2010 digital comm week 6 7

8/7/2019 2010 Digital Comm Week 6 7

1/27

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)

12/20/2010 Muhammad Ali Jinnah University, Islamabad Digital Communications II EE4723 1


2/27

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


The power outside the 1st null bandwidth is not negligible. That

is, the power in the sidelobes can be quite high


3/27

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)



4/27

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



5/27

Inter Symbol Interference

Input data stream and bit superposition


T e c anne output s t e sum o t e contr ut ons rom eac t


6/27

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



7/27

ISI Baseband Communication System Model

receivertheofresponseImpulse)(

channel,theofresponseImpulse)(

,

=

=

th

th

R

C

T

=

=nTn

nTthats ),()(

=== *=n sCTTn

,,

=

+= een tnnTthaty )()()( ),(*)(*)()( ththththwhere RCTe =


)(*)(*)()( ththtntn RCe =


8/27

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


h0 is an arbitrary constant


9/27

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



10/27

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 ,



11/27

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


If the received signal is not sampled at exactly the bit instant,

then ISI will occur


12/27

1st Nyquist Criterion: Time domain

t1

shaping function

TfN

=2

1

02t0t

t

Equally spaced zeros,

=1-1


fn2


13/27

Sample rate vs. bandwidth

Wis the channel bandwidth forP(f)

, ,

system with no ISI

P(f)



14/27

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 =


So the bandwidth becomes:s

( )rBB+=

1min


19/27

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



20/27

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)



21/27

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



22/27

Eye Patterns


Concept of the eye pattern


23/27

Eye Patterns


Concept of Eye diagram Mask. Waveform must not intrude into the shaded regions.


24/27

Cosine rolloff filter: Eye pattern

2nd Nyquist:

1st Nyquist: 2nd Nyquist:

1st Nyquist:

1st Nyquist

1st Nyquist: 1st Nyquist:

2nd Nyquist: 2nd Nyquist:



25/27

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)



26/27


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)



27/27


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)


2010 digital comm week 6 7

Documents