Dimensions of Uncertainty in Communication Engineering

By Ezio Biglieri

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.

• Uniquely brings together a variety of tools derived from statistics, information theory, moment theory, interval analysis and probability boxes, dependence bounds, nonadditive measures, and Dempster—Shafer theory
• Focuses on the essentials of various, wide-ranging methods with references to journal articles where more detail can be found if required
• Includes MIMO-related results throughout

• Language: English
• Publisher: Academic Press
• Release date: Jul 6, 2022
• ISBN: 9780323992763

Ezio Biglieri

Ezio Biglieri received his formal training in Electrical Engineering at Politecnico di Torino (Italy), where he received his Dr. Engr. degree in 1967. Before being an Honorary Professor at University Pompeu Fabra, he was a Professor at Università di Napoli (Italy), at Politecnico di Torino (Italy), and at UCLA (USA). He has held visiting positions with Bell Labs (USA), the École Nationale Supérieure des Télécommunications (Paris, France), the University of Sydney (Australia), the Yokohama National University (Japan), Princeton University (USA), the University of South Australia, the Munich Institute of Technology (Germany), the National University of Singapore, the National Taiwan University, the University of Cambridge (U.K.), ETH Zurich (Switzerland), and Monash University Melbourne (Australia). Among other honors, in 2000 he received the IEEE Third-Millennium Medal and the IEEE Donald G. Fink Prize Paper Award, in 2001 the IEEE Communications Society Edwin Howard Armstrong Achievement Award, in 2004, 2012, and 2015 the Journal of Communications and Networks Best Paper Award, in 2012 the IEEE Information Theory Society Aaron D. Wyner Distinguished Service Award, and in 2021 the IEEE Communications Society Heinrich Hertz Award. He is a Life Fellow of the IEEE.

Book preview

1: Model selection

Abstract

This initial chapter shows how wireless channel modeling can be done when epistemic uncertainty may play a major role in the prediction of system performance. Although most of the tools described here can be adapted to different situations, we focus our attention on the derivation, based on incomplete knowledge available, of the probability density function of the random fading attenuation process affecting wireless communications. We proceed as follows:

 We first describe how a probability density function of a given family, whose form is known but whose parameters are unspecified, can be fitted to experimental data: Rayleigh, Rice, and Nakagami-m fading models.

 If only incomplete information about a random variable is available, and in particular its probability density function has an unknown form, we describe how the maximum-entropy method can be used to determine a probability density function consistent with what is known about the random variable.

 Assuming a given class of fading models in which the true model, or at least a good approximation to it, is believed to lie, we show how the Akaike Information Criterion can be used to make the best model choice.

Keywords

Wireless channel models; Fading distributions; Differential entropy; Kullback–Leibler divergence; Spherically invariant processes; Maximum-entropy method; Akaike Information Criterion

In this initial chapter we show how channel modeling can be done when epistemic uncertainty may play a major role in the prediction of system performance. Although most of the tools described here can be adapted to different situations, we shall focus our attention on the derivation, based on incomplete knowledge available, of the probability density function (pdf) of the random fading attenuation process affecting wireless communications. We proceed as follows:

 We first describe how a pdf of a given family, whose form is known but whose parameters are unspecified, can be fitted to experimental data: Rayleigh, Rice, and Nakagami-m fading models.

 If only incomplete information about a random variable (RV) is available, and in particular its pdf has an unknown form, we describe how the maximum-entropy method can be used to determine a pdf consistent with what is known about the RV.

 Assuming a given class of fading models in which the true model, or at least a good approximation to it, is believed to lie, we show how the Akaike Information Criterion can be used to make the best model choice.

1.1 Parametric models

Here we consider the selection of a class of parametric models: although in common practice neither the model nor its parameters are perfectly known, we may accept to proceed under the assumption that the model structure is known and correct, while only its parameters need be determined. The specification of such parametric class carries more epistemic effort than the estimation of its parameters. In particular, models selected in a candidate set should make as much physical sense as possible. Moreover, a model should be selected with an eye on its practicality/usefulness (as an adage goes, all models are wrong, but some are useful [41, p. 20]). The ideal model should be simple enough to be mathematically convenient, thus satisfying an implicit law of parsimony, even at the cost of some inexactness, and hence should be chosen with the smallest number of parameters sufficient to represent the data in an adequate way. In any case, as suggested for example in [8, p. 144], models should not be taken too seriously, i.e., they should be understood as crude approximations to reality, and thus the choice of a certain class of models is often strongly influenced by mathematical convenience. Nonetheless, the assumption that the true model generating the available experimental data lies within the set of candidate models is generally implicit, although sometimes