Superdirective Beamforming Research Articles

A Superdirective Beamforming Approach based on MultiTransUNet-GAN

A Superdirective Beamforming Approach based on MultiTransUNet-GAN

A General Approach to the Design of the Fractional-Order Superdirective Beamformer

The superdirective beamformer (SD) with a linear array exhibits the maximum directivity factor (DF) in the isotropic noise field. Previously, a fractional-order SD (FO-SD) has been designed to achieve a compromise between the robustness and the DF. However, this method may suffer from two limitations. First, it only considers the Jacobi-Anger expansion-based beampattern synthesis. Second, it cannot control the DF in spherically isotropic noise field. To address these problems, we propose a general approach to the design of the FO-SD, which is a linear combination of two SDs with the integer order that can be designed with any beampattern synthesis method. Moreover, the proposed approach is able to control the WNG and the DF in both spherically and cylindrically isotropic noise field. Computer simulations substantiate the effectiveness of the proposed FO-SD over the existing SDs.

Robust superdirective beamforming for arbitrary sensor arrays

This paper presents a method of designing robust superdirective beamformers for arbitrary sensor arrays. First, the optimal weighting vector is transformed into an equivalent form based on the eigen–decomposition of the noise correlation matrix in an isotropic uniform noise field, and its entries will be indexed using mode orders instead of element numbers. Second, a parameter is weighted at the maximum–order entry in the modified weighting vector. The beampattern, directivity factor, and error sensitivity function can be expressed as functions of the parameter. Adjusting the parameter will achieve arbitrary–order superdirective beampatterns with different directivity factors or error sensitivity functions. Third, the closed–form expression of the parameter can be derived given a desired directivity factor or error sensitivity function. The final robust broadband superdirective beampatterns can then be readily synthesized. The proposed method, which is an extension of that previously proposed for circular sensor arrays, provides flexible schemes to designing robust broadband superdirective beamformers for arbitrary arrays in simulations and experiments.

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.

Frequency-invariant beamformer design via ADPM approach

Frequency-invariant (FI) beamformers play an important role in suppressing speech waveform distortions. Due to the perfect FI beampattern (FIB), differential microphone arrays (DMAs) have been widely used in practical applications like voice communication and human-machine interface systems. Superdirective beamforming generated by DMAs have many useful properties but suffer white noise amplification. To address this drawback, we formulate a least squares broadband FI problem, under the white noise output power constraints, to improve robustness of superdirective beamformers. The problem is challenging to solve since FI beamformers are designed on broadband and initialization parameters corresponding to each frequency are different. We devise broadband beampattern synthesis algorithm based on alternating direction penalty method (ADPM), which utilizes the relationship between residuals and penalty terms to reduce the iteration number under the improved framework of alternating direction method of multipliers (ADMM). The proposed ADPM method can decompose the optimization problem into multi-block convex optimization problems and solve them separately. The fast convergence property of our solution is demonstrated via numerical simulations.

A Neural Beamspace-Domain Filter for Real-Time Multi-Channel Speech Enhancement

Most deep-learning-based multi-channel speech enhancement methods focus on designing a set of beamforming coefficients, to directly filter the low signal-to-noise ratio signals received by microphones, which hinders the performance of these approaches. To handle these problems, this paper designs a causal neural filter that fully exploits the spectro-temporal-spatial information in the beamspace domain. Specifically, multiple beams are designed to steer towards all directions, using a parameterized super-directive beamformer in the first stage. After that, a deep-learning-based filter is learned by, simultaneously, modeling the spectro-temporal-spatial discriminability of the speech and the interference, so as to extract the desired speech, coarsely, in the second stage. Finally, to further suppress the interference components, especially at low frequencies, a residual estimation module is adopted, to refine the output of the second stage. Experimental results demonstrate that the proposed approach outperforms many state-of-the-art (SOTA) multi-channel methods, on the generated multi-channel speech dataset based on the DNS-Challenge dataset.

