Generalized radiation modes and microphone arrays for close-talking

In close-talking applications, such as mobile phones, selective measurement of the near-field sound is desirable as it can be used to improve the signal-to-noise ratio. In this study, the theory of generalized radiation modes is applied to the design of microphone arrays. The generalized radiation modes are formulated as a generalized eigenvalue problem related to the specific acoustic impedances on the array surface. The real eigenvalue corresponds to the near-to-far ratio for each mode and the real eigenvector indicates the modal shape, i.e., the amplitudes and phases of the individual microphones. The microphone array is designed according to the eigenvector with the largest eigenvalue so as to maximize the near-to-far ratio. The theory is verified based on computer simulations. The proposed method is also compared with conventional gradient microphones via numerical examples.