Spherical Microphone Array Research Articles

Perceived Quality of Binaural Rendering from Baffled Microphone Arrays Evaluated Without an Explicit Reference

The authors present a perceptual evaluation of the binaural rendering quality of signals from several types of baffled microphone arrays. They employ the multi-stimulus category rating (MuSCR) paradigm that does not require a reference stimulus. The tested conditions also comprise a very high numerical accuracy stimulus, given the highest quality rating in approximately half of the multi-stimulus trials. A comparison with the literature on spherical microphone arrays (SMAs) shows that MuSCR allows for drawing representative conclusions regarding the dependency of the perceived quality on the array and rendering parameters as in previous experiments with an explicit high-fidelity reference. The authors applied the MuSCR paradigm to evaluate the perceived reproduction quality of equatorial microphone arrays (EMAs) with microphones only along the equator of the spherical baffle and of equatorial arrays with a nonspherical baffle (XMAs). The results endorse the observations from SMAs that an increasing spherical harmonic order leads to improved perceived quality. The authors also confirm that EMAs lead to the same perceived quality as SMAs despite the substantial difference in the number of microphones. Magnitude equalization of artifacts from spatial undersampling can be very effective for XMAs the raw solution deviates significantly from the other array types at high frequencies.

Time-Aligned Spatial Upsampling of Spherical Microphone Array Recordings

With the Spherical Array Interpolation by Time Alignment (SARITA) method, the authors introduced an approach for spatial upsampling of spherical microphone array (SMA) signals (T. Lübeck, J. M. Arend, and C. Pörschmann, IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 31, pp. 1163–1174 [2023]). The basic idea of this method is to perform the interpolation after time-aligning adjacent microphone signals. The upsampled SMA signals can be represented as spherical harmonic coefficients of much higher spatial order than is possible with the sparsely measured signals. Instead of impulse responses, the method is now applied to SMA recordings. Binaural decoding of upsampled SMA recordings is compared technically and perceptually to a baseline Ambisonics decoding. The results show that the SARITA method can also be applied to low-order array recordings and significantly improves their binaural reproduction.

The Influence of Diffuse-Field Equalization on the Perception of Spatial Aliasing Introduced by Spherical Microphone Arrays

When a sound field is sampled by a finite number of microphones, the upper-frequency range of the recorded content is affected by spatial aliasing. The frequency beyond which aliasing-induced artifacts occur is related to the distance between a microphone and its nearest neighbors. In this study, ambisonics signals of order N = 7 were encoded from simulated recordings made by virtual spherical microphone arrays of varying characteristics (radius, sampling scheme, and sampling grid order). A diffuse-field equalization, the role of which is to lessen the aliasing-induced spectral coloration, was also considered in the tested conditions. These aliased stimuli were then compared with unaliased stimuli of order N = 7. Results showed that the diffuse-field equalization had a great impact on the perceived differences. A perceptual threshold was calculated in order to determine whether aliasing artifacts are likely to be audible based on the amount of aliasing-induced encoding error.

Sparsity-driven loudspeaker gain optimization for sound field reconstruction with spherical microphone array

The paper presents a sparsity-driven method utilizing loudspeakers to reconstruct spatial sound fields using measurements obtained from a spherical microphone array (SMA). Employing spherical harmonics decomposition (SHD), the SMA recordings are characterized in the spherical harmonics domain. The gains for the loudspeakers are determined through an optimization problem, equating spherical harmonics pressure coefficients from primary and secondary sources. Furthermore, the sparsity within the loudspeaker feeds is redefined as a constrained sparse optimization problem, integrating linearity and orthogonality constraints. This method effectively reduces the required loudspeakers while maintaining sound field quality. The Bregman iteration method is applied to solve the constrained optimization problem. Rigorous evaluation based on reconstructed sound fields and objective measures highlights significant enhancements compared to least square and compressed sensing methods.

Time-domain sound field reconstruction using a rigid spherical microphone array.

