Matrix filter design using semi-infinite programming with application to DOA estimation

We propose using a semi-infinite programming technique to design a matrix filter. The idea is to formulate the design problem into a semi-infinite optimization model where the mean square error between the desired response and the designed filter in the passband and stopband is minimized subject to a set of nonlinear functional inequalities. These inequality constraints are used to ensure that the stopband attenuation and the passband deviation satisfy the prescribed specifications. Simulations showed that the proposed method was better than the conventional matrix filter design techniques. The matrix filters based on the proposed design method was also applied to the direction-of-arrival (DOA) estimation problem. It was shown that the filter greatly improved the estimation accuracy at low signal-to-noise ratios (SNRs).