The Multiple Signal Classification (MUSIC) algorithm has become one of the most popular algorithms for estimating the direction-of-arrival (DOA) of multiple sources due to its simplicity and ease of implementation. Spherical microphone arrays can capture more sound field information than planar arrays. The collected multichannel speech signals can be transformed from the space domain to the spherical harmonic domain (SHD) for processing through spherical modal decomposition. The spherical harmonic domain MUSIC (SHD-MUSIC) algorithm reduces the dimensionality of the covariance matrix and achieves better DOA estimation performance than the conventional MUSIC algorithm. However, the SHD-MUSIC algorithm is prone to failure in low signal-to-noise ratio (SNR), high reverberation time (RT), and other multi-source environments. To address these challenges, we propose a novel joint spherical harmonic domain beam-space MUSIC (SHD-BMUSIC) algorithm in this paper. The advantage of decoupling the signal frequency and angle information in the SHD is exploited to improve the anti-reverberation property of the DOA estimation. In the SHD, the broadband beamforming matrix converts the SHD sound pressure to the beam domain output. Beamforming enhances the incoming signal in the desired direction and reduces the SNR threshold as well as the dimension of the signal covariance matrix. In addition, the 3D beam of the spherical array has rotational symmetry and its beam steering is decoupled from the beam shape. Therefore, the broadband beamforming constructed in this paper allows for the arbitrary adjustment of beam steering without the need to redesign the beam shape. Both simulation experiments and practical tests are conducted to verify that the proposed SHD-BMUSIC algorithm has a more robust adjacent source discrimination capability than the SHD-MUSIC algorithm.

Sensor arrays are gradually becoming a current research hotspot due to their flexible beam control, high signal gain, robustness against extreme interference, and high spatial resolution. Among them, spherical microphone arrays with complex rotational symmetry can capture more sound field information than planar arrays and can convert the collected multiple speech signals into the spherical harmonic domain for processing through spherical modal decomposition. The subspace class direction of arrival (DOA) estimation algorithm is sensitive to noise and reverberation, and its performance can be improved by introducing relative sound pressure and frequency-smoothing techniques. The introduction of the relative sound pressure can increase the difference between the eigenvalues corresponding to the signal subspace and the noise subspace, which is helpful to estimate the number of active sound sources. The eigenbeam estimation of signal parameters via the rotational invariance technique (EB-ESPRIT) is a well-known subspace-based algorithm for a spherical microphone array. The EB-ESPRIT cannot estimate the DOA when the elevation angle approaches 90°. Huang et al. proposed a two-step ESPRIT (TS-ESPRIT) algorithm to solve this problem. The TS-ESPRIT algorithm estimates the elevation and azimuth angles of the signal independently, so there is a problem with DOA parameter pairing. In this paper, the DOA parameter pairing problem of the TS-ESPRIT algorithm is solved by introducing generalized eigenvalue decomposition without increasing the computation of the algorithm. At the same time, the estimation of the elevation angle is given by the arctan function, which increases the estimation accuracy of the elevation angle of the algorithm. The robustness of the algorithm in a noisy environment is also enhanced by introducing the relative sound pressure into the algorithm. Finally, the simulation and field-testing results show that the proposed method not only solves the problem of DOA parameter pairing, but also outperforms the traditional methods in DOA estimation accuracy.

Sidelobe suppression is a major challenge in wideband beamforming for acoustic research, especially in high noise and reverberation environments. In this paper, we propose a multi-objective NSGA-II wideband beamforming method based on a spherical harmonic domain for spherical microphone arrays topology. The method takes white noise gain, directional index and maximum sidelobe level as the optimization objectives of broadband beamforming, adopts the NSGA-II optimization strategy with constraints to estimate the Pareto optimal solution, and provides three-dimensional broadband beamforming capability. Our method provides superior sidelobe suppression across different spherical harmonic orders compared to commonly used multi-constrained single-objective optimal beamforming methods. We also validate the effectiveness of our proposed method in a conference room setting. The proposed method achieves a white noise gain of 8.28 dB and a maximum sidelobe level of −23.42 dB at low frequency, while at high frequency it yields comparable directivity index results to both DolphChebyshev and SOCP methods, but outperforms them in terms of white noise gain and maximum sidelobe level, measuring 16.14 dB and −25.18 dB, respectively.