Partial Update Least Square Adaptive Filtering

Adaptive filters play an important role in the fields related to digital signal processing and communication, such as system identification, noise cancellation, channel equalization, and beamforming. In practical applications, the computational complexity of an adaptive filter is an important consideration. The Least Mean Square (LMS) algorithm is widely used because of its low computational complexity ($O(N)$) and simplicity in implementation. The least squares algorithms, such as Recursive Least Squares (RLS), Conjugate Gradient (CG), and Euclidean Direction Search (EDS), can converge faster and have lower steady-state mean square error (MSE) than LMS. However, their high computational complexity ($O(N^2)$) makes them unsuitable for many real-time applications. A well-known approach to controlling computational complexity is applying partial update (PU) method to adaptive filters. A partial update method can reduce the adaptive algorithm complexity by updating part of the weight vector instead of the entire vector or by updating part of the time. In the literature, there are only a few analyses of these partial update adaptive filter algorithms. Most analyses are based on partial update LMS and its variants. Only a few papers have addressed partial update RLS and Affine Projection (AP). Therefore, analyses for PU least-squares adaptive filter algorithms are necessary and meaningful. This monograph mostly focuses on the analyses of the partial update least-squares adaptive filter algorithms. Basic partial update methods are applied to adaptive filter algorithms including Least Squares CMA (LSCMA), EDS, and CG. The PU methods are also applied to CMA1-2 and NCMA to compare with the performance of the LSCMA. Mathematical derivation and performance analysis are provided including convergence condition, steady-state mean and mean-square performance for a time-invariant system. The steady-state mean and mean-square performance are also presented for a time-varying system. Computational complexity is calculated for each adaptive filter algorithm. Numerical examples are shown to compare the computational complexity of the PU adaptive filters with the full-update filters. Computer simulation examples, including system identification and channel equalization, are used to demonstrate the mathematical analysis and show the performance of PU adaptive filter algorithms. They also show the convergence performance of PU adaptive filters. The performance is compared between the original adaptive filter algorithms and different partial-update methods. The performance is also compared among similar PU least-squares adaptive filter algorithms, such as PU RLS, PU CG, and PU EDS. In addition to the generic applications of system identification and channel equalization, two special applications of using partial update adaptive filters are also presented. One application uses PU adaptive filters to detect Global System for Mobile Communication (GSM) signals in a local GSM system using the Open Base Transceiver Station (OpenBTS) and Asterisk Private Branch Exchange (PBX). The other application uses PU adaptive filters to do image compression in a system combining hyperspectral image compression and classification.

In this book, the authors provide insights into the basics of adaptive filtering, which are particularly useful for students taking their first steps into this field. They start by studying the problem of minimum mean-square-error filtering, i.e., Wiener filtering. Then, they analyze iterative methods for solving the optimization problem, e.g., the Method of Steepest Descent. By proposing stochastic approximations, several basic adaptive algorithms are derived, including Least Mean Squares (LMS), Normalized Least Mean Squares (NLMS) and Sign-error algorithms. The authors provide a general framework to study the stability and steady-state performance of these algorithms. The affine Projection Algorithm (APA) which provides faster convergence at the expense of computational complexity (although fast implementations can be used) is also presented. In addition, the Least Squares (LS) method and its recursive version (RLS), including fast implementations are discussed. The book closes with the discussion of several topics of interest in the adaptive filtering field.

Adaptive Filtering: Algorithms and Practical Implementation, Second Edition, presents a concise overview of adaptive filtering, covering as many algorithms as possible in a unified form that avoids repetition and simplifies notation. It is suitable as a textbook for senior undergraduate or first-year graduate courses in adaptive signal processing and adaptive filters. The philosophy of the presentation is to expose the material with a solid theoretical foundation, to concentrate on algorithms that really work in a finite-precision implementation, and to provide easy access to working algorithms. Hence, practicing engineers and scientists will also find the book to be an excellent reference. This second edition contains a substantial amount of new material: -Two new chapters on nonlinear and subband adaptive filtering; -Linearly constrained Weiner filters and LMS algorithms; -LMS algorithm behavior in fast adaptation; -Affine projection algorithms; -Derivation smoothing; -MATLAB codes for algorithms. An instructor's manual, a set of master transparencies, and the MATLAB codes for all of the algorithms described in the text are also available. Useful to both professional researchers and students, the text includes 185 problems; over 38 examples, and over 130 illustrations. It is of primary interest to those working in signal processing, communications, and circuits and systems. It will also be of interest to those working in power systems, networks, learning systems, and intelligent systems.

