Design of matrix filter with prescribed null

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.