Source Number Detectability by an Acoustic Vector Sensor Linear Array and Performance Analysis

The motivation of this work is to investigate the source number detectability by an oversampled or undersampled linear acoustic vector sensor (AVS) array. Sufficient conditions that ensure the extension of existing source number estimators and beamforming techniques from the acoustic pressure sensor (APS) array to the AVS array are established based on the linear independence of steering vectors of the AVS array, an issue closely related to the number of sources whose parameters [e.g., the direction of arrival (DOA)] can be uniquely determinable. The upper bound on the detectable number of sources with distinct DOAs under oversampled and undersampled array configurations is derived, where the difference of definitions of the distinct DOAs between the APS array and the AVS array is clarified. The number constraint on detectable sources with distinct spatial aliasing DOAs using the undersampled AVS array is also investigated. Under these conditions, advantages of eigenvalue-based source number estimators using AVS arrays are demonstrated, and the minimum description length (MDL) estimator is extended to the AVS array as an illustration to verify the established theories.