Randy L. Haupt

Thinned arrays using genetic algorithms

Large arrays are difficult to thin in order to obtain low sidelobes. Traditional statistical methods of aperiodic array synthesis fall far short of optimum configurations. Traditional optimization methods are not well suited for optimizing a large number of parameters or discrete parameters. This paper presents how to optimally thin an array using genetic algorithms. The genetic algorithm determines which elements are turned off in a periodic array to yield the lowest maximum relative sidelobe level. Simulation results for 200 element linear arrays and 200 element planar arrays are shown. The arrays are thinned to obtain sidelobe levels of less than -20 dB. The linear arrays are also optimized over both scan angle and bandwidth. >

Genetic Algorithms in Electromagnetics

Preface. Acknowledgments. 1. Introduction to Optimization in Electromagnetics. 1.1 Optimizing a Function of One Variable. 1.1.1 Exhaustive Search. 1.1.2 Random Search. 1.1.3 Golden Search. 1.1.4 Newtons Method. 1.1.5 Quadratic Interpolation. 1.2 Optimizing a Function of Multiple Variables. 1.2.1 Random Search. 1.2.2 Line Search. 1.2.3 Nelder-Mead Downhill Simplex Algorithm. 1.3 Comparing Local Numerical Optimization Algorithms. 1.4 Simulated Annealing. 1.5 Genetic Algorithm. 2. Anatomy of a Genetic Algorithm. 2.1 Creating an Initial Population. 2.2 Evaluating Fitness. 2.3 Natural Selection. 2.4 Mate Selection. 2.4.1 Roulette Wheel Selection. 2.4.2 Tournament Selection. 2.5 Generating Offspring. 2.6 Mutation. 2.7 Terminating the Run. 3. Step-by-Step Examples. 3.1 Placing Nulls. 3.2 Thinned Arrays. 4. Optimizing Antenna Arrays. 4.1 Optimizing Array Amplitude Tapers. 4.2 Optimizing Array Phase Tapers. 4.2.1 Optimum Quantized Low-Sidelobe Phase Tapers. 4.2.2 Phase-Only Array Synthesis Using Adaptive GAs. 4.3 Optimizing Arrays with Complex Weighting. 4.3.1 Shaped-Beam Synthesis. 4.3.2 Creating a Plane Wave in the Near Field. 4.4 Optimizing Array Element Spacing. 4.4.1 Thinned Arrays. 4.4.2 Interleaved Thinned Linear Arrays. 4.4.3 Array Element Perturbation. 4.4.4 Aperiodic Fractile Arrays. 4.4.5 Fractal-Random and Polyfractal Arrays. 4.4.6 Aperiodic Refl ectarrays. 4.5 Optimizing Conformal Arrays. 4.6 Optimizing Reconfi gurable Apertures. 4.6.1 Planar Reconfi gurable Cylindrical Wire Antenna Design. 4.6.2 Planar Reconfi gurable Ribbon Antenna Design. 4.6.3 Design of Volumetric Reconfi gurable Antennas. 4.6.4 Simulation Results-Planar Reconfi gurable Cylindrical Wire Antenna. 4.6.5 Simulation Results-Volumetric Reconfi gurable Cylindrical Wire Antenna. 4.6.6 Simulation Results-Planar Reconfi gurable Ribbon Antenna. 5. Smart Antennas Using a GA. 5.1 Amplitude and Phase Adaptive Nulling. 5.2 Phase-Only Adaptive Nulling. 5.3 Adaptive Reflector. 5.4 Adaptive Crossed Dipoles. 6. Genetic Algorithm Optimization of Wire Antennas. 6.1 Introduction. 6.2 GA Design of Electrically Loaded Wire Antennas. 6.3 GA Design of Three-Dimensional Crooked-Wire Antennas. 6.4 GA Design of Planar Crooked-Wire and Meander-Line Antennas. 6.5 GA Design of Yagi-Uda Antennas. 7. Optimization of Aperture Antennas. 7.1 Refl ector Antennas. 7.2 Horn Antennas. 7.3 Microstrip Antennas. 8. Optimization of Scattering. 8.1 Scattering from an Array of Strips. 8.2 Scattering from Frequency-Selective Surfaces. 8.2.1 Optimization of FSS Filters. 8.2.2 Optimization of Reconfi gurable FSSs. 8.2.3 Optimization of EBGs. 8.3 Scattering from Absorbers. 8.3.1 Conical or Wedge Absorber Optimization. 8.3.2 Multilayer Dielectric Broadband Absorber Optimization. 8.3.3 Ultrathin Narrowband Absorber Optimization. 9. GA Extensions. 9.1 Selecting Population Size and Mutation Rate. 9.2 Particle Swarm Optimization (PSO). 9.3 Multiple-Objective Optimization. 9.3.1 Introduction. 9.3.2 Strength Pareto Evolutionary Algorithm-Strength Value Calculation. 9.3.3 Strength Pareto Evolutionary Algorithm-Pareto Set Clustering. 9.3.4 Strength Pareto Evolutionary Algorithm-Implementation. 9.3.5 SPEA-Optimized Planar Arrays. 9.3.6 SPEA-Optimized Planar Polyfractal Arrays. Appendix: MATLAB(r) Code. Bibliography. Index.

