Robust blind beamforming algorithm using joint multiple matrix diagonalization (JMMD)

In real-world environments, the signals captured by a set of microphones in a speech communication system are mixtures of the desired signal, interference, and ambient noise. A promising solution for proper speech acquisition (with reduced noise and interference) in this context consists in using the linearly constrained minimum variance (LCMV) beamformer to reject the interference, reduce the overall mixture energy, and preserve the target signal. The minimum variance distortionless response beamformer (MVDR) is also commonly known to reduce the interference-plus-noise energy without distorting the desired signal. In either case, it is of paramount importance to accurately quantify the achieved noise and interference reduction. Indeed, it is quite reasonable to ask, for instance, about the price that has to be paid in order to achieve total removal of the interference without distorting the target signal when using the LCMV. Besides, it is fundamental to understand the effect of the MVDR on both noise and interference. In this correspondence, we investigate the performance of the MVDR and LCMV beamformers when the interference and ambient noise coexist with the target source. We demonstrate a new relationship between both filters in which the MVDR is decomposed into the LCMV and a matched filter (MVDR solution in the absence of interference). Both components are properly weighted to achieve maximum interference-plus-noise reduction. We investigate the performance of the MVDR, LCMV, and matched filters and elaborate new closed-form expressions for their output signal-to-interference ratio (SIR) and output signal-to-noise ratio (SNR). We theoretically demonstrate the tradeoff that has to be made between noise reduction and interference rejection. In fact, the total removal of the interference may severely amplify the residual ambient noise. Conversely, totally focussing on noise reduction leads to increased level of residual interference. The proposed study is finally supported by several numerical examples.

In this paper, we study the performance of the minimum variance distortionless response (MVDR) and linearly constrained minimum variance (LCMV) noise reduction filters when a source of interference and ambient noise coexist with the target signal. We demonstrate that both filters are related as we decompose the MVDR filter into the LCMV and a matched filter (MVDR solution in the absence of interference). Both components are properly weighted to achieve maximum interference-plus-noise reduction at each frequency bin. Furthermore, we elaborate new closed-form expressions for the signal-to-interference ratio (SIR) and signal-to-noise ratio (SNR) at the output of the LCMV, MVDR, and matched filters. These expressions theoretically prove that a tradeoff between noise reduction and interference rejection has to be made. In fact, the total removal of the interference may severely amplify the output ambient noise. Conversely, totally focussing on noise reduction leads to increased level of residual interference. The proposed study is finally supported by numerical examples.

This paper studies and discusses robust minimum variance distortionless response (MVDR) beamformer with subarray multistage processing for circular hydrophone arrays, which is an extension of the multistage MVDR beamformer with line microphone arrays for noise reduction. The basic theory is to divide the hydrophones into a certain number of groups with each group only having two hydrophones for MVDR beamforming. After the beamforming, it is equivalent that the number of hydrophones is half of that at the adjoining former stage. Then the grouping and beamfoming processing will be repeated till that there is only one hydrophone. This subarray multistage MVDR beamformer has the following properties in the isotropic noise field: first, it is much more robust than the conventional MVDR beamformer; second, its array gain is lower than that of the conventional MVDR beamformer; moreover, the larger the sensor number in each subarray is, the higher the array gain will be, but with lower white noise gain. By choosing a proper hydrophone number of each subarray, a tradeoff can be made between the array gain and robustness.

Microphone arrays based on the minimum variance distortionless response (MVDR) beamformer are among the most popular for speech enhancement applications. The original MVDR is excessively sensitive to source location and microphone gains. Previous research has made MVDR practical by successfully increasing the robustness of MVDR to source location, and MVDR-based microphone arrays are already commercially available. Nevertheless, MVDR performance is still weak in cases where microphone gain variations are too large, e.g., for circular arrays of directional microphones. In this paper we propose an improved MVDR beamformer which takes into account the effect of sensors (e.g. microphones) with arbitrary, potentially directional responses. Specifically, we form estimates of the relative magnitude responses of the sensors based on the data received at the array and include those in the original formulation of the MVDR beamforming problem. Experimental results on real-world audio data show an average 2.4 dB improvement over conventional MVDR beamforming, which does not account for the magnitude responses of the sensors.

