this
case the antenna and load are perfectly matched. When the
impedances are non-equal, part of the available power is lost
by being reflected at the connection interface.
3.1.6 Electrically small antennas
An antenna which is mechanically considerably smaller than
the wavelength on which is it designed to operate is said to be
electrically small. Such antennas exhibit considerable
differences compared to a larger antenna. There has been
considerable work done on studying the properties of
electrically small antennas, and ascertaining what exactly
constitutes an electrically small antenna. Initial work was
carried by Wheeler [8], Chu [7]. Refined by Hansen [15], and
more recently refined by Gustafson et al. for thin antennas
[9]. The initial, still commonly used, definition of an
electrically small antenna is an antenna with volume V
smaller than (2∗π∗r)/λ [8]. Although this is clearly a non-
ideal metric for our strip shaped antenna, it is still useful in
order to conclude that the antenna is indeed electrically small,
since λ = 3.guatda.com/cmx.p4...2.8 meters and r = 0.20 meters. For a small
antenna, the background work leads us to expect the
following properties
1. High current densities
2. Difficulty in matching the antenna
3. A very small radiation aperture
3.2 The NEC2 program
The NEC2 program uses a combination of the electric field
integral equation (EIFE) and magnetic field integral equation
(MFIE), as a basis for calculating the current distribution on
antennas [16]. From the current distribution, it is possible to
calculate both the impedance of the antenna and the radiation
pattern. EFIE is used for thin-wire structures, and MFIE is
used when calculating voluminous structures.
They are combined into a hybrid equation, and this is solved
numerically using the method of moments, by describing
each antenna segment by a number of base functions. The
current on wires and structures are then described in matrix
form.
The solution matrix is consequently solved by Gaussian
elimination. From this it is possible to and the requested
antenna impedance and the far field radiation pattern.

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3.2.1 NEC2 limitations
The NEC2 program has several known limitations, such as its
limited support for dielectric volumes, and the difficulty in
accurately simulating complex three-dimensional shapes.
These are of little consequence to the problem at hand, which
is entirely modeled as separate wires.
However, a less obvious limitation clearly has implications to
this problem: Due to the design assumption of each wire
segment being either end fed or open ended, an antenna
where segments intersect between end-points cannot be
simulated without exception.
This is normally not a problem since segments can simply be
split up so that they either begin or end in intersections, thus
avoiding violation of the model.
In this case though, that limitation presents a problem as
antenna segments may or may not cross depending entirely
on the result of the genetic algorithm convergence. As this is
not exception handled in the current genetic algorithm, it
casts some doubt over the validity of the simulation results in
the cases where this happens. Currently, solutions could be
screened manually for violations of this NEC2 limitation, as it
is not caught automatically by the genetic algorithm.
3.3 Genetic Algorithm Theory
A genetic algorithm is an specialized optimization method
which mimics the process of natural selection [17] for solving
a specific problem. This method was pioneered by Holland in
1975 [18]. By this method, genetic algorithms are able to
search a multi-dimensional solution space and find a solution
reasonably efficiently. Genetic algorithms are therefore well
suited to the area of antenna design, where the search space is
wide and multi-dimensional but straight-forward to simulate.
The two key features of the algorithm are
• A basic genome, through which a large set of potential
solutions for the problem at hand may be described.
• A fitness function, through which individual solutions are
evaluated and chosen for generating new solution.
The algorithm works by setting up a number of candidate
solutions, described by the genome. Each solution is then
simulated and evaluated by the fitness function. The top
ranking solutions are then chosen for reproduction into a new
generation, where the best solutions are combined in order to
find solutions which may be closer to the design target. The
process is repeated until a desirable solution is found [19].
Each population iteration is referred to as a generation, and
solutions are referred to as parents and children in analogy
with the process of natural selection. In order to maintain the
progress of the algorithm, it is essential that the basic genome
is able to describe the parameters relevant to the problem at
hand, and that those parameters may be transferred from
parent to child.
3.3.1 Chromosome Representation
The chromosome is the solution vector used for each
individual solution candidate. Each parameter in the
chromosome is referred to as a gene.