Partial-update adaptive signal processing algorithms not only permit significant complexity reduction in adaptive filter implementations, but can also improve adaptive filter performance in telecommunications applications. This book gives state-of-the-art methods for the design and development of partial-update adaptive signal processing algorithms for use in systems development. Partial-Update Adaptive Signal Processing provides a comprehensive coverage of key partial updating schemes, giving detailed information on the theory and applications of acoustic and network echo cancellation, channel equalization and multiuser detection. It also examines convergence and stability issues for partial update algorithms, providing detailed complexity analysis and a unifying treatment of partial-update techniques. Features: • Advanced analysis and design tools • Application examples illustrating the use of partial-update adaptive signal processing • MATLAB codes for developed algorithms This unique reference will be of interest to signal processing and communications engineers, researchers, R&D engineers and graduate students. "This is a very systematic and methodical treatment of an adaptive signal processing topic, of particular significance in power limited applications such as in wireless communication systems and smart ad hoc sensor networks. I am very happy to have this book on my shelf, not to gather dust, but to be consulted and used in my own research and teaching activities" – Professor A. G. Constantinides, Imperial College, London About the author: Kutluyil Dogançay is an associate professor of Electrical Engineering at the University of South Australia. His research interests span statistical and adaptive signal processing and he serves as a consultant to defence and private industry. He was the Signal Processing and Communications Program Chair of IDC Conference 2007, and is currently chair of the IEEE South Australia Communications and Signal Processing Chapter. Advanced analysis and design tools Algorithm summaries in tabular format Case studies illustrate the application of partial update adaptive signal processing

Edited by the original inventor of the technology. Includes contributions by the foremost experts in the field. The only book to cover these topics together.

Online learning from a signal processing perspective There is increased interest in kernel learning algorithms in neural networks and a growing need for nonlinear adaptive algorithms in advanced signal processing, communications, and controls. Kernel Adaptive Filtering is the first book to present a comprehensive, unifying introduction to online learning algorithms in reproducing kernel Hilbert spaces. Based on research being conducted in the Computational Neuro-Engineering Laboratory at the University of Florida and in the Cognitive Systems Laboratory at McMaster University, Ontario, Canada, this unique resource elevates the adaptive filtering theory to a new level, presenting a new design methodology of nonlinear adaptive filters. Covers the kernel least mean squares algorithm, kernel affine projection algorithms, the kernel recursive least squares algorithm, the theory of Gaussian process regression, and the extended kernel recursive least squares algorithm Presents a powerful model-selection method called maximum marginal likelihood Addresses the principal bottleneck of kernel adaptive filters—their growing structure Features twelve computer-oriented experiments to reinforce the concepts, with MATLAB codes downloadable from the authors' Web site Concludes each chapter with a summary of the state of the art and potential future directions for original research Kernel Adaptive Filtering is ideal for engineers, computer scientists, and graduate students interested in nonlinear adaptive systems for online applications (applications where the data stream arrives one sample at a time and incremental optimal solutions are desirable). It is also a useful guide for those who look for nonlinear adaptive filtering methodologies to solve practical problems.

In the fifth edition of this textbook, author Paulo S.R. Diniz presents updated text on the basic concepts of adaptive signal processing and adaptive filtering. He first introduces the main classes of adaptive filtering algorithms in a unified framework, using clear notations that facilitate actual implementation. Algorithms are described in tables, which are detailed enough to allow the reader to verify the covered concepts. Examples address up-to-date problems drawn from actual applications. Several chapters are expanded and a new chapter ‘Kalman Filtering’ is included. The book provides a concise background on adaptive filtering, including the family of LMS, affine projection, RLS, set-membership algorithms and Kalman filters, as well as nonlinear, sub-band, blind, IIR adaptive filtering, and more. Problems are included at the end of chapters. A MATLAB package is provided so the reader can solve new problems and test algorithms. The book also offers easy access to working algorithms for practicing engineers.

This three-volume proceedings contains revised selected papers from the Second International Conference on Artificial Intelligence and Computational Intelligence, AICI 2011, held in Taiyuan, China, in September 2011. The total of 265 high-quality papers presented were carefully reviewed and selected from 1073 submissions. The topics of Part I covered are: applications of artificial intelligence; applications of computational intelligence; automated problem solving; biomedical inforamtics and computation; brain models/cognitive science; data mining and knowledge discovering; distributed AI and agents; evolutionary programming; expert and decision support systems; fuzzy computation; fuzzy logic and soft computing; and genetic algorithms.