White Noise Gain Research Articles

A note on the design of frequency-invariant beamforming with uniform concentric circular microphone array

Compared to the frequency-invariant beamformer (FIB) with uniform circular microphone arrays, the FIB with uniform concentric circular microphone arrays (UCCAs) can mitigate the deep nulls problem in the white noise gain (WNG) and the directivity factor (DF). The WNG of the FIB-UCCAs can be improved by increasing the number of microphones. However, certain Jacobi-Anger expansion based methods for FIB-UCCAs utilize a linearly transformed version of the beamformer coefficients to optimize the WNG, which may result in severe beampattern distortion at high frequencies. In this paper, we present a beamformer design method that is based on the Jacobi-Anger expansion but optimizes the WNG directly. We analyze the effect of the truncation error of Jacobi-Anger expansion and demonstrate that the proposed method can effectively reduce the beampattern distortion. Computer simulations illustrate the performance advantages of the developed method in terms of the DF and WNG.

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.

Mode matching-based beamforming with frequency-wise truncation order for concentric circular differential microphone arrays.

It is desired that a fixed beamformer should maintain the frequency-invariant beampattern and achieve the high white noise gain (WNG), i.e., high robustness against the mismatch in practice. However, existing methods for the design of concentric circular differential microphone arrays (CCDMAs) cannot achieve a compromise between the high robustness and the frequency-invariant beampattern. To address this problem, a new analytical expression for the synthesized beampattern of CCDMAs is derived without any truncation error. Then CCDMAs are designed by matching mode coefficients of the approximated synthesized beampattern to that of the target differential beampattern, where an adjustable truncation order is utilized to enable a trade-off between the robustness and the beampattern distortion. A simple and effective procedure is presented to determine the frequency-wise truncation order. The proposed method reduces to three existing methods, i.e., the Jacobi-Anger method, the improved Jacobi-Anger method, and the minimum mean square error-based method, for a fixed truncation order, which in turn establishes a close connection with these methods and provides a unified view on the design of the CCDMAs. The superiority of the proposed method in terms of robustness and beampattern distortion is demonstrated through computer simulations.

Design of frequency-invariant uniform concentric circular arrays with first-order directional microphones

Most of the existing frequency-invariant beamformers (FIBs) with circular arrays are implemented with omnidirectional microphones, where uniform circular arrays (UCAs) and uniform concentric circular arrays (UCCAs) have been widely utilized. However, the resulting FIB usually suffers from the deep nulls problem in the white noise gain (WNG) and the white noise amplification problem at low frequencies even if the order of the target beampattern is one. Due to its simple implementation, first-order directional microphones are adopted to improve the robustness of the FIB with UCCAs (FIB-UCCAs) in this paper. We exploit the circular harmonics decomposition rather than the Jacobi–Anger expansion to approximate the beampattern of the FIB-UCCAs with first-order directional microphones, because the directivity pattern of directional microphones is related to the direction of the signal. We show that the FIB-UCCAs can completely avoid the deep nulls problem in the WNG as long as the ring with the largest radius utilizes first-order directional microphones. In addition, the white noise amplification problem at low frequencies can be greatly alleviated if first-order directional microphones are utilized. Specifically, we show that the inherent white noise amplification problem at low frequencies can be completely circumvented when the order of the desired beampattern is one.

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.

Design of performance-weighted blended mode filters for underwater experiments

Normal mode signals are valuable in ocean acoustic tomography and source localization, assuming that they can be separated using spatial or temporal filtering. Common spatial mode filters include the matched filter (MF) [Ferris, JASA, 1972] and the pseudo-inverse (PI) filter [Tindle et al., JASA, 1978]. Choosing a filter and its parameters, e.g., the PI filter rank, requires knowledge that is not readily available. For instance, it is unlikely that the levels of ambient noise or interference from other modes is known a priori. To address this problem, Chakrabarti and Wage [IEEE Oceans, 2021, 2022] developed a Performance-Weighted Blended mode filtering algorithm that adapts quickly to changing conditions and achieves better performance than a single fixed mode filter. The PWB filter blends a set of PI filters of varying ranks, including a rank-1 PI filter (MF). A PI filter can suppress interference from neighboring modes but is more vulnerable to noise than the MF, which has the maximum white noise gain. This talk explores practical aspects of the PWB implementation, including how to select the set of filters to blend given realistic underwater noise conditions. We will show experimental and simulated data to illustrate performance in different environments. [Work supported by ONR.]

