The document addresses intersymbol interference (ISI) in communication systems, explaining how it occurs when pulse spreading in a channel leads to overlap between adjacent pulses. It discusses various techniques to mitigate ISI, including the use of Nyquist's methods, raised cosine-rolloff pulse shaping, and equalizing filters to minimize distortion in transmitted signals. The document also covers the characteristics of Nyquist filters that prevent ISI at the system output.

1. Eeng 360 1
Chapter 3
INTERSYMBOL INTERFERENCE (ISI)
 Intersymbol Interference
 ISI on Eye Patterns
 Combatting ISI
 Nyquist’s First Method for zero ISI
 Raised Cosine-Rolloff Pulse Shape
 Nyquist Filter
Huseyin Bilgekul
Eeng360 Communication Systems I
Department of Electrical and Electronic Engineering
Eastern Mediterranean University

2. Eeng 360 2
Intersymbol Interference
Intersymbol Interference
 Intersymbol interference (ISI)
Intersymbol interference (ISI) occurs when a pulse spreads out in such a way that
occurs when a pulse spreads out in such a way that
it interferes with adjacent pulses
it interferes with adjacent pulses at the
at the sample instant
sample instant.
.
 Example: assume polar NRZ line code. The channel outputs are shown as spreaded
Example: assume polar NRZ line code. The channel outputs are shown as spreaded
(width
(width T
Tb
b becomes 2
becomes 2T
Tb
b) pulses shown (Spreading due to bandlimited channel
) pulses shown (Spreading due to bandlimited channel
characteristics).
characteristics).
Data 1
b
T
 0 b
T
0
b
T b
T

Data 0
b
T
 0 b
T
0
b
T b
T

Channel Input
Pulse width T
Tb
b
Channel Output
Pulse width T
Tb
b

3. Eeng 360 3
Intersymbol Interference
Intersymbol Interference
 For the input data stream:
For the input data stream:
 The channel output is the superposition of each bit’s output:
The channel output is the superposition of each bit’s output:
1 1
1
1
0 0
b
T b
T
2 b
T
3 b
T
4
0 b
T
5
A
b
T b
T
2 b
T
3 b
T
4
0 b
T
5
1 1
1
1
0 0
b
T b
T
2 b
T
3 b
T
4
0 b
T
5
Resultant
Channel Output
Waveform

4. Eeng 360 4
ISI on Eye Patterns
ISI on Eye Patterns
 The amount of ISI can be seen on an oscilloscope using an
The amount of ISI can be seen on an oscilloscope using an
Eye Diagram
Eye Diagram or
or Eye
Eye pattern
pattern.
.
Time (Tb)
Amplitude
Noise
Margin
Distortion
b
T Extension
Beyond Tb is
ISI

5. Eeng 360 5
Intersymbol Interference
 If the rectangular multilevel pulses are filtered improperly as they pass through a
communications system, they will spread in time, and the pulse for each symbol may be
smeared into adjacent time slots and cause Intersymbol Interference.
 How can we restrict BW and at the same time not introduce ISI? 3 Techniques.

6. Eeng 360 6
 Flat-topped multilevel input signal having pulse shape h(t) and values ak:
Intersymbol Interference
         
 
       
in
out
w ( )* *
1
Where Where pulses/s
*
n s n s n s
n n
s
n e
s
n s e
n
s
n
t a h t nT a h t t nT a t nT h t
t
h t
a h t
D
T
nT
T
w t a t nT h t
 

 
     
 
 
 
 
 
 
 
  

 
 
  

 
         
Equivalent impulse response: * * *
h t h t h t h t h t
e T C R

 he(t) is the pulse shape that will appear at the output of the receiver filter.

7. Eeng 360 7
   
out n e s
n
w t a h t nT
 

 Equivalent transfer function:
 Receiving filter can be designed to produce a needed He(f) in terms of HT(f) and HC(f):
 Output signal can be rewritten as:
Intersymbol Interference
 He(f), chosen such to minimize ISI is called EQUALIZING FILTER)
 
 
     
H e
R
T C
H f
f
H f H f H f

         
* * *
h t h t h t h t h t
e T C R

           
sin
H Where H s
e T C R s
s s
T f
t
f H f H f H f H f f F T
T T f


 
   
  
 
   
 
   
 

 Equivalent Impulse Response he(t) :

8. Eeng 360 8
Combating ISI
Combating ISI
 Three strategies for eliminating ISI:
Three strategies for eliminating ISI:

Use a line code that is absolutely bandlimited.
Use a line code that is absolutely bandlimited.
• Would require Sinc pulse shape.
Would require Sinc pulse shape.
• Can’t actually do this (but can approximate).
Can’t actually do this (but can approximate).

