1. Benjamin Baggett M.S. Thesis Project, Virginia Tech Advisor: Dr. Timothy Pratt Keywords: Genetic algorithm, particle swarm optimization, aperiodic array, space-tapered array, helix antenna, wideband

2. 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

3. 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

4. Genetic Algorithm Optimization algorithm which simulates evolutionary biology to obtain an optimal solution to a problem Semi-heuristic method 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 Initialize 1 st Generation Most “Fit” Chromosomes Survive (Natural Selection) Evaluate Fitness of each Chromosome Crossover / Mutation (Reproduction) New Chromosomes Created (Next Generation) Optimal Solution Is Desired Fitness Achieved? Yes No

5. Particle Swarm Optimization Optimization algorithm that simulates the “swarming” nature of bees when searching for food Semi-heuristic method Utilizes both local search and global search methods 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) Particle 1’s Best Position Particle 2’s Best Position Entire Swarm Best Position Initial Position New Position Original Velocity Velocity toward group best Velocity toward personal best Resultant velocity Parameter 1 Parameter 2

6. Issues to Consider Antenna Element Pattern Axial-mode helix Original design Mutual Coupling Effects Simulated results Antenna Feed Network Complicated for aperiodic array

7. 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

8. 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

9. 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?

10. 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)

11. Questions?