B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

10
PERFORMANCE ANALYSIS OF
DIGITAL COMMUNICATION
SYSTEMS
In analog communications, the user objective is to achieve high fidelity in waveform reproduction;
Hence, the suitable performance criterion is the output signal-to-noise ratio. The
choice of this criterion indicates that the signal-to-noise ratio reflects the quality of the
message and is related to the ability of a listener to interpret a message.
In digital communication systems, the transmitter input is chosen from a finite set of
possible symbols. The objective at the receiver is not to reproduce the waveform that carries
the symbol with fidelity; instead, the receiver aims to accurately determine which particular
symbol was transmitted among the set of possible ones. Because each symbol is represented by
a particular waveform at the transmitter, our goal is to decide, from the noisy received signal,
which particular waveform was originally transmitted. Logically, the appropriate figure of
merit in a digital communication system is the probability of error in this decision at the
receiver. In particular, the probability of bit error, also known as the bit error rate (BER), is a
direct quality measure of the communication system. Not only is the BER important to digital
signal sources, it is also directly related to the quality of signal reproduction for analog signal
sources.
In this chapter, we present two important aspects in the performance analysis of digital
communication systems. The first part focuses on the error analysis of several specific binary
detection receivers. The goal is for students to learn how to apply the fundamental tools of
probability theory and random processes for BER performance analysis. Our second focus is to
illustrate detailed derivation of optimum detection receivers for general digital communication
systems such that the receiver BER can be minimized.
10. 1 OPTIMUM LINEAR DETECTOR FOR BINARY
POLAR SIGNALING
In binary communication systems, the information is transmitted as O or 1 in each time interval
T 0 • To begin, we consider the binary polar signaling system of Fig. 10. la, in which the source
signal bit 1 and O are represented by ±p(t), respectively. Having passed a distortionless, but
506