MVDR Beamformer Research Articles

A Nyström-based low-rank unitary MVDR beamforming scheme

A Nyström-based scheme is devised to approximate the real symmetrical covariance matrix of the popular unitary MVDR (U-MVDR) beamformer with low-rank kernel matrix, based on which a novel lightweight and robust Nyström-based U-MVDR (NU-MVDR) beamformer is developed. Subsequently, the full-dimensional Nyström covariance matrix estimator’s signal subspace can be calculated by eigenvalue decomposition (EVD) of two reduced-dimensional matrices, which will save a significant amount of computing load at the EVD stage. This scheme has obvious computational efficiency and lightweight storage overheads. Meanwhile, we derive the effect of the Nyström covariance matrix’s rank on the output signal-to-interference-plus-noise ratio (SINR). Numerical results demonstrate that the proposed beamformer performs well in less snapshots and steering vector errors cases.

Mitigating Multiple Moving Interferers with the Hybrid Double Zero MVDR Beamformer

Mitigating Multiple Moving Interferers with the Hybrid Double Zero MVDR Beamformer

Performance Analysis of MVDR Beamformer Applied on an End-fire Microphone Array Composed of Unidirectional Microphones

Performance Analysis of MVDR Beamformer Applied on an End-fire Microphone Array Composed of Unidirectional Microphones

Frequency-Invariant Sensor Selection for MVDR Beamforming in Wireless Acoustic Sensor Networks

Wireless acoustic sensor network (WASN) has a wide range of applications in internet of things, where signal estimation is one of the network design objectives. Due to the existence of ambient noises, the recorded audio signals are inevitably corrupted, resulting in a low signal-to-noise ratio (SNR), which triggers the necessity of signal enhancement. As using all sensor measurements brings a large amount of data transmissions and computational cost, the narrowband sensor selection was proposed to choose an informative subset of sensors to perform noise reduction in the audio context. However, the resulting frequency-dependent selection status has to be switched across frequencies. In order to avoid the complicated switching operations, we consider frequency-invariant sensor selection in this work. We propose to minimize the total power consumption over the WASN by constraining the broadband SNR, which can be solved using broadband semi-definite optimization (BroadOpt) or narrowband voting (NaVo) approaches. In order to further reduce the time complexity, we propose two near-optimal greedy methods, including gradient removal (GradR) and weighted input SNR removal (SnrR). As comparison, we also show a broadband energy removal (EnergyR) method. The greedy methods remove one sensor at each iteration from the complete network until the performance constraint is not satisfied. Numerical results using a simulated large-scale WASN show that the greedy methods can achieve a comparable performance compared to the optimization based counterparts, while the corresponding time complexity is much lower. In general, the sensors around the target source and the fusion center are more likely to be selected.

Reduced‐dimension MVDR beamformer based on sub‐array optimization

A reduced-dimension minimum variance distortionless response based on sub-array optimization beamformer (SAMVDR) is proposed for large array systems or some hardware performance constrained scenarios. The SAMVDR allows to weigh between convergence rate and computational complexity by selecting the sizes of the sub-arrays. It is worth noting that, employing a sub-array strategy, the SAMVDR allows for computing the matrix inversion with flexibly choosing the size of the matrix. When the size of each sub-array is 1, namely single weight optimization MVDR (SWMVDR), the SAMVDR avoids matrix inversion. So the SWMVDR is easiest to implement in system than other sizes of sub-arrays in the SAMVDR. It is found that the SAMVDR has manageable computational complexity and fast convergence rate, which is verified by theoretical analysis and simulation results. Importantly, the output performance of the SAMVDR is very close to auxiliary vector (AV) scheme, and the SWMVDR has lower computational cost than the AV. In addition, the SAMVDR can be applied to parallel systems with higher tracking speed.

Microphone Array Beamforming With High Flexible Interference Attenuation and Noise Reduction

This paper studies the problem of microphone array beamforming to enhance a speech signal of interest in adverse acoustic environments, where interference and additive background noise coexist. The problem is formulated as one of convex optimization whose solution under a specified level of interference attenuation leads to an interference controlled maximum noise reduction (ICMR) beamformer, which can be expressed as a linear combination of two MVDR beamformers: one attempts to extract the desired source signal while the other attempts to extract the interference. The combination coefficients are functions of the array manifold vectors, noise coherence matrix, and the specified interference attenuation factor. By tuning the interference attenuation factor, the ICMR beamformer can be implemented to achieve aggressive interference attenuation or even eliminate interference completely; but this may lead to less additive noise suppression or even noise amplification. To control the maximum sacrifice in gain (SG) of the signal-to-noise ratio (SNR) that is acceptable for additive reduction, a variant of ICMR is derived, which is named as the ICMR-SG beamformer. Simulations are performed and the results show that the ICMR beamformer is able to control the amount of interference attenuation. In comparison, ICMR-SG controls the maximum SG of SNR while achieving the optimal possible level of interference attenuation.