Deep neural network-based generalized sidelobe canceller for dual-channel far-field speech recognition

The traditional generalized sidelobe canceller (GSC) is a common speech enhancement front end to improve the noise robustness of automatic speech recognition (ASR) systems in the far-field cases. However, the traditional GSC is optimized based on the signal level criteria, causing it not to guarantee the optimal ASR performance. To address this issue, we propose a novel dual-channel deep neural network (DNN)-based GSC structure, called nnGSC, which is optimized by using the objective of maximizing the ASR performance. Our key idea is to make each module of the traditional GSC fully learnable and use the acoustic model to perform joint optimization with GSC. We use the coefficients of the traditional GSC to initialize nnGSC, so that both traditional signal processing knowledge and large amounts of data can be used to guide the network learning. In addition, nnGSC can automatically track the target direction-of-arrival (DOA) frame-by-frame without the need for additional localization algorithms. In the experiments, nnGSC achieves a relative character error rate (CER) improvement of 23.7% compared to the microphone observation, 13.5% compared to the oracle direction-based super-directive beamformer, 12.2% compared to the oracle direction-based traditional GSC and 5.9% compared to the oracle mask-based minimum variance distortionless response (MVDR) beamformer. Moreover, we can improve the robustness of nnGSC against array geometry mismatches by training with multi-geometry data.

On the Robustness of the Superdirective Beamformer

In microphone array beamforming, a high directional gain is always desired for acoustic noise and reverberation suppression; as a result, the superdirective beamformer has been of great interest in many applications. However, this beamformer is well known to be very sensitive to array imperfections. While much effort has been made to improve its robustness, it is still a major problem. This paper is essentially devoted to the study of the robustness of the superdirective beamformer and derivation of better ways to deal with this important issue. We first prove that any distortionless fixed beamformer can be written as the sum of two orthogonal beamformers, i.e., the sum of the classical delay-and-sum (DS) beamformer and a reduced-rank beamformer. Based on this property, different kinds of robust superdirective beamformers are then developed. We also show that the robust design problem can be transformed into a quadratic eigenvalue problem (QEP), which leads to a solution that achieves the maximum possible directivity factor (DF) while meets the white noise gain (WNG) constraint over a frequency band of interest.

A Robust Wavenumber-Domain Superdirective Beamforming for Endfire Arrays

Among various array configurations, superdirective beamforming based on linear differential arrays has attracted much attention. It is well known that its directivity performance degrades at higher frequencies due to the limitation of finite difference approximation, and its robustness deteriorates due to the mismatch of practical systems. In this paper, we develop a wavenumber-domain superdirective beamforming for endfire arrays, an alternative way of phase mode beamforming that cannot be applied directly to linear arrays. Here, “wavenumber-domain” means the spatial derivatives are calculated in the wavenumber domain through multiplication operations. An important feature of proposed method is that it provides a novel way to obtain the higher order derivatives from the reconstructed sound field utilizing all sensors of array, which is valid when the Nyquist criterion is satisfied, resulting in a broadband frequency-independent beamformer. On the other hand, since the proposed $N\rm {th}$ -order superdirective beamformer has no upper limit of number of sensors, its robustness at lower frequencies can be enhanced through increasing the number of sensors and using an optimum truncation parameter which plays a role to remove small singular values sensitive to the mismatch of array. Although it is demonstrated that the proposed method and the weighted least-squares optimization method lead to almost identical performances, the main advantage of the proposed method is that an optimum truncation parameter determined by the experiment is adopted to increase the robustness of beamformers, where the high sensitivity of the higher eigenbeams to random errors is exploited.

On microphone array beamforming and insights into the underlying signal models in the short-time-Fourier-transform domain.

This paper studies signal models for microphone array beamforming in the short-time-Fourier-transform (STFT) domain with long acoustic impulse responses. The major contributions are as follows. First, the signal modeling problem is investigated in the STFT domain and a general decomposition is proposed for the convolved source signal. Second, new insights into the array manifold are presented: the STFT of the windowed acoustic impulse response from the source to the sensors. Third, the structure of the reference signal is analyzed: it can be viewed as the output of a beamformer without considering the noise in the observation signal. Fourth, based on the new perspectives and decomposition, a signal model is derived based on the use of the superdirective beamformer. Finally, three performance measures are defined, based on which three optimal/suboptimal signal models are derived and their performance is assessed under different acoustic environments and analysis window lengths. The performance of the well-known minimum variance distortionless response (MVDR) beamformer is evaluated, which justifies the properties of the developed signal models.

Near-Field Superdirectivity: An Analytical Perspective

The gain achieved by a superdirective beamformer operating in a diffuse noise-field is significantly higher than the gain attainable with conventional delay-and-sum weights. A classical result states that for a compact linear array consisting of $N$ sensors which receives a plane-wave signal from the end-fire direction, the optimal superdirective gain approaches $N^2$ . It has been noted that in the near-field regime higher gains can be attained. The gain can increase, in theory, without bound for increasing wavelength or decreasing source-receiver distance. We aim to address the phenomenon of near-field superdirectivity in a comprehensive manner. We derive the optimal performance for the limiting case of an infinitesimal-aperture array receiving a spherical-wave signal. This is done with the aid of a sequence of linear transformations. The resulting gain expression is a polynomial, which depends on the number of sensors employed, the wavelength, and the source-receiver distance. The resulting gain curves are optimal and outperform weights corresponding to other superdirectivity methods. The practical case of a finite-aperture array is discussed. We present conditions for which the gain of such an array would approach that predicted by the theory of the infinitesimal case. The white noise gain (WNG) metric of robustness is shown to increase in the near-field regime.