A time-domain approach for interior spherical near-field acoustic holography is proposed to achieve the low-delay reconstruction of time-domain sound fields using a rigid spherical microphone array. This reconstruction encompasses the incident pressure field, the incident radial particle velocity field, and the total pressure field, which includes scattering. The proposed approach derives time-domain radial propagators through the inverse Fourier transform of their frequency-domain counterparts. These propagators are then applied to the array measurements to obtain the time-domain spherical harmonic coefficients of the interior sound field. Given the fact that the time-domain radial propagators possess finite-time support and exhibit significant high-frequency attenuation characteristics, they can be efficiently implemented using finite impulse response (FIR) filters. The proposed approach processes the signal sample-by-sample through these FIR filters, avoiding a series of issues associated with time-frequency transformations in frequency-domain methods. As a result, the approach offers higher accuracy and lower latency in reconstructing non-stationary sound fields compared to its frequency-domain counterpart and thus holds greater potential for real-time applications. Additionally, owing to the scattering effect of the rigid sphere, the approach avoids the impact of spherical Bessel function nulls and does not require the measurement of particle velocities, which renders the measurements cost effective.

Room Impulse Response Dataset of a Recording Studio with Variable Wall Paneling Measured Using a 32-Channel Spherical Microphone Array and a B-Format Microphone Array

This paper introduces RSoANU, a dataset of real multichannel room impulse responses (RIRs) obtained in a recording studio. Compared to the current publicly available datasets, RSoANU distinguishes itself by featuring RIRs captured using both a 32-channel spherical microphone array (mh acoustics em32 Eigenmike) and a B-format soundfield microphone array (Rode NT-SF1). The studio incorporates variable wall panels in felt and wood options, with measurements conducted for two configurations: all panels set to wood or felt. Three source positions that emulate typical performance locations were considered. RIRs were collected over a planar receiver grid spanning the room, with the microphone array centered at a height of 1.7 m. The paper includes an analysis of acoustic parameters derived from the dataset, revealing notable distinctions between felt and wood panel environments. Felt panels exhibit faster decay, higher clarity, and superior definition in mid-to-high frequencies. The analysis across the receiver grid emphasizes the impact of room geometry and source–receiver positions on reverberation time and clarity. The study also notes spatial variations in parameters obtained from the two microphone arrays, suggesting potential for future research into their specific capabilities for room acoustic characterization.

Validation of auralized impulse responses considering masking, loudness and background noise

The use of outdoor virtual scenarios promises to have a lot of potential to facilitate reproducible sensory evaluation experiments in laboratory. Auralizations allow for the integration of simulated or measured sound sources and transfer paths between the sources and receivers. Nonetheless, pure simulations can lack perfect plausibility. This contribution investigates the augmentation of auralized outdoor scenes based on simulated impulse responses (IRs) by ambient or background sounds. For this purpose, foreground events such as car pass-bys are created by simplified simulation of impulse responses. Due to their large number of events, however, ambient sounds are typically not simulated. Instead, spherical microphone array recordings can be used to capture the background sound. Using synthesized car sounds, we examine how much the augmentation by background sound improves the auditory plausibility of simulated impulse responses in comparison with the equivalent measured ones.

Phoneme dependence of horizontal asymmetries in voice directivity.

Human voice directivity shows horizontal asymmetries caused by the shape of the lips or the position of the tooth and tongue during vocalization. This study presents and analyzes the asymmetries of voice directivity datasets of 23 different phonemes. The asymmetries were determined from datasets obtained in previous measurements with 13 subjects in a surrounding spherical microphone array. The results show that asymmetries are inherent to human voice production and that they differ between the phoneme groups with the strongest effect on the [s], the [l], and the nasals [m], [n], and [ŋ]. The least asymmetries were found for the plosives.

A proposed method to improve the WER of an ASR system in the noisy reverberant room

This paper proposes a novel approach to reducing the word error rate (WER) of an automatic speech recognition (ASR) system in a noisy reverberant room. This research utilizes the integration of beamforming, dereverberation, and ambisonic. Based on the demonstrated formula, the proposed system synthesizes the signal of desired points on the sphere surface from a combination of 32 signals of a uniform spherical microphone array (USMA). This method uses the non-parametric sound field reproduction technique in the spherical harmonics domain (SHD). Also, the suggested new geometry determines the place of the desired points. In addition to improving the dereverberation performance, the proposed method also improves the performance of the beamformer in terms of directivity factor (DF) and white noise gain (WNG). The results show that objective metrics such as PESQ are significantly improved, and the WER of the Kaldi and the WeNet ASR systems is reduced considerably.

