Collaborative adaptive filtering for machine learning

Quantitative performance criteria for the analysis of machine learning architectures and algorithms have long been established. However, qualitative performance criteria, which identify fundamental signal properties and ensure any processing preserves the desired properties, are still emerging. In many cases, whilst offline statistical tests exist such as assessment of nonlinearity or stochasticity, online tests which not only characterise but also track changes in the nature of the signal are lacking. To that end, by employing recent developments in signal characterisation, criteria are derived for the assessment of the changes in the nature of the processed signal. Through the fusion of the outputs of adaptive filters a single collaborative hybrid filter is produced. By tracking the dynamics of the mixing parameter of this filter, rather than the actual filter performance, a clear indication as to the current nature of the signal is given. Implementations of the proposed method show that it is possible to quantify the degree of nonlinearity within both real- and complex-valued data. This is then extended (in the real domain) from dealing with nonlinearity in general, to a more specific example, namely sparsity. Extensions of adaptive filters from the real to the complex domain are non-trivial and the differences between the statistics in the real and complex domains need to be taken into account. In terms of signal characteristics, nonlinearity can be both split- and fully-complex and complex-valued data can be considered circular or noncircular. Furthermore, by combining the information obtained from hybrid filters of different natures it is possible to use this method to gain a more complete understanding of the nature of the nonlinearity within a signal. This also paves the way for building multidimensional feature spaces and their application in data/information fusion. To produce online tests for sparsity, adaptive filters for sparse environments are investigated and a unifying framework for the derivation of proportionate normalised least mean square (PNLMS) algorithms is presented. This is then extended to derive variants with an adaptive step-size. In order to create an online test for noncircularity, a study of widely linear autoregressive modelling is presented, from which a proof of the convergence of the test for noncircularity can be given. Applications of this method are illustrated on examples such as biomedical signals, speech and wind data

Adaptive signal processing algorithms for noncircular complex data

The complex domain provides a natural processing framework for a large class of signals encountered in communications, radar, biomedical engineering and renewable energy. Statistical signal processing in C has traditionally been viewed as a straightforward extension of the corresponding algorithms in the real domain R, however, recent developments in augmented complex statistics show that, in general, this leads to under-modelling. This direct treatment of complex-valued signals has led to advances in so called widely linear modelling and the introduction of a generalised framework for the differentiability of both analytic and non-analytic complex and quaternion functions. In this thesis, supervised and blind complex adaptive algorithms capable of processing the generality of complex and quaternion signals (both circular and noncircular) in both noise-free and noisy environments are developed; their usefulness in real-world applications is demonstrated through case studies. The focus of this thesis is on the use of augmented statistics and widely linear modelling. The standard complex least mean square (CLMS) algorithm is extended to perform optimally for the generality of complex-valued signals, and is shown to outperform the CLMS algorithm. Next, extraction of latent complex-valued signals from large mixtures is addressed. This is achieved by developing several classes of complex blind source extraction algorithms based on fundamental signal properties such as smoothness, predictability and degree of Gaussianity, with the analysis of the existence and uniqueness of the solutions also provided. These algorithms are shown to facilitate real-time applications, such as those in brain computer interfacing (BCI). Due to their modified cost functions and the widely linear mixing model, this class of algorithms perform well in both noise-free and noisy environments. Next, based on a widely linear quaternion model, the FastICA algorithm is extended to the quaternion domain to provide separation of the generality of quaternion signals. The enhanced performances of the widely linear algorithms are illustrated in renewable energy and biomedical applications, in particular, for the prediction of wind profiles and extraction of artifacts from EEG recordings