Constant-Beamwidth LCMV Beamformer with Rectangular Arrays

This paper presents a novel approach utilizing uniform rectangular arrays to design a constant-beamwidth (CB) linearly constrained minimum variance (LCMV) beamformer, which also improves white noise gain and directivity. By employing a generalization of the convolutional Kronecker product beamforming technique, we decompose a physical array into virtual subarrays, each tailored to achieve a specific desired feature, and we subsequently synthesize the original array’s beamformer. Through simulations, we demonstrate that the proposed approach successfully achieves the desired beamforming characteristics while maintaining favorable levels of white noise gain and directivity. A comparative analysis against existing methods from the literature reveals that the proposed method performs better than the existing methods.

Design of a robust MVDR beamforming method with Low-Latency by reconstructing covariance matrix for speech enhancement

Aiming at solving the problems of the conventional minimum variance distortionless response (MVDR) beamformer in practical applications, such as the sensibility of the steering vector mismatch and beampattern distortion, a robust broadband MVDR beamforming method with low-latency by reconstructing covariance matrix is proposed and applied to speech enhancement with a linear microphone array in this paper. In this work, some important steps are optimized, and the main contribution is to consider the problem of correlation terms generated by the low latency. Firstly, the direction of arrival (DOA) is corrected and the steering vector is estimated based on the sparsity of the DOAs corresponding to the sound sources, which improves the ability of anti-mismatches in the steering vector. Secondly, the correlation terms between the sound sources and noise are estimated and eliminated by the Capon power within the eigen-subspace, and the indirect dominant method is used to eliminate the correlation terms between the sound sources, so that the covariance matrix is reconstructed to obtain a more robust MVDR beamformer. Thirdly, the problem of white noise amplification at low frequency bins is analyzed, and a white noise gain (WNG) modification method is proposed to obtain a compromise between the interference suppression and WNG. In the experiments, the TIMIT corpus is used to generate the multi-channel speech data set, and the performance of the proposed method is evaluated with different DOAs and input signal to interference plus noise ratios (SINRs). The experimental results show that the proposed method can effectively suppress the interferences and reduce the noise with strong robustness.

Design of Planar Differential Microphone Array Beampatterns with Controllable Mainlobe Beamwidth and Sidelobe Level.

The differential microphone array, or differential beamformer, has attracted much attention for its frequency-invariant beampattern, high directivity factor and compact size. In this work, the design of differential beamformers with small inter-element spacing planar microphone arrays is concerned. In order to exactly control the main lobe beamwidth and sidelobe level and obtain minimum main lobe beamwidth with a given sidelobe level, we design the desired beampattern by applying the Chebyshev polynomials at first, via exploiting the structure of the frequency-independent beampattern of a theoretical Nth-order differential beamformer. Next, the so-called null constrained and least square beamformers, which can obtain approximately frequency-invariant beampattern at relatively low frequencies and can be steered to any direction without beampattern distortion, are proposed based on planar microphone arrays to approximate the designed desired beampatterns. Then, for dealing with the white noise amplification at low-frequency bands and beampattern divergence problems at high-frequency bands of the null constrained and least square beamformers, the so-called minimum norm and combined solutions are deduced, which can compromise among the white noise gain, directivity factor and beampattern distortion flexibly. Preliminary simulation results illustrate the properties and advantages of the proposed differential beamformers.