Robust Widely Linear Beamforming With Multiple Uncertainty Sets

The widely linear minimum variance distortionless response (WL-MVDR) beamformer has a better performance than the conventional MVDR beamformer when the received signals are potentially noncircular. However, it is sensitive to the extended steering vector (ESV) mismatches which can be caused by direction of arrival (DOA) errors, noncircularity coefficient errors, array imperfections and so on. To improve the robustness against large ESV mismatches, a robust WL beamformer based on the worst-case performance optimization (WCPO) method with multiple uncertainty sets is proposed. The resultant beamformer has the mathematical form of a nonconvex optimization problem, which can be converted into a semidefinite programming (SDP) problem and solved iteratively. Simulation results show that, in comparison with several representative robust WL beamformers, the proposed method can achieve better performances, especially under large ESV mismatch conditions.

Mask-based blind source separation and MVDR beamforming in ASR

This paper presents a front-end enhancement system for automatic speech recognition to address the cocktail party problem. Cocktail party problem is focus on recognizing the target speech when multiple speakers talk in the noisy real-environments. Many conventional techniques have been proposed. In this work, we propose a new framework to integrate the conventional blind source separation and minimum variance distortionless response beamformer for the speech enhancement and source separation of the recent CHiME-5 challenge. In our experiments, we found that the time–frequency (T–F) mask estimation strategy based on the BSS algorithm should be different for speech enhancement and source separation. The main difference is that whether we need to account for background noise as an additional class during T–F mask estimation. Experimental results showed that the proposed framework was very beneficial to improve the speech recognition performance on the Single-array-track of CHiME-5. We obtained relative 13.5% WER reduction than the official baseline system by only improving the front-end speech enhancement framework.

Optimal Beamforming Design for Underwater Acoustic Communication With Multiple Unsteady Sub-Gaussian Interferers

Traditional beamforming (BF) methods can be used to suppress the Gaussian interferers in underwater acoustic communication systems. However, multiple unsteady sub-Gaussian interferers may exist that degrade the performance of BF. In this paper, a new beamformer is proposed for the suppression of multiple unsteady sub-Gaussian interferers (SMUSGI). The proposed BF combines the multiplier and the quasi-Newton methods to obtain the optimal weight vector. Simulation experiments are conducted to validate the performance of the proposed beamformer. In addition, the proposed beamformer is compared with the traditional methods including the MVDR, Subspace, Bartlett, MDDR, LCMD and LCMV beamformers. The obtained results demonstrate that the proposed beamformer can effectively suppress multiple unsteady sub-Gaussian interferers with a higher output signal-to-interference-plus-noise ratio (SINR), and faster convergence compared with the traditional methods.

Weighted Subspace-Constrained Adaptive Beamforming for Sidelobe Control

A weighted subspace-constrained minimum variance distortion-less response (WS-MVDR) beamformer is proposed for robustly controlling the peak sidelobe level (PSL) as well as the sidelobe shape of adaptive array pattern with stable mainlobe. The adaptive weight vector is projected onto the subspace constructed from the weighted sidelobe steering vectors. The norm of the projection is constrained below the derived constant value determined by the desired PSL. The only inequality constraint is introduced to the conventional MVDR beamformer, resulting in a second-order cone programming problem. The numerical results demonstrate that WS-MVDR outperforms existing ones in terms of beampattern control capability and computational complexity.

MVDR Beamformer with Subband Peak Energy Detector for Detection and Tracking of Fast Moving Underwater Targets Using Towed Array Sonars

MVDR Beamformer with Subband Peak Energy Detector for Detection and Tracking of Fast Moving Underwater Targets Using Towed Array Sonars

A Bayesian Hierarchical Model for Speech Enhancement With Time-Varying Audio Channel

We present a fully Bayesian hierarchical approach for multichannel speech enhancement with time-varying audio channel. Our probabilistic approach relies on a Gaussian prior for the speech signal and a Gamma hyperprior for the speech precision, combined with a multichannel linear-Gaussian state-space model for the acoustic channel. Furthermore, we assume a Wishart prior for the noise precision matrix. We derive a variational expectation-maximization VEM algorithm that uses a variant of a multichannel Wiener filter MCWF to infer the sound source and a Kalman smoother to infer the acoustic channel. It is further shown that the VEM speech estimator can be recasted as a multichannel minimum variance distortionless response MVDR beamformer followed by a single-channel variational postfilter. The proposed algorithm was evaluated using both simulated and real room environments with several noise types and reverberation levels. Both static and dynamic scenarios are considered. In terms of speech quality, it is shown that a significant improvement is obtained with respect to the noisy signal, and that the proposed method outperforms a baseline algorithm. In terms of channel alignment and tracking ability, a superior channel estimate is demonstrated.

