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 N2. 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.

Mobile devices for hands-free speech communication often show significant nonlinear distortion in the sound emitted by their loudspeakers. Therefore, conventional linear echo cancellation is not sufficient for maintaining a high conversation quality. In this work we propose a nonlinear echo canceller that uses two serially cascaded adaptive filters to compensate for the nonlinear and linear echo. We show that a stable operation of the cascaded structure is achieved by using the multi-channel Kalman algorithm in the frequency domain with filtered-x references. By modelling a nonlinearity with memory we further improve the performance. To reduce the computational complexity of the proposed solution we derive an efficient decimation scheme by exploiting useful properties of the cascaded approach.

Considering the dereverberation problem using multichannel processing, two main paradigms exist. The first paradigm utilizes the long-term correlation of the reverberant component for reducing it, e.g. Weighted Prediction Error (WPE) [1]. The second paradigm, treats the reverberation as a diffuse noise field, statically independent of the direct speech component, and aims to reduce it using a superdirective beamformer, e.g. [2]. Here we propose to combine the two paradigms in a two-stages algorithm. The first stage comprises of the WPE method, and the second stage comprises of a Minimum Variance Distortionless Response (MVDR) beamformer for treating the residual reverberant component. We conjecture that the coherence of the reverberant component at the output of the WPE is similar to the coherence of the reverberant component at the microphones which should theoretically correspond to a diffuse noise field. By estimating the coherence from the reverberant components, linearly predicted by the WPE, non-ideal factors such as microphone positions errors, non-equalized frequency responses and acoustic shading are accounted for. The advantageous performance of the proposed method is exemplified in an experiment study using simulations.

Speech enhancement and separation are core problems in audio signal processing, with commercial applications in devices as diverse as mobile phones, conference call systems, hands-free systems, or hearing aids. In addition, they are crucial preprocessing steps for noise-robust automatic speech and speaker recognition. Many devices now have two to eight microphones. The enhancement and separation capabilities offered by these multichannel interfaces are usually greater than those of single-channel interfaces. Research in speech enhancement and separation has followed two convergent paths, starting with microphone array processing and blind source separation, respectively. These communities are now strongly interrelated and routinely borrow ideas from each other. Yet, a comprehensive overview of the common foundations and the differences between these approaches is lacking at present. In this paper, we propose to fill this gap by analyzing a large number of established and recent techniques according to four transverse axes: 1) the acoustic impulse response model, 2) the spatial filter design criterion, 3) the parameter estimation algorithm, and 4) optional postfiltering. We conclude this overview paper by providing a list of software and data resources and by discussing perspectives and future trends in the field.

The problem of source separation using an array of microphones in reverberant and noisy conditions is addressed. We consider applying the well-known linearly constrained minimum variance (LCMV) beamformer (BF) for extracting individual speakers. Constraints are defined using relative transfer functions (RTFs) for the sources, which are ratios of acoustic transfer functions (ATFs) between any microphone and a reference microphone. The latter are usually estimated by methods that rely on single-talk time segments where only a single source is active and on reliable knowledge of the source activity. Two novel algorithms for estimation of RTFs using the “Triple N” ICA for convolutive mixtures (TRINICON) framework are proposed, not resorting to the usually unavailable source activity pattern. The first algorithm estimates the RTFs of the sources by applying multiple two-channel geometrically constrained (GC) TRINICON units, where approximate direction of arrival information for the sources is utilized for ensuring convergence to the desired solution. The GC-TRINICON is applied to all microphone pairs using a common reference microphone. In the second algorithm, we propose to estimate RTFs iteratively using GC-TRINICON, where instead of using a fixed reference microphone as before, we suggest to use the output signals of LCMV-BFs from the previous iteration as spatially processed references with improved signal-to-interference-and-noise ratio. For both algorithms, a simple detection of noise-only time segments is required for estimating the covariance matrix of noise and interference. We conduct an experimental study in which the performance of the proposed methods is confirmed and compared to corresponding supervised methods.

Microphone array processing utilize spatial separation between the desired speaker and interference signal for speech enhancement. The transfer functions (TFs) relating the speaker component at a reference microphone with all other microphones, denoted as the relative TFs (RTFs), play an important role in beamforming design criteria such as minimum variance distortionless response (MVDR) and speech distortion weighted multichannel Wiener filter (SDW-MWF). Two common methods for estimating the RTF are surveyed here, namely, the covariance subtraction (CS) and the covariance whitening (CW) methods. We analyze the performance of the CS method theoretically and empirically validate the results of the analysis through extensive simulations. Furthermore, empirically comparing the methods performances in various scenarios evidently shows thats the CW method outperforms the CS method.

