Performance Analysis of Cardioid and Omnidirectional Microphones in Spherical Sector Arrays for Coherent Source Localization

Traditional spherical sector microphone arrays using omnidirectional microphones face limitations in modal strength and spatial resolution, especially within spherical sector configurations. This study aims to enhance array performance by developing a spherical sector array employing first-order cardioid microphones. A model based on spherical sector harmonic (SSH) functions is introduced to extend the benefits of spherical harmonics to sector arrays. Modal strength analysis demonstrates that cardioid microphones in open spherical sectors enhance nonzero-order strengths and eliminate the nulls associated with spherical Bessel functions. We find that the spatial resolution of spherical cap arrays depends on the array's maximum order and the limiting polar angle, but is independent of the microphone gain pattern. We assess direction-of-arrival (DOA) estimation performance for coherent wideband sources using the array manifold interpolation method, and compare cardioid and omnidirectional arrays through simulations in both open and rigid hemispherical configurations. The results indicate that cardioid arrays outperform omnidirectional ones on DOA estimation tasks, with performance improving alongside increased microphone directivity in the open hemispherical configuration. Specifically, hypercardioid microphones yielded the best results in the open configuration, while subcardioid microphones (without nulls) were optimal in rigid configurations. These findings demonstrate that spherical sector arrays of first-order cardioid microphones offer improved modal strength and DOA estimation capabilities over traditional omnidirectional arrays, providing significantly enhancing performance in spherical sector array processing.