Distributed adaptive signal processing for frequency estimation

It is widely recognised that future smart grids will heavily rely upon intelligent communication and signal processing as enabling technologies for their operation. Traditional tools for power system analysis, which have been built from a circuit theory perspective, are a good match for balanced system conditions. However, the unprecedented changes that are imposed by smart grid requirements, are pushing the limits of these old paradigms. To this end, we provide new signal processing perspectives to address some fundamental operations in power systems such as frequency estimation, regulation and fault detection. Firstly, motivated by our finding that any excursion from nominal power system conditions results in a degree of non-circularity in the measured variables, we cast the frequency estimation problem into a distributed estimation framework for noncircular complex random variables. Next, we derive the required next generation widely linear, frequency estimators which incorporate the so-called augmented data statistics and cater for the noncircularity and a widely linear nature of system functions. Uniquely, we also show that by virtue of augmented complex statistics, it is possible to treat frequency tracking and fault detection in a unified way. To address the ever shortening time-scales in future frequency regulation tasks, the developed distributed widely linear frequency estimators are equipped with the ability to compensate for the fewer available temporal voltage data by exploiting spatial diversity in wide area measurements. This contribution is further supported by new physically meaningful theoretical results on the statistical behavior of distributed adaptive filters. Our approach avoids the current restrictive assumptions routinely employed to simplify the analysis by making use of the collaborative learning strategies of distributed agents. The efficacy of the proposed distributed frequency estimators over standard strictly linear and stand-alone algorithms is illustrated in case studies over synthetic and real-world three-phase measurements. An overarching theme in this thesis is the elucidation of underlying commonalities between different methodologies employed in classical power engineering and signal processing. By revisiting fundamental power system ideas within the framework of augmented complex statistics, we provide a physically meaningful signal processing perspective of three-phase transforms and reveal their intimate connections with spatial discrete Fourier transform (DFT), optimal dimensionality reduction and frequency demodulation techniques. Moreover, under the widely linear framework, we also show that the two most widely used frequency estimators in the power grid are in fact special cases of frequency demodulation techniques. Finally, revisiting classic estimation problems in power engineering through the lens of non-circular complex estimation has made it possible to develop a new self-stabilising adaptive three-phase transformation which enables algorithms designed for balanced operating conditions to be straightforwardly implemented in a variety of real-world unbalanced operating conditions. This thesis therefore aims to help bridge the gap between signal processing and power communities by providing power system designers with advanced estimation algorithms and modern physically meaningful interpretations of key power engineering paradigms in order to match the dynamic and decentralised nature of the smart grid.Open Acces

