Paper ID# 901225
USING A GENETIC ALGORITHM TO DETERMINE AN OPTIMAL POSITION FOR AN ANTENNA
MOUNTED ON A PLATFORM
Jamie M. Knapil Infantolino (1), M. Jeffrey Barney (1), and Randy L. Haupt (2)
(1) Remcom, Inc, State College, PA, USA
(2) The Applied Research Lab, State College, PA, USA
ABSTRACT
Determining an optimal position of an antenna on a
platform is not always intuitive. This paper examines the
implementation ofa Genetic Algorithm (GA) within XFdtd,
a Finite Difference Time Domain (FDTD) solver, for its
effectiveness in determining an optimal antenna position
when compared to a bruteforce method.
XFdtd uses the FDTD method [1J to solve general
electromagneticproblems. Built into XFdtd is the concept
of Feature Based Modeling (FBM), which uses relative
coordinate systems to position antennas in a geometry in
relation to other parts. The GA, written in C++, is
available to XFdtd's Scripting API Through scripting a
user specifies the antenna to move and provides bounded
regions where the antenna can be located for maximum
efficiency.
INTRODUCTION
Adding new wireless systems to existing platforms is
difficult due to physical and electromagnetic constraints.
Finding space on an already crowded platform is difficult.
Blockage, scattering, and interference with other
communications and radar systems must be taken into
account. For instance, jammers on a vehicle used to
disable improvised explosive devices (lED) can interfere
with the tactical communication systems on that same
vehicle as well as other nearby vehicles. Designers of these
jamming systems need a way to optimally place the
~ammer antennas on the platform while minimizing the
Im~act on tactical communication systems. Traditionally,
designers use experience and intuition to place the
antennas on a platform. The large number of wireless
systems on a platform, interactions between the antenna
and its environment, and complex requirements like low
radar cross section, contribute to the complexity of the
antenna placement problem.
~
full wave electromagnetics model like FDTD is required
In order to understand the antenna's behavior in the
presence of the platform and environment. An exhaustive
search of all combinations of the antenna shape, size,
material, and location is not practical, because an antenna
978-1-4244-5239-2/09/$26.00 ©2009 IEEE
designer must conduct many computationally and time
intensive simulations and evaluate each one against the
others to arrive at the best performing antenna. Not only is
the antenna design process time consuming and laborious,
but there are no guarantees that the design chosen is
optimal.
The Genetic Algorithm (GA) is a global optimization
computer program that automatically guides the engineer
towards the best performing antenna design for an
application. The GA begins with some random guesses for
the location of an antenna on a platform and proceeds to
finding an optimal location using rules based upon
genetics and natural selection.
This paper presents results from incorporating a GA in the
FDTD algorithm XFdtd in order to optimally place
antennas on platforms. XFdtd provides the needed
accuracy of the electromagnetics model while the GA is
capable of finding an excellent solution within a
reasonable run time. Results for the optimal placement of a
jamming antenna on a Humvee are much better than the
results obtained from the best intuitive guess.
GENETIC ALGORITHM
A GA works by evaluating a cost function to determine the
optimal solution to a problem. The cost function, in this
case, consists of the electromagnetic functions which are
to be minimized or maximized. Some examples of cost
~unctions are radiation pattern, radiation efficiency, input
Impedance, and S parameters. Some of these functions
may also involve manufacturing costs or other nonelectromagnetic factors such as antenna placement
location, frequency, dielectric value, or perhaps the cost of
a material used in the antenna design. Using a GA can
maximize or minimize the cost function that employs real
and integer variables in calculating the cost. Optimization
algorithms that minimize real and integer values are
known as mixed integer optimization algorithms, so this
GA is known as a mixed integer GA [2]. In order to
increase the GA's flexibility, all variables are mapped to
continuous values between 0 and 1.
The population
represented by;
p=
npop x nvar matrix for this GA is
vI,1
VI ,2
v 2,1
V 2 ,2
VI,nvar
v npop ,1
where
with 0 ::; vm,n
::;
parent #1= Vm,l
parent#2 =Vn,l
mask = 0
Vnpop,nvar
vm,n = variable
n
In
chromosome
m
offspring = Vn,l
V m,2
Vm,3
Vm,4
V m,5
V m,6
V m,7
V m,8
V n,2
V n,3
Vn,4
Vn,5
Vn,6
V n,7
Vn,8
0
1
0
0
1
0
1
Vn,2
Vm,3
Vn,4
V n,5
V m,6
Vn,7
Vm,8
1. Each row is a chromosome, and the
values are initially created by a uniform random number
generator. A continuous variable, vm,n is converted to
either a real variable, x n' an integer, In, or a binary digit,
s;
Xn
In
exploration of the cost surface than other approaches to
crossover [2], so it is implemented in this algorithm. First,
a random binary mask is created. A 1 in the mask column
means the offspring receives the variable value in
parent#1. If it has a 0, then the offspring receives the
variable value in parent#2.
