To locate the theory of Lie groups within mathematics, one can say that Lie
groups are groups with some additional structure that permits us to apply
analytic techniques such as differentiation in a group theoretic context.
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The very title of this book is borrowed from the information theory vocabulary,
and, quite naturally, it is an outline of this theory that will serve as an introduction.
The subject of information theory is the scientific study of communications. To this
end it defines a quantitative measurement of the communicated content, i.e. informa-
tion, and deals with two operations essential for communication techniques: source
coding and channel encoding.
This introduction takes a visionary look at ideal cognitive radios (CRs) that inte-
grate advanced software-defined radios (SDR) with CR techniques to arrive at
radios that learn to help their user using computer vision, high-performance
speech understanding, global positioning system (GPS) navigation, sophisticated
adaptive networking, adaptive physical layer radio waveforms, and a wide range
of machine learning processes.
While teaching classes on digital transmission and mobile communications for
undergraduate and graduate students, I was wondering if it would be possible to
write a book capable of giving them some insight about the practical meaning of the
concepts, beyond the mathematics; the same insight that experience and repetitive
contact with the subject are capable to construct; the insight that is capable of build-
ing the bridge between the theory and how the theory manifests itself in practice.
Wireless Fidelity (Wi-Fi) networks have become mainstream over the last few years. What
started out as cable replacement for static desktops in indoor networks has been extended
to fully mobile broadband applications involving moving vehicles, high-speed trains, and
even airplanes.
