Synthesis of Planar Arrays Based on Fast Iterative Shrinkage-Thresholding Algorithm

In this communication, a pattern synthesis method based on fast iterative shrinkage-thresholding algorithm (FISTA) is proposed for nonuniform planar arrays. In the proposed method, the array synthesis problem is first expressed as a weighted least absolute shrinkage and selection operator (LASSO) problem. Then, the weighted LASSO problem is solved iteratively by FISTA to acquire the locations of reconstructed array elements. At last, two kinds of methods are given to acquire the excitations of the reconstructed array elements. The first kind of method to obtain the excitations is based on the least-squares method. Another way to calculate the excitations is based on convex optimization. The characteristics of these two methods are discussed in this communication. A series of numerical examples are introduced to show the effectiveness and robustness of the proposed method.

I. Introduction

In modern society, planar arrays are widely used in communication systems, radar systems, and inertial navigation systems [1], [2]. With the increase of hardware cost and the increase of size of planar arrays, the synthesis of planar arrays with a minimum number of active elements has become a research hotspot because of its practical advantages including reduction of cost and weight as well as the simplification of the feeding network [3]. Because of the high nonlinearity of nonuniform planar array synthesis problems, the research of robust and numerically efficient nonuniform planar array synthesis methods is still an open field.