Sound field recording using distributed spherical microphone arrays based on a virtual spherical model

Binaural synthesis helps provide rich spatial information to users. Spherical microphone arrays and head-related transfer functions significantly aid in realizing the aforementioned approach. In a typical case, a spherical microphone array is set at the recording point, and listeners experience the sound binaurally as if they are at the recording point. However, in real situations, setting a microphone array at the recording point is not always feasible. In this study, we investigate binaural synthesis using an Auditory Display based on VIrtual SpherE (ADVISE) model with distributed spherical microphone arrays. In the proposed ADVISE-based method, the virtual sphere is set around the target point, and the sound pressure on the boundary of the virtual sphere is calculated based on recorded signals using spherical microphone arrays. The simulation results indicate that the proposed method can robustly synthesize sound fields even when the target point is far from the spherical microphone arrays.

CRNN-based spatial active noise control in spherical harmonics domain

In this work, an active noise control (ANC) in the spherical harmonics (SH) domain, along with a learning model, is developed. The traditional ANCs are built on the adaptive signal processing framework and fail in the presence of nonlinear distortions. Further, these algorithms are limited to the horizontal plane only. In contrast, the proposed work develops the ANC in the 3D space using the SH representation with the spherical microphone array (SMA) as the error microphone. The SH decomposition calculates the SH pressure coefficients from the SMA recordings. Subsequently, a convolutional recurrent neural network (CRNN) is trained to estimate the real and imaginary spectrograms from the SH coefficients as the input features. The output of the CRNN is the canceling signal that eliminates or attenuates the primary noise in the ANC system. A delay-compensated method addresses ANC system latency. According to simulations and experiments, the proposed learning-based spatial ANC reduces wideband noise and generalizes to untrained noises.

Evaluation of virtual sensing with spherical array surrounding head for directional noise

Active noise control (ANC) is expected to be applicable to public transportation modalities such as airplanes and trains. In these application systems, passengers may need to avoid wearing devices such as earphones and ear microphones. However, in conventional ANC systems, it is necessary to locate a physical microphone at the ear positions as an error sensor. To overcome this problem, virtual sensing techniques have been studied for estimating sound pressures at ear positions using remote microphones. In this study, we investigated the performance of a virtual sensing method for interpolating the sound pressures at ear positions using a spherical microphone array surrounding the head, based on a spherical harmonic expansion. The experiments were conducted using a rigid sphere instead of a head and dodecahedral spherical microphone array surrounding the sphere. The estimation errors were evaluated for various noise directions at low frequencies (100, 300, 500, and 700 Hz). The experimental results showed that the estimation errors were less than -20 dB for almost all conditions below 500 Hz. By comparison with other virtual sensing methods using a few microphones in the vicinity of the ear positions, we confirmed that our proposed method was effective for any noise direction.

Multi-Objective NSGA-II Optimization for Broadband Beamforming with Spherical Harmonic Domain Assistance.

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.

Physics-informed neural network assisted spherical microphone array signal processing

Thanks to their rotational symmetry that facilitates three-dimensional signal processing, spherical microphone arrays are the common array apertures used for spatial audio and acoustic applications. However, practical implementations of spherical microphone arrays suffer from two issues. First, at high frequency range, a large number of sensors are needed to accurately capture a sound field. Second, the accompanying signal processing algorithm, i.e., the spherical harmonic decomposition method, requires a variable radius array or a rigid surface array to circumvent the spherical Bessel function nulls. Such arrays are hard to design and introduce a scattering field. To address these issues, this paper proposes to assist a spherical microphone array with a physics-informed neural network (PINN) for three-dimensional signal processing. The PINN models the sound field around the array based on the sensor measurements and the acoustic wave equation, augmenting the sound field information captured by the array through prediction. This makes it possible to analyze a high frequency sound field with a reduced number of sensors and avoid the spherical Bessel function nulls with a simple single radius open-sphere microphone array.

Computation of spherical sector harmonics norm with application to blind source separation.

