Learning Algorithms for Complex-Valued Neural Networks in Communication Signal Processing and Adaptive Equalization as its Application

Learning Algorithms for Complex-Valued Neural Networks in Communication Signal Processing and Adaptive Equalization as its Application

Cheolwoo You (Myongji University, South Korea) and Daesik Hong (Yonsei University, South Korea)
DOI: 10.4018/978-1-60566-214-5.ch009
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Abstract

In this chapter, the complex Backpropagation (BP) algorithm for the complex backpropagation neural networks (BPN) consisting of the suitable node activation functions having multi-saturated output regions is presented and analyzed by the benchmark testing. And then the complex BPN is utilized as nonlinear adaptive equalizers that can deal with both quadrature amplitude modulation (QAM) and phase shift key (PSK) signals of any constellation sizes. In addition, four nonlinear blind equalization schemes using complex BPN for M-ary QAM signals are described and their learning algorithms are presented. The presented complex BP equalizer (CBPE) gives, compared with conventional linear complex equalizers, an outstanding improvement with respect to bit error rate (BER) when channel distortions are nonlinear.
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Background

Many authors have studied to solve equalization problems by using BP algorithm (Gibson, Siu, & Cowan, 1989, May) and have acquired the good results. Their applications, however, have been limited to binary {0, 1} or bipolar {-1, 1} valued signals, due to the sigmoid function or the tanh(ax/2) taken as the nonlinear activation function. The used channels are also the real-valued models. But, as applications of the BP algorithm have progressed in various fields, the BP algorithm for complex-valued channel models and complex-valued signals with bigger signal constellation, which have been used widely in many applications of the digital communications or signal processing, has been requisite. For instance, the modulation techniques such as M-ary QAM (Quadrature Amplitude Modulation) or MPSK (M-ary phase shift key) in digital communications use the signal that has two components, i.e., amplitude and phase. Therefore, algorithms for the complex BP and activation functions for signals with multi-level constellation communication are very important in related fields.

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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
$37.50
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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