Optimal design of nearfield wideband beamformers robust against errors in microphone array characteristics

Nearfield wideband beamformers for microphone arrays have wide applications, such as hands-free telephony, hearing aids, and speech input devices to computers. The existing design approaches for nearfield wideband beamformers are highly sensitive to errors in microphone array characteristics, i.e., microphone gain, phase, and position errors, as well as sound speed errors. In this paper, a robust design approach for nearfield wideband beamformers for microphone arrays is proposed. The robust nearfield wideband beamformers are designed based on the minimax criterion with the worst case performance optimization. The design problems can be formulated as second-order cone programming and be solved efficiently using the well-established polynomial time interior-point methods. Several interesting properties of the robust nearfield wideband beamformers are derived. Numerical examples are given to demonstrate the efficacy of the proposed beamformers in the presence of errors in microphone array characteristics.