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Dimensions of Uncertainty in Communication Engineering is a comprehensive and self-contained introduction to the problems of nonaleatory uncertainty and the mathematical tools needed to solve them. The book gathers together tools derived from statistics, information theory, moment theory, interval analysis and probability boxes, dependence bounds, nonadditive measures, and Dempster–Shafer theory. While the book is mainly devoted to communication engineering, the techniques described are also of interest to other application areas, and commonalities to these are often alluded to through a number of references to books and research papers. This is an ideal supplementary book for courses in wireless communications, providing techniques for addressing epistemic uncertainty, as well as an important resource for researchers and industry engineers. Students and researchers in other fields such as statistics, financial mathematics, and transport theory will gain an overview and understanding on these methods relevant to their field.
It is common practice in communication engineering to face uncertainty. Specifically, unknown outcomes of experiments run under similar conditions have to be dealt with. Probability theory has long become the tool of choice in this discipline, which implicitly assumes that all forms of uncertainty can be treated in terms of a single dimension. One should, however, realize that uncertainty presents itself under multiple dimensions: specifically, “aleatory” (or “stochastic”) uncertainty, caused by the randomness of system behavior, differs in a substantial way from “epistemic” uncertainty, which is caused by the imperfect knowledge of the factors affecting the behavior of a system. In other words, while aleatory uncertainty affects events that cannot be predicted, epistemic uncertainty is caused by imperfect information about the probabilistic model of aleatory uncertainty. Different types of information deficiency determine the type of the associated uncertainty, information may be incomplete, imprecise, fragmentary, unreliable, vague, or even contradictory. Epistemic uncertainty can be reduced by a deeper analysis, while aleatory uncertainty cannot. Probability theory is only sufficient once epistemic uncertainty is removed from the problem.
In wireless communication, a considerable amount of research activity has been spent in the search for accurate statistical models of the transmission channel. The model selected should satisfy the requirement of yielding a design that performs satisfactorily and provides reliable guidelines for decision making. A major problem there is caused by the fact that no single model (e.g., Rayleigh or Rice probability distributions modeling fading effects) can be accurate enough for a wide variety of channels appearing in practice. Considerable efforts have also been spent in the search for general classes of probability measures which are at the same time physically justified and flexible enough to fit a large mass of data gathered experimentally.
The material here does not demand any great mathematical knowledge. It only assumes a firm grasp of the fundamental concepts of probability, information, and communication theories as presented in senior-level college courses. Elementary notions of optimization theory may be useful to follow some arguments in a few sections of Chapters 1 to 3. Although readers would probably benefit the most by reading this book from cover to cover, I tried to keep each chapter standing on its own, so that individual chapters could be read separately, with no need to work through the entire text