Use a line code that is zero during adjacent sample instants.
Use a line code that is zero during adjacent sample instants.
• It’s okay for pulses to overlap somewhat, as long as there is no overlap at
It’s okay for pulses to overlap somewhat, as long as there is no overlap at
the sample instants.
the sample instants.
• Can come up with pulse shapes that don’t overlap during adjacent sample
Can come up with pulse shapes that don’t overlap during adjacent sample
instants.
instants.

Raised-Cosine Rolloff pulse shaping
Raised-Cosine Rolloff pulse shaping

Use a filter at the receiver to “undo” the distortion introduced by
Use a filter at the receiver to “undo” the distortion introduced by
the channel.
the channel.
• Equalizer.
Equalizer.

9. Eeng 360 9
Nyquist’s First Method for Zero ISI
 ISI can be eliminated by using an equivalent transfer function, He(f), such that the impulse
response satisfies the condition:
 
, 0
0, 0
e s
C k
h kT
k



 


k is an integer, is the symbol (sample) period
is the offset in the receiver sampling clock times
C is a nonzero constant
sin
Now choose the function for ( )
s
e
T
x
h t
x

Sampling Instants
ISI occurs but,
NO ISI is present at the
sampling instants
   
is a Sa function
sin
( )
out n e s
n
e
s
e
s
w t a h t nT
h
f t
h t
f t


 



10. Eeng 360 10
 There will be NO ISI and the bandwidth requirement will be minimum (Optimum
Filtering) if the transmit and receive filters are designed so that the overall transfer function He(f)
is:
 This type of pulse will allow signalling at a baud rate of D=1/Ts=2B (for Binary R=1/Ts=2B)
where B is the absolute bandwidth of the system.
Nyquist’s First Method for Zero ISI
   
sin
1 1
Where
s
e e s
s s s s
f t
f
H f h t f
f f f t T


 
  
 
 

s
MINIMUM BAND
Absolute bandwidth is:
2
Signalling Rate is: =1 2 Pulses/se
ID
c
W TH
s
f
B
D T B


0
f
He(f)
1/fs
fs/2
-fs/2

11. Eeng 360 11
Nyquist’s First Method for Zero ISI

12. Eeng 360 12
Nyquist’s First Method for Zero ISI
he(t)
0
f
He(f)
1/fs
fs/2
-fs/2
 Since pulses are not possible to create due to:
Since pulses are not possible to create due to:

Infinite time duration.
Infinite time duration.

Sharp transition band in the frequency domain.
Sharp transition band in the frequency domain.
 The Sinc pulse shape can cause significant ISI in the presence of timing errors.
The Sinc pulse shape can cause significant ISI in the presence of timing errors.

If the received signal is not sampled at
If the received signal is not sampled at exactly
exactly the bit instant (Synchronization
the bit instant (Synchronization
Errors), then ISI will occur.
Errors), then ISI will occur.
 We seek a pulse shape that:
We seek a pulse shape that:

Has a more gradual transition in the frequency domain.
Has a more gradual transition in the frequency domain.

Is more robust to timing errors.
Is more robust to timing errors.

