Hemispherical antenna arrays are subjected to linear and nonlinear synthesis and are optimized using adaptive based differential evolution (ADE) and fire fly (AFA) algorithm. The hemispherical shaped array with isotropic elements is considered. Antenna element parameters that are used for synthesis are excitation amplitude and angular position. Linear synthesis is termed as the variation in the element excitation amplitude and nonlinear synthesis is process of variation in element angular position. Both ADE and AFA are a high-performance stochastic evolutionary algorithm used to solve -dimensional problems. These methods are used to determine a set of parameters of antenna elements that provide the desired radiation pattern. The effectiveness of the algorithms for the design of conformal antenna array is shown by means of numerical results. Comparison with other methods is made whenever possible. The results reveal that nonlinear synthesis, aided by the discussed techniques, provides considerable enhancements compared to linear synthesis. 1. Introduction Design of antenna arrays that conforms an arbitrary shape has triggered the electromagnetic researchers since they have a potential of coverage, either with an omnidirectional beam, multiple beams, or a narrow beam that can be steered over . One of the geometrical solutions that can be provided through a hemispherical shape. The linear arrays have good directivity and they can form the narrowest main lobe in a given direction but cannot be steered in all azimuth directions. The circular array is a high side lobe geometry. The lacuna of the regular arrays leads to the aid of arrays that can perform/radiate in azimuth range also [1]. These arrays have to be mathematically formulated for their array factor. Since the array elements are conformal to the surface of the sphere, the phase at each element becomes critical for synthesizing low side lobe patterns [2, 3]. Primitive methods such as Schelkunoff, Fourier, and Woodwardlawson cannot be applied for this hemispherical array because of its curvature effects; the phase adjustments of each array element become complex. The stochastic pattern synthesis [4–7] can be adopted for these conformal shapes. The literature instructs the advantages of stochastic process over deterministic methods that can be stretched out for large size arrays [8–11]. One of the greatest advantages of using these evolutionary techniques such as Genetic Algorithm and Particle Swarm optimization [12–14] is their ability to deal with a huge parameter set up with out getting trapped in
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