ISI - DC error correction techniques in channel

isi

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 InterferenceIntersymbol 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 instantsample 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 TT
b b becomes 2becomes 2TT
bb) pulses shown (Spreading due to bandlimited channel ) pulses shown (Spreading due to bandlimited channel
characteristics).characteristics).
Data 1
bT 0
bT0
bT
bT
Data 0
bT 0
b
T0bT
b
T
Channel Input
Pulse width TT
bb
Channel Output
Pulse width TT
bb

3. Eeng 360 3
Intersymbol InterferenceIntersymbol 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 1110 0
b
T
b
T2
b
T3
b
T40
b
T5
A
bT
bT2
bT3
bT40
bT5
1 1110 0
bT
bT2
bT3
bT40
bT5
Resultant
Channel Output
Waveform

4. Eeng 360 4
ISI on Eye PatternsISI 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 DiagramEye Diagram or or EyeEye patternpattern..
Time (T
b
)
A
m
p
lit
u
d
e
Noise
Margin
Distortion
b
T Extension
Beyond T
b 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 a
k:
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


h
e(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 H
e
(f) in terms of H
T
(f) and H
C
(f):
 Output signal can be rewritten as:
Intersymbol Interference
 H
e(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 ft
f H f H f H f H f f F T
T T f


    
       
     

 Equivalent Impulse Response h
e(t) :

8. Eeng 360 8
Combating ISICombating 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 shapingRaised-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, H
e
(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 H
e(f)
is:
 This type of pulse will allow signalling at a baud rate of D=1/T
s
=2B (for Binary R=1/T
s
=2B)
where B is the absolute bandwidth of the system.
Nyquist’s First Method for Zero ISI
 
sin1 1
Where
s
e e s
s s s s
f tf
H f h t f
f f f t T


 
   
 

s
MINIMUM BANDAbsolute bandwidth is:
2
Signalling Rateis: =1 2 Pulses/se
ID
c
W TH
s
f
B
D T B


0
f
H
e(f)
1/f
s
f
s/2
-f
s
/2

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

12. Eeng 360 12
Nyquist’s First Method for Zero ISI
h
e(t)
0
f
H
e
(f)
1/f
s
f
s/2
-f
s
/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 exactlyexactly 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 , BistheAbsoluteBandwidth
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
sin2 cos2
2
2 1 4
o
b
e e
f
Rf
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=f
Δ
/f
o.
0
Rolloff factor: Bandwidth: B (1 )
2
b
Rf
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

    

 11
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
sin2 cos2
2
2 1 4
e e
f t f t
h t F H f f
f t f t
 

 

  
      
    
• The tails of h
e
(t) are now
decreasing much faster than the Sa
function (As a function of t
2
).
• 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 rr is transmitted over a baseband channel with bandwidth is transmitted over a baseband channel with bandwidth
BB..
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
  

    