2. Introduction
Introduction
– Intersymbol interference (ISI) is different from noise in
that it is a signal-dependent form of interference that
arises because of deviations in the frequency response of
a channel from the ideal channel.
• This non-ideal communication channel is also called
dispersive
– The result of these deviation is that the received pulse
corresponding to a particular data symbol is affected by
the tail ends of the pulses representing the previous
symbols and the front ends of the pulses representing the
subsequent symbols. E.2
4. Introduction
– Two scenarios
• The effect of ISI is negligible in comparison to that of
channel noise.
use a matched filter, which is the optimum linear
time-invariant filter for maximizing the peak pulse
signal-to-noise ratio.
• The received signal-to-noise ratio is high enough to
ignore the effect of channel noise (For example, a
telephone system)
control the shape of the received pulse.
E.4
5. Intersymbol Interference
Consider a binary system, the incoming binary sequence
{bk } consists of symbols 1 and 0, each of duration Tb .
The pulse amplitude modulator modifies this binary
sequence into a new sequence of short pulses
(approximating a unit impulse), whose amplitude ak is
+ 1 if bk = 1
represented in the polar form ak =
− 1 if bk = 0
{bk } Pulse- {ak } s (t ) xo (t ) x(t )
Transmit
amplitude Channel
filter g (t ) h(t )
modulator
w(t ) White noise
E.5
6. Intersymbol Interference
The short pulses are applied to a transmit filter of
impulse response g(t), producing the transmitted signal
s (t ) = ∑ ak g (t − kTb )
k
The signal s (t ) is modified as a result of transmission
through the channel of impulse response h(t ) . In
addition, the channel adds random noise to the signal.
{bk } Pulse- {ak } s (t ) xo (t ) x(t )
Transmit
amplitude Channel
filter g (t ) h(t )
modulator
w(t ) White noise
E.6
7. Intersymbol Interference
The noisy signal x(t ) is then passed through a receive
filter of impulse response c(t ) .The resulting output y (t )
is sampled and reconstruced by means of a decision
device.
x(t ) y(t) 1 if y > λ
Receive Decision
filter c(t ) device 0 if y < λ
Sample at ti = iTb
λ
The receiver output is
∑
y (t ) = µ a k p (t − kTb ) + n(t )
k
where µp (t ) = g (t ) ⊗ h(t ) ⊗ c(t ) and µ is a constant.
E.7
8. Intersymbol Interference
The sampled output is
∑
y (t i ) = µ ak p[(i − k )Tb ] + n(t i )
k
----- (1)
= µa i + µ ∑a
k
k p[(i − k )Tb ] + n(t i )
k ≠i
µai : contribution of the ith transmitted bit.
µ ∑ ak p[(i − k )Tb ] :
k
k ≠i
the residual effect of all other transmitted bits.
(This effect is called intersymbol interference)
E.8
9. Distortionless Transmission
In a digital transmission system, the frequency
response of the channel h(t ) is specified.
We need to determine the frequency responses of the
transmit g (t ) and receive filter c(t ) so as to reconstruct
the original binary data sequence
{bk } Pulse- {ak } s (t ) xo (t ) x(t )
Transmit
amplitude Channel
filter g (t ) h(t )
modulator
w(t ) White noise
x(t ) y(t) 1 if y > λ
Receive Decision
filter c(t ) device 0 if y < λ
Sample at ti = iTb
λ E.9
10. Distortionless Transmission
The decoding requires that
1 i = k
p (iTb − kTb ) = …..(2)
0 i ≠ k
(If this equation is satisfied and S/N is large,
equation (1) becomes y (ti ) = µai )
It can be shown that equation (2) is equivalent to
∞
∑ P( f − n / T ) = T
n = −∞
b b ….. (3)
E.10