Binaural Heterophasic Superdirective Beamforming.

The superdirective beamformer, while attractive for processing broadband acoustic signals, often suffers from the problem of white noise amplification. So, its application requires well-designed acoustic arrays with sensors of extremely low self-noise level, which is difficult if not impossible to attain. In this paper, a new binaural superdirective beamformer is proposed, which is divided into two sub-beamformers. Based on studies and facts in psychoacoustics, these two filters are designed in such a way that they are orthogonal to each other to make the white noise components in the binaural beamforming outputs incoherent while maximizing the output interaural coherence of the diffuse noise, which is important for the brain to localize the sound source of interest. As a result, the signal of interest in the binaural superdirective beamformer’s outputs is in phase but the white noise components in the outputs are random phase, so the human auditory system can better separate the acoustic signal of interest from white noise by listening to the outputs of the proposed approach. Experimental results show that the derived binaural superdirective beamformer is superior to its conventional monaural counterpart.

Personal audio system for neckband headset with low computational complexity.

Personal audio systems have been developed based on various approaches with the goal of synthesizing an isolated sound zone that avoids disturbing others in different locations. In this work, a near-field solution for a neckband headset using three loudspeakers positioned close to each ear is proposed. In particular, it is an attempt to derive a simple multichannel filter for reducing the computational cost in mobile devices. Unlike super-directive beamforming techniques, the controlled radiation pattern is not highly directional but can boost the near-field sound, thereby providing an extra sound level difference between the listener's ear locations and far-field surrounding areas. For this purpose, a multichannel filter is designed using a conventional pressure matching technique for reproducing a target signal at the ear location while suppressing sound radiation to a far-field. It is shown that the optimal filter weights can be successfully approximated in the form of a simple broadside differential array pattern. The simplified filter structure can be realized using only two second-order infinite impulse response filters for driving the middle and two side loudspeakers. Through various simulations and experiments, it is demonstrated that the proposed solution can effectively realize a personal audio system with a minimal loss of sound isolation performance.

Superdirective Robust Algorithms’ Comparison for Linear Arrays

Frequency-invariant beam patterns are often required by systems using an array of sensors to process broadband signals. In some experimental conditions (small devices for underwater acoustic communication), the array spatial aperture is shorter than the involved wavelengths. In these conditions, superdirective beamforming is essential for an efficient system. We present a comparison between two methods that deal with a data-independent beamformer based on a filter-and-sum structure. Both methods (the first one numerical, the second one analytic) formulate a mathematical convex minimization problem, in which the variables to be optimized are the filters coefficients or frequency responses. The goal of the optimization is to obtain a frequency invariant superdirective beamforming with a tunable tradeoff between directivity and frequency-invariance. We compare pros and cons of both methods measured through quantitative metrics to wrap up conclusions and further proposed investigations.

Microphone Array Geometries for Horizontal Spatial Audio Object Capture With Beamforming

Microphone array beamforming can be used to enhance and separate sound sources, with applications in the capture of object-based audio. Many beamforming methods have been proposed and assessed against each other. However, the effects of compact microphone array design on beamforming performance have not been studied for this kind of application. This study investigates how to maximize the quality of audio objects extracted from a horizontal sound field by filter-and-sum beamforming, through appropriate choice of microphone array design. Eight uniform geometries with practical constraints of a limited number of microphones and maximum array size are evaluated over a range of physical metrics. Results show that baffled circular arrays outperform the other geometries in terms of perceptually relevant frequency range, spatial resolution, directivity and robustness. Moreover, a subjective evaluation of microphone arrays and beamformers is conducted with regards to the quality of the target sound, interference suppression and overall quality of simulated music performance recordings. Baffled circular arrays achieve higher target quality and interference suppression than alternative geometries with wideband signals. Furthermore, subjective scores of beamformers regarding target quality and interference suppression agree well with beamformer onaxis and off-axis responses; with wideband signals the superdirective beamformer achieves the highest overall quality.