Speech enhancement is an important pre-processing step in a wide diversity of practical fields related to speech signals, and many signal-enhancement methods, such as fixed beamforming and adaptive beamforming, have already been proposed for speech enhancement. However, lack of comprehensive and quantitative performance evaluation of current enhancement methods when multi-speeches exist simultaneously, it is difficult to choose an appropriate enhancement method in a practical application. This work aims to study the implementation of several enhancement methods for multi-speech enhancement in indoor environment of T60 = 0 s and T60 = 0.3 s. We first propose and compare two types of enhancement approaches. The first type is the basic enhancement methods, including the delay-and-sum beamforming (DSB), minimum variance distortionless response (MVDR), linearly constrained minimum variance (LCMV), and independent component analysis (ICA); The second type is the improved enhancement methods, including the robust MVDR and LCMV, realized by eigen decomposition and diagonal loading. In addition, the online enhancement performance based on the iteration of single-frame speech signals is then researched. The experimental results show that the enhancement effect of LCMV and ICA is relatively more stable in the case of the basic enhancement methods; in the case of the improved enhancement algorithms, the methods which employed diagonal loading iterations are better. In the case of the online enhancement, the DSB with frequency masking yields the best performance on the signal-to-interferences ratio (SIR) and possesses the capacity to suppress interferences.

Most existing methods on beamformer design, such as the minimum variance distortionless response (MVDR) method and the linearly constrained minimum variance (LCMV) method, assume that the group delay is known and often heuristically preselected to be half of the filter length. However, the optimal group delay is problem-dependent in practice, and the beamformer design performance based on the optimal beamformer response can be significantly better than the one based on the preselected beamformer response in the reverberant environment. In this paper, we consider the optimal beamformer design problem, i.e., the joint beamformer response and beamformer design problem. We introduce a new variable to represent the beamformer response and formulate the joint beamformer response design and beamformer design problem as a structured constrained convex optimization (SCCO) problem. Moreover, we exploit the separable structures of the SCCO problem and propose to use the alternating direction method of multipliers (ADMM) to solve it, and give a simple proof for the analysis of convergence. Numerical simulation results show the effectiveness of the proposed method in the reverberant environment by comparing it with the LCMV method.

Beamforming techniques are becoming popular in a wide spectrum of applications thanks to their promising performance. We consider applying the minimum variance distortionless response (MVDR) beamformer in a dynamic scenario, where the desired speaker, the noise components or microphone array may move. The generalized sidelobe canceler (GSC) structure offers a convenient implementation of the MVDR, allowing to track the noise efficiently. Yet, noise reduction is degraded during speech tracking. We propose a QR Decomposition (QRD) based MVDR beamformer, which allows to track both speech and noise variations in dynamic scenarios without sacrificing noise reduction during speech segments. The proposed method utilizes the QRD algorithm for the implementation of a complete system required for the realization of an MVDR beamformer, which includes the identification of noisy speech or noise-only time-frequency bins, speech tracking and noise tracking. The proposed QRD based MVDR is efficiently implemented, and its overall computational complexity is O(M2), with M being the number of microphones. The advantages of the proposed method over the GSC are exemplified in a synthetically simulated scenario.

For multi-microphone speech enhancement, different microphones might have different contributions, assome are even marginal. This is more likely to happen in wireless acoustic sensor networks (WASNs), where somesensors might be distant. In this work, we therefore consider sensor selection for linearly-constrained beamformers. Theproposed sensor selection approach is formulated by minimizing the total output noise power and constraining thenumber of selected sensors. As the considered sensor selection problem requires the relative acoustic transfer function(RTF), the covariance whitening based RTF estimation or a direct-path RTF approximation is exploited. For a singletarget source, we can thus substitute the estimated RTF or the assumed RTF to the original problem formulation in orderto design a minimum variance distortionless response (MVDR) beamformer. Alternatively, we can integrate the two RTFsto design a linearly constrained minimum variance (LCMV) beamformer in order to alleviate the effects of RTFestimation/approximation errors. By leveraging the superiority of LCMV beamformers, the proposed approach can beapplied to the multi-source case. An evaluation using a simulated large-scale WASN demonstrates that the integration ofRTFs for the sensor selection based LCMV beamformer can be beneficial as opposed to relying on either of theindividual RTF steered sensor selection based MVDR beamformers. We conclude that the sensors that are close to thetarget source(s) and also some around the coherent interferers are more informative.