The chromosome representation used in the genome is highly
influential on the performance of the genetic algorithm. A too
constrained chromosome design will not allow the algorithm
to find the necessary solutions, but an overly exible design
may on the other hand slow down convergence or prevent
convergence altogether [19]. Apart from exibility, the
chromosome design should also be able to relate to the
problem at hand in a relevant way, so that relevant properties
of the solution may be transferred from parent to child during
cross-over between different parents, in order for desired
solutions to be able to propagate between generations.
4. Implementation
A multi-objective genetic algorithm was implemented in
Matlab, with the NEC2 program used as the simulation back-
end. Matlab is well suited to genetic algorithm tracking and
development, as several plotting and debugging tools needed
are readily available. Apart from that, almost any
programming language could have been employed for the
same purpose.
The NEC2 simulation software is a critical part of this thesis,
as it is well proven and easy to interface from an automated
algorithm. Its method-of-moments simulation foundation,
while unsuitable for certain types of antennas, is well suited
to the wire-type antennas studied in this thesis.
4.1 Genetic Algorithm
The genetic algorithm largely follows the theoretical
description as outlined. The genetic algorithm is implemented
in Matlab, and loops through each individual in each
generation until specific termination criteria are met. The
flow of the implemented algorithm is shown in figure 4.1. In
this thesis the termination criteria isis based on numbers of
generations.
4.2 Mechanical model
The mechanical model for the antenna simulation consists of
two fundamental parts. An overview of the mechanical model
is given in figure 4.2. The fixed part is made up of the static,
pre-existing, structure. This is two wires of 2mm stainless
steel. The shape of these wires is set by mechanical
requirements for the headset. They provide support for the
headset cups and give the necessary holding force for the ear-
cups. The exact dimensions for the fixed part are based on
measurements on real headsets.
The second part is the variable antenna surface, where the
genetic antenna is free to place wires to meet it optimization
targets. For simulation purposes the antenna elements are
considered to be thin wires segments, 1mm in diameter. In a
real product they would be at traces, etched on the exible
PCB.
A fixed diameter is chosen in order to make sure no wire
diameters may violate the manufacturing possibilities for the
flexible PCB.
The active antenna surface part is modeled as a thin section of
a cylindrical surface, where the antenna genetic algorithm
places a number of elements, the first being the fed element.

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The variable antenna surface is highlighted in blue in figure
4.2.
The coordinate system used for this model is a right-handed
Cartesian coordinate system, as used by NEC2. Specifically,
the end-user faces along the positive-Y axis, the end-user left-
right axis is X, while the user up direction coincides with the
Z axis.
Figure 4.1: Genetic algorithm, generation progress
Figure 4.2: Head-band model base, space for antenna
elements in blue
Figure 4.3: Chromosome representation for each solution
candidate
4.3 Chromosome Design
For this thesis a Cartesian coordinate system genome was
chosen, with five movable wire segments. The genome space
spans a [0:0]... [1:1] unity X-Y coordinate space, where each
wire start and stop coordinates is represented as X-Y pairs.
The number of wires may be varied, and the initial number
was arrived on after initial manual tests suggested that five
segments provided sufficient freedom of design. All wires are
fixed to be 1 mm in diameter, which is not adjustable by the
genome.
This straight-forward design makes debugging and range-
checking practical and easy to verify. The major drawback is
it may be non-ideal from an optimization point of view, since
rotational translation is not possible in a simple genome
cross-over scheme. This is left as the subject for a further
study, as a polar coordinate representation would be
considerably more complex to analyze from a theoretical
algorithm point of view.
4.4 Antenna Feed Point
The antenna feed-point is fixed by the algorithm to the center
of the first element in the genome. The starting coordinate of
this first element is forced to genome coordinates x, y = [0,
0]. The other coordinates of this element is subject to genetic
algorithm cross-over and noise like the other elements in the
genome. This ensures that while algorithm is able to move the

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free segment end, other end is fixed in the lower right corner.
The center feed point is therefore kept reasonably close to the
desired location.
.
4.5 Symmetry
Theoretically the antenna is fully symmetrical along the front-
to-back axis. This may havebeen employed to simplify the
genome, but this would have precluded the use of an
asymmetric left-side coax feed, as specified in the design
target. It was also believed that a future addition to the
simulation would be the addition of the asymmetrical left and
right handcircuit boards, which further removes symmetry
from the problem. Therefore the current genome design does
not employ any simplification due to symmetry.
