Synthesis of Concentric Ring Antenna Arrays Yielding Approximately Equal Side Lobes

Based on the Haar's theorem, known in the general approximation theory, a method of synthesizing an optimum concentric ring array is presented. The far field pattern function of such an array is first formulated in terms of the zeroth‐order first kind Bessel function. A numerical approach is used for obtaining a solution approximating any specified radiation pattern according to the “minimax” rather than the ordinary least‐mean‐square error criterion. With respect to a prespecified array size, the solution obtained has the following properties: (1) the maximum deviation between the synthesized and desired patterns is minimized, (2) the side lobes are approximately equal in level if the specified pattern is a Gaussian function, (3) a maximum directive gain can be realized, (4) a minimum number of elements required to achieve such a performance can be determined, and (5) the solution is unique under certain conditions. The theory and method to be presented are valid for arrays consisting of either isotropic sources or physical directional elements.