基于前后向矩阵束方法的赋形波束方向图综合

摘要

For the optimization problem of shaped-beam pattern,a new method based on forward-backward matrix pencil method(FBMPM) is proposed to reduce the number of elements,to solve the element locations and to design the excitations.Firstly,the shaped-beam pattern is sampled to form a discrete data set.Secondly,a Hankel-Toeplitz matrix is built and the singular value decomposition (SVD) can be performed.By discarding the insignificant singular values,an optimal low-rank approximation of the matrix which corresponds to sparse antenna array can be obtained.Finally,the generalized eigen-decomposition is employed to calculate the sparse linear array locations and excitations.The FBMPM places a necessary restriction on the poles which can guarantee to obtain more accurate result.Simulation results are presented to demonstrate the efficiency of the proposed approach.%针对阵列天线的方向图赋形问题,研究了一种基于前后向矩阵束方法(FBMPM).先确定适当的阵元数目,再优化设计激励幅度和阵元位置,最终设计出需要的赋形方向图.由期望方向图的均匀采样数据构造Hankel-Toeplitz矩阵；然后对它进行奇异值分解,舍弃不重要的奇异值,得到此矩阵的低秩逼近矩阵；最后基于广义特征值分解求得重构阵列的阵元位置和激励.FBMPM采用特殊的前后向矩阵来约束极点分布,保证了重构赋形波束方向图的精度可控.仿真实例证明了方法的快速性和有效性.