Design and Implementation of an Active Noise Control Headphone With Directional Hear-Through Capability

This article presents the design and implementation of an active noise control (ANC) headphone system with a directional hear-through capability and compares the performance of this system to that of a standard hear-through headphone system. The directional hear-through ANC headphones are a novel integration of microphone array beamforming and ANC technologies into a pair of headphones, which provide the consumer with additional functionality and new, digitally augmented ways to interact with their acoustic environment. As the microphone array is necessarily compact, superdirective beamforming is utilised to increase its low and mid frequency directional performance. In this unique integration of two current consumer technologies, first, the ANC subsystem attempts to maximise the attenuation and then the beamformer output is added to the control signal and reproduced by the headphones’ loudspeakers, with the appropriate compensation to avoid self-cancellation. The experimental study demonstrates that the proposed spatially selective ANC headphones provide a hear-through capability in the look direction, whilst reducing ambient noise and enabling the wearer to experience reduced noise communication in a noisy environment. The proposed system thus offers the consumer the potential for an electronically enhanced acoustic experience, allowing a selective reduction in environmental noise whilst desired exterior noise remains audible.

Wind Direction Estimation Using Small-Aperture HF Radar Based on a Circular Array

Compact high-frequency (HF) antenna arrays are convenient to deploy. However, using a small-aperture HF surface wave radar for wind direction measurement is still a challenging problem, since an unsatisfactory array pattern degrades the performance of Bragg ratio estimation. To address this issue, a digital beamforming method based on a superdirective synthesis technique for an HF receiving array that consists of seven elements positioned on a 5-m diameter circle is proposed. This superdirective beamforming method contains a sidelobe constraint. Subsequently, a hybrid superdirective beamforming and direction-finding method is adopted to estimate the wind direction using a multifrequency HF radar based on a circular array (MHF-C). The superdirective beamforming approach, as well as the wind direction estimation method, is presented in detail. The wind direction estimation method has been applied to the raw data sets that were collected with two MHF-C radars installed along the coast of the East China Sea in April 2015 and comparisons between radar-derived and in situ wind directions have been made. Ship-mounted anemometers were used to obtain in situ measurements at six sampling locations within the overlapping coverage of both radars. Another comparison between the radar-derived and anemometer-derived wind directions, which were obtained from June 15, 2015 to August 12, 2015, has also been made. The results indicate that the proposed method is effective for wind direction estimation with root-mean-square differences (RMSDs) between 24.1° and 33.1°, when wind speeds were higher than 5 m/s. The analysis encourages us to recommend a minimum wind speed of 5 m/s for reasonably assessing wind direction measurement performance.

Uniform Linear Arrays of First-Order Steerable Differential Microphones

We propose a spatial filtering method for linear arrays of First-Order Steerable Differential Microphones (FOSDMs), which operates in two layers. In the former, signals acquired by individual microphones are locally filtered to produce the outputs of the FOSDMs. In the latter, the outputs of the FOSDMs are processed by another filter. We analyse different design methodologies and study the conditions under which the two filtering layers can be decoupled. The proposed two-layer spatial filter can be flexibly controlled with a single scalar parameter, which can be chosen, for example, to maximize the White Noise Gain (like in a Delay-and-Sum beamformer); or to maximize the Directivity Factor (like in a Super-Directive beamformer); without needing any matrix inversion. The effectiveness of the proposed beamforming method is compared with traditional spatial filtering techniques using different metrics.

Efficient implementation of superdirective beamforming in a half-space environment

In this paper, the case considered is a planar microphone array placed in front of a wall of the room so that the microphone array plane is perpendicular to that of the wall. For this arrangement, a so-called half-space propagation model has been recently proposed, which accounts for the joint contribution of the direct path and the earliest reflection introduced by the adjacent wall. Based on this propagation model, a numerical process to estimate a model of the diffuse noise spatial coherence, which accounts for the presence of the reflecting surface, is proposed. The suggested noise covariance model is used in order to extend the superdirective beamformer in half-space, achieving notable improvements in performance in comparison to a more typical implementation that involves the spherical isotropic coherence model.

Superdirective beamforming applied to SWellEx96 horizontal arrays data for source localization.

Arrays employing superdirective beamforming can provide the same directivity and directivity index (or array gain) with less aperture as a large size array using conventional beamforming (CBF). Superdirective arrays offer a practical and significant improvement in the reception of low frequency signals and is useful for many applications where the array size is limited, such as a miniature microphone array or an underwater acoustic array with a limited aperture. Deconvolving the CBF is a method of superdirective beamforming. The improvement in directivity (beam width) and array gain is studied/illustrated using the SWellEx96 horizontal array data where only sub-arrays are used.