Fractal antenna engineering: the theory and design of fractal antenna arrays

A fractal is a recursively generated object having a fractional dimension. Many objects, including antennas, can be designed using the recursive nature of a fractal. In this article, we provide a comprehensive overview of recent developments in the field of fractal antenna engineering, with particular emphasis placed on the theory and design of fractal arrays. We introduce some important properties of fractal arrays, including the frequency-independent multi-band characteristics, schemes for realizing low-sidelobe designs, systematic approaches to thinning, and the ability to develop rapid beam-forming algorithms by exploiting the recursive nature of fractals. These arrays have fractional dimensions that are found from the generating subarray used to recursively create the fractal array. Our research is in its infancy, but the results so far are intriguing, and may have future practical applications.

Optimized Element Spacing for Low Sidelobe Concentric Ring Arrays

It is described how to optimize the element placement in a concentric ring array to obtain the lowest maximum sidelobe level at boresight.

Optimum population size and mutation rate for a simple real genetic algorithm that optimizes array factors

There has been an explosion of papers describing applications of a genetic algorithm (GA) to electromagnetics problems. Most of the work has followed traditional GA philosophy when choosing the population size and mutation rate of the genetic algorithm. This paper reports the results of experiments to determine the optimum population size and mutation rate for a simple real genetic algorithm. The choice of population size and mutation rate can cause the run time of the GA to vary by several orders of magnitude. The results of this investigation show that a small population size and relatively large mutation rate is far superior to the large population sizes and low mutation rates that is used by most of the papers presented in the electromagnetics community and by the GA community at large. The results of the numerical experiments presented in this paper suggest that the best mutation rate for GAs lies between 5 and 20% while the population size should be less than 16.

Antenna Design With a Mixed Integer Genetic Algorithm

Antenna design variables, such as size, have continuous values while others, such as permittivity, have a finite number of values. Having both variable types in one problem requires a mixed integer optimization algorithm. This paper describes a genetic algorithm (GA) that works with real and/or binary values in the same chromosome. The algorithm is demonstrated on designing low side-lobe phase tapers, circularly polarized patch antennas, and identically thinned subarrays

Interleaved thinned linear arrays

This paper presents three approaches to improving the efficiency of an array aperture by interleaving two arrays in the same aperture area. The interleaved arrays have aperiodic spacings that are integer multiples of a set minimum spacing and are optimized to reduce the maximum sidelobe level. Fully and partially interleaved sum arrays operating at the same frequencies are demonstrated as well as interleaved sum and difference arrays for a monopulse system. A genetic algorithm is used to optimize arrays of isotropic point sources as well as arrays of dipoles modeled using the method of moments. Narrow beamwidths are possible while avoiding high sidelobes. The available aperture area is efficiently used.

Optimized Weighting of Uniform Subarrays of Unequal Sizes

Amplitude weighting at the subarray outputs alone causes grating lobes in array factors. An approach that disrupts the periodic quantization by dividing the array into subarrays of unequal sizes and amplitude weighting at the subarray ports is presented. A hybrid genetic algorithm optimizes the subarray size and subarray weights to minimize the maximum sidelobe level

Comparison between genetic and gradient-based optimization algorithms for solving electromagnetics problems

This paper compares the application of genetic algorithms and traditional gradient-based algorithms to various optimization problems in electromagnetics. Gradient algorithms work well for a small number of continuous parameters. Genetic algorithms are best for a large number of quantized parameters. Both antenna array and scattering optimization examples are shown. >

Simultaneous nulling in the sum and difference patterns of a monopulse antenna

Most adaptive array research has not directly addressed the problem of nulling in a monopulse antenna. Placing a null in the sum does not automatically place a null in the difference pattern and vice versa. Nulls may be placed in the two patterns with the use of separate adaptive weights and controls for the sum and difference channels. However, this requires two sets of adaptive hardware for one antenna. A technique for simultaneous hulling in the sum and difference channels of a monopulse phased array using one set of adaptive weights shared by both channels is described. First, the technique is described for amplitude and phase nulling, then for phase only hulling. In each case, the ability to simultaneously null in both channels with one set of variable weights is theoretically demonstrated.