Polynomial eigenvalue decomposition for multichannel broadband signal processing

This article is devoted to the polynomial eigenvalue decomposition (PEVD) and its applications in broadband multichannel signal processing, motivated by the optimum solutions provided by the eigenvalue decomposition (EVD) for the narrow-band case [1], [2]. In general, the successful techniques from narrowband problems can also be applied to broadband ones, leading to improved solutions. Multichannel broadband signals arise at the core of many essential commercial applications such as telecommunications, speech processing, healthcare monitoring, astronomy and seismic surveillance, and military technologies like radar, sonar and communications [3]. The success of these applications often depends on the performance of signal processing tasks, including data compression [4], source localization [5], channel coding [6], signal enhancement [7], beamforming [8], and source separation [9]. In most cases and for narrowband signals, performing an EVD is the key to the signal processing algorithm. Therefore, this paper aims to introduce PEVD as a novel mathematical technique suitable for many broadband signal processing applications

Subband beamforming with higher order statistics for distant speech recognition

This dissertation presents novel beamforming methods for distant speech recognition (DSR). Such techniques can relieve users from the necessity of putting on close talking microphones. DSR systems are useful in many applications such as humanoid robots, voice control systems for automobiles, automatic meeting transcription systems and so on. A main problem in DSR is that recognition performance is seriously degraded when a speaker is far from the microphones. In order to avoid the degradation, noise and reverberation should be removed from signals received with the microphones. Acoustic beamforming techniques have a potential to enhance speech from the far field with little distortion since they can maintain a distortionless constraint for a look direction. In beamforming, multiple signals propagating from a position are captured with multiple microphones. Typical conventional beamformers then adjust their weights so as to minimize the variance of their own outputs subject to a distortionless constraint in a look direction. The variance is the average of the second power (square) of the beamformer\u27s outputs. Accordingly, it is considered that the conventional beamformer uses second orderstatistics (SOS) of the beamformer\u27s outputs. The conventional beamforming techniques can effectively place a null on any source of interference. However, the desired signal is also canceled in reverberant environments, which is known as the signal cancellation problem. To avoid that problem, many algorithms have been developed. However, none of the algorithms can essentially solve the signal cancellation problem in reverberant environments. While many efforts have been made in order to overcome the signal cancellation problem in the field of acoustic beamforming, researchers have addressed another research issue with the microphone array, that is, blind source separation (BSS) [1]. The BSS techniques aim at separating sources from the mixture of signals without information about the geometry of the microphone array and positions of sources. It is achieved by multiplying an un-mixing matrix with input signals. The un-mixing matrix is constructed so that the outputs are stochastically independent. Measuring the stochastic independence of the signals is based on the theory of the independent component analysis (ICA) [1]. The field of ICA is based on the fact that distributions of information-bearing signals are not Gaussian and distributions of sums of various signals are close to Gaussian. There are two popular criteria for measuring the degree of the non-Gaussianity, namely, kurtosis and negentropy. As described in detail in this thesis, both criteria use more than the second moment. Accordingly, it is referred to as higher order statistics (HOS) in contrast to SOS. HOS is not considered in the field of acoustic beamforming well although Arai et al. showed the similarity between acoustic beamforming and BSS [2]. This thesis investigates new beamforming