A new approach to implement minimum variance distortionless response (MVDR) beamforming is introduced for coherent plane-wave compounding (CPWC). MVDR requires the covariance matrix of the incoming signal to be estimated and a spatial smoothing approximation is usually adopted to prevent this calculation from being underconstrained. In the new approach, we analyze MVDR as a spatial filter that decorrelates signals received at individual channels before summation. Based on the analysis, we develop two MVDR beamformers without using any spatial smoothing. First, MVDR weights are applied to the received signals after accumulating the data over transmits at different angles, while the second involves weighting the data collected in individual transmits and compounding over the transducer elements. In both cases, the covariance matrix is estimated using a set of slightly different combinations of the echo data. We show the sufficient statistic for this estimation that can be described by approximating the correlation among the backscattered ultrasound signals to their spatial coherence. Using the van Cittert-Zernike theorem, their statistical similarity is assessed by relating the spatial coherence to the profile of the source intensity. Both spatial-coherence-based MVDR beamformers are evaluated on data sets acquired from simulation, phantom, and in vivo studies. Imaging results show that they offer improvements over simple coherent compounding in terms of spatial and contrast resolutions. They also outperform other existing MVDR-based methods in the literature that are applied to CPWC.

By comparing the disadvantages and advantages of conventional algorithms of adaptive beamformer, we put forward an adaptive beamformer based on weight iterative algorithm for suppressing RFI according to the distributing properties of radio frequency interference (RFI) in different range cell. We get the initial weight vector of the adaptive beamformer by using the algorithm of minimum variance distortionless response (MVDR). The other weight vectors are computed by the algorithm of linearly constrained minimum variance (LCMV) based on the last time weight vector. The covariance matrix of the two algorithms, i.e. MVDV and LCMV, are constructed with the array snapshots in the far range cells which have not useful radar echo. Thus the free degree of antenna array is increased. The feasibility of the adaptive beamformer is proved by using it to process the actual radar data.

Microphone array (MA) own substantial gain in evaluation due to the high spatial diversity to suppress unwanted noise, third-party talker, background noise, interfering signals coming from undesired directions. Minimum Variance Distortionless Response (MVDR) beamformer is an effective solution for extracting the clean speech data while mitigating all total noise power in different recording environment. However, in realistic situation, because of the moving head, the error of estimating transfer function, the complex and annoying recording scenario, the different microphone sensitivities, the inaccurate MA configuration, the imprecise estimation of other acoustic factors, MVDR beamformer’s evaluation often decreased in the the term of speech quality and speech intelligibility. The existence of remained noise, speech distortion decrease the overall MVDR beamformer’s performance. In this paper the author proposed using an appropriate spectral mask for reducing speech distortion. The obtained promising result has confirmed the effectiveness of the author’s method for improving the MVDR beamformer’s performance in adverse recording situations.

The optimal microphone array includes two processing blocks ‐ minimum variance distortionless response (MVDR) beamformer and the single‐channel Wiener filter, which acts as post‐filter. The main drawback of MVDR beamformer is the cancellation of the desired speech signal and its degradation in multi‐path wave propagation environment. To make the adaptive algorithm robust against room reverberation and to prevent desired signal cancellation, an estimation of the unknown desired speaker's transfer function was proposed. The estimation is based on the imperfect signal and the interference covariance matrices estimated from available microphone signals during speaker activity and pause of speech respectively. As MVDR beamformer suppresses coherent interference, post‐filter has to reduce diffuse acoustic noise. The post‐filter proposed in this paper is developed under assumption that complex coherence function is unknown but time invariant. The additional improvement of the post‐processing algorithm on low frequencies is obtained by combining a priori noise power attenuation factor for diffuse noise field with estimated one. The proposed algorithm is tested on simulated room with reverberation, and compared with some known post‐processing algorithms with rather good results.

