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EE4723 : Digital Communications II
Week 6 7:
Inter Symbol Interference (ISI)
N uist Criteria for ISI
Pulse Shaping and Raised-Cosine Filter
Eye Pattern
Error Performance Degradation (On Board)
Demodulation and Detection (On Board)
Eb/No and Error Probability (On Board)
Matched Filter and Correlator Receiver (On Board)
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Baseband Communication System We have been considering the following baseband system
The transmitted signal is created by the line coderaccording
to
where an is thesymbol mappingand g(t) is thepulse shape=
n
bn
One big problem with the line codes is that they are not bandlimited
The absolute bandwidth is infinite
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The power outside the 1st null bandwidth is not negligible. That
is, the power in the sidelobes can be quite high
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Intersymbol Interference (ISI)
If the transmission channel is bandlimited, then high frequency
components will be cut off
,
If the pulse spread out into the adjacent symbolperiods, then it is
said that intersymbol interference (ISI) has occurred
Intersymbol Interference (ISI)
Inters mbol interference ISI occurs when a ulse s reads out in
such a way that it interferes with adjacent pulses at thesample instant
Causes
Channel induced distortion which spreads or disperses the pulses
Multipath effects (echo)
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Pulse spreading
Due to improper filtering (@ Tx and/orRx), the received pulses overlap one
another thus making detection difficult xamp e o
Assume polar NRZ line code
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Inter Symbol Interference
Input data stream and bit superposition
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T e c anne output s t e sum o t e contr ut ons rom eac t
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ISI
Note:
can occur w enever a non- an m e ne co e s use
over a bandlimited channel
can occur on y a e samp ng ns an s
Overlapping pulses will not cause ISI if they have zeroamp u e a e me e s gna s samp e
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ISI Baseband Communication System Model
receivertheofresponseImpulse)(
channel,theofresponseImpulse)(
,
=
=
th
th
R
C
T
=
=nTn
nTthats ),()(
=== *=n sCTTn
,,
=
+= een tnnTthaty )()()( ),(*)(*)()( ththththwhere RCTe =
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)(*)(*)()( ththtntn RCe =
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ISI Baseband Communication System Model
Note that he(t) is the equivalent impulse response of the receiving filter
To recover the information sequence {an}, the outputy(t) is sampled at t = kT,
= , , ,
The sampled sequence is
or equivalently
=
+=n
een kTnnTkThakTy )()()(
AWGN term
=
= ++=+=
n knn
knknkknknk nhaahnhay,
0
,..2,1,0),(),(where === kkTnnkThh ekek
Effect of other symbols at thesampling instants t=kT
Desired symbol scaled bygain parameters h0
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h0 is an arbitrary constant
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Signal Design for Bandlimited Channel
Zero ISI
To remove ISI, it is necessary and sufficient to make the term=
=knn
eenk nnaay
,
0
Nyquist Criterion
0,0)(0
= handknfornTkThe
Pulse amplitudes can be detected correctly despite pulse
spreading or overlapping, if there is no ISI at the decision-
makin instants
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Nyquist Criterion: Time domain
p(t): impulse response of a transmission system (infinite length)
Suppose 1/T is the sample rate
e necessary an su c ent con t on or p t to sat s y yqu st
Criterion is
( )
( )
=
=
0,1 n
nTp ,
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1st Nyquist Criterion: Time domain
Pulse shape that satisfy this criteria is Sinc(.) function, e.g.,
t
The smallest value ofTfor which transmission with zero ISI isT
e
possible is
Problems with Sinc(.) function T
1
= It is not possible to create Sinc pulses due to
Infinite time duration
arp rans on an n e requency oma n Sinc(.) pulse shape can cause ISI in the presence of timing
errors
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If the received signal is not sampled at exactly the bit instant,
then ISI will occur
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1st Nyquist Criterion: Time domain
t1
shaping function
TfN
=2
1
02t0t
t
Equally spaced zeros,
=1-1
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fn2
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Sample rate vs. bandwidth
Wis the channel bandwidth forP(f)
, ,
system with no ISI
P(f)
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Sample rate vs. bandwidth
When 1/T = 2W(The Nyquist Rate), rectangular
function satisfy Nyquist condition
( ) ( ) ( ),otherwise,0
,;sinc
sin
excess bandwidth is 50 % Rolloff factor, r= 1 ===> excess bandwidth is 100 %
RC filter is used to realized Nyquist filter since the transition band can be
changed using the roll-off factor The sharpness of the filter is controlled by the parameter r
When r = 0 this corresponds to an ideal rectangular function
BandwidthB occupied by a RC filtered signal is increased from itsminimum value
B1
min =
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So the bandwidth becomes:s
( )rBB+=
1min
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Rolloff and bandwidth
Benefits of large roll off factor
implement with less processing delay Less signal overshoot, resulting in lower peak to mean
excursions of the transmitted signal
Less sensitivity to symbol timing accuracy wider eyeopen ng
r= 0 corresponds to Sinc(.) function
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Partial Response Signals
To improve the bandwidth efficiency
Widen the ulse the smaller the bandwidth.
But there is ISI. For binary case with two symbols, there isonly few possible interference patterns.
By adding ISI in a controlled manner, it is possible to
achieve a signaling rate equal to the Nyquist ratei.e.
Duobinar and Polibinar Si nalin
(Covered in the previous lectures)
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Eye Patterns
An eye pattern is obtained by superimposing the actual waveforms for large
numbers of transmitted or received symbols
- -,
alphabet of two digital waveforms encoding a binary signal (1s and 0s)
Actual eye patterns are used to estimate the bit error rate and thesignal to- noise ratio
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Eye Patterns
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Concept of the eye pattern
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Eye Patterns
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Concept of Eye diagram Mask. Waveform must not intrude into the shaded regions.
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Cosine rolloff filter: Eye pattern
2nd Nyquist:
1st Nyquist: 2nd Nyquist:
1st Nyquist:
1st Nyquist
1st Nyquist: 1st Nyquist:
2nd Nyquist: 2nd Nyquist:
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Eye Diagram Examples
0.8
1EYE DIAGRAM
0.4
0.6
-0.2
0
.
-
-0.6
-0.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1
.
Time (sec)
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Eye Diagram Examples
1.5EYE DIAGRAM WITH NOISE (Variance =0.1)
0.5
1
0
-1
-0.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1.5
Time (sec)
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Eye Diagram Examples
3EYE DIAGRAM WITH NOISE (Variance =0.5)
1
2
0
-2
-1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-3
Time (sec)
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