Underdetermined-order recursive least-squares adaptive filtering: The concept and algorithms

Published versio

Employing data fusion & diversity in the applications of adaptive signal processing

The paradigm of adaptive signal processing is a simple yet powerful method for the class of system identification problems. The classical approaches consider standard one-dimensional signals whereby the model can be formulated by flat-view matrix/vector framework. Nevertheless, the rapidly increasing availability of large-scale multisensor/multinode measurement technology has render no longer sufficient the traditional way of representing the data. To this end, the author, who from this point onward shall be referred to as `we', `us', and `our' to signify the author myself and other supporting contributors i.e. my supervisor, my colleagues and other overseas academics specializing in the specific pieces of research endeavor throughout this thesis, has applied the adaptive filtering framework to problems that employ the techniques of data diversity and fusion which includes quaternions, tensors and graphs. At the first glance, all these structures share one common important feature: invertible isomorphism. In other words, they are algebraically one-to-one related in real vector space. Furthermore, it is our continual course of research that affords a segue of all these three data types. Firstly, we proposed novel quaternion-valued adaptive algorithms named the n-moment widely linear quaternion least mean squares (WL-QLMS) and c-moment WL-LMS. Both are as fast as the recursive-least-squares method but more numerically robust thanks to the lack of matrix inversion. Secondly, the adaptive filtering method is applied to a more complex task: the online tensor dictionary learning named online multilinear dictionary learning (OMDL). The OMDL is partly inspired by the derivation of the c-moment WL-LMS due to its parsimonious formulae. In addition, the sequential higher-order compressed sensing (HO-CS) is also developed to couple with the OMDL to maximally utilize the learned dictionary for the best possible compression. Lastly, we consider graph random processes which actually are multivariate random processes with spatiotemporal (or vertex-time) relationship. Similar to tensor dictionary, one of the main challenges in graph signal processing is sparsity constraint in the graph topology, a challenging issue for online methods. We introduced a novel splitting gradient projection into this adaptive graph filtering to successfully achieve sparse topology. Extensive experiments were conducted to support the analysis of all the algorithms proposed in this thesis, as well as pointing out potentials, limitations and as-yet-unaddressed issues in these research endeavor.Open Acces

Improved Signal Processing Techniques for Passive Radar Applications. Design of a Technological Demonstrator

Las sociedades modernas deben hacer frente a numerosas situaciones críticas en las que la detección y el seguimiento de blancos es un problema de especial interés. En este contexto, los radares pasivos son tecnologías emergentes que están siendo objeto de una intensa actividad investigadora a nivel internacional. Su principal ventaja frente a los radares activos es la utilización de la señal transmitida por sistemas de comunicación, en lugar de un transmisor propio. La ausencia del transmisor da lugar a una importante reducción de costes de diseño, desarrollo, despliegue y mantenimiento, y elimina los problemas asociados a la emisión de ondas electromagnética (salud pública e interferencias) y la necesidad de una asignación de frecuencias. Por otro lado, la utilización de transmisores no controlados diseñados para garantizar una calidad de servicio en un sistema de comunicación, y no con propósitos de detección, complica las tareas de detección y seguimiento de los blancos. El objetivo de la Tesis doctoral es el estudio de los radares pasivos y el desarrollo de un demostrador para la adquisición de datos reales en condiciones controladas, que permita el diseño de mejoras en las técnicas de procesado de señal. La capacidad detectora de estos sistemas en escenarios aéreos ha sido probada en numerosos trabajos, por lo que la presente Tesis se ha centrado en escenarios terrestres, caracterizados por blancos con bajo retorno radar, bajo Doppler y entornos semiurbanos con diferentes tipos de relieve y la presencia de edificios. La naturaleza multiestática de los radares pasivos requiere de un análisis detallado del impacto de la geometría del sistema en las resoluciones alcanzables y en la definición de requisitos específicos de los sistemas de antenas y las cadenas receptoras. Este estudio se ha realizado para sistemas basados en iluminadores terrestres y satelitales, cuyas geometrías y pérdidas de propagación son completamente diferentes. Se han analizado sistemas basados en la Televisión Digital Terrestre, la Televisión Digital vía Satélite (con iluminadores embarcados en satélites geoestacionarios) y en sistemas radar de observación de la Tierra (con sensores embarcados en satélites de órbita baja, cuyo movimiento genera geometrías variables con el tiempo). El estudio se ha completado con la caracterización de la sección radar biestática de los blancos de interés. Una vez desarrolladas las cadenas de adquisición del demostrador, se realizaron numerosas campañas de medidas y los datos adquiridos se utilizaron en un estudio detallado de las técnicas de reducción de las interferencias debidas a la señal del iluminador captada por la antena de vigilancia y otras fuentes de clutter. Se propuso una metodología de análisis y diseño basada en la definición de parámetros directamente relacionados con las capacidades detectoras del sistema. La metodología propuesta permitió el diseño de mejoras en las etapas de reducción de interferencias que fueron validadas en nuevas campañas de medidas con blancos colaborativos provistos de receptores GPS. Durante el desarrollo de la Tesis, se produjo la liberalización del dividendo digital y una nueva asignación de frecuencias caracterizada por una gran variabilidad y dispersión de los canales. Ante este nuevo escenario, las cadenas de adquisición se actualizaron con el objetivo de aumentar su robustez respecto de los canales disponibles en el emplazamiento elegido. Se propuso una solución de bajo coste basada en conversores de frecuencia comerciales y etapas de calibrado diseñadas para compensar los elevados “offsets” frecuenciales de estos sistemas. Con el fin de mejorar la cobertura y la resolución angular del demostrador, se abordó el estudio de los requisitos de diseño de sistemas de antenas basados en arrays, con el fin de incorporar técnicas de beamforming que permitiesen la mejora de las técnicas de reducción de interferencias y el diseño de detectores y etapas de seguimiento en el espacio rango-Doppler-azimuth, así como la implementación de técnicas de estimación de la dirección de llegada

