零点约束矩阵滤波设计

Design of matrix filter with prescribed null

为解决在空域预滤波阶段抑制强噪声的问题,提出了零点约束矩阵滤波设计方法,并给出了解的表达式。通过设计凸规划问题,在严格约束阻带响应等于零的情况下,使通带误差最小。将凸规划问题转换为线性约束二阶最优化问题,构造Lagrange函数并得到最优解,重排后得出滤波矩阵。仿真可知,本方法可设计出强干扰离散分布或处于某扇面的预滤波器,可用于解决常规波束形成算法受强干扰影响方位估计性能的问题。

To solve the problem of strong noise suppression in the period of spatial pre-filtering, design of the matrix filter with prescribed null is proposed and expression of the solution is presented. Through the convex programming, the pass-band response error is minimized on the condition that the stop-band response is strictly forced to zero. The convex programming is converted to a second-order optimization problem with a linear constraint and the optimal solution is obtained by constructing a Lagrange function. Finally, the filtering matrix is achieved by rearranging the solution. Result of the simulation has proved that the designed prefilter can suppress the strong interference with discrete distribution or in a sector and performance of the DOA estimation in conventional beamforming （CBF） can be improved in presence of strong interference by using this method.