扩展酉矩阵束算法实现稀疏可重构天线阵的优化设计

针对方向图可重构天线阵列的稀疏布阵问题，提出一种基于扩展酉矩阵束算法的优化设计算法。首先建立以阵元位置和多组激励为变量的多方向图联合稀疏优化模型，并利用期望方向图采样数据构建Hankel块矩阵。然后通过centro-Hermitian化处理和酉变换将采样矩阵从复数域转换到实数域，舍弃实矩阵中较小的奇异值对可重构线阵进行稀疏。最后通过对等价矩阵束的广义特征值分解估计稀布阵元位置，进而得到每个方向图对应的激励。仿真验证了该方法能够以阵元非均匀稀疏分布的阵列形式有效实现多个方向图的精确重构。

Extended unitary matrix pencil algorithm for optimal design of sparse reconfigurable antenna arrays

An innovative method, extended unitary matrix pencil (EUMP) algorithm, is proposed for the optimal design of sparse reconfigurable antenna arrays. The joint sparse optimization model is established with element positions and excitations as the design variables, and an extended block-Hankel matrix can be constructed according to sample data of the desired pattern. Then through centro-Hermitian matrix and unitary transformation, this complex-valued sample matrix can be transformed into real-valued one, of which smaller singular values are discarded to reduce the number of antenna elements. The generalized eigenvalues of equivalent matrix pencil are exploited to estimate the sparse array element positions and their corresponding excitations accurately. Simulation results validate that multiple-patterns can be reconfigured with non-uniform arrangements by this algorithm efficiently.