Comparison of Kernel Methods Applied to Smart Antenna Array Processing

Comparison of Kernel Methods Applied to Smart Antenna Array Processing

Christos Christodoulou (University of New Mexico, USA) and Manel Martínez-Ramón (Universidad Carlos III de Madrid, Spain)
Copyright: © 2007 |Pages: 21
DOI: 10.4018/978-1-59904-042-4.ch008
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Abstract

Support vector machines (SVMs) are a good candidate for the solution of antenna array processing problems such as beamforming, detection of the angle of arrival, or sidelobe suppression, due to the fact that these algorithms exhibit superior performance in generalization ability and reduction of computational burden. Here, we introduce three new approaches for antenna array beamforming based on SVMs. The first one relies on the use of a linear support vector regressor to construct a linear beamformer. This algorithm outperforms the minimum variance distortionless method (MVDM) when the sample set used for training is small. It is also an advantageous approach when there is non-Gaussian noise present in the data. The second algorithm uses a nonlinear multiregressor to find the parameters of a linear beamformer. A multiregressor is trained off line to find the optimal parameters using a set of array snapshots. During the beamforming operation, the regressor works in the test mode, thus finding a set of parameters by interpolating among the solutions provided in the training phase. The motivation of this second algorithm is that the number of floating point operations needed is smaller than the number of operations needed by the MVDM since there is no need for matrix inversions. Only a vector-matrix product is needed to find the solution. Also, knowledge of the direction of arrival of the desired signal is not required during the beamforming operation, which leads to simpler and more flexible beamforming realizations. The third one is an implementation of a nonlinear beamformer using a non-linear SVM regressor. The operation of such a regressor is a generalization of the linear SVM one, and it yields better performance in terms of bit error rate (BER) than its linear counterparts. Simulations and comparisons with conventional beamforming strategies are provided, demonstrating the advantages of the SVM approach over the least-squares-based approach.

Complete Chapter List

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Table of Contents
Foreword
Bernhard Schölkopf
Preface
Gustavo Camps-Valls, José Luis Rojo-Álvarez, Manel Martínez-Ramón
Acknowledgments
Gustavo Camps-Valls, José Luis Rojo-Álvarez, Manel Martínez-Ramón
List of Reviewers
Chapter 1
Nello Cristianini, John Shawe-Taylor, Craig Saunders
During the past decade, a major revolution has taken place in pattern-recognition technology with the introduction of rigorous and powerful... Sample PDF
Kernel Methods: A Paradigm for Pattern Analysis
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Chapter 2
Jean-Philippe Vert
Support vector machines and kernel methods are increasingly popular in genomics and computational biology due to their good performance in... Sample PDF
Kernel Methods in Genomics and Computational Biology
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Chapter 3
Nathalie L.M.M. Pochet, Fabian Ojeda, Frank De Smet, Tijl De Bie, Johan A.K. Suykens
Clustering techniques like k-means and hierarchical clustering have shown to be useful when applied to microarray data for the identification of... Sample PDF
Kernel Clustering for Knowledge Discovery in Clinical Microarray Data Analysis
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Chapter 4
Stanislaw Osowski, Tomasz Markiewicz
This chapter presents an automatic system for white blood cell recognition in myelogenous leukaemia on the basis of the image of a bone-marrow... Sample PDF
Support Vector Machine for Recognition of White Blood Cells of Leukaemia
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Chapter 5
Manel Martínez-Ramón, Vladimir Koltchinskii, Gregory L. Heileman, Stefan Posse
Pattern recognition in functional magnetic resource imaging (fMRI) is a novel technique that may lead to a quantity of discovery tools in... Sample PDF
Classification of Multiple Interleaved Human Brain Tasks in Functional Magnetic Resonance Imaging
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Chapter 6
José Luis Rojo-Álvarez, Manel Martínez-Ramón, Gustavo Camps-Valls, Carlos E. Martínez-Cruz, Carlos Figuera
Digital signal processing (DSP) of time series using SVM has been addressed in the literature with a straightforward application of the SVM kernel... Sample PDF
Discrete Time Signal Processing Framework with Support Vector Machines
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Chapter 7
M. Julia Fernández-Getino García, José Luis Rojo-Álvarez, Víctor P. Gil-Jiménez, Felipe Alonso-Atienza, Ana García-Armada
Most of the approaches to digital communication applications using support vector machines (SVMs) rely on the conventional classification and... Sample PDF
A Complex Support Vector Machine Approach to OFDM Coherent Demodulation
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Chapter 8
Christos Christodoulou, Manel Martínez-Ramón
Support vector machines (SVMs) are a good candidate for the solution of antenna array processing problems such as beamforming, detection of the... Sample PDF
Comparison of Kernel Methods Applied to Smart Antenna Array Processing
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Chapter 9
Joseph Picone, Aravind Ganapathiraju, Jon Hamaker
Automated speech recognition is traditionally defined as the process of converting an audio signal into a sequence of words. Over the past 30 years... Sample PDF
Applications of Kernel Theory to Speech Recognition
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Chapter 10
Vincent Wan
This chapter describes the adaptation and application of kernel methods for speech processing. It is divided into two sections dealing with speaker... Sample PDF
Building Sequence Kernels for Speaker Verification and Word Recognition
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Chapter 11
Blaž Fortuna, Nello Cristianini, John Shawe-Taylor
We present a general method using kernel canonical correlation analysis (KCCA) to learn a semantic of text from an aligned multilingual collection... Sample PDF
A Kernel Canonical Correlation Analysis for Learning the Semantics of Text
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Chapter 12
Gökhan Bakir, Bernhard Schölkopf, Jason Weston
In this chapter, we are concerned with the problem of reconstructing patterns from their representation in feature space, known as the pre-image... Sample PDF
On the Pre-Image Problem in Kernel Methods
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Chapter 13
Juan Gutiérrez, Gabriel Gómez-Perez, Jesús Malo, Gustavo Camps-Valls
Support vector machine (SVM) image coding relies on the ability of SVMs for function approximation. The size and the profile of the e-insensitivity... Sample PDF
Perceptual Image Representations for Support Vector Machine Image Coding
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Chapter 14
Francesca Odone, Alessandro Verri
In this chapter we review some kernel methods useful for image classification and retrieval applications. Starting from the problem of constructing... Sample PDF
Image Classification and Retrieval with Kernel Methods
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Chapter 15
Daniel Cremers, Timo Kohlberger
We present a method of density estimation that is based on an extension of kernel PCA to a probabilistic framework. Given a set of sample data, we... Sample PDF
Probabilistic Kernel PCA and its Application to Statistical Modeling and Inference
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Chapter 16
Lorenzo Bruzzone, Luis Gomez-Chova, Mattia Marconcini, Gustavo Camps-Valls
The information contained in hyperspectral images allows the characterization, identification, and classification of land covers with improved... Sample PDF
Hyperspectral Image Classification with Kernels
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