published_or_final_version / Education / Master / Master of Education

Os problemas de separação cega de fontes e desconvolução cega multiusuário vêm sendo intensamente estudados nas últimas décadas, principalmente devido às inúmeras possibilidades de aplicações práticas. A desconvolução multiusuário pode ser compreendida como um problema particular de separação de fontes em que o sistema misturador é convolutivo, e as estatísticas das fontes, que possuem alfabeto finito, são bem conhecidas. Dentre os desafios atuais nessa área, cabe destacar que a obtenção de soluções adaptativas para o problema de separação cega de fontes com misturas convolutivas não é trivial, pois envolve ferramentas matemáticas avançadas e uma compreensão aprofundada das técnicas estatísticas a serem utilizadas. No caso em que não se conhece o tipo de mistura ou as estatísticas das fontes, o problema é ainda mais desafiador. Na área de Processamento Estatístico de Sinais, soluções vêm sendo propostas para resolver casos específicos. A obtenção de algoritmos adaptativos eficientes e numericamente robustos para realizar separação cega de fontes, tanto envolvendo misturas instantâneas quanto convolutivas, ainda é um desafio. Por sua vez, a desconvolução cega de canais de comunicação vem sendo estudada desde os anos 1960 e 1970. A partir de então, várias soluções adaptativas eficientes foram propostas nessa área. O bom entendimento dessas soluções pode sugerir um caminho para a compreensão aprofundada das soluções existentes para o problema mais amplo de separação cega de fontes e para a obtenção de algoritmos eficientes nesse contexto. Sendo assim, neste trabalho (i) revisitam-se a formulação dos problemas de separação cega de fontes e desconvolução cega multiusuário, bem como as relações existentes entre esses problemas, (ii) abordam-se as soluções existentes para a desconvolução cega multiusuário, verificando-se suas limitações e propondo-se modificações, resultando na obtenção de algoritmos com boa capacidade de separação e robustez numérica, e (iii) relacionam-se os critérios de desconvolução cega multiusuário baseados em curtose com os critérios de separação cega de fontes. / Blind source separation and blind deconvolution of multiuser systems have been intensively studied over the last decades, mainly due to the countless possibilities of practical applications. Blind deconvolution in the multiuser case can be understood as a particular case of blind source separation in which the mixing system is convolutive, and the sources, which exhibit a finite alphabet, have well known statistics. Among the current challenges in this area, it is worth noting that obtaining adaptive solutions for the blind source separation problem with convolutive mixtures is not trivial, as it requires advanced mathematical tools and a thorough comprehension of the statistical techniques to be used. When the kind of mixture or source statistics are unknown, the problem is even more challenging. In the field of statistical signal processing, solutions aimed at specific cases have been proposed. The development of efficient and numerically robust adaptive algorithms in blind source separation, for either instantaneous or convolutive mixtures, remains an open challenge. On the other hand, blind deconvolution of communication channels has been studied since the 1960s and 1970s. Since then, various types of efficient adaptive solutions have been proposed in this field. The proper understanding of these solutions can suggest a path to further understand the existing solutions for the broader problem of blind source separation and to obtain efficient algorithms in this context. Consequently, in this work we (i) revisit the problem formulation of blind source separation and blind deconvolution of multiuser systems, and the existing relations between these problems, (ii) address the existing solutions for blind deconvolution in the multiuser case, verifying their limitations and proposing modifications, resulting in the development of algorithms with proper separation performance and numeric robustness, and (iii) relate the kurtosis based criteria of blind multiuser deconvolution and blind source separation.

