Generalized analytical technique for the synthesis of unequally spaced arrays with linear, planar, cylindrical or spherical geometry

An effective method for optimizing the performance of a fixed current distribution, uniformly spaced antenna array has been to adjust its element positions to provide performance improvement. In comparison with the default uniform structure, this approach yields performance improvements such as smaller sidelobe levels or beamwidth values. Additionally, it provides practical advantages such as reductions in size, weight and number of antenna elements. The objective of this paper is to describe a unified mathematical approach to nonlinear optimization of multidimensional array geometries. The approach utilizes a class of limiting properties of sinusoidal, Bessel or Legendre functions that are dictated by the array geometry addressed. The efficacy of the method is demonstrated by its generalized application to synthesis of rectangular, cylindrical and spherical arrays. The unified mathematical approach presented below is a synthesis technique founded on the mathematical transformation of the desired field pattern, followed by the application of limiting forms of the transformation, and resulting in the development of a closed form expression for the element positions. The method offers the following advantages over previous techniques such as direct nonlinear optimization or genetic algorithms. First, it is not an iterative, searching algorithm, and provides element spacing values directly in a single run of the algorithm, thereby saving valuable CPU time and memory storage. Second, It permits the array designer to place practical constraints on the array geometry, (e.g., the minimum/maximum spacing between adjacent elements)