= x max
= rounddown
-
xmin
I max -
+ Xmin
I min + 1 Vm,n + I min
vm,n
b; = round vm,n
Where min and max represent variable bounds specified by
the GA. X m i n ::; Xn ::; X m a, rounddown is a function that
rounds to the next lowest integer, and round is a function
that rounds to the nearest integer. A grouping of binary
digits forms a gene in the binary GA. The benefit of this
approach is that all the scaling, quantizing, and rounding
happen in the cost function, so the GA operates
independent of the variable type. There is no need for a
binary GA, a real GA, and a mixed integer GA, because
the operators work with any combination of variable types.
A chromosome can have any mix of real, integer, and
binary variables. For instance, the chromosome may
contain the number of antennas (integer), the location of
the antennas in three-dimensional space (constrained
continuous), the material properties of a nearby object
(binary), and the location of a handrail.
Chromosome survival may be determined in a number of
different ways. Here, the top 50% of the chromosomes
survive to be part of the mating pool. Tournament
selection with two chromosomes per tournament is used.
Roulette wheel selection with rank ordering would give
nearly equivalent results [2].
At this point, mating between two selected chromosomes
can be done using one of the many different real GA or
binary crossovers [2]. Uniform crossover provides a larger
In this approach, only one offspring is created for every
two parents selected. This type of crossover results in a
diversity of values if the values are binary, but only
interchanges values between chromosomes if the values
are integer or continuous. Consequently, the mutation
introduces new values within the population of continuous
values. A continuous crossover would also work in this
algorithm.
One approach to mutation is to randomly select variables
in the population and replace them with uniform random
values. Another approach is to add a random correction
factor. The correction factor may be created by
multiplying each element within a chromosome by a
random number ( -1 s firm s 1) and multiplying the entire
chromosome by a mutation factor ( 0 ::; a, S 1).
where rem is the remainder function (digits to the left of
the decimal point are dropped). This type of mutation
modifies the entire chromosome rather than a single
variable.
GENETIC ALGORITHM IN XFDTD
XFdtd' s theory is based on the FDTD method presented by
Kunz and Luebbers [1]. Built into XFdtd is the concept of
Feature Based Modeling (FBM), which allows relative
coordinate system definitions among parts in a model. The
GA [2], written in C++, is available through XFdtd's
Scripting API. Through scripting, a user defines the
antenna and the acceptable regions on a platform where
the antenna can be located.
This GA has a population size of 8 and a mutation rate of
15%. During an optimization, a single region from the list
of possible regions, as well as a position on that region, are
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randomly selected. The resulting spatial location is where
the antenna is placed for the next cost function evaluation.
Each cost function evaluation is a call to a script function
that executes the calculation engine, calculates the cost
(antenna pattern, impedance, bandwidth, etc.) and passes
that value back to the GA as the cost. The GA keeps 50%
of the best chromosomes then performs mating and
mutation to find the next generation. This process
continues until an acceptable solution is found or a set
number of iterations are performed. Figure 1 is a
flowchart of the process.
dipole --+
I
1
19 mm
1
90 =
j
PEe plate
1
I
+
, -- - - - - - -
C++ GA
Initial pop ulation = 8
Movab le structure and acceptab le regions
mut ation rate = 15%
2000 rnm
---------t,1
Figure 2: Analytic geometry
Results
1
IscriPti ng Language
Passes cost to GA
The cost threshold was set at 4.5dBi and the GA optimized
for a maximum cost. The cost function executed XFdtd's
calculation engine (CalcFDTD) which calculated the far
zone gain. The minimum gain was returned as the cost.
By maximizing the minimum gain, an omni-directional
pattern was found. After 29 evaluations of the cost
function, the GA reached its cost threshold at 4.53dBi.
The associated dipole location was at (le-24, 1.8) mm.
The optimization occurred in 22min.
1
SIDPMODEL
C++GA
Translates GA chromoso me into
XFdtd design variables
1
XFdtd
Builds model
Performs gridding
Does calculations
1
1Performs natural
C++GA
selection. mating..1
A crude model of a ship was generated inside XFdtd and is
shown in Figure 3. The dimensions were as follows:
and mut ation. then iterates
Figure 1: Flowchart for GA process
•
DIPOLE OVER METAL PLATE
•
•
XFdtd's GA implementation was first verified with an
analytic model with a known solution before proceeding to
a more complicated model, with an unknown solution. The
analytic model consisted of a dipole located over a circular
plate (Figure 2). It used a design frequency of 1.5 GHz
with a wavelength of 200mm. The vertically polarized
short dipole had a length of 19mm. The dipole was placed
over a circular PEC plate a distance of 90mm. The plate
had a 1000mm radius and is centered at (0,0).
The dipole was constrained to being directly over the plate.
The optimization attempted to find a position that
produced an omni-directional pattern. The center of the
plate was the obvious solution. An initial test was run with
a centered dipole and a minimum gain of 4.76dBi is
computed. The grid contains 0.325 million FDTD cells,
the calculation engine uses 52MB, and it took 49s to run
the initial test.
