Page 27 - Fundamentals of Communications Systems

Preface xxv

texts was there a method to compute the spectral content of finite length
transmissions even though this must be done in engineering practice. To
be mathematically consistent with the standard practice for defining the
power spectrum of random processes, I settled on the concept of an average
energy spectrum. Here the average is over the random data sequences that
are transmitted. For students to understand this concept they only need to
understand the concept of expectation over a random experiment. This av-
erage energy spectrum is defined for any modulation format and for finite
or infinite length transmissions. In contrast, many professors who teach
communications are wed to the idea of computing the power spectrum of
digital transmissions by
(a) Assuming an infinite length transmission
(b) Defining cyclostationarity
(c) Averaging over the period of the correlation function of a cyclostationary
process to get a one parameter correlation function
(d) Taking the Fourier transform of this one parameter correlation function
to get a power spectrum

This procedure has four drawbacks: (1) it introduces a completely new
type of random process (to undergraduates who struggle with random pro-
cesses more than anything else), (2) it introduces a time averaging for no
apparent logical reason (this really confused me as a student and as a young
engineer), (3) it only is precise for infinite length transmissions (no station-
arity argument can be used on a finite length transmission), and (4) these
operations are not consistent with the theory of operation of a spectrum
analyzer that will be used in practice. Hopefully it is apparent why this
traditional approach seems less logical than computing the average energy
spectrum. In addition, the approach used in this book gives the same an-
swers in the cases when cyclostationarity can be used (without the strange
concept of cyclostationarity) and gives answers in cases where cyclostation-
arity cannot be used, and is consistent with spectral analyzer operations.
Unfortunately, I have learned (perhaps too late in life) that when you are a
heretic, logic does not help your case against true believers of the status quo.
9. Orthogonal Modulations. My professional career has led me on many in-
teresting rides in terms of understanding of communication theory. Early
in my career the communciation field was roiled by a debate of narrowband
modulation versus wideband modulation sparked by Qualcomm’s introduc-
tion of IS-95. At the time I felt wideband modulation was a special case of a
general modulation theory. I remember at the time (roughly 1990) someone
making the comment during a discussion that narrowband modulation was
3
a special case of wideband modulation and at the time I was dismissive of

3 I believe this discussion was with Wayne Stark or Jim Lehnert.