Yet still satisfies Nyquist’s first method for zero ISI.
Yet still satisfies Nyquist’s first method for zero ISI.
Zero crossings at non-zero integer multiples of the bit period

13. Eeng 360 13
Raised Cosine-Rolloff Nyquist Filtering
 
 
1
1
1
0 1 0
1,
1
1 cos , B is the Absolute Bandwidth
2 2
0,
e
f f
f f
H f f f B
f
f B
f B f f f f



 

 
 
 
  
   
 
  
 
  
 
 




   
   
 
0
1 0
0 2
0
Where is the 6-dB bandwidth of the filter
Rolloff factor: Bandwidth: B (1 )
2
sin 2 cos2
2
2 1 4
o
b
e e
f
R
f
r r
f
f t f t
h t F H f f
f t f t
 



 

  
 
 
 
   
 
 

 
   
 Because of the difficulties caused by the Sa type pulse shape, consider other
pulse shapes which require more bandwidth such as the Raised Cosine-rolloff
Nyquist filter but they are less affected by synchrfonization errors.
 The Raised Cosine Nyquist filter is defined by its rollof factor number r=fΔ/fo.
0
Rolloff factor: Bandwidth: B (1 )
2
b
R
f
r r
f

  

14. Eeng 360 14
Raised Cosine-Rolloff Nyquist Filtering
0
Rolloff factor: Bandwidth: B (1 ) (1 )
2 2
f R D
r r r
f

    
 
 
1
1
1
2
c s
o
2
e
f f
f
H f


 

 
 
 
 
 
 
 
 
 
 Now filtering requirements are relaxed because absolute bandwidth is
increased.
 Clock timing requirements are also relaxed.
 The r=0 case corresponds to the previous Minimum bandwidth case.
o
B f f
 

15. Eeng 360 15
Raised Cosine-Rolloff Nyquist Filtering
 Impulse response is given by:    
 
1 0
0 2
0
sin 2 cos2
2
2 1 4
e e
f t f t
h t F H f f
f t f t
 

 

 
 
 
   
 
 

 
   
• The tails of he(t) are now
decreasing much faster than the Sa
function (As a function of t2
).
• ISI due to synchronization errors
will be much lower.

16. Eeng 360 16
Raised Cosine-Rolloff Nyquist Filtering
Frequency response and impulse
responses of Raised Cosine pulses for
various values of the roll off parameter.
r B
r ISI
  
  

17. Eeng 360 17
Raised Cosine-Rolloff Nyquist Filtering
 Illustrating the received bit stream of Raised Cosine pulse shaped
transmission corresponding to the binary stream of 1 0 0 1 0 for 3 different
values of r=0, 0.5, 1.
1 0 0 1 0 1 0 0 1 0

18. Eeng 360 18
 The bandwidth of a Raised-cosine (RC) rolloff pulse shape is a function of the
The bandwidth of a Raised-cosine (RC) rolloff pulse shape is a function of the
bit rate and the rolloff factor:
bit rate and the rolloff factor:
 Or solving for bit rate yields the expression:
Or solving for bit rate yields the expression:

This is the maximum transmitted bit rate when a RC-rolloff pulse shape
This is the maximum transmitted bit rate when a RC-rolloff pulse shape
with Rolloff factor
with Rolloff factor r
r is transmitted over a baseband channel with bandwidth
is transmitted over a baseband channel with bandwidth
B
B.
.
2
1
B
R
r


Bandwidth for Raised Cosine Nyquist Filtering
 
 
 
1 1
1
2
1 Multilevel Signalling
2
o o o
o
f
B f f f f r
f
R
B r
D
B r


 
     
 
 
 
 

19. Eeng 360 19
Nyquist Filter
 
  0
0
,
2
0, Elsewhere
e
f
Y f f f
H f f
f
  
  
  
  


 
 
0
0
0 0 0
( ) is a real function and even symmetric about = 0:
( ), 2
Y is odd symmetric about :
( ),
Y f f
Y f Y f f f
f f
Y f f Y f f f f
  

    
0
2
s
D f f
 
 Theorem: A filter is said to be a Nyquist filter if the effective transfer function is :
 There will be no intersymbol interference at the system output if the symbol rate is
 Raised Cosine Filter is also called a NYQUIST FILTER.
 NYQUIST FILTERS refer to a general class of filters that satisfy the
NYQUIST’s First Criterion.

20. Eeng 360 20
 
  0
0
,
2
0, Elsewhere
e
f
Y f f f
H f f
f
  
  
  
  


Nyquist Filter Characteristics
 
 
0
0
0 0 0
( ) is a real function and even symmetric about = 0:
( ), 2
Y is odd symmetric about :
( ),
Y f f
Y f Y f f f
f f
Y f f Y f f f f
  

    