algorithms which take into consideration higher-order statistics (HOS). The new beamforming methods adjust the beamformer\u27s weights based on one of the following criteria: • minimum mutual information of the two beamformer\u27s outputs, • maximum negentropy of the beamformer\u27s outputs and • maximum kurtosis of the beamformer\u27s outputs. Those algorithms do not suffer from the signal cancellation, which is shown in this thesis. Notice that the new beamforming techniques can keep the distortionless constraint for the direction of interest in contrast to the BSS algorithms. The effectiveness of the new techniques is finally demonstrated through a series of distant automatic speech recognition experiments on real data recorded with real sensors unlike other work where signals artificially convolved with measured impulse responses are considered. Significant improvements are achieved by the beamforming algorithms proposed here.Diese Dissertation präsentiert neue Methoden zur Spracherkennung auf Entfernung. Mit diesen Methoden ist es möglich auf Nahbesprechungsmikrofone zu verzichten. Spracherkennungssysteme, die auf Nahbesprechungsmikrofone verzichten, sind in vielen Anwendungen nützlich, wie zum Beispiel bei Humanoiden-Robotern, in Voice Control Systemen für Autos oder bei automatischen Transcriptionssystemen von Meetings. Ein Hauptproblem in der Spracherkennung auf Entfernung ist, dass mit zunehmendem Abstand zwischen Sprecher und Mikrofon, die Genauigkeit der Spracherkennung stark abnimmt. Aus diesem Grund ist es elementar die Störungen, nämlich Hintergrundgeräusche, Hall und Echo, aus den Mikrofonsignalen herauszurechnen. Durch den Einsatz von mehreren Mikrofonen ist eine räumliche Trennung des Nutzsignals von den Störungen möglich. Diese Methode wird als akustisches Beamformen bezeichnet. Konventionelle akustische Beamformer passen ihre Gewichte so an, dass die Varianz des Ausgangssignals minimiert wird, wobei das Signal in "Blickrichtung" die Bedingung der Verzerrungsfreiheit erfüllen muss. Die Varianz ist definiert als das quadratische Mittel des Ausgangssignals.Somit werden bei konventionellen Beamformingmethoden Second-Order Statistics (SOS) des Ausgangssignals verwendet. Konventionelle Beamformer können Störquellen effizient unterdrücken, aber leider auch das Nutzsignal. Diese unerwünschte Unterdrückung des Nutzsignals wird im Englischen signal cancellation genannt und es wurden bereits viele Algorithmen entwickelt um dies zu vermeiden. Keiner dieser Algorithmen, jedoch, funktioniert effektiv in verhallter Umgebung. Eine weitere Methode das Nutzsignal von den Störungen zu trennen, diesesmal jedoch ohne die geometrische Information zu nutzen, wird Blind Source Separation (BSS) [1] genannt. Hierbei wird eine Matrixmultiplikation mit dem Eingangssignal durchgeführt. Die Matrix muss so konstruiert werden, dass die Ausgangssignale statistisch unabhängig voneinander sind. Die statistische Unabhängigkeit wird mit der Theorie der Independent Component Analysis (ICA) gemessen [1]. Die ICA nimmt an, dass informationstragende Signale, wie z.B. Sprache, nicht gaußverteilt sind, wohingegen die Summe der Signale, z.B. das Hintergrundrauschen, gaußverteilt sind. Es gibt zwei gängige Arten um den Grad der Nichtgaußverteilung zu bestimmen, Kurtosis und Negentropy. Wie in dieser Arbeit beschrieben, werden hierbei höhere Momente als das zweite verwendet und somit werden diese Methoden als Higher-Order Statistics (HOS) bezeichnet. Obwohl Arai et al. zeigten, dass sich Beamforming und BSS ähnlich sind, werden HOS beim akustischen Beamforming bisher nicht verwendet [2] und beruhen weiterhin auf SOS. In der hier vorliegenden Dissertation werden neue Beamformingalgorithmen entwickelt und evaluiert, die auf HOS basieren. Die neuen Beamformingmethoden passen ihre Gewichte anhand eines der folgenden Kriterien an: • Minimum Mutual Information zweier Beamformer Ausgangssignale • Maximum Negentropy der Beamformer Ausgangssignale und • Maximum Kurtosis der Beamformer Ausgangssignale. Es wird anhand von Spracherkennerexperimenten (gemessen in Wortfehlerrate) gezeigt, dass die hier entwickelten Beamformingtechniken auch erfolgreich Störquellen in verhallten Umgebungen unterdrücken, was ein klarer Vorteil gegenüber den herkömmlichen Methoden ist

