Digital Communications

7Optimum Receiver in AWGN Channel

In Chapter 6 we considered the matched filter reception of baseband pulses in an AWGN channel, and the ISI due to band‐limiting and multipath. We also considered pulse shaping and other techniques for ISI mitigation. In this chapter, we will consider the details of the receiver design for the reception of sequences of M‐ary symbols and the resulting error probability in a baseband channel in the presence of AWGN.

7.1 Introduction

Consider a digital communication system with a block diagram as shown in Figure 7.1, where a message source emits every T seconds one symbol from an alphabet of M symbols, m₁, m₂,…, m_M with a priory probabilities p₁, p₂,…., p_M. In most cases of interest, M symbols of the alphabet are equally likely:

(7.1)

Figure 7.1 Block Diagram of a Baseband Digital Communication System.

Transmitter converts the message source output m_i into a distinct electrical signal s_i(t), suitable for transmission over the channel. Hence the transmission of digital information is accomplished by using one of the M signals every T seconds:

(7.2)

The energy of the real‐valued energy signal s_i(t) over the symbol duration T:

(7.3)

Depending on the ...