I. Introduction
Phased antenna arrays are potentially the most versatile and consequently the most expensive type of electromagnetic sensor [1]–[4]. In large part, cost can be directly tied to the size of the array, or more precisely the total number of elements in the array, making it important to use the minimum number of elements required to satisfy cost-sensitive applications. A survey of the literature will reveal that the vast majority of planar, 2-D array apertures are in fact based on a square lattice, as it is generally the simplest for construction, has the appeal of geometric symmetry, and so on. Yet, though the square array lattice is the most common in practice, it is well known that an optimally sampled triangular lattice can achieve an additional 15.5% reduction in array element counts over the optimally sampled square lattice with the same aperture area and grating-lobe-free scan operation [3]–[6]. Very large phased arrays (or more precisely, phased arrays with large element counts) favor triangular lattices for this reason. As an example, the famous Precision Acquisition Vehicle Entry Phased Array Warning System (PAVE PAWS) is a very large array of dual-polarized dipole radiators benefiting from the lower element counts of a triangular grid [7].