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In this work, a novel technique using closed-form expressions is rigorously surveyed to collaboratively nullsteer uniformly distributed, planar ring, and volumetric shell distributions. To assess the radiation behavior of these geometries circular tapers is of interest for their attractiveness in derivation, design, application, and mathematical simplicity. A rigorous mathematical derivation is used for the generation of closed-form expressions of the mean-valued radiation characteristics. The numerical simulations are performed using both ANSYS HFSS and MATLAB using a finite-element distribution. To validate the analytical models, we include the measured results of a uniformly distributed ring array topology, constrained to a set of 18 elements and a uniformly distributed shell array topology constrained to 16 elements. The results of all methods are compared to demonstrate exceptional agreement in the recommended theoretical analysis. This process follows differently from traditional phased array nulling methods, which apply the unique amplitude tapers along individual phased array elements. Unlike typical adaptive beamforming algorithms, this process does not require the estimation of second-order statistical metrics and avoids expansions of large polynomial equations. It uses shared aperture characteristics in order to generate null beams simultaneously. This can also be extended to widen null widths from the compounding of these shared aperture distributions, which is shown in simulation. [ABSTRACT FROM AUTHOR]

This work investigates beam pattern behavior of an isotropic point source and a collection of sources distributed amongst a spherical volume. Pattern behavior is compared to the tapering of a plane wave expansion of spherical waves demonstrating self-adjoint characteristics. Beampatterns of atomic like orbitals and Zernike polynomials are provided as connections to common applications. [ABSTRACT FROM AUTHOR]

Random arrays bound by a spherical volume are rigorously analyzed through a stochastic approach for uniform and Gaussian element distributions. The full mathematical derivation and process to determine the array characteristics are discussed and a key result is the form solution which describes both the sidelobe behavior and main beam characteristics. It is also shown that the proposed approach shares many conceptual similarities to the probabilistic approach applied to circular random arrays and comparisons are made. The 3-dB beamwidth, directivity, grating lobes, and sidelobe level are examined analytically and in numerical simulation for a conceptual system of isotropic wide-band radiators with a 100:1 bandwidth. [ABSTRACT FROM PUBLISHER]