Interaural Coherence Preservation for Binaural Noise Reduction Using Partial Noise Estimation and Spectral Postfiltering

The objective of binaural speech enhancement algorithms is to reduce the undesired noise component, while preserving the desired speech source and the binaural cues of all sound sources. For the scenario of a single desired speech source in a diffuse noise field, an extension of the binaural multichannel Wiener filter (MWF), namely the MWF-IC, has been recently proposed, which aims to preserve the interaural coherence (IC) of the noise component. However, due to the large complexity of the MWF-IC, in this paper we propose several alternative algorithms at a lower computational complexity. First, we consider a quasi-distortionless version of the MWF-IC, denoted as minimum-variance-distortionless response (MVDR-IC). Second, we propose to preserve the IC of the noise component using the binaural MWF with partial noise estimation (MWF-N) and the binaural MVDR beamformer with partial noise estimation (MVDR-N), for which closed-form expressions exist. In addition, we show that for the MVDR-N a closed-form expression can be derived for the tradeoff parameter yielding a desired magnitude squared coherence (MSC) for the output noise component. Since contrary to the MWF-IC and the MWF-N the MVDR-IC and the MVDR-N do not take into account the spectro-temporal properties of the speech and the noise components, we propose to apply a spectral postfilter to the filter outputs, improving the noise reduction performance. The performance of all algorithms is compared in several diffuse noise scenarios. The simulation results show that both the MVDR-IC and the MVDR-N are able to preserve the MSC of the noise component, while generally the MVDR-IC shows a slightly better noise reduction performance at a larger complexity. Further, simulation results show that applying a spectral postfilter leads to a very similar performance for all considered algorithms in terms of noise reduction and speech distortion.

A parallel complex divider architecture based on DCD iterations for computing complex division in MVDR beamformer

A parallel complex divider architecture based on DCD iterations for computing complex division in MVDR beamformer

A Comparison of MVDR and LCMV Beamformers’ Floating Point Implementations on FPGAs

Adaptive beamformers are designed with the aim of detection of noise and intentional destructive interference and then removing them from the desired signal. This is done by placing high attenuation in the direction of the destructive signal in the radiation pattern of antenna arrays without attenuating the signal from a known direction. Minimum variance distortionless response and linearly constrained minimum variance are among such algorithms in mobile communications. A short explanation of the theory and weights formulae of these beamformers will be given. Two designs for weights calculations in Simulink with the added library of DSP-Builder tool from Altera will be presented. Quadrature Rectangular decomposition with Modified Gram-Schmidt algorithm is used instead of the direct matrix inversion. All calculations are done in single floating point mode for the required high accuracy. Modelsim has been used for hardware simulation and measuring the required clock cycles. The target FPGA is Aria10 from Altera which has floating point DSP blocks for high-performance computations. Hardware resources usage, power consumption, maximum clock frequency and update rate for different matrix sizes of these two beamformers are compared and discussed. The results are also compared with some other relevant reported works.

Online MVDR Beamformer Based on Complex Gaussian Mixture Model With Spatial Prior for Noise Robust ASR

This paper considers acoustic beamforming for noise robust automatic speech recognition. A beamformer attenuates background noise by enhancing sound components coming from a direction specified by a steering vector. Hence, accurate steering vector estimation is paramount for successful noise reduction. Recently, time-frequency masking has been proposed to estimate the steering vectors that are used for a beamformer. In particular, we have developed a new form of this approach, which uses a speech spectral model based on a complex Gaussian mixture model CGMM to estimate the time-frequency masks needed for steering vector estimation, and extended the CGMM-based beamformer to an online speech enhancement scenario. Our previous experiments showed that the proposed CGMM-based approach outperforms a recently proposed mask estimator based on a Watson mixture model and the baseline speech enhancement system of the CHiME-3 challenge. This paper provides additional experimental results for our online processing, which achieves performance comparable to that of batch processing with a suitable block-batch size. This online version reduces the CHiME-3 word error rate WER on the evaluation set from 8.37% to 8.06%. Moreover, in this paper, we introduce a probabilistic prior distribution for a spatial correlation matrix a CGMM parameter, which enables more stable steering vector estimation in the presence of interfering speakers. In practice, the performance of the proposed online beamformer degrades with observations that contain only noise or/and interference because of the failure of the CGMM parameter estimation. The introduced spatial prior enables the target speaker's parameter to avoid overfitting to noise or/and interference. Experimental results show that the spatial prior reduces the WER from 38.4% to 29.2% in a conversation recognition task compared with the CGMM-based approach without the prior, and outperforms a conventional online speech enhancement approach.

