A simple algorithm to achieve desired patterns for arbitrary arrays

A simple iterative algorithm which can be used to find array weights that produce array patterns with a given look direction and an arbitrary sidelobe specification is presented. The method can be applied to nonuniform array geometries in which the individual elements have arbitrary (and differing) radiation patterns. The method is iterative and uses sequential updating to ensure that peak sidelobe levels in the array meet the specification. Computation of each successive pattern is based on the solution of a linearly constrained least-squares problem. The constraints ensure that the magnitude of the sidelobes at the locations of the previous peaks takes on the prespecified values. Phase values for the sidelobes do not change during this process, and problems associated with choosing a specific phase value are therefore avoided. Experimental evidence suggests that the procedure terminates in remarkably few iterations, even for arrays with significant numbers of elements.>