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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)
Copyright: © 2009 |Pages: 42
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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