一种平面稀疏阵列的快速综合方法

A Fast Synthesis Method for Planar Sparse Array

以快速综合出满足期望方向图以及阵元数最少的平面阵列为目标,提出一种基于迭代加权l_1范数的平面阵列综合方法。该方法将平面稀疏阵列综合问题转化为加权l_1范数最小化的稀疏信号重构过程,并利用拉格朗日乘数法求解每次迭代中的阵列加权向量的闭式解,由于二维平面的空间采样导致闭式解中存在大规模矩阵的求逆运算,进而引入共轭梯度法以促进算法加速收敛。当满足迭代终止条件时,由加权向量的非零值确定平面阵列的阵元位置及其激励。仿真结果表明,该方法能有效提高平面稀疏阵列综合的收敛速度。

In order to fast synthesize the planar array to satisfy the desired pattern and minimize the number of radiating elements,a planar array synthesis method based on iteratively reweighted l1 norm minimization is proposed. The problem of planar array synthesis is transformed into a process of the sparse signal recon-struction based on reweighted l1 norm minimization,and the closed-form solution of the array weight vector at each iteration is obtained by the Lagrange multiplier method. Due to the inverse operation of the large-scale matrix caused by the two dimensional spatial sampling in the closed-form solution,the conjugate Gra-dient method is introduced to promote the convergence speed of the proposed method. The excitations and locations of sensors in the planar sparse array are determined by the nonzero elements in the solved weight vector until the iteration termination condition is satisfied. Simulation results show that the proposed meth-od can effectively speed up the planar sparse array synthesis.