Acoustic Array Systems: Paper ICA2016-731 Spherical harmonic smoothing for DOA estimation of fully coherent sources

The subspace-based estimation of direction of arrivals (DOAs) of multiple sound sources requires multiple observation data from a microphone array, such that basis of signal subspace can be fully identified. For coherent sources, however, multiple measurements only produce linearly dependent observations, which makes it difficult to separate signal subspace from noise subspace. In order to obtain linearly independent observations from fully coherent sources, various smoothing techniques including spatial, temporal, and frequency smoothing have been proposed. In principle, smoothing techniques acquire linearly independent observations by separating a single measurement into multiple subarray data. For constructing subarrays, however, several constraints on the array shape or waveform are need to be satisfied. In this work, we develop a smoothing technique based on spherical harmonic expansion that can be applied without any constraint on the array shape or waveform. The proposed technique directly produces linearly independent observations from spherical harmonic coefficients of measured data. Spherical harmonic coefficients of measured data are separated into multiple subsets in spherical harmonics domain, which correspond to linearly independent observations of fully coherent sources. The proposed smoothing technique is processed in the spherical harmonics domain, so it is compatible with various eigenbeam-based approaches such as EB-MUSIC and EB-ESPRIT, as far as spherical harmonic coefficients can be measured up to a finite order greater than one.