Functional delay and sum beamforming for three-dimensional acoustic source identification with solid spherical arrays

• Novel DAS and FDAS algorithms are created for 3D acoustic source identification with solid spherical arrays.
• Spherical harmonics degree׳s truncated upper limit is determined as a function of wavenumber and array radius.
• DAS׳s performance is not inferior to SHB׳s, and quantification accuracy is almost irrespective of focus distance.
• FDAS can attenuate sidelobes both significantly and efficiently, thus quickly achieve clear 3D acoustic imaging.
• Scale-and-integrate method can commendably compensate for FDAS׳s quantification deviation.

Solid spherical arrays have become particularly attractive tools for doing acoustic sources identification in cabin environments. Spherical harmonics beamforming (SHB) is the popular conventional algorithm. Regrettably, its results suffer from severe sidelobe contaminations and the existing solutions are incapable of removing these contaminations both significantly and efficiently. This paper focuses on conquering these problems by creating a novel functional delay and sum (FDAS) algorithm. First and foremost, a new delay and sum (DAS) algorithm is established, and for which, the point spread function (PSF) is derived, the determination principle of the truncated upper limit of the spherical harmonics degree is explored, and the performance is examined as well as compared with that of SHB. Next, the FDAS algorithm is created by combining DAS and the functional beamforming (FB) approach initially suggested for planar arrays, and its merits are demonstrated. Additionally, performances of DAS and FDAS are probed into under the situation that the source is not at the focus point. Several interesting results have emerged: (1) the truncated upper limit of the spherical harmonics degree, capable of making DAS meet FB׳s requirement, exists and its minimum value depends only on the wave number and the array radius. (2) DAS can accurately locate and quantify the single source and the incoherent or coherent sources, and its comprehensive performance is not inferior to that of SHB. (3) For single source or incoherent sources, FDAS can not only accurately locate and quantify the source, but also significantly and efficiently attenuate sidelobes, effectively detect weak sources and acquire somewhat better spatial resolution. In contrast to that, for coherent sources, FDAS is not available. (4) DAS can invariably quantify the source accurately, irrespectively of the focus distance, whereas FDAS is burdened with a quantification deviation growing with the increase of the exponent parameter, when the focus distance is unequal to the distance from the source to the array center or the focus directions do not embrace the source direction. Fortunately, the deviation can be commendably compensated for by the introduced scale-and-integrate method. This study will be of great significance to the accurate and quick localization and quantification of acoustic sources in cabin environments.