Considerations for the design of directional microphone arrays based on error analysis

For spherical array processing, such as beamforming, rigid sphere arrays are often used to solve the forbidden frequency problem that occurs in open sphere arrays composed of omnidirectional microphones. However, these arrays are known to exhibit performance degradation at low frequencies due to noise sensitivity. To address this problem, directional arrays with hypercardioid microphones, which utilize higher-order pressure gradients to achieve narrow directivity, have been proposed. These arrays are expected to provide more stable performance at low frequencies. In this study, we first compare the performance of rigid sphere arrays and directional arrays through detailed simulations that analyze various error components. Then, we investigate how microphone directivity and the number of microphones jointly affect array performance. Results show that directional arrays are superior to rigid sphere arrays at low frequencies. However, using highly directional microphones with an insufficient microphone count caused performance degradation across the entire frequency band, indicating the need for a number of microphones appropriate for their directivity. This finding provides an important guideline for selecting microphone directivity and the number of microphones in the array according to the intended application. Work supported by JSPS KAKENHI Grant No. JP24K03222.