基于多凸优化的稀疏线性阵列综合方法

Synthesis of sparse linear arrays based on multi-convex optimization

提出了一种基于迭代算法的稀疏阵列综合方法,通过减少阵列单元数量以简化波束形成网络。该方法在每一步迭代过程中使用多凸优化方法,将控制主瓣波纹大小的非凸函数转化成凸函数,并将稀疏阵列综合问题转化为一系列迭代加权L1范数最小化的稀疏重构问题。通过该算法综合出来的阵列天线具有较少单元数与较高的方向图性能。算例表明,与传统算法相比较,文中提出的方法可以节省大量天线单元。

A sparse array synthesis method is proposed based on the iterative algorithm, in which the number of antenna array elements is reduced to simplify the beam forming network. The multi-convex optimization method is used in each step of iterative process where the nonconvex function that controls the size of the mainlobe is converted into the convex function, and the sparse array synthesis problem is cast as a sparse reconfiguration problem of minimizing a series of iterative weighted L1 norms. Therefore, the sparse array antenna features fewer antenna elements and better pattern performance. Examples concerning the design of linear arrays show relevant savings of array elements with respect to conventional architectures.