Os problemas de separação cega de fontes e desconvolução cega multiusuário vêm sendo intensamente estudados nas últimas décadas, principalmente devido às inúmeras possibilidades de aplicações práticas. A desconvolução multiusuário pode ser compreendida como um problema particular de separação de fontes em que o sistema misturador é convolutivo, e as estatísticas das fontes, que possuem alfabeto finito, são bem conhecidas. Dentre os desafios atuais nessa área, cabe destacar que a obtenção de soluções adaptativas para o problema de separação cega de fontes com misturas convolutivas não é trivial, pois envolve ferramentas matemáticas avançadas e uma compreensão aprofundada das técnicas estatísticas a serem utilizadas. No caso em que não se conhece o tipo de mistura ou as estatísticas das fontes, o problema é ainda mais desafiador. Na área de Processamento Estatístico de Sinais, soluções vêm sendo propostas para resolver casos específicos. A obtenção de algoritmos adaptativos eficientes e numericamente robustos para realizar separação cega de fontes, tanto envolvendo misturas instantâneas quanto convolutivas, ainda é um desafio. Por sua vez, a desconvolução cega de canais de comunicação vem sendo estudada desde os anos 1960 e 1970. A partir de então, várias soluções adaptativas eficientes foram propostas nessa área. O bom entendimento dessas soluções pode sugerir um caminho para a compreensão aprofundada das soluções existentes para o problema mais amplo de separação cega de fontes e para a obtenção de algoritmos eficientes nesse contexto. Sendo assim, neste trabalho (i) revisitam-se a formulação dos problemas de separação cega de fontes e desconvolução cega multiusuário, bem como as relações existentes entre esses problemas, (ii) abordam-se as soluções existentes para a desconvolução cega multiusuário, verificando-se suas limitações e propondo-se modificações, resultando na obtenção de algoritmos com boa capacidade de separação e robustez numérica, e (iii) relacionam-se os critérios de desconvolução cega multiusuário baseados em curtose com os critérios de separação cega de fontes. / Blind source separation and blind deconvolution of multiuser systems have been intensively studied over the last decades, mainly due to the countless possibilities of practical applications. Blind deconvolution in the multiuser case can be understood as a particular case of blind source separation in which the mixing system is convolutive, and the sources, which exhibit a finite alphabet, have well known statistics. Among the current challenges in this area, it is worth noting that obtaining adaptive solutions for the blind source separation problem with convolutive mixtures is not trivial, as it requires advanced mathematical tools and a thorough comprehension of the statistical techniques to be used. When the kind of mixture or source statistics are unknown, the problem is even more challenging. In the field of statistical signal processing, solutions aimed at specific cases have been proposed. The development of efficient and numerically robust adaptive algorithms in blind source separation, for either instantaneous or convolutive mixtures, remains an open challenge. On the other hand, blind deconvolution of communication channels has been studied since the 1960s and 1970s. Since then, various types of efficient adaptive solutions have been proposed in this field. The proper understanding of these solutions can suggest a path to further understand the existing solutions for the broader problem of blind source separation and to obtain efficient algorithms in this context. Consequently, in this work we (i) revisit the problem formulation of blind source separation and blind deconvolution of multiuser systems, and the existing relations between these problems, (ii) address the existing solutions for blind deconvolution in the multiuser case, verifying their limitations and proposing modifications, resulting in the development of algorithms with proper separation performance and numeric robustness, and (iii) relate the kurtosis based criteria of blind multiuser deconvolution and blind source separation.

This dissertation deals with dynamics of engineering structures and principally discusses the identification of the modal parameters (i.e., natural frequencies, damping ratios and vibration modes) using output-only information, the excitation sources being considered as unknown and unmeasurable. To solve these kind of problems, a quite large selection of techniques is available in the scientific literature, each of them possessing its own features, advantages and limitations. One common limitation of most of the methods concerns the post-processing procedures that have proved to be delicate and time consuming in some cases, and usually require good users expertise. The constant concern of this work is thus the simplification of the result interpretation in order to minimize the influence of this ungovernable parameter. A new modal parameter estimation approach is developed in this work. The proposed methodology is based on the so-called Blind Source Separation techniques, that aim at reducing large data set to reveal its essential structure. The theoretical developments demonstrate a one-to-one relationship between the so-called mixing matrix and the vibration modes. Two separation algorithms, namely the Independent Component Analysis and the Second-Order Blind Identification, are considered. Their performances are compared, and, due to intrinsic features, one of them is finally identified as more suitable for modal identification problems. For the purpose of comparison, numerous academic case studies are considered to evaluate the influence of parameters such as damping, noise and nondeterministic excitations. Finally, realistic examples dealing with a large number of active modes, typical impact hammer modal testing and operational testing conditions, are studied to demonstrate the applicability of the proposed methodology for practical applications.