Differential constant-beamwidth beamforming with cube arrays

In this paper, we present an azimuth and elevation constant-beamwidth (CB) differential beamforming approach for cube arrays. We decompose a global cube beamformer into a Kronecker-product (KP) of three sub-beamformers: two constant-beamwidth beamformers along the y and z axes, and a tunable super-directive (SD) beamformer along the x-axis. We propose two design methods to derive cube beamformers whose either white noise gain (WNG) or directivity factor (DF) may be set by design. We show that the CB threshold frequency with respect to the azimuth and elevation angles, and the WNG and DF performance, can be controlled by the number of microphones along each axis. In addition, we focus on the particular case of merely a single microphone along the x-axis, which yields a rectangular azimuth and elevation CB beamformer. We demonstrate that its CB threshold frequencies are controlled by the number of microphones along the y and z axes, and show that the WNG and DF performance measures are maximized when the two axes are equal in size. Finally, we analyze the performance of the proposed beamformers through simulations of speech signals in various reverberant scenarios, including deviations in the desired speech signal’s direction of arrival (DOA). We show that the proposed beamformers outperform previously-presented beamformers and the traditional SD and delay-and-sum (DS) beamformers, particularly in terms of the intelligibility of their corresponding time-domain enhanced signals.

A double zero MVDR beamformer that is universal over number of second-order notches

Adaptive beamformers, like the minimum variance distortionless response (MVDR) beamformer, suffer from interferer direction mismatch due to interferer motion. This mismatch reduces interferer suppression and degrades the beamformer’s performance. Applying a flatter and broader notch near the interferer location effectively suppresses moving interferers. The double zero MVDR (DZ MVDR) adaptive beamformer [Tuladhar & Buck, JASA, 2015] produces second-order notches in the interferer’s directions by squaring the array polynomial of a subarray SMI MVDR beamformer. The performance of the DZ MVDR beamformer depends on the chosen number of second-order notches by applying different subarray aperture sizes. If the number of interferers in a dynamic environment is known, then the ideal number of second-order notches can be implemented. In practice, the number of interferers is an unknown and often time-varying parameter. To address this challenge, we propose a universal DZ (UDZ) MVDR beamformer that is universal over the number of second-order notches. This universal beamformer requires fewer degrees of freedom than competing beamformers to suppress the interferers, thus providing a better white noise gain in the array output. We present simulation results illustrating the benefits of the UDZ MVDR beamformer in the presence of multiple moving interferers. [Work supported by ONR 321US.]

Source separation with an acoustic vector sensor for terrestrial bioacoustics

Passive acoustic monitoring is emerging as a low-cost, non-invasive methodology for automated species-level population surveys. However, systems for automating the detection and classification of vocalizations in complex soundscapes are significantly hindered by the overlap of calls and environmental noise. We propose addressing this challenge by utilizing an acoustic vector sensor to separate contributions from different sound sources. More specifically, we describe and implement an analytical pipeline consisting of (1) calculating direction-of-arrival, (2) decomposing the azimuth estimates into angular distributions for individual sources, and (3) numerically reconstructing source signals. Using both simulation and experimental recordings, we evaluate the accuracy of direction-of-arrival estimation through the active intensity method (AIM) against the baselines of white noise gain constraint beamforming (WNC) and multiple signal classification (MUSIC). Additionally, we demonstrate and compare source signal reconstruction with simple angular thresholding and a wrapped Gaussian mixture model. Overall, we show that AIM achieves higher performance than WNC and MUSIC, with a mean angular error of about 5°, robustness to environmental noise, flexible representation of multiple sources, and high fidelity in source signal reconstructions. Finally, we illustrate applications of AVS-based source separation for spatiotemporal analysis of birdsong in dawn chorus recordings.

A Perspective on Fully Steerable Differential Beamformers for Circular Arrays

Both the null-constrained method and the Jacobi-Anger expansion method are commonly adopted to design the fully steerable circular differential microphone arrays (CDMAs). So far, these two methods have been independently studied, and it is unclear why they exhibit pronounced performance difference and whether they have a potential connection. In this letter, we develop a unified framework for the design of the fully steerable CDMA, which jointly utilizes the null constraints and the Jacobi-Anger expansion. We show that the existing two methods can be treated as special cases of the proposed approach and they can indeed be connected. We then reveal that the null-constrained CDMA can be viewed as the regularized Jacobi-Anger expansion-based CDMA, which theoretically explains why the former can alleviate the deep nulls problem in white noise gain in certain cases and why it still suffers from the severe deep nulls in other cases. We further explain why the magnitude of the synthesized beampattern of the Jacobi-Anger expansion-based method in nulls' direction can be much larger than that of the null-constrained method. Simulations support the theoretical results well.

