Efficient pattern synthesis of large scale four-dimensional heterogeneous antenna arrays

Abstract

Due to the inherent sideband radiation feature and the non-convexity in four-dimensional (4D) antenna arrays synthesis problems, the conventional global optimization algorithms face critical challenges, especially for large scale 4D heterogeneous arrays. In this work, an efficient method based on convex optimization is proposed for the synthesis of large scale 4D heterogeneous arrays. By designing suitable time sequences with different dynamic range ratios (DRRs), the synthesis problem is firstly summarized as a programming problem. Due to the fact that the constraint conditions contain multi-extreme values function, the programming problem is thus a non-convex problem in essence. However, mathematical transformations can be introduced to address the constraint condition with respect to excitation coefficients, thus converting the corresponding non-convex problem into a convex-problem. Therefore, the programming problem is reduced to two dependent convex optimization problems corresponding to the patterns at the center frequency and the first sideband, and convex optimization can be efficiently used to solve the two simplified problems, respectively. Owing to the efficiency of the convex optimization, the proposed method is much more efficient than conventional methods of using brute-force evolutionary optimizations. Numerical examples are presented to show the effectiveness of the proposed method for the pattern synthesis of large scale 4D heterogeneous arrays based on simple airplane platform.