4.6 Coordinate Projection
Since the genome design is based on a Cartesian coordinate
space, as is the output simulationthree dimensional (3D)
spaces, it is possible to map genome space directly to 3D
space with asimple coordinate mapping. A study of the
mechanical design gives the following coordinateprojection.
The mapping function is visualized in figure 4.4.
Figure 4.4: Coordinate mapping. The antenna feed point is
marked with an X
For any short wire segment of the output antenna, a straight
line between the mapped beginning and end coordinates is
sufficient. For wire segments with larger x-coordinate
separation, a segmentation scheme is needed to keep the
antenna segment sufficiently in-plane due to the curved
nature of the output 3D space. In the case where a wire spans
a longer section of the curved plane, a segmentation function
is used to keep the wire segment sufficiently in-plane.
4.7 Solution Mating And Selection Process
The solution mating and the selection process determine a
genetic algorithm convergence performance [19]. It is
generally desirable to select the top ranking solutions for
mating into new solutions. There is a clear trade of between
focusing solely on the top individuals and maintaining the
genetic diversity of the rest of the generation with lower
rankings. A too tight focus on top individuals will tend to
converge to a solution relatively quick, but may employ a
poor exploration of the solution space. A too high focus on
the lower rating solutions may, on the other hand, completely
fail to converge on an acceptable solution or cause very slow
progress. There are several mating schemes that have been
successfully employed in similar cases, such as best-mates-
worst, adjacent-fitness-pairing and emperor-selective. In a
study of mating schemes carried out by B.K Yeo in 1999, the
emperor-selective was found to give the best solution
convergence [20], and this method was therefore selected.
The emperor-selective matching scheme starts by identifying
the highest ranking solution for each generation. This
solution, dubbed the emperor, is then mated with the
remaining top-ranking solutions to produce the desired
number of ospring solutions. A certain amount of overlap
between generations is usually also employed, where a
percentage of the previous generation top-ranking individuals
are kept on to the next generation. This is done to maintain
genetic diversity and ensure that the solution set does not
degrade if all offspring in a generation should rank lower than
the previous generation. In this thesis an overlap of 10 % is
used, as it was found to give acceptable progress results.
4.8 Solution Cross-Over Function
The cross-over function, used for producing ospring
solutions, selects antenna segments from either parent by the
following random selection:
• By a 31% probability, the wire coordinates are copied from
the first parent
• By a 31% probability, the wire coordinates are copied from
the second parent
• By a 31% probability the wire is generated as a mean
between the coordinates used by the rst and second parent. •
By a 7% probability, the wire is subject to a randomization,
where the coordinates are replaced with a 0..1 square
probability distribution random coordinate regardless of
parent coordinates.
4.9 Fitness Evaluation
In a multi-objective genetic algorithm, fitness evaluation is
central to the progress of the optimization. In this thesis, the
two fitness determining factors are the radiation pattern shape
and the impedance matching of the antenna. These factors are
evaluated separately as two parameters, pattern fitness Pf and
impedance fitness Zf . The overall fitness for each solution is
evaluated as
F = Pf + Zf
4.10 Pattern Fitness
As stated above, the radiation pattern should ideally be
completely rotationally symmetrical, vertically polarized, and
exhibit some gain. To rate the fitness, each solution vertical
gain Av [dBi] is evaluated at center frequency λ0 in
the polar Φ plane, maintaining Θ = 90. This vertical gain data
set is available directly from the NEC simulation. For each
solution:

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Figure 4.5: Φ plane vertical gain Av, Θ = 90 : Fitness rating
of radiation pattern
the maximum gain Avmax, minimum gain Avmin is found, and
the average gain Avmin is calculated. A typical pattern is
shown in figure 4.5.
4.12 Population Size and Termination Criteria
In any genetic algorithm, there is an obvious tradeoff between
evolution speed and search width. With a small population
size, each generation will obviously be simulated quicker
than a large population, since the total time to simulate each
generation
Tgeneration = T individual * Nindividuals.
The solutions in a genetic algorithm with a small population
size will therefore also tend to evolve quicker than a large
one. A small population size may not efficiently explore the
given solution space. Such an algorithm runs the risk of
converging on a sub-optimal local solution, taking an
excessive number of generations to converge on a solution or
being unable to converge on a solution at all[6].