Ultra Wideband Communications: from Analog to Digital

Ultrabreitband-Signale (Ultra Wideband [UWB]) können einen signifikanten Nutzen im Bereich drahtloser Kommunikationssysteme haben. Es sind jedoch noch einige Probleme offen, die durch Systemdesigner und Wissenschaftler gelöst werden müssen. Ein Funknetzsystem mit einer derart großen Bandbreite ist normalerweise auch durch eine große Anzahl an Mehrwegekomponenten mit jeweils verschiedenen Pfadamplituden gekennzeichnet. Daher ist es schwierig, die zeitlich verteilte Energie effektiv zu erfassen. Außerdem ist in vielen Fällen der naheliegende Ansatz, ein kohärenter Empfänger im Sinne eines signalangepassten Filters oder eines Korrelators, nicht unbedingt die beste Wahl. In der vorliegenden Arbeit wird dabei auf die bestehende Problematik und weitere Lösungsmöglichkeiten eingegangen. Im ersten Abschnitt geht es um „Impulse Radio UWB”-Systeme mit niedriger Datenrate. Bei diesen Systemen kommt ein inkohärenter Empfänger zum Einsatz. Inkohärente Signaldetektion stellt insofern einen vielversprechenden Ansatz dar, als das damit aufwandsgünstige und robuste Implementierungen möglich sind. Dies trifft vor allem in Anwendungsfällen wie den von drahtlosen Sensornetzen zu, wo preiswerte Geräte mit langer Batterielaufzeit nötigsind. Dies verringert den für die Kanalschätzung und die Synchronisation nötigen Aufwand, was jedoch auf Kosten der Leistungseffizienz geht und eine erhöhte Störempfindlichkeit gegenüber Interferenz (z.B. Interferenz durch mehrere Nutzer oder schmalbandige Interferenz) zur Folge hat. Um die Bitfehlerrate der oben genannten Verfahren zu bestimmen, wurde zunächst ein inkohärenter Combining-Verlust spezifiziert, welcher auftritt im Gegensatz zu kohärenter Detektion mit Maximum Ratio Multipath Combining. Dieser Verlust hängt von dem Produkt aus der Länge des Integrationsfensters und der Signalbandbreite ab. Um den Verlust durch inkohärentes Combining zu reduzieren und somit die Leistungseffizienz des Empfängers zu steigern, werden verbesserte Combining-Methoden für Mehrwegeempfang vorgeschlagen. Ein analoger Empfänger, bei dem der Hauptteil des Mehrwege-Combinings durch einen „Integrate and Dump”-Filter implementiert ist, wird für UWB-Systeme mit Zeit-Hopping gezeigt. Dabei wurde die Einsatzmöglichkeit von dünn besetzten Codes in solchen System diskutiert und bewertet. Des Weiteren wird eine Regel für die Code-Auswahl vorgestellt, welche die Stabilität des Systems gegen Mehrnutzer-Störungen sicherstellt und gleichzeitig den Verlust durch inkohärentes Combining verringert. Danach liegt der Fokus auf digitalen Lösungen bei inkohärenter Demodulation. Im Vergleich zum Analogempfänger besitzt ein Digitalempfänger einen Analog-Digital-Wandler im Zeitbereich gefolgt von einem digitalen Optimalfilter. Der digitale Optimalfilter dekodiert den Mehrfachzugriffscode kohärent und beschränkt das inkohärente Combining auf die empfangenen Mehrwegekomponenten im Digitalbereich. Es kommt ein schneller Analog-Digital-Wandler mit geringer Auflösung zum Einsatz, um einen vertretbaren Energieverbrauch zu gewährleisten. Diese Digitaltechnik macht den Einsatz langer Analogverzögerungen bei differentieller Demodulation unnötig und ermöglicht viele Arten der digitalen Signalverarbeitung. Im Vergleich zur Analogtechnik reduziert sie nicht nur den inkohärenten Combining-Verlust, sonder zeigt auch eine stärkere Resistenz gegenüber Störungen. Dabei werden die Auswirkungen der Auflösung und der Abtastrate der Analog-Digital-Umsetzung analysiert. Die Resultate zeigen, dass die verminderte Effizienz solcher Analog-Digital-Wandler gering ausfällt. Weiterhin zeigt sich, dass im Falle starker Mehrnutzerinterferenz sogar eine Verbesserung der Ergebnisse zu beobachten ist. Die vorgeschlagenen Design-Regeln spezifizieren die Anwendung der Analog-Digital-Wandler und die Auswahl der Systemparameter in Abhängigkeit der verwendeten Mehrfachzugriffscodes und der Modulationsart. Wir zeigen, wie unter Anwendung erweiterter Modulationsverfahren die Leistungseffizienz verbessert werden kann und schlagen ein Verfahren zur Unterdrückung schmalbandiger Störer vor, welches auf Soft Limiting aufbaut. Durch die Untersuchungen und Ergebnissen zeigt sich, dass inkohärente Empfänger in UWB-Kommunikationssystemen mit niedriger Datenrate ein großes Potential aufweisen. Außerdem wird die Auswahl der benutzbaren Bandbreite untersucht, um einen Kompromiss zwischen inkohärentem Combining-Verlust und Stabilität gegenüber langsamen Schwund zu erreichen. Dadurch wurde ein neues Konzept für UWB-Systeme erarbeitet: wahlweise kohärente oder inkohärente Empfänger, welche als UWB-Systeme Frequenz-Hopping nutzen. Der wesentliche Vorteil hiervon liegt darin, dass die Bandbreite im Basisband sich deutlich verringert. Mithin ermöglicht dies einfach zu realisierende digitale Signalverarbeitungstechnik mit kostengünstigen Analog-Digital-Wandlern. Dies stellt eine neue Epoche in der Forschung im Bereich drahtloser Sensorfunknetze dar. Der Schwerpunkt des zweiten Abschnitts stellt adaptiven Signalverarbeitung für hohe Datenraten mit „Direct Sequence”-UWB-Systemen in den Vordergrund. In solchen Systemen entstehen, wegen der großen Anzahl der empfangenen Mehrwegekomponenten, starke Inter- bzw. Intrasymbolinterferenzen. Außerdem