Page 169 - Fundamentals of Communications Systems

Analog Communications Basics 5.9

■ Complexity – This metric almost always translates directly into cost.
■ Fidelity – This metric typically measures how accurate the received message
estimate is given the amount of transmitted power.
■ Spectral Efficiency – This metric measures how much bandwidth a modula-
tion uses to implement the communication.
Complexity is a quantity that requires engineering judgment to estimate.
Often the cost of a certain level of complexity changes over time. What were seen
as good design choices in terms of complexity in the 1930s when vacuum tubes
were prevalent seem somewhat silly today with the prevalance of integrated
circuits and complex electronic devices.
The fidelity of the communication system is typically a measure of how well
the message is reconstructed at the demodulator output. The message at the
output of the demodulator can always be classified as

ˆ m(t) = Am(t) + N L (t) = m e (t) + N L (t) (5.9)

where A is an amplitude gain on the signal, m e (t) is the effective message
estimate, and N L (t) is a combination of the noise and distortion produced in
demodulation. Engineers in practice have many ways to characterize the fidelity
of the message estimate. In this introductory course we will concentrate on the
idea of signal power-to-noise power ratio (SNR). The demodulator output SNR
is defined as
2
A P m P m e
SNR = = (5.10)
P N P N
where P m is defined in Eq. (5.1) and the noise or distortion power will require
the tools in Chapter 9 to define. The SNR is typically a function of the received
signal power, the noise power, and the demodulator processing. It should be
noted in this text that since the channel model that is being adopted is r z (t) =
x z (t)e j φ p this implies that the received power is equal to the transmitted power
). This is obviously not the case in a real communication system but
(P r z = P x z
is true in the idealized models assumed in this book.
Communications engineers usually like to compare performance to an ideal-
ized standard to get a metric for fidelity produced by a communication system.
The idealized metric for performance used in this text is the system where the
message is transmitted directly across a baseband channel. The block diagram
of this system is shown in Figure 5.9. The resulting output SNR from this system
will be denoted SNR b . The figure of merit in assessing system performance is
the ratio of the output SNR to the reference SNR for a common received signal
. We denote this quantity as the transmission efficiency, i.e.,
power, P r z
SNR
E T = (5.11)
SNR b