Robust Multichannel Microphone Beamforming

In this thesis, a method for the design and implementation of a spatially robust multichannel microphone beamforming system is presented. A set of spatial correlation functions are derived for 2D and 3D far-field/near-field scenarios based on von Mises(-Fisher), Gaussian, and uniform source location distributions. These correlation functions are used to design spatially robust beamformers and blocking beamformers (nullformers) designed to enhance or suppress a known source, where the target source location is not perfectly known due to either an incorrect location estimate or movement of the target while the beamformers are active. The spatially robust beam/null-formers form signal and interferer plus noise references which can be further processed via a blind source separation algorithm to remove mutual components - removing the interference and sensor noise from the signal path and vice versa. The noise reduction performance of the combined beamforming and blind source separation system approaches that of a perfect information MVDR beamformer under reverberant conditions. It is demonstrated that the proposed algorithm can be implemented on low-power hardware with good performance on hardware similar to current mobile platforms using a four-element microphone array

Broadband adaptive beamforming with low complexity and frequency invariant response

This thesis proposes different methods to reduce the computational complexity as well as increasing the adaptation rate of adaptive broadband beamformers. This is performed exemplarily for the generalised sidelobe canceller (GSC) structure. The GSC is an alternative implementation of the linearly constrained minimum variance beamformer, which can utilise well-known adaptive filtering algorithms, such as the least mean square (LMS) or the recursive least squares (RLS) to perform unconstrained adaptive optimisation.A direct DFT implementation, by which broadband signals are decomposed into frequency bins and processed by independent narrowband beamforming algorithms, is thought to be computationally optimum. However, this setup fail to converge to the time domain minimum mean square error (MMSE) if signal components are not aligned to frequency bins, resulting in a large worst case error. To mitigate this problem of the so-called independent frequency bin (IFB) processor, overlap-save based GSC beamforming structures have been explored. This system address the minimisation of the time domain MMSE, with a significant reduction in computational complexity when compared to time-domain implementations, and show a better convergence behaviour than the IFB beamformer. By studying the effects that the blocking matrix has on the adaptive process for the overlap-save beamformer, several modifications are carried out to enhance both the simplicity of the algorithm as well as its convergence speed. These modifications result in the GSC beamformer utilising a significantly lower computational complexity compare to the time domain approach while offering similar convergence characteristics.In certain applications, especially in the areas of acoustics, there is a need to maintain constant resolution across a wide operating spectrum that may extend across several octaves. To attain constant beamwidth is difficult, particularly if uniformly spaced linear sensor array are employed for beamforming, since spatial resolution is reciprocally proportional to both the array aperture and the frequency. A scaled aperture arrangement is introduced for the subband based GSC beamformer to achieve near uniform resolution across a wide spectrum, whereby an octave-invariant design is achieved. This structure can also be operated in conjunction with adaptive beamforming algorithms. Frequency dependent tapering of the sensor signals is proposed in combination with the overlap-save GSC structure in order to achieve an overall frequency-invariant characteristic. An adaptive version is proposed for frequency-invariant overlap-save GSC beamformer. Broadband adaptive beamforming algorithms based on the family of least mean squares (LMS) algorithms are known to exhibit slow convergence if the input signal is correlated. To improve the convergence of the GSC when based on LMS-type algorithms, we propose the use of a broadband eigenvalue decomposition (BEVD) to decorrelate the input of the adaptive algorithm in the spatial dimension, for which an increase in convergence speed can be demonstrated over other decorrelating measures, such as the Karhunen-Loeve transform. In order to address the remaining temporal correlation after BEVD processing, this approach is combined with subband decomposition through the use of oversampled filter banks. The resulting spatially and temporally decorrelated GSC beamformer provides further enhanced convergence speed over spatial or temporal decorrelation methods on their own

