Page 25 - Fundamentals of Communications Systems

Preface xxiii

2. Fidelity, Complexity, and Spectral Efficiency. Everything in electronic
communications engineering comes down to a trade-off between fidelity of
message reconstruction, complexity/cost of the electronic systems used to
implement this communication, and the spectral efficiency of the transmis-
sion. I have decided to adopt this approach in my teaching. This approach
clearly deviates from past practice and has not proven to be universally
popular.
3. Stationary versus Wide-Sense Stationary. An interesting characteris-
tic in my education was that a big deal was made out of the difference be-
tween stationary and wide-sense stationary random processes – and most
likely for all communication engineers of my generation. As I went through
my life as a communication engineering professional I came to the real-
ization that this additional level of abstraction was only needed because
the concept of stationarity was arbitrarily introduced before the concept of
Gaussianity. For my book, I introduce Gaussian processes first and then the
idea of wide-sense stationarity is never needed. My view is clearly not ap-
1
preciated by all but my book has only stationary Gaussian processes and
random variables. I felt the less new concepts in random processes that
are introduced in teaching students how to analyze the fidelity of message
reconstruction, the better the student learning experience would be.
4. Information Theory Bounds. My view is that digital communication is
an exciting field to work in because there are some bounds to motivate what
we do. Claude Shannon introduced a bound on the achievable fidelity and
spectral efficiency in the 1940s [Sha48]. Communication engineers have
been pursuing how to achieve these bounds in a reasonable complexity
ever since. Many people feel strongly that Shannon’s bounds cannot be
introduced to undergraduates and I disagree with that notion! It is arguable
that Claude Shannon has a bigger impact on modern life than does Albert
Einstein yet name recognition among engineering and science students
is not high for Claude Shannon. Hopefully introducing Shannon and his
bounds to undergraduates can give him part of his due.
5. Erfc(•) versus Q(•). The tail probability of a Gaussian random variable
comes up frequently in digital communications. The tail probability of a
Gaussian random variable is not given by a simple expression but instead
must be evaluated numerically. Past authors have used three different tran-
scendental functions to specify tail probabilities: Erfc(•), (•), and the Q(•).
Historically, communication engineers have gravitated to the use of Q(•)as
its definition matches more closely how the usage comes up in digital com-
munications. I have chosen to buck this trend because of one simple fact:
Matlab is the most common tool used in modern communications engineer-
ing and Matlab uses Erfc(•). Most people who read this text after having

1 Some reviewers went so far as to suggest I needed to review my random processes background
to get it right!