Convex Optimization of Pencil Beams Through Large-Scale 4-D Antenna Arrays

An efficient pattern synthesis approach is proposed for the synthesis of large-scale 4-D antenna arrays in this paper. A 4-D antenna array is separated into two dependent “conventional arrays” with identical array structures, whose far-field radiation patterns correspond to the patterns at the center frequency and the sidebands, respectively. It is demonstrated that the problem can be formulated as a nonconvex programming problem. Mathematical transformation is then applied to change the nonconvexity with respect to the excitation coefficients. Therefore, the programming problem can be reduced to two dependent convex optimization problems, and convex optimization can be efficiently used to optimize the two problems. Owing to the introduction of the convex optimization, the proposed method is much more efficient than conventional approaches using brute-force evolutionary optimizations. Numerical examples of 4-D linear/planar arrays (≥1000 elements for each) are presented to demonstrate the effectiveness of the proposed method.