Phase-mode versus delay-and-sum spherical microphone array processing

Phase-mode spherical microphone array processing, also known as spherical harmonic array processing, has been recently studied for various applications. The spherical array configuration provides desired three-dimensional symmetry, while the phase modes provide frequency-independent spatial processing. This letter employs the spherical harmonic framework to compare the well-known delay-and-sum to the phase-mode processing for spherical arrays. The two approaches show similar performance at frequencies where the upper spherical harmonic order equals the product of the wave number and sphere radius. However, at lower frequencies, phase-mode processing maintains the same directivity, limited by signal-to-noise ratio, while for delay-and-sum, spatial resolution deteriorates.