Signal_Processing_Noise-Vyacheslav_P._Tuzlukov-CRC

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Signal_Processing_Noise-Vyacheslav_P._Tuzlukov-CRC


Preface
The performance of complex signal processing systems is limited by the additive
and multiplicative noise present in the communication channel through
which the information signal is transmitted.
Multiplicative noise is distortion in the amplitude and phase structure of
the information signal. Multiplicative noise can occur in the generation, transmission,
and processing of the information signal. The main characteristics
of complex signal processing systems that are used, for example, in radar,
communications, wireless communications, mobile communications, sonar,
acoustics, underwater signal processing, remote sensing, navigation systems,
geophysical signal processing, and biomedical signal processing, deteriorate
as a result of the effect of multiplicative noise. The impact of multiplicative
noise on the main characteristics of complex signal processing systems in various
areas of signal processing is great in those cases in which complex signal
processing systems use signals with complex phase structure, for example,
frequency-modulated signals, phase-modulated signals, and so on, or when
complex signal processing systems use signal processing of coherent signals
of large duration.
In recent years the problems of signal processing that result from the combined
stimulus of additive Gaussian noise and multiplicative noise are of
great interest for systems that deploy complex signal processing and coherent
signal processing.
In this book we discuss the following problems:
• The main statistical characteristics of multiplicative noise
• The main statistical characteristics of the signals distorted by multiplicative
noise
• The main statistical characteristics of the process at the output of linear
systems impacted by multiplicative noise
• The main principles of the generalized approach to signal processing in
additive Gaussian noise and multiplicative noise
• The main statistical characteristics of the signal at the output of the generalized
detector impacted by multiplicative noise
• Impact of multiplicative noise on the detection performances of the signals
that are processed by the generalized detector, on the estimation of
measurement of the signal parameters, and on the signal resolution
© 2002 by CRC Press LLC
As a starting point, in Chapter 1 we discuss the main concepts of probability
and statistics upon which all results and all conclusions in this book
are based. The main results and conclusions discussed in this book are based
on the generalized approach to signal processing in the presence of additive
Gaussian noise and multiplicative noise. This is based on a seemingly abstract
idea: the introduction of an additional noise source (that does not carry any
information about the signal) in order to improve the qualitative performance
of complex signal processing systems. Theoretical and experimental studies
carried out by the author lead to the conclusion that the proposed generalized
approach to signal processing impacted by additive Gaussian noise and
multiplicative noise allows us to formulate a decision-making rule based on
the determination of the jointly sufficient statistics of the mean and variance of the
likelihood function (or functional). Classical and modern signal processing
theories allow us to define only the sufficient statistic of the mean of the likelihood
function (or functional). Additional information about the statistical
characteristics of the likelihood function (or functional) leads to better quality
signal detection in compared with the optimal signal detection algorithms of
classical and modern theories.
The generalized approach to signal processing in the presence of additive
Gaussian noise and multiplicative noise allows us to extend the well-known
boundaries of the potential noise immunity set by classical and modern signal
detection theories. Employing complex signal processing systems constructed
on the basis of the generalized approach to signal processing in the presence
of additive Gaussian noise and multiplicative noise allows us to obtain better
detection of signals with noise components present compared with complex
signal processing systems that are constructed on the basis of classical and
modern theories. The optimal and asymptotic signal detection algorithms (of
classical and modern theories), for signals with amplitude-frequency-phase
structure characteristics that can be known and unknown a priori, are the
components of the signal detection algorithms that are designed on the basis
of the generalized approach to signal detection theory.The problems discussed
in this book show that it is possible to raise the upper boundary of
the potential noise immunity for any complex signal processing system including
signal processing systems with associated noise immunity defined
by classical and modern signal detection theories.
To better understand the fundamental statements and concepts of the generalized
approach to signal processing in the presence of additive Gaussian
noise and multiplicative noise the reader should consultmytwo earlier books:
Signal Processing in Noise: A New Methodology (IEC, Minsk, 1998) and Signal
Detection Theory (Springer-Verlag, New York, 2001).
I am extremely grateful tomycolleagues in the field of signal processing for
very useful discussion about the main results, in particular, Prof. V. Ignatov,
Prof. A. Kolyada, Prof. I. Malevich, Prof. G. Manshin, Prof. V. Marakhovsky,
Prof. B. Levin, Prof. D. Johnson, Prof. B. Bogner, Prof. Yu. Sedyshev,
© 2002 by CRC Press LLC
Prof. J. Schroeder, Prof. Yu. Shinakov, Prof. V. Varshavsky, Prof. A. Kara,
Prof. X. R. Lee, Prof. Y. Bar-Shalom, Dr. V. Kuzkin, Dr. A. Dubey, and Dr.
O. Drummond.
I thank my colleagues at the University of Aizu, Japan, for very valuable
discussion about the main statements and concepts of the book.
I especially thank my dear mother, Natali Tuzlukova, and my lovely wife,
Elena Tuzlukova, for their understanding, endless patience, and tremendous
support during the course of my work on this book.
I also wish to express my life-long, heartfelt gratitude to Dr. Peter G.
Tuzlukov, my father and teacher, who introduced me to science.
Vyacheslav P. Tuzlukov

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