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Journal of Applied Mathematics
Volume 2014, Article ID 564976, 8 pages
Research Article

Optimal Spatial Matrix Filter Design for Array Signal Preprocessing

1Department of Communication Engineering, Dalian Naval Academy, Dalian 116018, China
2Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China

Received 12 February 2014; Revised 21 March 2014; Accepted 24 March 2014; Published 17 April 2014

Academic Editor: Guiming Luo

Copyright © 2014 Haiyong Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An efficient technique of designing spatial matrix filter for array signal preprocessing based on convex programming was proposed. Five methods were considered for designing the filter. In design method 1, we minimized the passband fidelity subject to the controlled overall stopband attenuation level. In design method 2, the objective function and the constraint in the design method 1 were reversed. In design method 3, the optimal matrix filter which has the general mean square error was considered. In design method 4, the left stopband and the right stopband were constrained with specific attenuation level each, and the minimized passband fidelity was received. In design method 5, the optimization objective function was the sum of the left stopband and the right stopband attenuation levels with the weighting factors 1 and γ, respectively, and the passband fidelity was the constraints. The optimal solution of the optimizations above was derived by the Lagrange multiplier theory. The relations between the optimal solutions were analyzed. The generalized singular value decomposition was introduced to simplify the optimal solution of design methods 1 and 2 and enhanced the efficiency of solving the Lagrange multipliers. By simulations, it could be found that the proposed method was effective for designing the spatial matrix filter.