Determining an Optimal Antenna Placement using a Genetic Algorithm
M. Jeffrey Barney*(1), Jamie M. Knapil (1), and Dr. Randy L. Haupt(2)
(1) Remcom, Inc, State College, PA, USA
(2) The Applied Research Lab, State College, PA, USA
E-mail: Jamie.Knapil@remcom.com
Introduction
Determining the optimal location for an antenna on a platform is limited by the humans
involved. Best guesses are based on previous experience and rules of thumb. As
platforms become more complicated, determining the placement for antennas becomes an
increasing challenge. This paper looks at XFdtd's, a Finite-Difference Time-Domain
solver, implementation of a Genetic Algorithm (GA) for its effectiveness in determining
the optimal placement of an antenna on a platform.
Background
XFdtd uses the Finite-Difference Time-Domain (FDTD) method [1] to solve general
electromagnetic problems. 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
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.
XFdtd's GA implementation was first verified with an analytic model with a known
solution. After the results were verified, a more complicated model, with an unknown
solution, was optimized. The analytic model consisted of a dipole located over a circular
plate (Figure 2). It used a design frequency of 1.5 GHz, wavelength of 200mm. The
vertically polarized short dipole has a length of 19mm. The dipole was placed over a
circular PEC plate a distance of 90mm. The plate had a 1000mm radius and was 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 is the
obvious solution. An initial test was run with a centered dipole and a minimum gain of
4.76dBi was computed. The grid contained 0.325 million FDTD cells, CalcFDTD used
52MB, and it took 49s to run the initial test.
978-1-4244-3647-7/09/$25.00 ©2009 IEEE
C++GA
Initial population = 8
Movable structure and acceptable regions
mutation rate = 15%
C++GA
Translates GA chromosome into
XFdtd design variables
XFdtd
Builds model
Perform s gridding
Does calculations
C++GA
Performs natural selection, mating,
and mutation, then iterates
Figure 1: Flowchart for GA process
dipole --+
I
!
19mm
1
90mm
PEe plate
I
1
I
+-t- - - - - - - - -
2000 mm
I
----------+~
Figure 2: Analytic geometry
Results
The cost threshold was set at 4.5dBi and the optimization was set to optimize 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 ran in 22min.
A crude model of a ship was generated inside XFdtd and is shown in Figure 3.
Dimensions are as follows:
• The smoke stack has a 1m radius, is 4m long, 3.577m tall
• The box is 3 x 3 x 1.5m
• The distance between the base of the smoke stack and box is '""7.24m
• The deck is a maximum of 8.3m wide and 17.7m long
• The vertically polarized monopole is O.09375m tall which is a quarterwavelength at 800MHz
Figure 3: Crude model of ship
An initial test was run with the monopole located half way between the smoke stack and
box. This created a discretized model containing 0.839 million FDTD cells. CalcFDTD
used 80MB and took 3min 30sec to determine a solution. The computed radiation pattern
had values ranging from 5.8dBi to 41.9dBi.
For the optimization, 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 omni-directional pattern will be found. A
cost threshold of 20dBi was set.
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 ran in 29 min. The
optimal location found is represented by the yellow dot in Figure 4. The optimized far
zone radiation pattern ranges from 21.2dBi to 54.8dBi. The full 3D pattern can be seen
in Figure 5. Figure 6 compares a slice around theta = 75 degrees (theta is measured from
the z-axis) for the pattern from the optimal location, drawn in green, as well as from the
monopole centered between the smoke stack and box, drawn in blue.
Figure 4: Optimal location of monopole
Figure 5: Optimized far zone radiation pattern
Gain vs. Angle
90
135
45
225
315
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.
Conclusions
XFdtd's GA implementation successfully found optimal solutions for the two models
used in this paper. Defining the antenna to optimize and the acceptable regions where
the antenna can be located was done through the Scripting API. Also, the cost was
determined in a script function and passed to the GA for use in natural selection.
References
[1] K.S. Kunz and R.J. Luebbers, The Finite Difference Time Domain Methodfor
Electromagnetics, 1st edition, CRC Press, 1993.
[2] R.L. Haupt and S.E. Haupt, Practical Genetic Algorithms, 2nd edition, New York:
John Wiley & Sons, 2004.