Pattern synthesis with null constraints for circular arrays of equally spaced isotropic elements

In the paper we deal with the null synthesis of radiation pattern for single-ring circular arrays of equally spaced isotropic elements. The problem that we consider consists in finding the array pattern which minimises the mean-square distance from a given pattern, while being simultaneously null at assigned directions. We present a simple and efficient method of solution that uses a discrete Fourier transform (DFT) approach. At first, the unconstrained problem is solved in closed form, then the unconstrained optimum array pattern is modified in such a way as to produce the required nulls