Spherical microphone arrays (SMAs) are widely being used for source localization and separation. However, it is uneconomical to build a full SMA when sources are present in restricted regions of environment. Hence, a spherical sector microphone array is utilized for blind source separation for the first time. In particular, the norm of the spherical sector harmonics basis function is computed for mixing matrix estimation. The estimated steering vectors are clustered using mean-shift algorithm. The number of sources is estimated automatically from the number of clusters. The developed mathematical framework is verified using various simulations and experiments on real data.

Multizone reproduction by matching the velocity vectors

This paper proposes a velocity-based multizone reproduction method, which reproduces the velocity vectors throughout each listening zone. Velocity vectors are related to the localization of sound below 700 Hz. Previous work considered reproducing the velocity vectors at sweet spots or on the listening zone’s boundary, and usually involved measurements using multiple velocity sensors. In this paper, in each listening zone, the velocity vectors are calculated from the spherical harmonic coefficients of the pressure, which are obtained by a spherical microphone array. The calculation of the velocity vectors is based on the sound field translation formula. Moreover, by reproducing the desired velocity vectors throughout each listening zone, listener's movement within each zone is allowed. To enlarge the size of the listening zone, the sound field in each listening zone is expressed by a sparse distribution of plane waves that results in the same velocity vectors. The pressure transfer functions between each loudspeaker and each listening zone are measured by placing a spherical microphone array at multiple spatial sampling points within each listening zone. The loudspeaker driving functions are calculated by matching the velocity vectors due to the sparse distribution of plane waves in each listening zone.

Time domain virtual sensing method based on a rigid-sphere transfer function for active noise control headrests

Active noise control (ANC) is expected to be used in public transportation such as airplanes and trains. While using these applications, passengers prefer not to wear earphones or ear microphones, if possible, to reduce ear strain. However, conventional ANC systems require a physical microphone, which acts as an error sensor, at the ear position. To address this issue, a virtual sensing technique has been studied that uses a microphone mounted on a seat’s headrest to estimate the sound pressure at the ear position. In this study, we propose a virtual sensing technique that interpolates the sound pressure at the ear position using a spherical microphone array surrounding the head. This method improves robustness to variations in noise arrival direction using spherical harmonic coefficients without directional dependence. In general, the interpolation formula using spherical harmonic expansion is obtained in the frequency domain. By contrast, the proposed method designs the interpolation process as an IIR filter by considering the minimum phase and estimates the noise signal directly in the time domain, achieving the real-time processing required for ANC. The effectiveness of the proposed method in reducing noise was investigated for various noise arrival directions.

Three-dimensional sound recording using directional beams

The recording of three-dimensional spatial audio is typically carried out using microphone arrays that produce higher-order B-format responses, which are defined by spherical harmonics. Spherical harmonics provide a compact, orthonormal representation of the sound field, but can be intuitively challenging for general users because they do not have a direction, as opposed to typical microphones used in the audio industry. Furthermore, spherical microphone arrays typically use microphone angles based on Platonic solids which do not have intuitive directions such as front, rear, left, right, up, and down. This paper considers the use of sets of directional beams that have orthonormal properties in a similar manner to spherical harmonics. Sets of angles that have intuitive directions are used, and a method of approximating orthonormal beams is developed. The approach can also be applied to angles obtained from Platonic solids. Finally, a prototype microphone array that implements the directional recording format is described.

Clear imaging method based on far-field beamforming for substation noise source identification

The noise problem of substations has become increasingly prominent in recent years, and the accurate identification of noise sources has been the prerequisite for substation noise control. By virtue of the advantages of long measurement distance and panoramic acoustic imaging, far-field beamforming based on solid spherical microphone arrays has broad application prospects in large substation noise source identification. Spherical harmonics beamforming (SHB) is a classical algorithm matched with spherical microphone arrays. However, its sound source identification results suffer from problems such as wide mainlobes at low frequencies and abundant sidelobes at high frequencies, which lead to limited acoustic imaging clarity. In order to achieve clear acoustic imaging of noise sources in large substations, the output of far-field SHB is reconstructed and the method of clear SHB (C-SHB) is proposed. The simulations and experiment show that C-SHB can significantly reduce the mainlobe width and suppress the sidelobe contamination, thus effectively improving the imaging clarity of SHB and enhancing its weak source identification capability.

An Improved Two-Stage Spherical Harmonic ESPRIT-Type 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.