MVDR broadband beamforming using polynomial matrix techniques

This thesis addresses the formulation of and solution to broadband minimum variance distortionless response (MVDR) beamforming. Two approaches to this problem are considered, namely, generalised sidelobe canceller (GSC) and Capon beamformers. These are examined based on a novel technique which relies on polynomial matrix formulations. The new scheme is based on the second order statistics of the array sensor measurements in order to estimate a space-time covariance matrix. The beamforming problem can be formulated based on this space-time covariance matrix. Akin to the narrowband problem, where an optimum solution can be derived from the eigenvalue decomposition (EVD) of a constant covariance matrix, this utility is here extended to the broadband case. The decoupling of the space-time covariance matrix in this case is provided by means of a polynomial matrix EVD. The proposed approach is initially exploited to design a GSC beamformer for a uniform linear array, and then extended to the constrained MVDR, or Capon, beamformer and also the GSC with an arbitrary array structure. The uniqueness of the designed GSC comes from utilising the polynomial matrix technique, and its ability to steer the array beam towards an off-broadside direction without the pre-steering stage that is associated with conventional approaches to broadband beamformers. To solve the broadband beamforming problem, this thesis addresses a number of additional tools. A first one is the accurate construction of both the steering vectors based on fractional delay filters, which are required for the broadband constraint formulation of a beamformer, as for the construction of the quiescent beamformer. In the GSC case, we also discuss how a block matrix can be obtained, and introduce a novel paraunitary matrix completion algorithm. For the Capon beamformer, the polynomial extension requires the inversion of a polynomial matrix, for which a residue-based method is proposed that offers better accuracy compared to previously utilised approaches. These proposed polynomial matrix techniques are evaluated in a number of simulations. The results show that the polynomial broadband beamformer (PBBF) steersthe main beam towards the direction of the signal of interest (SoI) and protects the signal over the specified bandwidth, and at the same time suppresses unwanted signals by placing nulls in their directions. In addition to that, the PBBF is compared to the standard time domain broadband beamformer in terms of their mean square error performance, beam-pattern, and computation complexity. This comparison shows that the PBBF can offer a significant reduction in computation complexity compared to its standard counterpart. Overall, the main benefits of this approach include beam steering towards an arbitrary look direction with no need for pre-steering step, and a potentially significant reduction in computational complexity due to the decoupling of dependencies of the quiescent beamformer, blocking matrix, and the adaptive filter compared to a standard broadband beamformer implementation.This thesis addresses the formulation of and solution to broadband minimum variance distortionless response (MVDR) beamforming. Two approaches to this problem are considered, namely, generalised sidelobe canceller (GSC) and Capon beamformers. These are examined based on a novel technique which relies on polynomial matrix formulations. The new scheme is based on the second order statistics of the array sensor measurements in order to estimate a space-time covariance matrix. The beamforming problem can be formulated based on this space-time covariance matrix. Akin to the narrowband problem, where an optimum solution can be derived from the eigenvalue decomposition (EVD) of a constant covariance matrix, this utility is here extended to the broadband case. The decoupling of the space-time covariance matrix in this case is provided by means of a polynomial matrix EVD. The proposed approach is initially exploited to design a GSC beamformer for a uniform linear array, and then extended to the constrained MVDR, or Capon, beamformer and also the GSC with an arbitrary array structure. The uniqueness of the designed GSC comes from utilising the polynomial matrix technique, and its ability to steer the array beam towards an off-broadside direction without the pre-steering stage that is associated with conventional approaches to broadband beamformers. To solve the broadband beamforming problem, this thesis addresses a number of additional tools. A first one is the accurate construction of both the steering vectors based on fractional delay filters, which are required for the broadband constraint formulation of a beamformer, as for the construction of the quiescent beamformer. In the GSC case, we also discuss how a block matrix can be obtained, and introduce a novel paraunitary matrix completion algorithm. For the Capon beamformer, the polynomial extension requires the inversion of a polynomial matrix, for which a residue-based method is proposed that offers better accuracy compared to previously utilised approaches. These proposed polynomial matrix techniques are evaluated in a number of simulations. The results show that the polynomial broadband beamformer (PBBF) steersthe main beam towards the direction of the signal of interest (SoI) and protects the signal over the specified bandwidth, and at the same time suppresses unwanted signals by placing nulls in their directions. In addition to that, the PBBF is compared to the standard time domain broadband beamformer in terms of their mean square error performance, beam-pattern, and computation complexity. This comparison shows that the PBBF can offer a significant reduction in computation complexity compared to its standard counterpart. Overall, the main benefits of this approach include beam steering towards an arbitrary look direction with no need for pre-steering step, and a potentially significant reduction in computational complexity due to the decoupling of dependencies of the quiescent beamformer, blocking matrix, and the adaptive filter compared to a standard broadband beamformer implementation

