Design of Irregular Embedded Antenna Arrays for Shaped-Beam Radiation Using Reciprocity and Sparse Optimization

In this article, the sparse optimization based methodology for designing irregular arrays of antenna radiating in free space for various beam pattern objectives is extended to the case of realistic antennas embedded in an arbitrary hosting structure. To reduce the computational complexity involved in this extension, which lies in the need to numerically calculate the far-fields of the antennas for many possible placements while accounting for the effect of the embedding structure, we resort to the reciprocity theorem. Once the far-fields have been computed, we can proceed and employ any sparse optimizer to design the array. To demonstrate this approach, we apply it to the design of an electrically short dipole array embedded in a dielectric substrate above a finite ground plane for various beam pattern objectives. The sparse optimization is shown to yield arrays with more desirable beam patterns (better in terms of least squares error) than achieved by commonly used uniformly spaced planar arrays.