Optimal Spatial Matrix Filter Design for Array Signal Preprocessing

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

Optimal matrix-filter design

A matrix filter produces N output values given a block of N input values. Matrix filters are particularly useful for filtering short data records (e.g., N ≤ 20). In this correspondence, we introduce a new set of matrix-filter design criteria and show that the design of a matrix filter can be formulated as a convex optimization problem. Several examples are given of lowpass and bandpass designs as well as a Hilbert transformer design. © 1996 IEEE