Polynomial matrix algebra with applications

[Abstract unavailable

Modelling the nonstationarity of speech in the maximum negentropy beamformer

State-of-the-art automatic speech recognition (ASR) systems can achieve very low word error rates (WERs) of below 5% on data recorded with headsets. However, in many situations such as ASR at meetings or in the car, far field microphones on the table, walls or devices such as laptops are preferable to microphones that have to be worn close to the user\u27s mouths. Unfortunately, the distance between speakers and microphones introduces significant noise and reverberation, and as a consequence the WERs of current ASR systems on this data tend to be unacceptably high (30-50% upwards). The use of a microphone array, i.e. several microphones, can alleviate the problem somewhat by performing spatial filtering: beamforming techniques combine the sensors\u27 output in a way that focuses the processing on a particular direction. Assuming that the signal of interest comes from a different direction than the noise, this can improve the signal quality and reduce the WER by filtering out sounds coming from non-relevant directions. Historically, array processing techniques developed from research on non-speech data, e.g. in the fields of sonar and radar, and as a consequence most techniques were not created to specifically address beamforming in the context of ASR. While this generality can be seen as an advantage in theory, it also means that these methods ignore characteristics which could be used to improve the process in a way that benefits ASR. An example of beamforming adapted to speech processing is the recently proposed maximum negentropy beamformer (MNB), which exploits the statistical characteristics of speech as follows. "Clean" headset speech differs from noisy or reverberant speech in its statistical distribution, which is much less Gaussian in the clean case. Since negentropy is a measure of non-Gaussianity, choosing beamformer weights that maximise the negentropy of the output leads to speech that is closer to clean speech in its distribution, and this in turn has been shown to lead to improved WERs [Kumatani et al., 2009]. In this thesis several refinements of the MNB algorithm are proposed and evaluated. Firstly, a number of modifications to the original MNB configuration are proposed based on theoretical or practical concerns. These changes concern the probability density function (pdf) used to model speech, the estimation of the pdf parameters, and the method of calculating the negentropy. Secondly, a further step is taken to reflect the characteristics of speech by introducing time-varying pdf parameters. The original MNB uses fixed estimates per utterance, which do not account for the nonstationarity of speech. Several time-dependent variance estimates are therefore proposed, beginning with a simple moving average window and including the HMM-MNB, which derives the variance estimate from a set of auxiliary hidden Markov models. All beamformer algorithms presented in this thesis are evaluated through far-field ASR experiments on the Multi-Channel Wall Street Journal Audio-Visual Corpus, a database of utterances captured with real far-field sensors, in a realistic acoustic environment, and spoken by real speakers. While the proposed methods do not lead to an improvement in ASR performance, a more efficient MNB algorithm is developed, and it is shown that comparable results can be achieved with significantly less data than all frames of the utterance, a result which is of particular relevance for real-time implementations.Automatische Spracherkennungssysteme können heutzutage sehr niedrige Wortfehlerraten (WER) unter 5% erreichen, wenn die Sprachdaten mit einem Headset oder anderem Nahbesprechungsmikrofon aufgezeichnet