Two-Stage Beamforming With Arbitrary Planar Arrays of Differential Microphone Array Units

Differential Microphone Arrays (DMAs) are of great interest in the literature on small-sized microphone arrays, due to their good directivity properties and nearly frequency-invariant spatial responses. Recently developed beamforming techniques combine multiple DMA units to form flexible two-stage spatial filtering systems, where the output of each DMA is fed into a higher-level filter, called virtual filter, for further processing. In this manuscript, we analyze and discuss some properties of a broad class of two-stage beamformers with arbitrary planar geometry. In this context, the DMA units are all assumed to have the same directivity pattern of arbitrary order and can be characterized by a variable number of omnidirectional sensors organized in an arbitrary geometry. For any given choice of the virtual array filter, we introduce a closed-form optimization procedure to design DMA filters that maximize the White Noise Gain (WNG) or the Directivity Factor (DF) of the resulting two-stage beamformer at any frequency. Based on this frequency-dependent design, we propose a frequency-invariant design of the two-stage beamformer and we compare the performance of the two approaches. Finally, we propose two possible computational schemes for the proposed generic two-stage spatial filtering system and discuss their efficiency in performing filtering, steering, and changing beampattern.

Design of Maximum Directivity Beamformers With Linear Acoustic Vector Sensor Arrays

This paper studies the design of maximum directivity factor (MDF) beamformers based on uniform linear arrays (ULAs) consisting of acoustic vector sensors (AVSs). We first derive the main lobe constraints, which ensure that the beamformer's beampattern achieves a maximum in the look direction, and prove that any beamformer that satisfies the proposed constraints can be written as the sum of two orthogonal beamformers: the maximum white noise gain (MWNG) beamformer and a reduced-rank beamformer. Then, we derive the MDF beamformer by maximizing the directivity factor (DF) under the deduced constraints. We also derive a robust version of the MDF beamformer, which can keep the WNG above a pre-specified level. Compared to the conventional MDF beamformer based on ULAs with omnidirectional microphones, the designed MDF beamformer with uniform linear AVS arrays (ULAVSAs) can steer the beampattern to any look direction in the 3-dimensional space and achieves a higher directivity. The proposed MDF beamformer also outperforms the two-step MDF beamformer with ULAVSAs since it maximizes the DF. The proposed methods are validated through simulations as well as real experiments.

Beamforming for Small-Spacing Acoustic Vector Sensor Array Using Optimal Beampattern Synthesis Technique

Traditional low-frequency acoustic senor arrays will always be very large and not easy to be implemented. So it is meaningful to study small-spacing underwater acoustic sensor arrays. The superdirectivity beamforming technique can achieve high array gains for sensor arrays with small apertures, and we study superdirectivity beamforming for small-spacing acoustic vector sensor (AVS) arrays in this letter. We use the beampattern synthesis technique and establish the optimization problem by both considering the approximation of the beampattern to a Dirac delta function and constraint for white noise gain of the beamformer. The superdirectivity beamformers for AVS arrays are then obtained by solving this optimization problem. Simulation results show that the proposed method can achieve high directivity factors for small-spacing AVS arrays. Experimental results of an AVS array with aperture being less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{1}\,\text{m}$</tex-math></inline-formula> are also presented in this letter and around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{7.9}\,\text{dB}$</tex-math></inline-formula> array gain is obtained at the frequency of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{200}\,\text{Hz}$</tex-math></inline-formula> .

Optimal beamformer design in spherical sector harmonics domain

Beamforming using spherical microphone arrays (SMAs) with processing in spherical harmonics (SH) domain is widely being studied. This is due to the ease of array processing in SH domain with no spatial ambiguity. Despite the widespread applications of SMA in beamforming, its size makes it inconvenient for practical or commercial use. Building of SMA over a rigid sphere is also a challenging task. Additionally, use of the entire sphere comes at the cost of more microphones and signals to process. Hence, it is uneconomic to use full SMA when sources are only present in restricted regions of the environment. Attempts have been made in literature to use hemispherical microphone array for beamforming. Acoustic image principle was utilized to enable application of SH but with greater computational complexity. In this paper, the use of a spherical sector microphone array is proposed for beamforming. An orthonormal spherical sector harmonics (S2H) basis function is used for data model development. An ideal direction-invariant beampattern using S2H basis function is utilized. Subsequently, to make the beamformer robust against sensor noise with a sharp directivity pattern at the direction of arrival and zero elsewhere, a new maximum directivity and white noise gain (MD-WNG) beamformer is designed for a spherical sector microphone array. Performance analysis of the proposed beamformer is presented using various experiments on directivity pattern and array gain. The proposed method is additionally compared with several existing beamforming techniques. The comparison reveals that the S2H based beamforming provides reasonably better results compared to the existing methods.

