TABLE OF CONTENTS In this chapter we study the performance of digital communication systems in the presence of additive noise as measured by the probability of error and introduce the concept of the optimum signal detection. We assume throughout a distortionless channel, so the received signal is free of intersymbol interference (ISI). We also assume additive white gaussian noise (AWGN) with zero mean value, independent of the signal.
Figure 9-1 portrays the operations of a binary receiver. The transmitted signal over a symbol interval(O, T) is represented by
The received signal r( t) by the receiver is represented by
where n( t) is a zero-mean AWGN.
There are two separate steps involved in signal detection. The first step consists of reducing the receive signal r( t) to a single number z( T). This operation can be performed by a linear filter followed by a sampler, as shown in block 1 of Fig. 9-1. The output of receiver (block 1), sampled at t = T, yields
where a i( T) is the signal component of z( T) and n o( T) is the noise component. We often write Eq.( 9.3a) as
Note that the noise component n o is a zero-mean gaussian random variable, and thus z is a gaussian random variable with a mean of either a 1