The initial compromise was therefore set at 50 individuals per
generation. This was found to be the largest population size
where algorithm development was still practical. At larger
generation sizes, the time to simulate each generation
considerably hindered algorithm development. As a
validation of the 50 individual generation size, tests were
carried out using larger generation sizes. This did not notably
change the evolution progress, apart from reducing algorithm
progress speed, and the choice was therefore deemed
acceptable. As termination criteria, the fixed number of
generations’ method was chosen. While this is known to be a
suboptimal method from a computational efficiency point of
view, it was found to be acceptable for this problem.
4.13 Tracing And Debugging Tools
As the run-time for this genetic algorithm is in the multi-hour
range, direct feedback of the progress, as well as methods to
perform post-run analysis is needed. Several methods for
assessing progress were developed. The most obvious result
to plot is the best-individual performance, as a function of
generations passed. This gives a clear feedback of the
algorithm evolution progress. Also, impedance matching
ratings and pattern rating progress may be 21 plotted in the
same graph, in order for their individual progress to be
assessed.
Figure 4.7: Typical progress plot, 150 generations elapsed
The optional visualization of each solution output data is also
employed. This allows the fitness rating functions, and
genome antenna wire design to be assessed in real-time. The
visualization makes it possible to catch unexpected behavior
of the fitness functions, or their reaction to unexpected input
from the NEC simulations. As the genetic algorithm will
converge on whatever solutions that give the highest ranking,
it is very important that the rating functions be carefully
debugged. Without these visualization functions, these core
functions would be very difficult to debug. As the genetic
algorithm convergence is highly nonlinear, it is also desirable
to provide means for detailed post-analysis of each run, so
that what appears to be undesirable behavior may be analyzed
and rectied. As an analogy to natural evolution, the genetic
algorithm is therefore fitted with means to create fossil
records at certain intervals. These are complete records of a
generation, stored to separate each 50 generations. After each
run a complete fossil strata is therefore present for analysis,
should this be necessary. After the genetic algorithm
terminates, a 3D surface is plotted which displays individual
rating as a function of generations passed. This allows the
total convergence progress to be assessed.
4.14 Noise Between Generations
In order to keep the genetic algorithm from converging on a
solution which relies too heavily on close tolerances, a certain
amount of noise is added between generations. This makes
sure that solutions may not require unrealistic manufacturing
tolerances. It also avoids convergence on any mathematical
Singularities, should they arise. A random noise with
continuous uniform distribution and with max amplitude of
0.01 mm is added to all coordinates of generated offspring
solutions. A uniform distribution is chosen as a first-order
approximation of the expected error distribution in production

_______________________________________________________________________________________
of a printed antenna. This is caused by a production process
where any position within a tight tolerance is accepted, and
any outliers are discarded.
5. RESULTS
5.1 Genetic Algorithm
The genetic algorithm appears to be functioning as intended.
Antennas are produced within the given mechanical
constraint. There is a clear progress of evolution where initial
solutions can be clearly seen to replace their previous, less fit,
predecessors. As the algorithm is started with a different
random seed for each run, each run is dierent. All runs show
clear progress toward the intended target. It is clear that the
impedance problem is not handled nearly as well as the
radiation pattern problem.
5.1.1 Initial Solutions
The top-ranking solutions of the very rst generations
generally exhibit very poor matching. At this stage, a solution
with acceptable, or close-to acceptable omnidirectionality
may often be found. Note that the antenna is acceptably
omnidirectional, but that the average gain is only around
1.3dBi, varying around 0.5dB. From the 3D diagram it is
noted that this is caused by the radiation pattern being front-
to-back tilted approximately 40 degrees.
5.1.2 Late Solutions
The top-ranking solutions of the final generation generally
still exhibit very poor matching, with little or no improvement
from the initial solutions. At this stage, however, the solution
usually exhibits very good omnidirectionality. This now
exhibits 2.2dBi gain, within a +/- 0.01dB tolerance.
5.2 OBJECTIVES
5.2.1 Radiation Pattern
Radiation pattern optimization works well. The resulting
radiation pattern show a high degree of omnidirectionality,
and would likely to perform well in a real-world application.