•
•
The smoke stack had a 1m radius, was 4m long,
3.577m tall
The box was 3 x 3 x 1.5m
The distance between the base of the smoke stack
and box was - 7.24m
The deck was a maximum of 8.3m wide and
17.7m long
The vertically polarized monopole was 0.09375m
tall which is a quarter-wavelength at 800MHz
Figure 3: Crude model of ship
An initial test started with the monopole located half way
between the smoke stack and box. The discretized model
contained 0.839 million FDTD cells. CalcFDTD used
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Gain vs An91e
90
80MB and took 3min 30sec to determine a solution. The
computed radiation pattern had values ranging from 5.8dBi
to 41.9dBi.
The local origin of the monopole was constrained to the
top of the deck, excluding regions around the smoke stack
and box. The cost function executed CalcFDTD, analyzed
the far zone pattern, and returned the minimum gain value
found. Again, by maximizing the minimum gain, an omnidirectional pattern was found. The cost threshold was
20dBi.
After 22 evaluations of the cost function, the threshold was
reached at 21.2dBi when the monopole was placed in front
of the smokestack. The optimization took 29 min. The
optimal location is represented by the red dot in Figure 4.
The optimized far zone radiation pattern ranged from
21.2dBi to 54.8dBi. The full 3D pattern can be seen in
Figure 5. Figure 6 compares a conical surface (theta=75
degrees from the vertical axis) from the optimal pattern,
drawn in green, with the same conical surface from the
starting pattern, drawn in blue.
180
270
Figure 6: Optimized vs unoptimized location comparison
This optimization found that placing the monopole in front
of the smoke stack generated a more omni-directional
pattern and produced greater gain at nearly all angles when
compared to a location between the smoke stack and box.
RESULTS
The GA was used to find an optimal location for an lED
jammer antenna on a Humvee. The first location was
chosen to mimic an antenna that was already located on
the platform. Figure 7 depicts the first guess for the
optimal antenna location. This was the first guess used to
initialize the GA.
Figure 4: Optimal location of monopole
Figure 7: First Guess for Optimal Antenna Location
z
x
Figure 5: Optimized far zone radiation pattern
The goal of the jammer was to project as much power on
the target (the suspected lED) as possible. This can be
simulated using XFdtd. It was assumed the lED was close
to the ground. Figure 8 depicts the results of the first
guess for optimal antenna location. XFdtd indicates that
very little energy from the transmitter reached the ground.
This seed was placed into the initial GA population to see
if a better location for the antenna could be found. By the
sixth generation, all of the locations that were on the front
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bumper were discarded. This seems counterintuitive, but
the GA determined it was not the optimal location.
It turns out that the optimal location was on the front hood
and not on the front bumper. This might be due to the fact
the air intake acted like a reflector. The second most
optimal location was on the driver side front bumper.
FUTURE WORK
.35
The next step is to start using more complex geometries
with the GA. The Humvee is a simple model compared to
other military applications. For example, a platform that
already has a dozen antennas on it has more interactions
than the Humvee. Further investigation is needed to
determine how complex of a geometry the GA can handle.
·28
Figure 8 Cross Section SSE of First Guess
Antenna Location
The GA ran 13 generations. The optimal location found is
depicted in Figure 9 with the power down range depicted
in Figure 10.
One of the problems with the current GA is runtime
limitations. This GA takes 13 generations for a total of 36
hours to complete. This is an unrealistic runtime for some
applications. One way to help with the runtime is to use a
Graphic Processor Unit (GPU) to do the calculations.
More research is required to better utilize these devices;
initial studies have shown speed ups of 20X, and speed ups
of 30X-50X are theoretically possible.
The Humvee
example took 2 hours with the use of a GPU, making this
technology more practical.
CONCLUSIONS
The GA was useful in determining the location for an lED
jammer antenna on a platform like a Humvee. It provided
an answer with very little guess work.
The GA was also able to account for interactions with
other elements of the platform. The Humvee has irregular
surfaces which could impact the performance of an
antenna due to interactions between the antenna and the
environment. XFdtd was able to model these interactions
properly and then feed the GA the correct data.
Figure 9: Optimal Location Found by GA
It has been demonstrated that the GA can produce an
optimal location for an antenna on a platform. It takes
away some of the guess work that is currently employed
within this field. The GA can be used to solve problems,
such as designing effective jammers, faster and more
efficient than what is being used currently.
REFERENCES
-70
-56
Figure 10: Power down range for Optimally Placed
Antenna
[1] K.S. Kunz and RJ. Luebbers, The Finite Difference
Time Domain Method for Electromagnetics, 1sl
edition, CRC Press, 1993.
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[2] R.L. Haupt and S.E. Haupt, Practical Genetic
Algorithms, 2nd edition, New York: John Wiley &
Sons, 2004.
[3] R.L. Haupt, "A Mixed Integer Genetic Algorithm for
Electromagnetics Applications," IEEE AP-S
Trans., Vol. 55, No.3, Mar 2007.
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