Performance Enhancement of Functional Delay and Sum Beamforming for Spherical Microphone Arrays

Functional delay and sum (FDAS) beamforming for spherical microphone arrays can achieve 360° panoramic acoustic source identification, thus having broad application prospects for identifying interior noise sources. However, its acoustic imaging suffers from severe sidelobe contamination under a low signal-to-noise ratio (SNR), which deteriorates the sound source identification performance. In order to overcome this issue, the cross-spectral matrix (CSM) of the measured sound pressure signal is reconstructed with diagonal reconstruction (DRec), robust principal component analysis (RPCA), and probabilistic factor analysis (PFA). Correspondingly, three enhanced FDAS methods, namely EFDAS-DRec, EFDAS-RPCA, and EFDAS-PFA, are established. Simulations show that the three methods can significantly enhance the sound source identification performance of FDAS under low SNRs. Compared with FDAS at SNR = 0 dB and the number of snapshots = 1000, the average maximum sidelobe levels of EFDAS-DRec, EFDAS-RPCA, and EFDAS-PFA are reduced by 6.4 dB, 21.6 dB, and 53.1 dB, respectively, and the mainlobes of sound sources are shrunk by 43.5%, 69.0%, and 80.0%, respectively. Moreover, when the number of snapshots is sufficient, the three EFDAS methods can improve both the quantification accuracy and the weak source localization capability. Among the three EFDAS methods, EFDAS-DRec has the highest quantification accuracy, and EFDAS-PFA has the best localization ability for weak sources. The effectiveness of the established methods and the correctness of the simulation conclusions are verified by the acoustic source identification experiment in an ordinary room, and the findings provide a more advanced test and analysis tool for noise source identification in low-SNR cabin environments.