In this paper, we consider the design of multi-dimensional broadband beamformers. This problem can be formulated as an optimization problem, where the performance is to select the coefficients of the FIR filters such that the error between the actual response and the desired response is minimized. However, this problem cannot be readily solved by optimization due to the curse of dimensions. We propose a novel approach here to tackle this problem. We prove that the optimal beamformer response can be obtained by a onedimensional optimization problem. A minimax optimization is then formulated to find the optimal window function to approach the optimized beamformer response. These steps decrease significantly the complexity of the multi-dimensional beamformer design method.
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