This paper proposes a distributed multiple constraints generalized sidelobe canceler (GSC) for speech enhancement in anN-node fully connected wireless acoustic sensor network (WASN) comprisingMmicrophones. Our algorithm is designed to operate in reverberant environments with constrained speakers (including both desired and competing speakers). Rather than broadcastingMmicrophone signals, a significant communication bandwidth reduction is obtained by performing local beamforming at the nodes, and utilizing only transmission channels. Each node processes its own microphone signals together with the N + P transmitted signals. The GSC-form implementation, by separating the constraints and the minimization, enables the adaptation of the BF during speech-absent time segments, and relaxes the requirement of other distributed LCMV based algorithms to re-estimate the sources RTFs after each iteration. We provide a full convergence proof of the proposed structure to the centralized GSC-beamformer (BF). An extensive experimental study of both narrowband and (wideband) speech signals verifíes the theoretical analysis.

Beamforming with wireless acoustic sensor networks (WASNs) has recently drawn the attention of the research community. As the number of microphones grows it is difficult, and in some applications impossible, to determine their layout beforehand. A common practice in analyzing the expected performance is to utilize statistical considerations. In the current contribution, we consider applying the speech distortion weighted multi-channel Wiener filter (SDW-MWF) to enhance a desired source propagating in a reverberant enclosure where the microphones are randomly located with a uniform distribution. Two noise fields are considered, namely, multiple coherent interference signals and a diffuse sound field. Utilizing the statistics of the acoustic transfer function (ATF), we derive a statistical model for two important criteria of the beamformer (BF): the signal to interference ratio (SIR), and the white noise gain. Moreover, we propose reliability functions, which determine the probability of the SIR and white noise gain to exceed a predefined level. We verify the proposed model with an extensive simulative study.

Modern high performance speech processing applications incorporate large microphone arrays. Complicated scenarios comprising multiple sources, motivate the use of the linearly constrained minimum variance (LCMV) beamformer (BF) and specifically its efficient generalized sidelobe canceler (GSC) implementation. The complexity of applying the GSC is dominated by the blocking matrix (BM). A common approach for constructing the BM is to use a projection matrix to the null-subspace of the constraints. The latter BM is denoted as the eigen-space BM, and requires M2complex multiplications, where M is the number of microphones. In the current contribution, a novel systematic scheme for constructing a multiple constraints sparse BM is presented. The sparsity of the proposed BM substantially reduces the complexity to K × (M - K) complex multiplications, where K is the number of constraints. A theoretical analysis of the signal leakage and of the blocking ability of the proposed sparse BM and of the eigen-space BM is derived. It is proven analytically, and tested for narrowband signals and for speech signals, that the blocking abilities of the sparse and of the eigen-space BMs are equivalent.

A randomly distributed microphone array is considered in this work. In many applications exact design of the array is impractical. The performance of these arrays, characterized by a large number of microphones deployed in vast areas, cannot be analyzed by traditional deterministic methods. We therefore derive a novel statistical model for performance analysis of the MWF beamformer. We consider the scenario of one desired source and one interfering source arriving from the far-field and impinging on a uniformly distributed linear array. A theoretical model for the MMSE is developed and verified by simulations. The applicability of the proposed statistical model for speech signals is discussed.

In this paper we introduce a novel algorithm for extracting desired speech signals uttered by moving speakers contaminated by competing speakers and stationary noise in a reverberant environment. The proposed beamformer uses eigenvectors spanning the desired and interference signals subspaces. It relaxes the common requirement on the activity patterns of the various sources. A novel mechanism for tracking the desired and interferences subspaces is proposed, based on the projection approximation subspace tracking (deflation) (PASTd) procedure and on a union of subspaces procedure. This contribution extends previously proposed methods to deal with multiple speakers in dynamic scenarios.

In many practical environments we wish to extract several desired speech signals, which are contaminated by nonstationary and stationary interfering signals. The desired signals may also be subject to distortion imposed by the acoustic room impulse responses (RIRs). In this paper, a linearly constrained minimum variance (LCMV) beamformer is designed for extracting the desired signals from multimicrophone measurements. The beamformer satisfies two sets of linear constraints. One set is dedicated to maintaining the desired signals, while the other set is chosen to mitigate both the stationary and nonstationary interferences. Unlike classical beamformers, which approximate the RIRs as delay-only filters, we take into account the entire RIR [or its respective acoustic transfer function (ATF)]. The LCMV beamformer is then reformulated in a generalized sidelobe canceler (GSC) structure, consisting of a fixed beamformer (FBF), blocking matrix (BM), and adaptive noise canceler (ANC). It is shown that for spatially white noise field, the beamformer reduces to a FBF, satisfying the constraint sets, without power minimization. It is shown that the application of the adaptive ANC contributes to interference reduction, but only when the constraint sets are not completely satisfied. We show that relative transfer functions (RTFs), which relate the desired speech sources and the microphones, and a basis for the interference subspace suffice for constructing the beamformer. The RTFs are estimated by applying the generalized eigenvalue decomposition (GEVD) procedure to the power spectral density (PSD) matrices of the received signals and the stationary noise. A basis for the interference subspace is estimated by collecting eigenvectors, calculated in segments where nonstationary interfering sources are active and the desired sources are inactive. The rank of the basis is then reduced by the application of the orthogonal triangular decomposition (QRD). This procedure relaxes the common requirement for nonoverlapping activity periods of the interference sources. A comprehensive experimental study in both simulated and real environments demonstrates the performance of the proposed beamformer.