The demonstrated omnidirectionality and relative gain is
equal to, or better then what can be expected from a
traditional whip-based antenna design in this type of
application. This objective is considered met.
5.2.2 Antenna matching
Antenna matching has proven di-cult to archive, and the
matching goals have not been met. The resulting antennas
show too poor matching to be usable in a real product. While
it is clear that the genetic algorithm is able to reward
solutions with improved matching performance, these
solutions do not seem to propagate well through the genome.
With the dimensions for our antenna at hand, R = 0.2 m, and
λ = 3 m we get Rr = 0, 035 Ohm. This is a very small value,
and we may therefore expect that such a small dipole would
be a very poor radiator. It should be noted that Herzian
dipoles, when dl ≪ λ, but it gives us a reasonable indication
of performance. By increasing the number of segment in the
algorithm, and hence the antenna length we expect that the
impedance should improve slightly since short antennas have
low impedance. A system that rewards useful SWRs at any
frequency in the band would also likely improve the
algorithms development of matching.
6. CONCLUSIONS
A multi-objective genetic algorithm for creating an
omnidirectional antenna inside the headband of an existing
headset is demonstrated. The algorithm is demonstrated to
show convergence towards the desired solutions. Typical
average gains are shown to start out at 1.3dBi, with a
rotational variation of 0.5dB and end up at 2.2dBi with a
rotational variation of 0.01. This shows that the algorithm is
able to generate antennas with a directional radiation pattern
in close accordance to the design target. The algorithm is not
able to solve the problem of matching the antenna; the
possible reasons for this are discussed in the following
chapter. Polarization optimization is not included but could
be added as a secondary requirement. Several possible
additions to the original scope of the thesis work have been
identified.
7. PRACTICAL LIMITATIONS
Some known limitations in this work are listed below
• Intersected segments are present, even though this violates
the fundamental NEC2 assumptions. A way to avoid this
would be to replace NEC2 with simulation software
which does not suffer from this limitation.
• A model for the end-user head is not included. This is due
to the fact that NEC2 it not able to handle dielectric
bodies well, and it was therefore decided to omit the head
from the model. The antenna designs in this thesis could
be easily tested in real-life without an end-user head, in
order to verify the simulation accuracy. The presence of a
real head is not expected to invalidate any of the prior
results.
• The printed circuit boards for the headset electronics are
also not included. These could easily be simulated by
NEC2, if so desired, but it was believed that they could
safely be omitted in order to speed up the simulations.
Like with the head model, an antenna could be tested in real-
life without printed circuit boards, in order to validate the
antenna simulation results.
8. IDEAS FOR FUTURE IMPROVEMENTS
During the development of this thesis, some ideas for future
developments have been noted. These have not been possible
to investigate during the thesis work, but could be the subject
of future studies.
• A thorough analysis of the problem from a theoretical
point of view could be conducted, extending from the
basic review above. With the recent results provided by
Gustafsson et. al., it should be able to theoretically
establish the fundamental limitations present for a thin
antenna of this shape [9]. This may establish if the

_______________________________________________________________________________________
problems encountered are due to fundamental physics or
merely technical limitations of the algorithm. A careful
study of the recent advances in this field may additionally
provide further insight into possible ways to avoid the
most severe limitations, and ultimately provide a more
successful antenna design.
• A different genome which would allow complex
structures to better transfer between solutions could be
investigated. This should allow matching structures to
better survive between generations and cross-overs and
may also provide an improved stability of the matching
solutions. At the same time a corresponding cross-over
function could be investigated. A study could be
conducted of the feasibility of different genomes and their
cross-over functions described in recent literature, and
their suitability to the problem on-hand. A basic literature
study does not present a great deal on the subject which is
directly applicable to this problem. The two-dimensional,
small size, nature of the problem appears to make the
subject relatively rare.
• A fitness rating rewarding vertical polarization could be
added. This would allow for a shift towards vertical
polarization in the final antennas, should the specification
be changed to request this.
• The termination criteria could be updated with suitable
fitness-based termination criteria, should the major
obstacle of impedance fitness rating be overcome. This
would allow the time to convergence to be assessed in
greater detail and most likely result in a shorter average
time to convergence [19].
