Second-Order Cone Programming for Scan-Plane Reconstruction for the Wavelength-Scaled Array

The wavelength-scaled array architecture reduces the element count in large, ultrawideband antenna arrays by segmenting the aperture into subapertures of varying sizes and bandwidths. This results in an asymmetrical aperture of dissimilar elements with associated patterns that require significant correction. Here, we assess narrowband array performance using its far-field pattern as obtained in two steps. First, we characterize individual elements using planar near-field measurements. Second, we use second-order cone programming to optimize the complex element weights that generate the desired individual far-field element patterns derived from those measurements. This document details the far-field optimization technique, referred to here as optimized scan-plane reconstruction, and uses it to demonstrate that the asymmetric wavelength-scaled array can support low global sidelobe reduction, deep localized nulls, and/or mainbeam scanning like a conventional symmetric array.