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I
Preliminaries
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Chapter 1
Introduction
In this chapter we provide a brief and concise review of foundational topics that are of broad interest and usefulness in wireless communication engineering technologies. The notation used throughout is introduced in Section 1.1, and the basics of electrical circuits and signals are reviewed in Section 1.4, we focus on signals and systems concepts specifically for communications systems. The reader is expected to have come across much of the material in this chapter in a typical undergraduate electrical engineering program. Therefore, this chapter is written in review form; it is not meant for a student who is encountering all this material for the first time.
Similarly, reviews of foundational topics are provided in Chapters 2, 6, and 10 for the following areas:
- Chapter 2: review of selected topics in electromagnetics, transmission lines, and testing, as a foundation for radio frequency (RF), antennas, and propagation
- Chapter 6: review of selected topics in digital signal processing, digital communcations over wireless links, the cellular concept, spread spectrum, and othogonal frequency-division multiflexing (OFDM), as a foundation for wireless access technologies 5
- Chapter 10: review of selected topics in fundamental networking concepts, Internet protocol (IP) networking, and teletraffic analysis, as a foundation for network and service architectures
Compared to the present chapter, the topics in Chapters 2, 6, and 10 are generally more specific to particular areas. Also, we selectively develop some of the topics in those chapters in more detail than we do in this chapter.
1.1 Notation
In this section we discuss the conventions we use in this book for mathematical notation. A list of symbols is provided in Appendix D.
and
represent the real and complex numbers, respectively. Membership in a set is represented by
(e.g.,
means that
x is a real number). For
, we write
and
for the real and imaginary parts of
x, respectively.
log represents base-10 logarithms unless otherwise indicated (e.g., log2 for base-2 logarithms), or where an expression is valid for all bases.
Scalars, which may be real or even complex valued, are generally represented by italic type (e.g., x, y), whereas vectors and matrices will be represented by bold type (e.g., G, H). We represent a complex conjugate of a complex number, say an impedance Z, by Z*. We represent the magnitude of a complex number x by |x|. Thus, |x|2=xx*.
For
,
is the largest integer
n such that
n<
x. For example,
and
.
If G is a matrix, GT represents its transpose.
When we refer to a matrix, vector, or polynomial as being over something (e.g., over the integers), we mean that the components (or coefficients, in the case of polynomials) are numbers or objects of that sort.
If
x(
t) is a random signal, we use <
x(
t)> to refer to the time average and
to refer to the ensemble average.
1.2 Foundations
Interconnections of electrical elements (resistors, capacitors, inductors, switches, voltage and current sources) are often called a circuit. Sometimes, the ter...