This thesis proposes a decision-feedback equalizer (DFE) scheme for blind ADC-based receivers to overcome the challenges introduced by blind sampling. It presents the design, simulation, and implementation of a 5Gb/s speculative DFE for a 2x blind ADC-based receiver. The complete receiver, including the ADC, the DFE, and a 2x blind clock and data recovery (CDR) circuit, is implemented in Fujitsu’s 65-nm CMOS process. Measurements of the fabricated test-chip confirm 5Gb/s data recovery with bit error rate (BER) less than 1e−12 in the presence of a test channel introducing 13.3dB of attenuation at the Nyquist frequency of 2.5GHz. The receiver tolerates 0.24UIpp of high-frequency sinusoidal jitter (SJ) in this case. Without the DFE, the BER exceeds 1e−8 even when no SJ is applied.

This thesis proposes a decision-feedback equalizer (DFE) scheme for blind ADC-based receivers to overcome the challenges introduced by blind sampling. It presents the design, simulation, and implementation of a 5Gb/s speculative DFE for a 2x blind ADC-based receiver. The complete receiver, including the ADC, the DFE, and a 2x blind clock and data recovery (CDR) circuit, is implemented in Fujitsu’s 65-nm CMOS process. Measurements of the fabricated test-chip confirm 5Gb/s data recovery with bit error rate (BER) less than 1e−12 in the presence of a test channel introducing 13.3dB of attenuation at the Nyquist frequency of 2.5GHz. The receiver tolerates 0.24UIpp of high-frequency sinusoidal jitter (SJ) in this case. Without the DFE, the BER exceeds 1e−8 even when no SJ is applied.

The objective of the dissertation research is to investigate noise reduction methods for binaural hearing aids based on array and statistical signal processing and inspired by a human auditory model. In digital hearing aids, wide dynamic range compression (WDRC) is the most successful technique to deal with monaural hearing losses. This WDRC processing is usually performed after a monaural noise reduction algorithm. When hearing losses are present in both ears, i.e., a binaural hearing loss, independent monaural hearing aids have been shown not to be comfortable for most users, preferring a processing that involves synchronization between both hearing devices. In addition, psycho-acoustical studies have identified that under hostile environments, e.g., babble noise at very low SNR conditions, users prefer to use linear amplification rather than WDRC. In this sense, the noise reduction algorithm becomes an important component of a digital hearing aid to provide improvement in speech intelligibility and user comfort. Including a wireless link between both hearing aids offers new ways to implement more efficient methods to reduce the background noise and coordinate processing for the two ears. This approach, called binaural hearing aid, has been recently introduced in some commercial products but using very simple processing strategies. This research analyzes the existing binaural noise-reduction techniques, proposes novel perceptually-inspired methods based on blind source separation (BSS) and multichannel Wiener filter (MWF), and identifies different strategies for the real-time implementation of these methods. The proposed methods perform efficient spatial filtering, improve SNR and speech intelligibility, minimize block processing artifacts, and can be implemented in low-power architectures.

We live in a dynamic world full of noises and interferences. The conventional acoustic echo cancellation (AEC) framework based on the least mean square (LMS) algorithm by itself lacks the ability to handle many secondary signals that interfere with the adaptive filtering process, e.g., local speech and background noise. In this dissertation, we build a foundation for what we refer to as the system approach to signal enhancement as we focus on the AEC problem. We first propose the residual echo enhancement (REE) technique that utilizes the error recovery nonlinearity (ERN) to "enhances" the filter estimation error prior to the filter adaptation. The single-channel AEC problem can be viewed as a special case of semi-blind source separation (SBSS) where one of the source signals is partially known, i.e., the far-end microphone signal that generates the near-end acoustic echo. SBSS optimized via independent component analysis (ICA) leads to the system combination of the LMS algorithm with the ERN that allows for continuous and stable adaptation even during double talk. Second, we extend the system perspective to the decorrelation problem for AEC, where we show that the REE procedure can be applied effectively in a multi-channel AEC (MCAEC) setting to indirectly assist the recovery of lost AEC performance due to inter-channel correlation, known generally as the "non-uniqueness" problem. We develop a novel, computationally efficient technique of frequency-domain resampling (FDR) that effectively alleviates the non-uniqueness problem directly while introducing minimal distortion to signal quality and statistics. We also apply the system approach to the multi-delay filter (MDF) that suffers from the inter-block correlation problem. Finally, we generalize the MCAEC problem in the SBSS framework and discuss many issues related to the implementation of an SBSS system. We propose a constrained batch-online implementation of SBSS that stabilizes the convergence behavior even in the worst case scenario of a single far-end talker along with the non-uniqueness condition on the far-end mixing system. The proposed techniques are developed from a pragmatic standpoint, motivated by real-world problems in acoustic and audio signal processing. Generalization of the orthogonality principle to the system level of an AEC problem allows us to relate AEC to source separation that seeks to maximize the independence, hence implicitly the orthogonality, not only between the error signal and the far-end signal, but rather, among all signals involved. The system approach, for which the REE paradigm is just one realization, enables the encompassing of many traditional signal enhancement techniques in analytically consistent yet practically effective manner for solving the enhancement problem in a very noisy and disruptive acoustic mixing environment.

