isi & pulse shaping_good

5/25/2018 ISI & Pulse Shaping_good

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Eeng 360 1

Chapter 3

INTERSYMBOL INTERFERENCE (ISI)

Intersymbol Interference

ISI on Eye Patterns

Combatting ISI

Nyquists First Method for zero ISI

Raised Cosine-Rolloff Pulse Shape

Nyquist Filter

Huseyin Bilgekul

Eeng360 Communication Systems IDepartment of Electrical and Electronic Engineering

Eastern Mediterranean University


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Intersymbol interference (ISI)occurs when a pulse spreads out in such a way thatit interferes with adjacent pulses at thesample instant.

Example: assume polar NRZ line code. The channel outputs are shown as spreaded(width Tbbecomes 2Tb) pulses shown (Spreading due to bandlimited channelcharacteristics).

Data 1

bT 0 bT0bT bT

Data 0

bT 0 bT0bT bT

Channel Input

Pulse width Tb

Channel Output

Pulse width Tb


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For the input data stream:

The channel output is the superposition of each bits output:

1 11100

bT bT2 bT3 bT40 bT5

A

bT bT2 bT3 bT40 bT5

1 1110 0

bT bT2 bT3 bT40 bT5

Resultant

Channel OutputWaveform


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ISI on Eye Patterns

The amount of ISI can be seen on an oscilloscope using an EyeDiagramor Eyepattern.

Time (Tb)

Amplitude

NoiseMargin

Distortion

bT Extension

Beyond TbisISI


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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.


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Flat-topped multilevel input signal having pulse shape h(t) and values ak:


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

th t

a h t

DT

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.


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out n e sn

w t a h t nT

Equivalent transfer function:

Receiving filter can be designed to produce a neededHe(f)in terms ofHT(f)andHC(f):

Output signal can be rewritten as:


He(f), chosen such to minimize ISI is called EQUALIZING FILTER)

H

e

R

T C

H ff

H f H f H f

* * *h t h t h t h t h t e T C R

sin

H Where H se T C R ss s

T ftf H f H f H f H f f F T

T T f

Equivalent Impulse Response he(t) :


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Combating ISI Three strategies for eliminating ISI:

Use a line code that is absolutely bandlimited.

Would require Sinc pulse shape.

Cant actually do this (but can approximate).

Use a line code that is zero during adjacent sample instants.

Its okay for pulses to overlap somewhat, as long as there is no overlap atthe sample instants.

Can come up with pulse shapes that dont overlap during adjacent sampleinstants.

Raised-Cosine Rolloff pulse shaping

Use a filter at the receiver to undo the distortion introduced bythe channel.

Equalizer.


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Nyquists First Method for Zero ISIISI can be eliminated by using an equivalent transfer function,He(f), such that the impulse

response satisfies the condition:

, 00, 0

e sC kh kT

k

k is an integer, is the symbol (sample) period

is the offset in the receiver sampling clock times

C is a nonzero constantsin

Now choose the function for ( )

s

e

T

xh t

x

Sampling Instants

ISI occurs but,

NO ISI is present at thesampling instants

is a Sa function

sin (

)

out n e s

n

e

se

s

w t a h t nT

h

f th t

f t


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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 functionHe(f)

is:

This type of pulse will allow signalling at a baud rate ofD=1/Ts=2B(for BinaryR=1/Ts=2B)

whereBis the absolute bandwidth of the system.

Nyquists First Method for Zero ISI

sin1 1

Wherese e ss s s s

f tfH f h t f

f f f t T

s

MINIMUM BANDAbsolute bandwidth is:

2Signalling Rate is: =1 2 Pulses/se

ID

c

W THsf

B

D T B

0f

He(f)1/fs

fs/2

-fs/2


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he(t)

0f

He(f)

1/fs

fs/2-fs/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 Nyquists first method for zero ISI.

Zero crossings at non-zero integer multiples of the bit period


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Raised Cosine-Rolloff Nyquist Filtering

1

1

1

0 1 0

1,

1

1 cos , B is the Absolute Bandwidth2 2

0,

e

f f

f f

H f f f Bf

f B

f B f f f f

0

1 00 2

0

Where is the 6-dB bandwidth of the filter

Rolloff factor: Bandwidth: B (1 )2

sin2 cos22

2 1 4

o

b

e e

f

Rf

r rf

f t f th t F H f f

f t f t

Because of the difficulties caused by the Sa type pulse shape, consider otherpulse shapes which require more bandwidthsuch 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/fo.

0

Rolloff factor: Bandwidth: B (1 )2

bRfr rf


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0Rolloff factor: Bandwidth: B (1 ) (1 )2 2

f R Dr r rf

11

12

c so2

e

f f

fH f

Now filtering requirements are relaxed because absolute bandwidth isincreased.

Clock timing requirements are also relaxed.

The r=0 case corresponds to the previous Minimum bandwidth case.

oB f f


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Impulse response is given by:

1 00 2

0

sin2 cos2 2

2 1 4e e

f t f th 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 errorswill be much lower.


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Frequency response and impulse

responses of Raised Cosine pulses for

various values of the roll off parameter.

r B

r ISI

d ll ff l


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Raised Cosine-Rolloff Nyquist FilteringIllustrating the received bit stream of Raised Cosine pulse shapedtransmission 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

B d d h f R d N F l


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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 bandwidthB.

2

1

BR

r

Bandwidth for Raised Cosine Nyquist Filtering

1 1

12

1 Multilevel Signalling

2

o o o

o

fB f f f f rf

RB r

DB r

N F l


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Nyquist Filter

00

,

20, Elsewhere

e

fY f f f

H f ff

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

02sD f f

Theorem: A filter is said to be aNyquist filterif 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 theNYQUISTs First Criterion.

N F l Ch


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00,

2

0, Elsewhere

e

fY 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

isi & pulse shaping_good

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