Parametric direction-of-arrival estimation with three recurrence relations of spherical harmonics

Direction-of-Arrival Estimation of Electromagnetic Wave Impinging on Spherical Antenna Array in the Presence of Mutual Coupling Using a Multiple Signal Classification Method

A spherical antenna array (SAA) is the configuration of choice in obtaining an antenna array with isotropic characteristics. An SAA has the capacity to receive an electromagnetic wave (EM) with equal intensity irrespective of the direction-of-arrival (DoA) and polarization. Therefore, the DoA estimation of electromagnetic (EM) waves impinging on an SAA with unknown mutual coupling needs to be considered. In the spherical domain, the traditional multiple signal classification algorithm (SH-MUSIC) is faced with a computational complexity problem. This paper presents a one-dimensional MUSIC method (1D-MUSIC) for the estimation of the azimuth and elevation angles. An intermediate mapping matrix that exists between Fourier series and the spherical harmonic function is designed, and the Fourier series Vandermonde structure is used for the realization of the polynomial rooting technique. This mapping matrix can be computed prior to the DoA estimation, and it is only a function of the array configuration. Based on the mapping matrix, the 2-D angle search is transformed into two 1-D angle findings. Employing the features of the Fourier series, two root polynomials are designed for the estimation of the elevation and azimuth angles, spontaneously. The developed method avoids the 2-D spectral search, and angles are paired in automation. Both numerical simulation results, and results from experimental measured data (i.e., with mutual coupling effect incorporated), show the validity, potency, and potential practical application of the developed algorithm.

Generalized intensity vector and energy density in the spherical harmonic domain: Theory and applications

The acoustic intensity vector and energy density are perceptually relevant physical measures of a sound field that can be used in the context of sound field reproduction or acoustic parameter estimation. In this work, weighted spatial averaging of the intensity vector and energy density is investigated, and the results are expressed in terms of the spherical harmonic coefficients of the sound field. Higher-order spherical harmonic coefficients are incorporated by considering radial averaging. This radial averaging is then generalized, yielding the proposed generalized intensity vector and energy density. Direction-of-arrival and diffuseness estimators are constructed based on the generalized intensity vector and energy density. In the evaluation, the proposed parameter estimators are compared to existing state-of-the-art estimators using simulated signals containing directional, diffuse, and sensor-noise components.

Spherical sector harmonics representation of sound fields using a microphone array over spherical sector

Spherical microphone arrays (SMAs) are widely used for sound recording and analysis, with processing being done in the spherical harmonics (SH) domain. This is due to the ease of array processing in the SH domain without spatial ambiguity. However, it is uneconomical to construct a full SMA when sources are present in restricted regions of the environment. Additionally, the use of a full SMA comes at the cost of more microphone signals to process. Attempts have been made to use hemispherical microphone arrays on the basis of the acoustic image principle, enabling application of SH but with greater computational complexity. In this paper, the use of a spherical sector microphone array instead of a full SMA is proposed. An orthonormal spherical sector harmonics (S²H) basis function is developed for accurate representation of pressure over the sector. The orthonormality of the S²H function is established using orthogonality of shifted associated Legendre polynomials and a scaled exponential function. An addition theorem for S²H basis functions is derived. The S²H basis function is applied to the decomposition of a sound field over a sector array. The S²H basis function has potential applications to brain source localization and physiological shape description.

Three-dimensional source localization using sparse Bayesian learning on a spherical microphone array

The identification of acoustic sources in a three-dimensional (3D) domain based on measurements with an array of microphones is a challenging problem: it entails the estimation of the angular position of the sources (direction of arrival), distance relative to the array (range), and the quantification of the source amplitudes. A 3D source localization model using a rigid spherical microphone array with spherical wave propagation is proposed. In this study, sparse Bayesian learning is used to perform localization in 3D space and examine the use of principal component analysis to denoise the measurement data. The performance of the proposed method is examined numerically and experimentally, which is tested both in a free-field and in a reverberant environment. The numerical and experimental investigations demonstrate that the approach offers accurate localization in a 3D domain, resolving closely spaced sources and making it possible to identify sources located at different ranges.