La mayor parte de los sistemas de comunicaciones requieren el conocimiento previo del canal, el cual se suele estimar a partir de una secuencia de entrenamiento. Sin embargo, la transmisión de símbolos piloto se traduce en una reducción de la eficiencia espectral del sistema, lo que imposibilita que se alcancen los límites predichos por la Teoría de la Información. Este problema ha motivado el desarrollo de un gran número de técnicas para la estima e igualación ciega de canal, es decir, para la obtención del canal o la fuente sin necesidad de transmitir una señal de entrenamiento. Normalmente, estas técnicas se basan en el conocimiento previo de ciertas características de la señal, tales como su pertenencia a un alfabeto finito, o sus estadísticos de orden superior. Sin embargo, en el caso de sistemas de múltiples entradas y salidas (MIMO), se ha demostrado que los estadísticos de segundo orden de las observaciones proporcionan la información suficiente para resolver el problema ciego.El objetivo de esta Tesis consiste en la obtención de nuevas técnicas para la estima e igualación ciega de canales MIMO, tanto en sistemas con redundancia espacial, como en casos más generales en los que las fuentes no presentan ningún tipo particular de estructura. De manera general, los métodos propuestos se basan en los estadísticos de segundo orden de las observaciones. Sin embargo, las técnicas se presentan desde un punto de vista determinista, es decir, los algoritmos propuestos explotan directamente la estructura de las matrices de datos, lo que permite obtener resultados más precisos cuando se dispone de un número reducido de observaciones. Adicionalmente, la reformulación de los criterios propuestos como problemas clásicos del análisis estadístico de señales, ha permitido la obtención de algoritmos adaptativos eficientes para la estima e igualación de canales MIMO. En primer lugar se aborda el caso de sistemas sin redundancia. Más concretamente, se analiza el problema de igualación ciega de canales MIMO selectivos en frecuencia, el cual se reformula como un conjunto de problemas de análisis de correlaciones canónicas (CCA). La solución de los problemas CCA se puede obtener de manera directa mediante un problema de autovalores generalizado. Además, en esta Tesis se presenta un algoritmo adaptativo basado en la reformulación de CCA como un conjunto de problemas de regresión lineal acoplados. De esta manera, se obtienen nuevos algoritmos bloque y adaptativos para la igualación ciega de canales MIMO de una manera sencilla. Finalmente, el método propuesto se basa, como muchas otras técnicas ciegas, en el conocimiento a priori del orden del canal, lo que constituye un problema casi tan complicado como el de la estima o igualación ciega. Así, en el caso de canales de una entrada y varias salidas (SIMO), la combinación de la técnica propuesta con otros métodos para la estima ciega del canal permite obtener un nuevo criterio para extracción del orden de este tipo de canalesEn segundo lugar se considera el problema de estima ciega de canal en sistemas con algún tipo de redundancia o estructura espacial, con especial interés en el caso de sistemas con codificación espacio-temporal por bloques (STBC). Específicamente, se propone una nueva técnica para la estima ciega del canal, cuya complejidad se reduce a la extracción del autovector principal de una matriz de correlación modificada. El principal problema asociado a este tipo de sistemas viene dado por la existencia de ciertas ambigüedades a la hora de estimar el canal. En esta Tesis se plantea el problema de identificabilidad de una manera general, y en el caso de códigos ortogonales (OSTBCs) se presentan varios nuevos teoremas que aseguran la identificabilidad del canal en un gran número de casos. Adicionalmente, se proponen varias técnicas para la resolución de las ambigüedades, tanto en el caso OSTBC como para códigos más generales. En concreto, se introduce el concepto de diversidad de código, que consiste en la combinación de varios códigos STBC. Esta técnica permite resolver las indeterminaciones asociadas a un gran número de problemas, y en su versión más sencilla se reduce a una precodificación no redundante consistente en una simple rotación o permutación de las antenas transmisoras.En definitiva, en esta Tesis se abordan los problemas de estima e igualación ciega de canal en sistemas MIMO, y se presentan varias