Selected Topics in Applied Signal Processing - Digital Signal Processing: An Introduction with MATLAB and Applications - page 163

3.5.9 Application of Adaptive Filtering to Channel
Equalization

3.5.9.1 Reducing Intersymbol Interference

A communication channel can introduce noise and other forms of distortion which
adversely affect the transmitted data. One kind of distortion which is particularly
important in communication systems is so-called intersymbol interference.
Consider the scenario where it is desired to transmit a square pulse across a
communications channel. This pulse has a sinc function spectrum, which has an
infinite bandwidth. The square pulse is therefore compact in time, but infinite in
frequency extent. If the square pulse enters a communications channel which
acts as an ideal low-pass filter, the output signal will be bandlimited in fre-
quency, but it will be stretched in the time-domain. In fact it will have infinite
extent in the time-domain, due to the fact that the output is the convolution of
the input with the filter impulse response, and the latter is infinitely long. This is
in accord with the fact that any signal with finite frequency spectrum is infinitely
long in the time domain. As will be seen in the following paragraphs, this fact
has significant implications for digital pulse transmission in communication

systems.
A communication channel has normally a limited bandwidth, B c , and hence acts
like a LPF (with transfer function H c (f)). Consider for simplicity a baseband
antipodal signal transmission, where rectangular data bits are transmitted as ± 1,
with symbol duration T (see Sect. 3.2.2 ). The channel will cause each data symbol
to be stretched in time beyond its allocated interval T, and this stretching will
interfere with the receiver's ability to reliably detect the true data value at any given
time. This kind of interference is referred to as intersymbol interference (ISI). ISI
tends to become worse as the data rate R = 1/T bps increases. The number of other
'parasitic' symbols incorporated into the current symbol period depends on the data
rate R and the channel bandwidth B c . The higher the data rate the worse the ISI, and
the lower the bandwidth the more the ISI becomes a problem.
In practice, there is a significant effect on ISI from only a finite number of
symbols on either side of the current symbol. The practical effect of the ISI can
therefore be modeled via a distortion or filtering with a finite impulse response. i.e.
one can model the ISI as a filtering produced by a tapped delay line with a finite
number of taps f h o ; h 1 ; ... ; h M g . If the channel is distortionless, then h o = 1 and
h k ¼ 0 8 k 6¼ 0. For practical channels which have some distortion, at least some
of the h k 8 k 6¼ 0 are non-zero.
In the case of baseband antipodal binary transmission, the distortionless channel
output (i.e., the observed signal seen at the matched filter detector) would be
y(k) =±1 + noise, assuming a sampling rate at the receiver similar to that at the
transmitter. A decision here can be made as follows: if y(k) C 0, then +1 was
transmitted, otherwise -1 was transmitted. This decision is not reliable if sig-
nificant if ISI exists; and the matched filter is insufficient for detection.