kann die Funktionalität des Systems durch Mehrnutzerinterferenz und Schmalbandstörungen deutlich beeinflusst werden. Um sie zu eliminieren, wird die „Widely Linear”-Rangreduzierung benutzt. Dabei verbessert die Rangreduzierungsmethode das Konvergenzverhalten, besonders wenn der gegebene Vektor eine sehr große Anzahl an Abtastwerten beinhaltet (in Folge hoher einer Abtastrate). Zusätzlich kann das System durch die Anwendung der R-linearen Verarbeitung die Statistik zweiter Ordnung des nicht-zirkularen Signals vollständig ausnutzen, was sich in verbesserten Schätzergebnissen widerspiegelt. Allgemeine kann die Methode der „Widely Linear”-Rangreduzierung auch in andern Bereichen angewendet werden, z.B. in „Direct Sequence”-Codemultiplexverfahren (DS-CDMA), im MIMO-Bereich, im Global System for Mobile Communications (GSM) und beim Beamforming.The aim of this thesis is to investigate key issues encountered in the design of transmission schemes and receiving techniques for Ultra Wideband (UWB) communication systems. Based on different data rate applications, this work is divided into two parts, where energy efficient and robust physical layer solutions are proposed, respectively. Due to a huge bandwidth of UWB signals, a considerable amount of multipath arrivals with various path gains is resolvable at the receiver. For low data rate impulse radio UWB systems, suboptimal non-coherent detection is a simple way to effectively capture the multipath energy. Feasible techniques that increase the power efficiency and the interference robustness of non-coherent detection need to be investigated. For high data rate direct sequence UWB systems, a large number of multipath arrivals results in severe inter-/intra-symbol interference. Additionally, the system performance may also be deteriorated by multi-user interference and narrowband interference. It is necessary to develop advanced signal processing techniques at the receiver to suppress these interferences. Part I of this thesis deals with the co-design of signaling schemes and receiver architectures in low data rate impulse radio UWB systems based on non-coherent detection.● We analyze the bit error rate performance of non-coherent detection and characterize a non-coherent combining loss, i.e., a performance penalty with respect to coherent detection with maximum ratio multipath combining. The thorough analysis of this loss is very helpful for the design of transmission schemes and receive techniques innon-coherent UWB communication systems.● We propose to use optical orthogonal codes in a time hopping impulse radio UWB system based on an analog non-coherent receiver. The “analog” means that the major part of the multipath combining is implemented by an integrate and dump filter. The introduced semi-analytical method can help us to easily select the time hopping codes to ensure the robustness against the multi-user interference and meanwhile to alleviate the non-coherent combining loss.● The main contribution of Part I is the proposal of applying fully digital solutions in non-coherent detection. The proposed digital non-coherent receiver is based on a time domain analog-to-digital converter, which has a high speed but a very low resolution to maintain a reasonable power consumption. Compared to its analog counterpart, itnot only significantly reduces the non-coherent combining loss but also offers a higher interference robustness. In particular, the one-bit receiver can effectively suppress strong multi-user interference and is thus advantageous in separating simultaneously operating piconets.The fully digital solutions overcome the difficulty of implementing long analog delay lines and make differential UWB detection possible. They also facilitate the development of various digital signal processing techniques such as multi-user detection and non-coherent multipath combining methods as well as the use of advanced modulationschemes (e.g., M-ary Walsh modulation).● Furthermore, we present a novel impulse radio UWB system based on frequency hopping, where both coherent and non-coherent receivers can be adopted. The key advantage is that the baseband bandwidth can be considerably reduced (e.g., lower than 500 MHz), which enables low-complexity implementation of the fully digital solutions. It opens up various research activities in the application field of wireless sensor networks. Part II of this thesis proposes adaptive widely linear reduced-rank techniques to suppress interferences for high data rate direct sequence UWB systems, where second-order non-circular signals are used. The reduced-rank techniques are designed to improve the convergence performance and the interference robustness especially when the received vector contains a large number of samples (due to a high sampling rate in UWB systems). The widely linear processing takes full advantage of the second-order statistics of the non-circular signals and enhances the estimation performance. The generic widely linear reduced-rank concept also has a great potential in the applications of other systems such as Direct Sequence Code Division Multiple Access (DS-CDMA), Multiple Input Multiple Output (MIMO) system, and Global System for Mobile Communications (GSM), or in other areas such as beamforming