Source separation with an acoustic vector sensor for terrestrial bioacoustics.

Passive acoustic monitoring is emerging as a low-cost, non-invasive methodology for automated species-level population surveys. However, systems for automating the detection and classification of vocalizations in complex soundscapes are significantly hindered by the overlap of calls and environmental noise. We propose addressing this challenge by utilizing an acoustic vector sensor to separate contributions from different sound sources. More specifically, we describe and implement an analytical pipeline consisting of (1) calculating direction-of-arrival, (2) decomposing the azimuth estimates into angular distributions for individual sources, and (3) numerically reconstructing source signals. Using both simulation and experimental recordings, we evaluate the accuracy of direction-of-arrival estimation through the active intensity method (AIM) against the baselines of white noise gain constraint beamforming (WNC) and multiple signal classification (MUSIC). Additionally, we demonstrate and compare source signal reconstruction with simple angular thresholding and a wrapped Gaussian mixture model. Overall, we show that AIM achieves higher performance than WNC and MUSIC, with a mean angular error of about 5°, robustness to environmental noise, flexible representation of multiple sources, and high fidelity in source signal reconstructions.

Multistage approach for steerable differential beamforming with rectangular arrays

This paper presents a multistage rectangular approach for steerable differential beamforming. As a first step, we propose employing a two-dimensional (2-D) differentiation scheme that operates independently on the columns and rows of a uniform rectangular array (URA). This yields a differentials matrix controlled by two parameters, Pc and Pr, which indicate the number of differential stages for the URA columns and rows. Then, as a second step, we design a rectangular differential beamformer and apply it to the vector form of the differentials matrix. We show that the proposed differentiation scheme may significantly improve the directivity of the resulted beamformer at the expense of white noise amplification. This improvement is heavily tied to selecting the (Pc,Pr) configuration per the desired signal incident angle. Next, we propose four rectangular differential beamformers and analyze their performances in terms of the white noise gain (WNG) and directivity factor (DF) measures. In addition, we address reverberant scenarios with three distinct incident angles of the desired signal. We examine the performances of each beamformer in terms of four reduction factors calculated from the noisy and enhanced signals and investigate their quality and intelligibility. We demonstrate that the proposed rectangular differential beamformers outperform common linear and differential beamformers in these measures, mainly when the incident angle is far from the endfire direction. Finally, we compare the proposed approach to two existing rectangular differential beamforming approaches from the literature. We show the proposed method to be preferable, considering both the quality and intelligibility of the enhanced signals.

Constant-Beamwidth Kronecker Product Beamforming With Nonuniform Planar Arrays

In this paper, we address the problem of constant-beamwidth beamforming using nonuniform planar arrays. We propose two techniques for designing planar beamformers that can maintain different beamwidths in the XZ and YZ planes based on constant-beamwidth linear arrays. In the first technique, we utilize Kronecker product beamforming to find the weights, thus eliminating matrix inversion. The second technique provides a closed-form solution that allows for a tradeoff between white noise gain and directivity factor. The second technique is applicable even when only a subset of the sensors is used. Since our techniques are based on linear arrays, we also consider symmetric linear arrays. We present a method that determines where sensors should be placed to maximize the directivity and increase the frequency range over which the beamwidth remains constant, with a minimal number of sensors. Simulations demonstrate the advantages of the proposed design methods compared to the state-of-the-art. Specifically, our method yields a 1000-fold faster runtime than the competing method, while improving the wideband directivity factor by over 8 dB without compromising the wideband white noise gain in the simulated scenario.