técnicas ciegas, cuyas prestaciones se evalúan mediante un gran número de ejemplos de simulación. / The majority of communication systems need the previous knowledge of the channel, which is usually estimated by means of a training sequence. However, the transmission of pilot symbols provokes a reduction in bandwidth efficiency, which precludes the system from reaching the limits predicted by the Information Theory. This problem has motivated the development of a large number of blind channel estimation and equalization techniques, which are able to obtain the channel or the source without the need of transmitting a training signal. Usually, these techniques are based on the previous knowledge of certain properties of the signal, such as its belonging to a finite alphabet, or its higher-order statistics. However, in the case of multiple-input multiple-output (MIMO) systems, it has been proven that the second order statistics of the observations provide the sufficient information for solving the blind problem.The aim of this Thesis is the development of new blind MIMO channel estimation and equalization techniques, both in systems with spatial redundancy, and in more general cases where the sources do not have any particular spatial structure. In general, the proposed methods are based on the second order statistics of the observations. However, the techniques are presented from a deterministic point of view, i.e., the proposed algorithms directly exploit the structure of the data matrices, which allows us to obtain more accurate results when only a reduced number of observations is available. Additionally, the reformulation of the proposed criteria as classical statistical signal processing problems is exploited to obtain efficient adaptive algorithms for MIMO channel estimation and equalization.Firstly, we consider the case of systems without spatial redundancy. Specifically, we analyze the problem of blind equalization of frequency selective MIMO channels, which is reformulated as a set of canonical correlation analysis (CCA) problems. The solution of the CCA problems can be obtained by means of a generalized eigenvalue problem. In this Thesis, we present a new adaptive algorithm based on the reformulation of CCA as a set of coupled linear regression problems. Therefore, new batch and adaptive algorithms for blind MIMO channel equalization are easily obtained. Finally, the proposed method, as well as many other blind techniques, is based on the previous knowledge of the channel order, which is a problem nearly as complicated as the blind channel estimation or equalization. Thus, in the case of single-input multiple-output (SIMO) channels, the combination of the proposed technique with other blind channel estimation methods provides a new criterion for the order extraction of this class of channels.Secondly, we consider the problem of blind channel estimation in systems with some kind of redundancy or spatial structure, with special interest in space-time block coded (STBC) systems. Specifically, a new blind channel estimation technique is proposed, whose computational complexity reduces to the extraction of the principal eigenvector of a modified correlation matrix. The main problem in these cases is due to the existence of certain ambiguities associated to the blind channel estimation problem. In this Thesis the general identifiability problem is formulated and, in the case of orthogonal codes (OSTBCs), we present several new theorems which ensure the channel identifiability in a large number of cases. Additionally, several techniques for the resolution of the ambiguities are proposed, both in the OSTBC case as well as for more general codes. In particular, we introduce the concept of code diversity, which consists in the combination of several STBCs. This technique avoids the ambiguities associated to a large number of problems, and in its simplest version it reduces to a non-redundant precoding consisting of a single rotation or permutation of the transmit antennas.In summary, in this Thesis the blind MIMO channel estimation and equalization problems are analyzed, and several blind techniques are presented, whose performance is evaluated by means of a large number of simulation examples.

Thesis (Ph.D.)--Mississippi State University. Department of Counseling and Educational Psychology. / Title from title screen. Includes bibliographical references.