最小误差空域预滤波矩阵求解及误差分析

建立了空域矩阵滤波器设计最优化问题，利用两种方法给出该最优化问题的最优解。第一种方法是通过将最优化问题转化为以向量为未知数的另一个最优化问题，并求解稳定点，重排获得原问题的最优解。第二种方法是利用对原最优化问题求偏导数的方式，直接获得最优解。利用广义奇异值分解，给出了最优解的简化形式。通过仿真，给出了不同阵元数情况下，预滤波的响应效果，通过对比可知，与恒定阻带抑制滤波器相比，最小误差空域预滤波矩阵有更小的归一化响应误差。

Solving of Least Error Spatial Prefilter Matrix and Error Analysis

In this paper, the design optimization problem of spatial matrix filter is built, two methods are used for solving the optimization problem. The first method changes the optimization problem into another optimization problem with inde- pendent variable of unknown vector. The stable point is derived, and the solution of the optimal spatial matrix filter is re- shaped by the vector solved. The second method gets the optimal solution by the derivation of Lagrange function. By using the generalized singular value decomposition, the simplified solution is given. By simulation, the filter responses are given with different sensor number. The least error spatial matrix filter has less normalized response error than the filter of constant stop -band response restriction.