Digital Front-End Signal Processing with Widely-Linear Signal Models in Radio Devices

Necessitated by the demand for ever higher data rates, modern communications waveforms have increasingly wider bandwidths and higher signal dynamics. Furthermore, radio devices are expected to transmit and receive a growing number of different waveforms from cellular networks, wireless local area networks, wireless personal area networks, positioning and navigation systems, as well as broadcast systems. On the other hand, commercial wireless devices are expected to be cheap, be relatively small in size, and have a long battery life. The demands for flexibility and higher data rates on one hand, and the constraints on production cost, device size, and energy efficiency on the other, pose difficult challenges on the design and implementation of future radio transceivers. Under these diametric constraints, in order to keep the overall implementation cost and size feasible, the use of simplified radio architectures and relatively low-cost radio electronics are necessary. This notion is even more relevant for multiple antenna systems, where each antenna has a dedicated radio front-end. The combination of simplified radio front-ends and low-cost electronics implies that various nonidealities in the remaining analog radio frequency (RF) modules, stemming from unavoidable physical limitations and material variations of the used electronics, are expected to play a critical role in these devices. Instead of tightening the specifications and tolerances of the analog circuits themselves, a more cost-effective solution in many cases is to compensate for these nonidealities in the digital domain. This line of research has been gaining increasing interest in the last 10-15 years, and is also the main topic area of this work. The direct-conversion radio principle is the current and future choice for building low-cost but flexible, multi-standard radio transmitters and receivers. The direct-conversion radio, while simple in structure and integrable on a single chip, suffers from several performance degrading circuit impairments, which have historically prevented its use in wideband, high-rate, and multi-user systems. In the last 15 years, with advances in integrated circuit technologies and digital signal processing, the direct-conversion principle has started gaining popularity. Still, however, much work is needed to fully realize the potential of the direct-conversion principle. This thesis deals with the analysis and digital mitigation of the implementation nonidealities of direct-conversion transmitters and receivers. The contributions can be divided into three parts. First, techniques are proposed for the joint estimation and predistortion of in-phase/quadrature-phase (I/Q) imbalance, power amplifier (PA) nonlinearity, and local oscillator (LO) leakage in wideband direct-conversion transmitters. Second, methods are developed for estimation and compensation of I/Q imbalance in wideband direct-conversion receivers, based on second-order statistics of the received communication waveforms. Third, these second-order statistics are analyzed for second-order stationary and cyclostationary signals under several other system impairments related to circuit implementation and the radio channel. This analysis brings new insights on I/Q imbalances and their compensation using the proposed algorithms. The proposed algorithms utilize complex-valued signal processing throughout, and naturally assume a widely-linear form, where both the signal and its complex-conjugate are filtered and then summed. The compensation processing is situated in the digital front-end of the transceiver, as the last step before digital-to-analog conversion in transmitters, or in receivers, as the first step after analog-to-digital conversion. The compensation techniques proposed herein have several common, unique, attributes: they are designed for the compensation of frequency-dependent impairments, which is seen critical for future wideband systems; they require no dedicated training data for learning; the estimators are computationally efficient, relying on simple signal models, gradient-like learning rules, and solving sets of linear equations; they can be applied in any transceiver type that utilizes the direct-conversion principle, whether single-user or multi-user, or single-carrier or multi-carrier; they are modulation, waveform, and standard independent; they can also be applied in multi-antenna transceivers to each antenna subsystem separately. Therefore, the proposed techniques provide practical and effective solutions to real-life circuit implementation problems of modern communications transceivers. Altogether, considering the algorithm developments with the extensive experimental results performed to verify their functionality, this thesis builds strong confidence that low-complexity digital compensation of analog circuit impairments is indeed applicable and efficient

