Complex-Valued Neural Networks for Equalization of Communication Channels

Complex-Valued Neural Networks for Equalization of Communication Channels

Rajoo Pandey (National Institute of Technology - Kurukshetra, India)
DOI: 10.4018/978-1-60566-214-5.ch008
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Abstract

The equalization of digital communication channel is an important task in high speed data transmission techniques. The multipath channels cause the transmitted symbols to spread and overlap over successive time intervals. The distortion caused by this problem is called inter-symbol interference (ISI) and is required to be removed for reliable communication of data over communication channels. In this task of ISI removal, the signals are complex-valued and processing has to be done in a complex multidimensional space. The growing interest in complex-valued neural networks has spurred the development of many new algorithms for equalization of communication channels in the recent past. This chapter illustrates the application of various types of complex-valued neural networks such as radial basis function networks (RBFN), multilayer feedforward networks and recurrent neural networks for training sequence-based as well as blind equalization of communication channels. The structures and algorithms for these equalizers are presented and performances based on simulation studies are analyzed highlighting their advantages and the important issues involved.
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Introduction

The complex-valued neural networks have attracted a great deal of interest in recent years. The growing interest could be attributed to superior learning ability of complex-valued neural networks in comparison with the real valued counterparts. A number of new low complexity and fast learning algorithms have also been proposed by the researchers for complex-valued neural networks, facilitating their use in various applications (Nitta, 1997; Leung & Haykin, 1991). The applications of complex-valued neural networks have emerged in the areas of seismic, sonar and radar signal processing, speech and image processing, environmental science and wireless communications where signals are typically complex valued (Haykin, 1994a; Mandic & Chambers, 2001).

Digital communication through multipath channels is subject to intersymbol interference and its cancellation using adaptive equalizers has been studied for several years by the signal processing community. Also, in order to maximize efficiency of digital radio links, the transmitter high-power amplifiers are often required to operate near saturation, introducing nonlinearities which in turn cause degradation of the received signal. The nonlinearity may affect both amplitude and phase of the signal. It is well known that the signals like QAM are very sensitive to nonlinear distortion which causes spectral spreading, inter-symbol interference (ISI) and constellation warping. The classical approaches to equalization rely on the existence of a training sequence in the transmitted signal to identify the channel (Proakis, 1995).

In adaptive equalization, when the channel is varying, even slowly, the training sequence has to be sent periodically to update the equalizer. Since the inclusion of reference training signals in conventional equalizers sacrifices valuable channel capacity, adaptation without using the training signals i.e. blind equalization is preferred (Godard, 1980; Haykin, 1994b).

With the development of complex-valued versions of training algorithms, the nonlinear adaptive filters can be realized as neural networks for both conventional as well as blind equalization as they are well suited to deal with the complex-valued communication signals. Although, the real valued and complex-valued networks have been both extensively studied for equalization of communication channels, the advantages of using complex-valued neural networks instead of a real valued counterpart fed with a pair of real values is well established. Among neural network equalizers, the application of radial basis function networks (RBFN) has been extensively covered in the literature. The studies of Chen, Mulgrew and, Grant (1993), Cha and Kassam (1995), Jianping, Sundarrajan, and, Saratchandran (2002) and Li, Huang, Saratchandran and, Sundarrajan (2006) are some of the examples. The technique proposed by Chen et al. (1993) is based on the clustering of data and uses a real valued network. Cha and Kassam (1995) have proposed an adaptive complex-valued RBFN for equalization. In their approach, the inputs and outputs of the network are both complex-valued while the radial basis functions are real valued. Jianping et al. (2002) and Li et al. (2006) have considered RBFN- based equalization of channels, where growing and pruning strategy is used for selection of nodes. All these approaches show a remarkable improvement in the performance of the equalizers in comparison with conventional equalizers.

Uncini, Vecci, Campolucci, and Piazza (1999) have presented a study on the use of complex-valued neural networks with adaptive activation functions. An intelligent use of activation function has been shown to reduce the number of synaptic interconnections while preserving the universal approximation and regularization properties of the network, resulting in efficient implementation of nonlinear filters.