Reduced complexity adaptive filtering algorithms with applications to communications systems

This thesis develops new adaptive filtering algorithms suitable for communications applications with the aim of reducing the computational complexity of the implementation. Low computational complexity of the adaptive filtering algorithm can, for example, reduce the required power consumption of the implementation. A low power consumption is important in wireless applications, particularly at the mobile terminal side, where the physical size of the mobile terminal and long battery life are crucial. We focus on the implementation of two types of adaptive filters: linearly-constrained minimum-variance (LCMV) adaptive filters and conventional training-based adaptive filters. For LCMV adaptive filters, normalized data-reusing algorithms are proposed which can trade off convergence speed and computational complexity by varying the number of data-reuses in the coefficient update. Furthermore, we propose a transformation of the input signal to the LCMV adaptive filter, which properly reduces the dimension of the coefficient update. It is shown that transforming the input signal using successive Householder transformations renders a particularly efficient implementation. The approach allows any unconstrained adaptation algorithm to be applied to linearly constrained problems. In addition, a family of algorithms is proposed using the framework of set-membership filtering (SMF). These algorithms combine a bounded error specification on the adaptive filter with the concept of data-reusing. The resulting algorithms have low average computational complexity because coefficient update is not performed at each iteration. In addition, the adaptation algorithm can be adjusted to achieve a desired computational complexity by allowing a variable number of data-reuses for the filter update. Finally, we propose a framework combining sparse update in time with sparse update of filter coefficients. This type of partial-update (PU) adaptive filters are suitable for applications where the required order of the adaptive filter is conflicting with tight constraints for the processing power.reviewe

System approach to robust acoustic echo cancellation through semi-blind source separation based on independent component analysis

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.PhDCommittee Chair: Biing-Hwang Juang; Committee Member: Brani Vidakovic; Committee Member: David V. Anderson; Committee Member: Jeff S. Shamma; Committee Member: Xiaoli M

Distributed Signal Processing Algorithms for Wireless Networks

Distributed signal processing algorithms have become a key approach for statistical inference in wireless networks and applications such as wireless sensor networks and smart grids. It is well known that distributed processing techniques deal with the extraction of information from data collected at nodes that are distributed over a geographic area. In this context, for each specific node, a set of neighbor nodes collect their local information and transmit the estimates to a specific node. Then, each specific node combines the collected information together with its local estimate to generate an improved estimate. In this thesis, novel distributed cooperative algorithms for inference in ad hoc, wireless sensor networks and smart grids are investigated. Low-complexity and effective algorithms to perform statistical inference in a distributed way are devised. A number of innovative approaches for dealing with node failures, compression of data and exchange of information are proposed and summarized as follows: Firstly, distributed adaptive algorithms based on the conjugate gradient (CG) method for distributed networks are presented. Both incremental and diffusion adaptive solutions are considered. Secondly, adaptive link selection algorithms for distributed estimation and their application to wireless sensor networks and smart grids are proposed. Thirdly, a novel distributed compressed estimation scheme is introduced for sparse signals and systems based on compressive sensing techniques. The proposed scheme consists of compression and decompression modules inspired by compressive sensing to perform distributed compressed estimation. A design procedure is also presented and an algorithm is developed to optimize measurement matrices. Lastly, a novel distributed reduced-rank scheme and adaptive algorithms are proposed for distributed estimation in wireless sensor networks and smart grids. The proposed distributed scheme is based on a transformation that performs dimensionality reduction at each agent of the network followed by a reduced–dimension parameter vector