The phenomena of inter-symbol interference in band limited channels, pose severe limitations on the rate of data that can be transferred in digital communications. Equalizers are often being used in order to reduce inter-symbol interference and allow recovery of the transmitted symbols. Blind deconvolution techniques found to be efficient in carrying an online estimation of the equalizer lter, while relying on the transmitted signal statistics only. As a result, the recovered signal is obtained by convolving the impulse response of the estimated lter with the distorted received signal.
Over the years, many algorithms for the solution of the blind equalization problem have been developed. However, not much was written on their different features, explaining the advantages and drawbacks. This book not only explains the whole story behind blind adaptive equalization in such a way, that also a beginner in this eld will feel comfortable with but also supplies new developments, new ideas where simulation results are supplied to support the theory. This book can be used as a teaching book and may be of particular interest to advanced undergraduate students, graduate ones, university instructors and research scientists in related disciplines.
Dean, Faculty of Engineering
Ariel University Center of Samaria
The problem of blind deconvolution arises comprehensively in various applications such as digital communications, seismic signal processing, speech modeling and synthesis, ultrasonic nondestructive evaluation and image restoration. Many papers are written on blind adaptive equalizers using the cost function approach or Bayes rules. But, up to now there is no book available that makes order in the various techniques, namely, explains the differences, advantages, disadvantages and relationship between the cost function and Bayesian approach.
It is well known that the equalizer's tap length, step-size parameter, channel power and source signal have a great affect on the convergence speed as well as on the residual Intersymbol Interference (ISI). Thus, it is important to understand the relationship between the equalization performance and the various parameters involved in the system in order to obtain optimal equalization performance from the residual ISI point of view and convergence speed. In this book, a whole chapter deals with the relationship between the equalizer's parameters and the equalization performance. Closed-form approximated expressions are given for the mean square error (MSE) as a function of time (for the real valued and two independent quadrature carrier case and low ISI) and residual ISI for type of serially blind adaptive equalizers where the error that is fed into the adaptive mechanism which updates the equalizer's taps can be expressed as a polynomial function of order three of the equalized output.
The book explains why higher order statistics (HOS) are used in the blind equalization eld and why HOS based blind equalization methods can not be applied to Gaussian sources. In addition, it explains the two di erent classes of HOS-based equalization methods used in the literature and supplies examples for each class.
The book describes the single input single output (SISO) and single input multiple output (SIMO) system where the condition for perfect equalization performance from the residual ISI point of view is given for each case.
In the literature, the convolutional noise is often assumed to be a Gaussian process. In this book we propose a new model for the convolutional noise probability density function (pdf). The new model is based on the Edgeworth expansion which is close related to the Gaussian model. Based on this new model for the convolutional noise pdf, a new closed-form approximated expression for the conditional expectation is obtained. It should be pointed out that the new derived expression for the conditional expectation, is also based on the Maximum Entropy approach, Laplace integral method and is valid for the noiseless, real valued and two independent quadrature carrier case. According to simulation results carried out for signal to noise ratio (SNR) SNR = 30 [dB], the new derived expression leads to improved equalization performance for the 16QAM input constellation case.
In summary, this book not only explains the whole story behind blind adaptive equalizers/blind deconvolution in such a way, that also a beginner in this eld will feel comfortable with the book but also supplies new developments, new ideas where simulation results are supplied to support the theory and a simple Matlab program for a blind adaptive equalizer (Godard's algorithm) for the 16QAM constellation input which is sent via an easy channel (FIR channel). This book can be used as a teaching book and may be of particular interest to advanced undergraduate students, graduate students, university instructors and research scientists in related disciplines.
Department of Electrical and Electronic Engineering, Ariel University
Center of Samaria, Ariel 40700, ISRAEL
List of Contributors
Ariel University Center of Samaria