Pencil-beam synthesis for large circular arrays

A method is developed which permits the synthesis of a pencil beam for a circular array with an arbitrary number of directive elements. A desired pattern specified in the azimuth and elevation directions is approximated in the least-mean-square-error sense, and the synthesis procedure, which requires the inversion of a matrix, is made quite straightforward. When the total number of array elements is large, computational difficulties arise in the inversion of a large matrix. These difficulties are circumvented by diagonalising the matrix in question with a unitary matrix composed of the eigenvectors of a rotational operator. The optimum excitations in the array ÿlements can then be determined readily, even for a large circular array with many directive elements. Numerical examples are presented to illustrate the procedures and results.