Design and performance limit of near-field broadband IIR beamformers

This paper considers the design of near-field broadband beamformer based on IIR filters, performing both spatial and frequency filtering. The design problem is formulated as an optimal minimax problem to minimize the error between the desired response and the actual response. To demonstrate the theoretical advantage of the proposed IIR-based beamformer over conventional FIR designs, we introduce a novel performance limit analysis framework in which the filter length is treated as an arbitrary design parameter. This performance limit can be efficiently computed by solving a sequence of functional optimization subproblems. A key theoretical contribution of this work is the proof that both FIR and IIR beamformers converge to the same performance bound. However, the proposed IIR structure achieves this bound with significantly fewer filter coefficients. This finding provides valuable guidance for selecting appropriate filter lengths in practical applications. Furthermore, we propose a novel reduced structure in which all array elements share a common feedback section, offering additional simplification without sacrificing performance. The proposed method is evaluated by means of a room simulation model for various reverberation times. Numerical experiments have shown that the optimal value of the IIR design method can approach the limit faster than FIR-based beamformers, and all reduced structures achieved significant reduction in terms of filter lengths comparing with FIR beamformers in the performance limit.