Tài liệu SEC 06 pdf

VI AdaptiveFiltering ScottC.Douglas UniversityofUtah 18IntroductiontoAdaptiveFilters ScottC.Douglas WhatisanAdaptiveFilter? • TheAdaptiveFilteringProblem • FilterStructures • TheTaskofan AdaptiveFilter • ApplicationsofAdaptiveFilters • Gradient-BasedAdaptiveAlgorithms • Conclu- sions 19ConvergenceIssuesintheLMSAdaptiveFilter ScottC.DouglasandMarkusRupp Introduction • CharacterizingthePerformanceofAdaptiveFilters • AnalyticalModels,Assump- tions,andDefinitions • AnalysisoftheLMSAdaptiveFilter • PerformanceIssues • Selecting Time-VaryingStepSizes • OtherAnalysesoftheLMSAdaptiveFilter • AnalysisofOtherAdaptive Filters • Conclusions 20RobustnessIssuesinAdaptiveFiltering AliH.SayedandMarkusRupp MotivationandExample • AdaptiveFilterStructure • PerformanceandRobustnessIssues • Er- rorandEnergyMeasures • RobustAdaptiveFiltering • EnergyBoundsandPassivityRelations • Min-MaxOptimalityofAdaptiveGradientAlgorithms • ComparisonofLMSandRLSAlgo- rithms • Time-DomainFeedbackAnalysis • Filtered-ErrorGradientAlgorithms • Referencesand ConcludingRemarks 21RecursiveLeast-SquaresAdaptiveFilters AliH.SayedandThomasKailath ArrayAlgorithms • TheLeast-SquaresProblem • TheRegularizedLeast-SquaresProblem • The RecursiveLeast-SquaresProblem • TheRLSAlgorithm • RLSAlgorithmsinArrayForms • Fast TransversalAlgorithms • Order-RecursiveFilters • ConcludingRemarks 22TransformDomainAdaptiveFiltering W.KennethJenkinsandDanielF.Marshall LMSAdaptiveFilterTheory • OrthogonalizationandPowerNormalization • Convergenceofthe TransformDomainAdaptiveFilter • DiscussionandExamples • Quasi-NewtonAdaptiveAlgo- rithms • The2-DTransformDomainAdaptiveFilter • Block-BasedAdaptiveFilters 23AdaptiveIIRFilters GeoffreyA.Williamson Introduction • TheEquationErrorApproach • TheOutputErrorApproach • Equation- Error/Output-ErrorHybrids • AlternateParametrizations • Conclusions 24AdaptiveFiltersforBlindEqualization ZhiDing Introduction • ChannelEqualizationinQAMDataCommunicationSystems • Decision-Directed AdaptiveChannelEqualizer • BasicFactsonBlindAdaptiveEqualization • AdaptiveAlgorithms andNotations • MeanCostFunctionsandAssociatedAlgorithms • InitializationandConvergence ofBlindEqualizers • GloballyConvergentEqualizers • FractionallySpacedBlindEqualizers • ConcludingRemarks c  1999byCRCPressLLC A FILTER IS, IN ITS MOST BASIC SENSE, a device that enhances and/or rejects certain components of a signal. To adapt is to change one’s characteristics according to some knowledge about one’s environment. Taken together, these two terms suggest the goal of an adaptive filter: to alter its selectivity based on the specific characteristics of the signals that are being processed. In digital signal processing, the term adaptive filters refers to a particular set of computational structures and methods for processing digital signals. While many of the most popular techniques used in adaptive filters have been developed and refined within the past forty years, the field of adaptive filters is part of the larger field of optimization theory that has a history dating back to the scientific work of both Galileo and Gauss in the 18th and 19th centuries. Modern developments in adaptive filters began in the 1930s and 1940s with the efforts of Kolmogorov, Wiener, and Levinson to formulate and solve linear estimation tasks. For those who desire an overview of many of the structures, algorithms, analyses, and applications of adaptive filters, the seven chapters in this section provide an excellent introduction to several prominent topics in the field. Chapter 18 presents an overview of adaptive filters, describing many of the applications for which these systems are used today. This chapter considers basic adaptive filtering concepts while providing an introduction to the popular least-mean-square (LMS) adaptive filter that is often used in these applications. Chapters 19 and 20 focus on the design of the LMS adaptive filter from two different viewpoints. In the former chapter, the behavior of the LMS adaptive filter is analyzed within a statistical framework that has proven to be quiteusefulforestablishinginitialchoicesof the parameter values of this system. The latter chapter studies the behavior of the LMS adaptive filter from a deterministic viewpoint, showing why this system behaves robustly evenwhen modeling errors and finite-precision calculation errors continually perturb the state of this adaptive filter. Chapter 21 presents the techniques used in another popular class of adaptive systems collectively known as recursive least-squares (RLS) adaptive filters. Focusing on the numerical methods that are typically employed in the implementations of these systems, the chapterprovides a detailed summary of both conventional and “fast” computational methods for these high-performance systems. Transform domain adaptive filtering is discussed in Chapter 22. Using the frequency-domain and fast convolution techniques described in this chapter, it is possible both to reduce the computational complexityand to increase the performance of LMS adaptive filters when implemented in block form. The first five chapters of this section focus almost exclusively on adaptive structures of a finite- impulse response (FIR) form. In Chapter 23, the subtle performance issues surrounding methods for adaptive infinite-impulse-response (IIR) filters are carefully described. The most recent technical results concerning the convergence behavior and stability of each major adaptive IIR algorithm class is provided in an easy-to-follow format. Finally, Chapter 24 presents an important emerging application area for adaptive filters: blind equalization. This section indicates how an adaptive filter can be adjusted to produce a desirable input/output characteristic without having an example desired output signal on which to be trained. While adaptive filters have had a long history, new adaptive filter structures and algorithms are continually being developed. In fact, the range of adaptive filtering algorithms and applications is so great that no one paper, chapter, section, or even book can fully cover the field. Those who desire more information on the topics presented in this section should consult works within the extensive reference lists that appear at the end of each chapter. c  1999 by CRC Press LLC . one paper, chapter, section, or even book can fully cover the field. Those who desire more information on the topics presented in this section should consult. adaptive filters when implemented in block form. The first five chapters of this section focus almost exclusively on adaptive structures of a finite- impulse