Spatial Matrix Filter with Dimension Reduction Design

The performance of spatial filter matrix degrades sharply in the presence of matrix dimension reduction. To solve the problem, a method using K-L (Karhunen-Loeve) Trans-form to reduce the matrix dimension is proposed. Theoretical derivation show the eigenvalues of the spatial-filter matrix and its conjugate transpose matrix product, has two characteristics. Firstly, there exists some eigenvalues that are much greater than the other eigenvalues. Secondly, the number of greater eigenvalues depends on the bandwidth of filter matrix pass-band. Based on those characteristics, K-L Trans-form was used to realize matrix dimension reduction through abandoning the eigenvectors corresponding to small eigenvalues. The proposed reduction dimension filter matrix has the advantage of orthogonality. Simulation results show the proposed reduction matrix and matrix with maximum dimension have similar filter capability.