A weighted MVDR beamformer based on SVM learning for sound source localization

A weighted minimum variance distortionless response (WMVDR) algorithm for near-field sound localization in a reverberant environment is presented. The steered response power computation of the WMVDR is based on a machine learning component which improves the incoherent frequency fusion of the narrowband power maps. A support vector machine (SVM) classifier is adopted to select the components of the fusion. The skewness measure of the narrowband power map marginal distribution is showed to be an effective feature for the supervised learning of the power map selection. Experiments with both simulated and real data demonstrate the improvement of the WMVDR beamformer localization accuracy with respect to other state-of-the-art techniques.

Spatially Robust Far-field Beamforming Using the von Mises(-Fisher) Distribution

This paper presents spatially robust far-field microphone beamformers and nullformers derived using the von Mises and von Mises-Fisher distributions to model the expected direction of arrival. Simple analytic expressions are presented for 2D and 3D far-field correlation functions and used to design spatially robust beamformers and nullformers. It is demonstrated that the spatially robust beamformers show a modest improvement in tolerating uncertainty in the target direction of arrival without incurring a significant penalty in terms of SINR performance compared with the MVDR beamformer. In addition, the spatially robust formulation shows significantly improved numerical robustness, indicating improved ability in tolerating intrinsic array errors.

Theoretical Analysis of Binaural Transfer Function MVDR Beamformers with Interference Cue Preservation Constraints

The objective of binaural noise reduction algorithms is not only to selectively extract the desired speaker and to suppress interfering sources (e.g., competing speakers) and ambient background noise, but also to preserve the auditory impression of the complete acoustic scene. For directional sources this can be achieved by preserving the relative transfer function (RTF) which is defined as the ratio of the acoustical transfer functions relating the source and the two ears and corresponds to the binaural cues. In this paper, we theoretically analyze the performance of three algorithms that are based on the binaural minimum variance distortionless response (BMVDR) beamformer, and hence, process the desired source without distortion. The BMVDR beamformer preserves the binaural cues of the desired source but distorts the binaural cues of the interfering source. By adding an interference reduction (IR) constraint, the recently proposed BMVDR-IR beamformer is able to preserve the binaural cues of both the desired source and the interfering source. We further propose a novel algorithm for preserving the binaural cues of both the desired source and the interfering source by adding a constraint preserving the RTF of the interfering source, which will be referred to as the BMVDR-RTF beamformer. We analytically evaluate the performance in terms of binaural signal-to-interference-and-noise ratio (SINR), signal-to-interference ratio (SIR), and signal-to-noise ratio (SNR) of the three considered beamformers. It can be shown that the BMVDR-RTF beamformer outperforms the BMVDR-IR beamformer in terms of SINR and outperforms the BMVDR beamformer in terms of SIR. Among all beamformers which are distortionless with respect to the desired source and preserve the binaural cues of the interfering source, the newly proposed BMVDR-RTF beamformer is optimal in terms of SINR. Simulations using acoustic transfer functions measured on a binaural hearing aid validate our theoretical results.

Combination of MVDR beamforming and single-channel spectral processing for enhancing noisy and reverberant speech

This paper presents a system aiming at joint dereverberation and noise reduction by applying a combination of a beamformer with a single-channel spectral enhancement scheme. First, a minimum variance distortionless response beamformer with an online estimated noise coherence matrix is used to suppress noise and reverberation. The output of this beamformer is then processed by a single-channel spectral enhancement scheme, based on statistical room acoustics, minimum statistics, and temporal cepstrum smoothing, to suppress residual noise and reverberation. The evaluation is conducted using the REVERB challenge corpus, designed to evaluate speech enhancement algorithms in the presence of both reverberation and noise. The proposed system is evaluated using instrumental speech quality measures, the performance of an automatic speech recognition system, and a subjective evaluation of the speech quality based on a MUSHRA test. The performance achieved by beamforming, single-channel spectral enhancement, and their combination are compared, and experimental results show that the proposed system is effective in suppressing both reverberation and noise while improving the speech quality. The achieved improvements are particularly significant in conditions with high reverberation times.