• Finally, different weighting functions of the antenna
fitness parameters could be considered. While the
weighting functions have been the subject of considerable
work in this study, without much progress, it cannot be
completely ruled out that it may be possible to improve
them further.
9. REFERENCES
[1] D. Marcano and F. Duran, “Synthesis of linear and planar
arrays using genetic algorithms,” in Electromagnetic
Optimization by Genetic Algorithms, 1999, pp. 157-180.
[2] E. E. Altschuler and D. S. Linden, “Design of wire
antennas using genetic algorithms,” in Electromagnetic
Optimization by Genetic Algorithms, 1999, pp. 211-248.
[3] D. S. Linden, “Rules of thumb for ga parameters, ga
monitoring, ga parameter optimization, and enhancement of
ga e-ciency,” in Electromagnetic Optimization by Genetic
Algorithms, 1999, pp. 67-94.
[4] E. E. Altshuler, “Electrically small self-resonant wire
antennas optimized using a genetic algorithm,” in IEEE
transactions on antennas and propagation, vol. 50 no. 3,
March
2002, pp. 297-300.
[5] A. S. James Dietrich, “Automating nec2 with matlab for
antenna analysis and design,” inProceedings of the 2002
Canadian Conference on Electrical and Computer
Engineering, 2002, pp. 342-346.
[6] Y. R. Tsoy, “The inuence of population size and search
time limit on genetic algorithm," in Proceedings KORUS
2003, vol. 7, June 2003, pp. 181-187.
[7] L. J. Chu, “Physical limitations of omni-directional
antennas,” in Applied physics, vol. 19, May 1948, pp. 1163-
1175.
[8] H. A. Wheeler, “Fundamental limitations of small
antennas,” in Proceedings of the I.R.E,vol. 35(12), December
1947, pp. 1479-1484.
[9] M. Gustafsson, C. Sohl, and G. Kristensson, “Illustrations
of new physical bounds on linearly polarized antennas,” in
IEEE transactions on antennas and propagation, vol. 57
no. 5, May 2009, pp. 1319-1327.
[10] S. M. Jain, S. K. Koul, A. Basu, and M. P. Abegaonkar,
“Recongurable conformalantenna array for non-rigid
platforms,” in Proceedings of Asia-Pacic Microwave
Conference2010, 2010, pp. 20642067.
[11] I. T. Union, “Bs.450 : Transmission standards for fm
sound broadcasting at vhf,” 2001,http://www.itu.int/rec/R-
REC-BS.450-3-200111-I/en.
[12] C. Inc, “Castronic volume ex pcb,” 2003-2007,
castronic.com/pcb_volumeex.htm.
[13] D. K. Cheng, Field and Wave Electromagnetics. Addison
Wesley, 1989. ISBN 0-201-52820-7
[14] N. K. Shrauger and K. L. Taylor, “Initial vhf propagation
results using xeledop techniques and low antenna heights,”
1966, www.dtic.mil/cgi-bin/GetTRDoc?AD=AD0653609.
[15] R. C. Hansen, “Fundamental limitations in antennas,” in
Proceedings of the IEEE, vol. 69(2), February 1981, pp. 170-
182.
[16] G. Burke and A. Poggio, “Numerical electromagnetics
code (nec) - method of moments,” 1981, part II: Program
description - code.
[17] C. R. Darwin, On the origin of species by means of
natural selection. London, JohnMurray, 1859.
[18] J. H. Holland, Adaptation in Natural and Artificial
systems. University of Michiganpress, 1975. ISBN
9780262581110
[19] Y. Rahmat-Samii and E. Michielssen, Electromagnetic
Optimization by Genetic Algorithms.Wiley, 1999. ISBN 0-
471-29545-0
[20] B. K. Yeo and Y. Lu, “Array failure correction with a
genetic algorithm,” in IEEEtransactions on antennas and
propagation, vol. 47 no. 5, May 1999, pp. 823828.
10. BIOGRAPHIES
Aatish Gandotra, a student of Electronics
and Communication Engineering in his final
year with deep interest in telecommunication
and networking.
Publications :- 1. Replication of attacks in
wireless sensor network using NS2.
Tejaswi Singh, a student of computer science
engineering in his final year with a knack for
network security.
Publications :- 1. Replication of attacks in
wireless sensor network using NS2.

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