The utility of convex optimization for weight selection in arrays

In this paper, the versatility and usefulness of convex optimization is illustrated. A sidelobe-minimizing weighting method will be presented that returns optimal weights given a set of specifications, including: scan direction, beamwidth, array geometry, set of null constraints and smoothness criteria. The method also takes into account the radiation patterns of the elements, which do not have to be identical. While this amount of versatility would be intractable via standard analytical methods, convex optimization makes this problem fairly straightforward. The method will be shown for a 1d array; extension to 2d arrays is straightforward.