The minimum variance distortionless response (MVDR) beamformer is very sensitive to errors, such as the the finite snapshots and the steering vector errors. A small mismatch can lead to serious degradation to its performance, especially at high signal-to-noise ratio(SNR). In this paper, a new robust MVDR beamformer is proposed. Our analysis starts from the physical meaning of the MVDR weight vector formula. Based on this analysis, DOA matrix is constructed in the single uniform linear array. Through the decomposition of this DOA matrix, we could obtain the actual signal modes contained in the covariance matrix of the snapshots. Then the weight vector could be modified to solve the robustness problem of MVDR beamforming. The computer simulation shows the effectiveness of this method.

In order to improve the robustness of microphone array beamformer in existing mismatch errors, robust beamforming algorithm based on linear constrained minimum variance and diagonal loading method is proposed. The proposed algorithm incorporates the spatial response variation function into the linear constrainted minimum variance criterion to design the frequency invariant beamformer and improve the robustness against microphone array mismatch errors in the actual environment by diagonal loading method. Simulation results and analyses illustrate that the array response within passband is robust, the stopband amplitude is controlled in the appropriate range, and the proposed algorithm based closed solution is better than the proposed algorithm based on convex optimization algorithm. Introduction As one of the key technologies for microphone arrays, broadband beamforming has been used in a wide range of audio and speech processing applications[1]. In many popular methods, the traditional linear constrained minimum variance(LCMV) beamforming method is mainly used to design narrow-band antenna beamformer[2]. If it is used to design a broadband beamformer of microphone array, it isn’t fit. It is necessary for microphone array to design broadband beamformer without specific arrays[3][4]. In order to achieve broadband frequency invariant beamformer[3], it is necessary to consider frequency invariant beamformer with mismatch errors caused by the gain, phase and position of the microphone[5][6]. For this purpose, in this paper, frequency invariant beamforming algorithm based on the linear constrainted minimum variance (LCMV), the spatial response variation function(SRV) of the microphone array, and diagonal loading method are used to design frequency invariant beamformer and improve the robustness on the given frequency range and the region. Array Model Consider a M-element linear microphone array in the far-field (not general, this method can be applied to arbitrary array structure), FIR subfilter with tap length L is added to microphone. The array output signal can be expressed as ( ) ( ) H k k = y w x , where H denotes conjugate transpose.The weight vector of microphone array response is written as 11 1 1 ( ) [ ( ), , ( ), , ( ), , ( )] T M L ML k w k w k w k w k = w L L L , T denotes transpose. 11 1 1 ( ) [ ( ), , ( ), , ( ), , ( )] T M L ML k x k x k x k x k = x L L L and it denotes the received signal of microphone array, the definition of the angle between the direction of the sound source and the line array is θ , the beam-pattern at frequency f and angle θ of arrival can be expressed as ( , ) | ( , )| T H f f θ θ = w d ,where frequency f is belongs to [ , ] l h f f ,the angle θ of the received signal is in[ , ] l h θ θ , and ( , ) f θ d denotes the array response vector. 4th International Conference on Computer, Mechatronics, Control and Electronic Engineering (ICCMCEE 2015) © 2015. The authors Published by Atlantis Press 102 Frequency Invariant Beamforming Algorithm and Diagonal Loading Method The spatial response variation function(SRV) is given by

Acoustic signals received by platform mounted sonar arrays can be spatially processed to enhance the detection of targets in the presence of both ambient and platform generated (self) noise. Ambient noise in the ocean, such as that due to distant shipping or biological choruses, are known to be spatially correlated. The platform generated noise will be of near-field origin and may not be received by all elements in the array. In this paper we investigate the performance of the minimum variance distortionless response (MVDR) beamformer and the recently introduced Fourier integral method (FIM) and compare their performances with the conventional beamformer. Real passive sonar data, obtained from a platform mounted sparse linear array of hydrophones, is used to study the performance of the beamformers in a typical sonar environment. It is shown that in the absence of self noise, when the array is accurately calibrated the MVDR beamformer will perform very well, but when sensor gain or phase errors are present the performance of the MVDR beamformer is degraded. Further, the MVDR beamformer is unable to reject the self noise which is not "seen" by the entire array. FIM however seems to perform well and a modified version of FIM, which we call weighted FIM (WFIM), is shown to perform better and is at worst comparable to a well calibrated MVDR beamformer.