Download Optimization of Aperiodically Spaced Antenna Arrays for Wideband

Keywords: Genetic algorithm, particle swarm optimization, aperiodic
array, space-tapered array, helix antenna, wideband
Benjamin Baggett
M.S. Thesis Project, Virginia Tech
Advisor: Dr. Timothy Pratt
The Goal
 Design an aperiodically spaced antenna array which
satisfies the following:
 Requires fewer elements than periodic counterpart

Cheaper and lighter
 Electronic scan range of ±45° in azimuth
 Achieve approx. 2-to-1 operational bandwidth
 Achieve comparable results to periodic array in terms of:



Sidelobe level
3-dB beamwidth
Directivity
The Optimization
 Optimization algorithms will be utilized to search the
solution space for the optimal set of element locations
 Genetic Algorithm
 Particle Swarm Optimization
 Solution will be optimized for a ±45° scan
 Ensures sidelobes will be lower and gain will be higher
during broadside case
 Fitness function will be based on a combination of
sidelobe level, 3-db beamwidth, and directivity
Genetic Algorithm
 Optimization algorithm which
simulates evolutionary biology to
obtain an optimal solution to a
problem
 Semi-heuristic method
Initialize 1st Generation
Evaluate Fitness of
each Chromosome
 Each solution is represented by a
chromosome
 Chromosomes evolve through
reproduction, mutation, and
natural selection
 Each chromosome is assigned a
“fitness”

The more “fit” chromosomes survive
and repeat the process
Most “Fit”
Chromosomes Survive
(Natural Selection)
Is Desired Fitness
Achieved?
No
Yes
Optimal Solution
New Chromosomes
Created
(Next Generation)
Crossover / Mutation
(Reproduction)
Particle Swarm Optimization
 Optimization algorithm that
simulates the “swarming” nature of
bees when searching for food
 Semi-heuristic method
 Utilizes both local search and


Each particle (bee) has an initial
location and velocity vector
Bees (particles) are “pulled” towards
optimal solutions that have
previously been found by:
 The Individual bee
 Other bees in the swarm
Eventually bees “swarm” around and
converge to the optimal solution
 Easier to code and less book
keeping required than the Genetic
Algorithm (GA)
Parameter 2
global search methods

Original Velocity
Velocity toward group best
Velocity toward personal best
Resultant velocity
New
Position
Initial
Position
Initial
Position
Entire Swarm
Best Position
Particle 1’s
Best
Position
Particle 2’s
Best
Position
Parameter 1
New
Position
Issues to Consider
 Antenna Element Pattern
 Axial-mode helix
 Original design
 Mutual Coupling Effects
 Simulated results
 Antenna Feed Network
 Complicated for aperiodic array
Helix Antenna Element
 Using axial-mode helix antenna as
element
 Provides end-fire operation of
element
 Element requires:




2-to-1 Bandwidth
90° Half-Power Beamwidth (HPBW)
Circular polarization
 Traveling Wave Antenna
Helix element must be designed using
FEKO software package
 Element must be designed
 Radiator design problem
 Designed FEKO software package
Mutual Coupling Analysis
 Array design is optimized with a minimum element
spacing of λ at the highest frequency
 Ensures 2-to-1 operation bandwidth of array
 Mutual coupling issue becomes less severe with λ/2 spacing
 FEKO Mutual Coupling Analysis
 Simulate array of helix antenna elements spaced λ/2 apart
 Check input impedance and far field pattern as array is
scanned


Makes sure coupling is not a major factor!
Test over operational bandwidth to ensure 2-to-1 bandwidth
capabilities
Feeding Network
 Not part of the scope of this project
 Complicated because of the variable
element spacing
 Would require additional phase
shifters or varying cable lengths to
compensate for phase difference
between each element
 Assumed to be a “black box” corporate
feed
 Matching network assumed to exist
 Future project?
Deliverables
 Optimized array design will be presented for both:
 Genetic Algorithm (GA)
 Particle Swarm Optimization (PSO)
 GA and PSO arrays will be compared and final design will
be chosen
 Chosen design will be compared to periodic array
counterpart
 Should achieve comparable performance to periodic array
 Aperiodic array will require:
 Fewer elements / fewer attenuators / fewer phase shifters
 Cheaper
 Lighter
 Great option for very high frequency applications (less compact)
Questions?