Dirty RF Signal Processing for Mitigation of Receiver Front-end Non-linearity

Moderne drahtlose Kommunikationssysteme stellen hohe und teilweise gegensätzliche Anforderungen an die Hardware der Funkmodule, wie z.B. niedriger Energieverbrauch, große Bandbreite und hohe Linearität. Die Gewährleistung einer ausreichenden Linearität ist, neben anderen analogen Parametern, eine Herausforderung im praktischen Design der Funkmodule. Der Fokus der Dissertation liegt auf breitbandigen HF-Frontends für Software-konfigurierbare Funkmodule, die seit einigen Jahren kommerziell verfügbar sind. Die praktischen Herausforderungen und Grenzen solcher flexiblen Funkmodule offenbaren sich vor allem im realen Experiment. Eines der Hauptprobleme ist die Sicherstellung einer ausreichenden analogen Performanz über einen weiten Frequenzbereich. Aus einer Vielzahl an analogen Störeffekten behandelt die Arbeit die Analyse und Minderung von Nichtlinearitäten in Empfängern mit direkt-umsetzender Architektur. Im Vordergrund stehen dabei Signalverarbeitungsstrategien zur Minderung nichtlinear verursachter Interferenz - ein Algorithmus, der besser unter "Dirty RF"-Techniken bekannt ist. Ein digitales Verfahren nach der Vorwärtskopplung wird durch intensive Simulationen, Messungen und Implementierung in realer Hardware verifiziert. Um die Lücken zwischen Theorie und praktischer Anwendbarkeit zu schließen und das Verfahren in reale Funkmodule zu integrieren, werden verschiedene Untersuchungen durchgeführt. Hierzu wird ein erweitertes Verhaltensmodell entwickelt, das die Struktur direkt-umsetzender Empfänger am besten nachbildet und damit alle Verzerrungen im HF- und Basisband erfasst. Darüber hinaus wird die Leistungsfähigkeit des Algorithmus unter realen Funkkanal-Bedingungen untersucht. Zusätzlich folgt die Vorstellung einer ressourceneffizienten Echtzeit-Implementierung des Verfahrens auf einem FPGA. Abschließend diskutiert die Arbeit verschiedene Anwendungsfelder, darunter spektrales Sensing, robuster GSM-Empfang und GSM-basiertes Passivradar. Es wird gezeigt, dass nichtlineare Verzerrungen erfolgreich in der digitalen Domäne gemindert werden können, wodurch die Bitfehlerrate gestörter modulierter Signale sinkt und der Anteil nichtlinear verursachter Interferenz minimiert wird. Schließlich kann durch das Verfahren die effektive Linearität des HF-Frontends stark erhöht werden. Damit wird der zuverlässige Betrieb eines einfachen Funkmoduls unter dem Einfluss der Empfängernichtlinearität möglich. Aufgrund des flexiblen Designs ist der Algorithmus für breitbandige Empfänger universal einsetzbar und ist nicht auf Software-konfigurierbare Funkmodule beschränkt.Today's wireless communication systems place high requirements on the radio's hardware that are largely mutually exclusive, such as low power consumption, wide bandwidth, and high linearity. Achieving a sufficient linearity, among other analogue characteristics, is a challenging issue in practical transceiver design. The focus of this thesis is on wideband receiver RF front-ends for software defined radio technology, which became commercially available in the recent years. Practical challenges and limitations are being revealed in real-world experiments with these radios. One of the main problems is to ensure a sufficient RF performance of the front-end over a wide bandwidth. The thesis covers the analysis and mitigation of receiver non-linearity of typical direct-conversion receiver architectures, among other RF impairments. The main focus is on DSP-based algorithms for mitigating non-linearly induced interference, an approach also known as "Dirty RF" signal processing techniques. The conceived digital feedforward mitigation algorithm is verified through extensive simulations, RF measurements, and implementation in real hardware. Various studies are carried out that bridge the gap between theory and practical applicability of this approach, especially with the aim of integrating that technique into real devices. To this end, an advanced baseband behavioural model is developed that matches to direct-conversion receiver architectures as close as possible, and thus considers all generated distortions at RF and baseband. In addition, the algorithm's performance is verified under challenging fading conditions. Moreover, the thesis presents a resource-efficient real-time implementation of the proposed solution on an FPGA. Finally, different use cases are covered in the thesis that includes spectrum monitoring or sensing, GSM downlink reception, and GSM-based passive radar. It is shown that non-linear distortions can be successfully mitigated at system level in the digital domain, thereby decreasing the bit error rate of distorted modulated signals and reducing the amount of non-linearly induced interference. Finally, the effective linearity of the front-end is increased substantially. Thus, the proper operation of a low-cost radio under presence of receiver non-linearity is possible. Due to the flexible design, the algorithm is generally applicable for wideband receivers and is not restricted to software defined radios

