chapter 3 intersymbol interference (isi)

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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 BilgekulEeng360 Communication Systems I

Department of Electrical and Electronic Engineering Eastern Mediterranean University

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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 TTb b becomes 2becomes 2TTbb) pulses shown (Spreading due to bandlimited channel ) pulses shown (Spreading due to bandlimited channel characteristics).characteristics).

Data 1

bT 0 bT0bT bT

Data 0

bT 0 bT0bTbT

Channel Input

Pulse width TTbb

Channel Output

Pulse width TTbb

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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

bT bT2 bT3 bT40 bT5

A

bT bT2 bT3 bT40 bT5

1 1110 0

bT bT2 bT3 bT40 bT5

Resultant Channel Output

Waveform

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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 (Tb)

Am

plitu

de

NoiseMargin

Distortion

bT Extension Beyond Tb is

ISI

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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:

Intersymbol Interference

in

out

w ( )* *

1 Where Where pulses/s

*

n s n s n sn n

s

n e

s

n s en

sn

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 te 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 needed He(f) in terms of HT(f) and HC(f):

Output signal can be rewritten as:

Intersymbol Interference

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

H eR

T C

H ff

H f H f H f

* * *h t h t h t h t h te T C R

sinH Where H s

e 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 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.

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Nyquist’s First Method for Zero ISI ISI can be eliminated by using an equivalent transfer function, He(f), such that the impulse response satisfies the condition:

, 0

0, 0e s

C 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 constant

sinNow choose the function for ( )

s

e

T

xh t

x

Sampling Instants

ISI occurs but,

NO ISI is present at the sampling instants

is a Sa function

sin (

)

out n e sn

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 function He(f) is:

This type of pulse will allow signalling at a baud rate of D=1/Ts=2B (for Binary R=1/Ts=2B) where B is the absolute bandwidth of the system.

Nyquist’s First Method for Zero ISI

sin1 1 Where s

e e ss s s s

f tfH 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 THsfB

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: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

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Raised Cosine-Rolloff Nyquist Filtering

1

1

1

0 1 0

1,

11 cos , B is the Absolute Bandwidth

2 2

0,

e

f f

f fH f f f B

f

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

sin 2 cos 22

2 1 4

o

b

e e

f

Rfr r

f

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 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=fΔ/fo.

0

Rolloff factor: Bandwidth: B (1 )2

bRfr r

f

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0

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

f R Dr r r

f

111

2 c s o

2e

f f

fH 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.

oB f f

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Raised Cosine-Rolloff Nyquist Filtering Impulse response is given by:

1 0

0 20

sin 2 cos 2 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 errors will 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

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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

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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

BR

r

Bandwidth for Raised Cosine Nyquist Filtering

1 1

12

1 Multilevel Signalling2

o o oo

fB f f f f r

f

RB r

DB r

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Nyquist Filter

00

,2

0, Elsewheree

fY 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

02sD 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.

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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

chapter 3 intersymbol interference (isi)

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