ISI and Pulse shaping.ppt

pulse shaping

1. INTERSYMBOL INTERFERENCE (ISI)
IntersymbolInterference
ISI on Eye Patterns
Combatting ISI
Nyquist’s First Method for zero ISI
Raised Cosine-RolloffPulse Shape
Nyquist Filter

2. Eeng 3602
Intersymbol Interference
Intersymbol interference (ISI)occurs when a pulse spreads out in such a way that
it interferes with adjacent pulses at the sample instant.
Example: assume polar NRZ line code. The channel outputs are shown as spreaded
(width T
b becomes 2T
b) pulses shown (Spreading due to bandlimited channel
characteristics).
Data 1bT 0 bT 0 bT bT
Data 0bT 0 bT 0 bT bT
Channel Input
Pulse width T
b
Channel Output
Pulse width T
b

3. Eeng 3603
Intersymbol Interference
For the input data stream:
The channel output is the superposition of each bit’s output:
1 1110 0bT bT2 bT3 bT4 0 bT5 A bT bT2 bT3 bT4 0 bT5
1 1110 0bT bT2 bT3 bT4 0 bT5
Resultant
Channel Output
Waveform

4. Eeng 3604
ISI on Eye Patterns
The amount of ISI can be seen on an oscilloscope using an Eye
Diagramor Eyepattern.
Time (T
b)
Amplitude
Noise
Margin
Distortionb
T
Extension
Beyond T
bis
ISI

5. Eeng 3605
Intersymbol Interference
Iftherectangularmultilevelpulsesarefilteredimproperlyastheypassthrougha
communicationssystem,theywillspreadintime,andthepulseforeachsymbolmaybe
smearedintoadjacenttimeslotsandcauseIntersymbolInterference.
How can we restrict BW and at the same time not introduce ISI? 3 Techniques.

6. Eeng 3606
Combating ISI
Three strategies for eliminating ISI:
Use a line code that is absolutely bandlimited.
•Would require Sinc pulse shape.
•Can’t actually do this (but can approximate).
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
the sample instants.
•Can come up with pulse shapes that don’t overlap during adjacent sample
instants.
Raised-Cosine Rolloff pulse shaping
Use a filter at the receiver to “undo” the distortion introduced by
the channel.
•Equalizer.

7. Eeng 3607
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
es
Ck
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
ht
x

Sampling Instants
ISI occursbut,
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
ft
ht
ft






8. Eeng 3608
There will be NOISI 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 Bis the absolute bandwidth of the system.
Nyquist’s First Method for Zero ISI 
sin11
Where
s
e e s
s s s s
ftf
H f h t f
f f f t T



  

 s
MINIMUM BANDAbsolute bandwidth is:
2
Signalling Rate is: =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

9. Eeng 3609
Nyquist’s First Method for Zero ISI

10. Eeng 36010
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:
Infinite time duration.
Sharp transition band in the frequency domain.
The Sinc pulse shape can cause significant ISI in the presence of timing errors.
If the received signal is not sampled at exactlythe bit instant (Synchronization
Errors), then ISI will occur.
We seek a pulse shape that:
Has a more gradual transition in the frequency domain.
Is more robust to timing errors.
Yet still satisfies Nyquist’s first method for zero ISI.
Zero crossings at non-zero integer multiples of the bit period

11. Eeng 36011
Raised Cosine-Rolloff Nyquist Filtering
 
1
1
1
0 1 0
1,
1
1 cos , B is the Absolute Bandwidth
22
0,



e
ff
ff
H f f f B
f
fB
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 14
o
b
ee
f
Rf
rr
f
ft ft
h t F H f f
ft ft
 



 

  

 
 
Because of the difficulties caused by the Sa type pulse shape, consider other
pulse shapes which require more bandwidthsuch as the Raised Cosine-rolloff
Nyquist filterbut 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
rr
f

  

12. Eeng 36012
Raised Cosine-Rolloff Nyquist Filtering0
Rolloff factor: Bandwidth: B (1 ) (1 )
22
f RD
r r r
f

     
 11
1
2
c s o
2
e
ff
f
Hf









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



13. Eeng 36013
Raised Cosine-Rolloff Nyquist Filtering
Impulse response is given by: 

1 0
0 2
0
sin 2 cos2
2
2 14
ee
ft ft
h t F H f f
ft ft
 

 


 
 
•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.

14. Eeng 36014
Raised Cosine-Rolloff Nyquist Filtering
Frequency response and impulse
responses of Raised Cosine pulses for
various values of the roll off parameter. rB
r ISI
  
  

15. Eeng 36015
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

16. Eeng 36016
The bandwidth of a Raised-cosine (RC) rolloff pulse shape is a function of the
bit rate and the rolloff factor:
Or solving for bit rate yields the expression:
This is the maximum transmitted bit rate when a RC-rolloff pulse shape with
Rolloff factor ris transmitted over a baseband channel with bandwidth B.2
1
B
R
r


Bandwidth for Raised Cosine Nyquist Filtering


11
1
2
1 Multilevel Signalling
2
o o o
o
f
B f f f f r
f
R
Br
D
Br



     




17. Eeng 36017
P(f)

18. Gaussian pulse shaping
Eeng 36018

19. Gaussian filter
Eeng 36019