Cramer-Rao bound and optimal amplitude estimator of superimposed sinusoidal signals with unknown frequencies

This dissertation addresses optimally estimating the amplitudes of superimposed sinusoidal signals with unknown frequencies. The Cramer-Rao Bound of estimating the amplitudes in white Gaussian noise is given, and the maximum likelihood estimator of the amplitudes in this case is shown to be asymptotically efficient at high signal to noise ratio but finite sample size. Applying the theoretical results to signal resolutions, it is shown that the optimal resolution of multiple signals using a finite sample is given by the maximum likelihood estimator of the amplitudes of signals

On optimal design and applications of linear transforms

Linear transforms are encountered in many fields of applied science and engineering. In the past, conventional block transforms provided acceptable answers to different practical problems. But now, under increasing competitive pressures, with the growing reservoir of theory and a corresponding development of computing facilities, a real demand has been created for methods that systematically improve performance. As a result the past two decades have seen the explosive growth of a class of linear transform theory known as multiresolution signal decomposition. The goal of this work is to design and apply these advanced signal processing techniques to several different problems. The optimal design of subband filter banks is considered first. Several design examples are presented for M-band filter banks. Conventional design approaches are found to present problems when the number of constraints increases. A novel optimization method is proposed using a step-by-step design of a hierarchical subband tree. This method is shown to possess performance improvements in applications such as subband image coding. The subband tree structuring is then discussed and generalized algorithms are presented. Next, the attention is focused on the interference excision problem in direct sequence spread spectrum (DSSS) communications. The analytical and experimental performance of the DSSS receiver employing excision are presented. Different excision techniques are evaluated and ranked along with the proposed adaptive subband transform-based excises. The robustness of the considered methods is investigated for either time-localized or frequency-localized interferers. A domain switchable excision algorithm is also presented. Finally, sonic of the ideas associated with the interference excision problem are utilized in the spectral shaping of a particular biological signal, namely heart rate variability. The improvements for the spectral shaping process are shown for time-frequency analysis. In general, this dissertation demonstrates the proliferation of new tools for digital signal processing