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31 Channel Equalization as a Regularized Inverse Problem

In this article we examine the problem of communication channel equalization and how it relates to the inversion of a linear system of equations. | Doherty J.F. Channel Equalization as a Regularized Inverse Problem Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 31 Channel Equalization as a Regularized Inverse Problem John F. Doherty Pennsylvania State University 31.1 Introduction 31.2 Discrete-Time Intersymbol Interference Channel Model 31.3 Channel Equalization Filtering Matrix Formulation of the Equalization Problem 31.4 Regularization 31.5 Discrete-Time Adaptive Filtering Adaptive Algorithm Recapitulation Regularization Properties of Adaptive Algorithms 31.6 Numerical Results 31.7 Conclusion References 31.1 Introduction In this article we examine the problem of communication channel equalization and how it relates to the inversion of a linear system of equations. Channel equalization is the process by which the effect of a band-limited channel may be diminished i.e. equalized at the sink of a communication system. Although there are many ways to accomplish this we will concentrate on linear filters and adaptive filters. It is through the linear filter approach that the analogy to matrix inversion is possible. Regularized inversion refers to a process in which noise dominated modes of the observed signal are attenuated. 31.2 Discrete-Time Intersymbol Interference Channel Model Intersymbol interference ISI is a phenomenon observed by the equalizer caused by frequency distortion of the transmitted signal. This distortion is usually caused by the frequency selective characteristics of the transmission medium. However it can also be due to deliberate time dispersion of the transmitted pulse to affect realizable implementations of the transmit filter. In any case the purpose of the equalizer is to remove deleterious effects of the ISI on symbol detection. The ISI generation mechanism is described next with a description of equalization techniques to follow. The information transmitted by a digital communication system is .