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Editorial Advisory Board
Table of Contents
Foreword
Sven Buchholz
Acknowledgment
Tohru Nitta
Chapter 1
Masaki Kobayashi
Information geometry is one of the most effective tools to investigate stochastic learning models. In it, stochastic learning models are regarded as... Sample PDF
Complex-Valued Boltzmann Manifold
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Chapter 2
Takehiko Ogawa
Network inversion solves inverse problems to estimate cause from result using a multilayer neural network. The original network inversion has been... Sample PDF
Complex-Valued Neural Network and Inverse Problems
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Chapter 3
Boris Igelnik
This chapter describes the clustering ensemble method and the Kolmogorovs Spline Complex Network, in the context of adaptive dynamic modeling of... Sample PDF
Kolmogorovs Spline Complex Network and Adaptive Dynamic Modeling of Data
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Chapter 4
V. Srinivasa Chakravarthy
This chapter describes Complex Hopfield Neural Network (CHNN), a complex-variable version of the Hopfield neural network, which can exist in both... Sample PDF
A Complex-Valued Hopfield Neural Network: Dynamics and Applications
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Chapter 5
Mitsuo Yoshida, Takehiro Mori
Global stability analysis for complex-valued artificial recurrent neural networks seems to be one of yet-unchallenged topics in information science.... Sample PDF
Global Stability Analysis for Complex-Valued Recurrent Neural Networks and Its Application to Convex Optimization Problems
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Chapter 6
Yasuaki Kuroe
This chapter presents models of fully connected complex-valued neural networks which are complex-valued extension of Hopfield-type neural networks... Sample PDF
Models of Complex-Valued Hopfield-Type Neural Networks and Their Dynamics
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Chapter 7
Sheng Chen
The complex-valued radial basis function (RBF) network proposed by Chen et al. (1994) has found many applications for processing complex-valued... Sample PDF
Complex-Valued Symmetric Radial Basis Function Network for Beamforming
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Chapter 8
Rajoo Pandey
The equalization of digital communication channel is an important task in high speed data transmission techniques. The multipath channels cause the... Sample PDF
Complex-Valued Neural Networks for Equalization of Communication Channels
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Chapter 9
Cheolwoo You, Daesik Hong
In this chapter, the complex Backpropagation (BP) algorithm for the complex backpropagation neural networks (BPN) consisting of the suitable node... Sample PDF
Learning Algorithms for Complex-Valued Neural Networks in Communication Signal Processing and Adaptive Equalization as its Application
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Chapter 10
Donq-Liang Lee
New design methods for the complex-valued multistate Hopfield associative memories (CVHAMs) are presented. The author of this chapter shows that the... Sample PDF
Image Reconstruction by the Complex-Valued Neural Networks: Design by Using Generalized Projection Rule
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Chapter 11
Naoyuki Morita
The author proposes an automatic estimation method for nuclear magnetic resonance (NMR) spectra of the metabolites in the living body by magnetic... Sample PDF
A Method of Estimation for Magnetic Resonance Spectroscopy Using Complex-Valued Neural Networks
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Chapter 12
Michele Scarpiniti, Daniele Vigliano, Raffaele Parisi, Aurelio Uncini
This chapter aims at introducing an Independent Component Analysis (ICA) approach to the separation of linear and nonlinear mixtures in complex... Sample PDF
Flexible Blind Signal Separation in the Complex Domain
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Chapter 13
Nobuyuki Matsui, Haruhiko Nishimura, Teijiro Isokawa
Recently, quantum neural networks have been explored as one of the candidates for improving the computational efficiency of neural networks. In this... Sample PDF
Qubit Neural Network: Its Performance and Applications
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Chapter 14
Shigeo Sato, Mitsunaga Kinjo
The advantage of quantum mechanical dynamics in information processing has attracted much interest, and dedicated studies on quantum computation... Sample PDF
Neuromorphic Adiabatic Quantum Computation
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Chapter 15
G.G. Rigatos, S.G. Tzafestas
Neural computation based on principles of quantum mechanics can provide improved models of memory processes and brain functioning and is of primary... Sample PDF
Attractors and Energy Spectrum of Neural Structures Based on the Model of the Quantum Harmonic Oscillator
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Chapter 16
Teijiro Isokawa, Nobuyuki Matsui, Haruhiko Nishimura
Quaternions are a class of hypercomplex number systems, a four-dimensional extension of imaginary numbers, which are extensively used in various... Sample PDF
Quaternionic Neural Networks: Fundamental Properties and Applications
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