wurden. Allerdings hat das Tragen eines mundnahen Mikrofons in vielen Situationen, wie z.B. der Spracherkennung im Auto oder während einer Besprechung, praktische Nachteile, und ein auf dem Tisch, an der Wand oder am Laptop befestigtes Mikrofon wäre in dem Fall vorteilhaft. Bei einer größeren Distanz zwischen Mikrofon und Sprecher werden andererseits aber verstärkt Hintergrundgeräusche und Hall aufgenommen, wodurch die Wortfehlerraten häufig in einen unakzeptablen Bereich von 30—50% und höher steigen. Ein Mikrofonarray, d.h. eine Gruppe von Mikrofonen, kann hierbei durch räumliches Filtern in gewissem Maße Abhilfe schaffen: sogenannte Beamforming-Methoden können die Daten der einzelnen Sensoren so kombinieren, dass der Fokus auf eine bestimmte Richtung gerichtet wird. Wenn nun ein Zielsignal aus einer anderen Richtung als die Störgeräusche kommt, kann dieser Prozess die Signalqualität erhöhen und WER-Werte reduzieren, indem die Geräusche aus den nicht-relevanten Richtungen herausgefiltert werden. Da Beamforming-Techniken sich aus der Forschung an nicht-sprachlichen Daten wie Sonar und Radar entwickelt haben, sind die wenigsten Methoden in diesem Bereich speziell auf das Problem der Spracherkennung ausgerichtet. Während eine Anwendungsunabhängigkeit von Vorteil sein kann, bedeutet sie aber auch, dass Eigenschaften der Spracherkennung ignoriert werden, die zur Verbesserung des Ergebnisses genutzt werden könnten. Ein Beispiel für einen Beamforming-Algorithmus, der speziell für die Verarbeitung von Sprache entwickelt wurde, ist der Maximum Negentropy Beamformer (MNB). Der MNB nutzt die Tatsache, dass "saubere" Sprache, die mit einem Nahbesprechungsmikrofon aufgenommen wurde, eine andere Wahrscheinlichkeitsverteilung aufweist als verrauschte oder verhallte Sprache: Die Verteilung sauberer Sprache unterscheidet sich von der Normalverteilung sehr viel stärker als die von fern aufgezeichneter Sprache. Der MNB wählt Beamforming-Gewichte, die den Negentropy-Wert maximieren, und da Negentropy misst, wie sehr sich eine Verteilung von der Normalverteilung unterscheidet, ähnelt die vom MNB produzierte Sprache statistisch gesehen sauberer Sprache, was zu verbesserten WER-Werten geführt hat [Kumatani et al., 2009]. Das Thema dieser Dissertation ist die Entwicklung und Evaluierung von verschiedenen Modifikationen des MNB. Erstens wird eine Anzahl von praktisch und theoretisch motivierten Veränderungen vorgeschlagen, die die Form der Wahrscheinlichkeitsverteilung zur Sprachmodellierung, die Schätzung der Parameter dieser Verteilung und die Berechnung der Negentropy-Werte betreffen. Zweitens wird ein weiterer Schritt zur Berücksichtigung der Eigenschaften von Sprache unternommen, indem die Zeitabhängigkeit der Verteilungsparameter eingeführt wird; im ursprünglichen MNB-Algorithmus sind diese für eine Äußerung konstant, was im Gegensatz zur nicht-konstanten Eigenschaft von Sprache steht. Mehrere zeitabhängige Varianz-Schätzungmethoden werden beschrieben und evaluiert, von einem einfachen gleitenden Durchschnittswert bis zum komplexeren HMM-MNB, der die Varianz aus Hidden-Markov-Modellen ableitet. Alle Beamforming-Algorithmen, die in dieser Arbeit vorgestellt werden, werden durch Spracherkennungsexperimente mit dem Multi-Channel Wall Street Journal Audio-Visual Corpus evaluiert. Dieser Korpus wurde nicht durch Simulation erstellt, sondern besteht aus Äußerungen von Personen, die mit echten Sensoren in einer realistischen akustischen Umgebung aufgenommen wurden. Die Ergebnisse zeigen, dass mit den bisher entwickelten Methoden keine Verbesserung der Wortfehlerrate erreicht werden kann. Allerdings wurde ein effizienterer MNB-Algorithmus entwickelt, der vergleichbare Erkennungsraten mit deutlich weniger Sprachdaten erreichen kann, was vor allem für eine Echtzeitimplementierung relevant ist