基于前后向矩阵束方法的赋形波束方向图综合

Shaped-beam Pattern Synthesis Using Forward-backward Matrix Pencil Method

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。

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.