Intersymbol Interference FDM TDM - GUCeee.guc.edu.eg/Courses/Communications/COMM502... · 1 Dr. Ahmed El-Mahdy Comm 502: Communication Theory Comm 502: Communication Theory Lecture

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Comm 502: Communication Theory Dr. Ahmed El-Mahdy

Comm 502: Communication Theory

Lecture 5

Intersymbol Interference

FDM TDM

2


Time Limited Waveforms

Time-Limited Signal = Frequency Unlimited Spectrum

TS 0

Fourier Transform

1/TS 2/TS 3/TS -1/TS -2/TS -3/TS 0

The transmitted pulses are filtered to be band-limited

(To have a limited frequency spectrum)

The pulses are spread in Time domain

Effect in Time domain

Limited Signal-Square Pulse is a Time

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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 spread (width Tb becomes more than Tb) pulses shown (Spreading due to

bandlimited channel characteristics).

Data 1

2/bT 0 2/3 bTbT 2/bT

Data 0

2/bT

0 bT

Channel Input

Pulse width Tb

Channel Output

Pulse width 2Tb

2/3 bT

2/3 bT

2/bT 2/3 bT

0

0

bT

bT

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symbol Interference (ISI)-Inter • Spreading of the pulses causes inter-symbol interference (ISI) • ISI results due to: (1) improper filtering of the pulses in the transmitter to reduce BW. (2) Effect of channel. Effect: Neighboring symbols affect the measured value and this introduces errors in the decision device at the receiver which results in increasing the bit error rate.

How can we restrict BW and at the same time not introduce ISI? 3 Techniques.

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Combating ISI • Three strategies for eliminating ISI:

1-Nyquist’s First Method for Zero ISI

– Use a line code that is absolutely band-limited. • Would require Sinc pulse shape.

• It is difficult to do this.

2- Raised Cosine filtering

– 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

– 3- Equalization

– Use a filter at the receiver to “undo” the distortion introduced by the channel.

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Combating ISI

)(the)(th

Input

pulse

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1-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:

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

,....2,0

0)(

ss

eTTt

tCth

t

Sinc function

(in time domain)

satisfies this condition if its

duration in freq. domain

is 1/Ts

Ts

0

-Ts 2Ts -2Ts

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1-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:

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

,....2,0

0)(

ss

eTTt

tCth

)( se Tth

t

Sinc function

(in time domain)

satisfies this condition if its

duration in freq. domain

is 1/Ts

Ts

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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.


sin1 1

Where se e s

s s s s

f tfH f h t f

f f f t T

0 f

He(f)

ratesignalingiswhere22

1bandwidth absolute minimum The 0 s

s

s

RR

TW

sT2

1

sT

sT2

1Ts

0

-Ts

t

10



he(t)

0f

He(f)

Ts

• Sinc pulses are not possible to create due to: – 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 exactly the 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. – Still satisfies Nyquist’s first method for zero ISI.

sT2

1

sT2

1

0W0Wt

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2-Raised Cosine Filtering Because of the difficulties caused by the Sinc type pulse shape, consider other

pulse shapes which require more bandwidth such as the Raised Cosine-rolloff

filter but they are less affected by synchronization errors.

The Raised Cosine filter is defined by its rollof factor number r.

o

o

WWrwhen

WWrwhen

2,1

,0

)1(2

rR

WBandwidth s

)1( rWo

e

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Raised Cosine Filtering-2 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.

)1(2

)1(2

1

rR

rT

WBandwidth

s

s

s s s s s s s s

WW

2,0

,1

0s

s

RWWthenrif

RWthenrif

e

=

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Cosine Filter-Shaping with Raised-Pulse-2

Impulse response

He(f) TS: symbol interval RS: symbol rate r: roll-off factor

Raised Cosine Filter Bandwidth = RS(1+r)/2

)(the

• The tails of he(t)

are now decreasing

much faster than

the Sinc function.

• ISI due to

synchronization

errors will be much

lower.

Ts 2Ts 3Ts -Ts -2Ts -3Ts

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3-Equalization for Wireless Channel

)(th

channeltheofresponseimpulsetheis)(

)(*)()(

:domaintimeIn

th

txthty

)(tyChannel

)(tx

)()()()()()()(ˆ

)()()(

:domainfrequencyIn

1 fXfXfHfHfYfGfX

fXfHfY

)()( Equalizer 1 fHfG Equalizer inverses the

effect of the channel

Equalizer

)(ˆ tx

)( fG

Receiver

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Multiplexing

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Frequency Division Multiplexing (FDM)

FDM is a technique for transmitting multiple messages

simultaneously over a wideband channel. Each user has a specified

frequency band and between these bands, there is a Guard interval.

Guard band

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Frequency Division Multiplexing (FDM)

• The disadvantage of this system is the limitation of the users due to the limitation in the frequency band.

• The advantage of this system is that all the channels are available for all the users all the time.

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6.18

Five channels, each with a 100-kHz bandwidth, are to be multiplexed

together. What is the minimum bandwidth of the link if there is a

need for a guard band of 10 kHz between the channels to prevent

interference?

Solution For five channels, we need at least four guard bands. This means that

the required bandwidth is at least

5 × 100 + 4 × 10 = 540 kHz,

as shown in the following Figure.

Example:

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Time Division Multiplexing (TDM)

• TDM is the time interleaving of samples from several sources so that the information from these sources can be transmitted serially over a single communication channel.

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Time Division Multiplexing (TDM) • The following Fig. shows the concept of TDM as applied to three analog sources

that are multiplexed over a PCM system.

• At the receiver, the samples from individual channels are separated and distributed by another sampler (rotary switch called distributer). The samples from each channel are filtered to reproduce the original message signal.

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Time Division Multiplexing (TDM)

Sec.

Sec.

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Time Division Multiplexing

• The disadvantage of this system is the delay caused especially in case of large number of users.

• The advantage of this system is that all the frequency band is available for all the users.

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6.23

Example:

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d. The frame rate is always the same as any input

rate. So the frame rate is 1,000,000 frames per

second. Because we are sending 4 bits in each

frame, we can verify the result of the previous

question by multiplying the frame rate by the

number of bits per frame.

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Applications of TDM In modern telephony a remote concentrator is a unit to which

Subscribers' analogue telephone lines are connected to it. They have the

following main functions, namely:

Digitize, that is, turn voice from analogue into a digital form.

Multiplex, interleaving many calls together on a single wire or

optical fiber.

Only a few hundred telephone lines attach to each remote concentrator.

https://en.wikipedia.org/wiki/File:VZ_SAI_workers_Secaucus_jeh.JPG

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• When a user picks up their phone, the concentrator produces

the dial tone.

• When the user dials, the concentrator reads the tones. Once

the user has completed dialing, the concentrator's

microcomputer sends the dialing data to the central switch,

which allocates a time slot for the dialing phone on the wire

pairs that pass through the concentrator and through the

central switch.

• After the central switch tells the concentrator which time slot

to use, the concentrator "opens" a time-slot on the loop to a

local phone.

Applications of TDM (Cont.)

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To arrange a connection, the central switch just completes the

circle between the user's phone and the remote phone. It

interchanges the data from one to the other. In this limited

sense, telephone "exchange" is exactly correct terminology

The allocated time slot on the wiring out of the concentrator

(with the same time slot number) carries data from the local

phone to the remote phone.

Telephone operator manually connecting calls

with cord pairs at a telephone switchboard

A modern central office

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Intersymbol Interference FDM TDM - GUCeee.guc.edu.eg/Courses/Communications/COMM502... · 1 Dr. Ahmed El-Mahdy Comm 502: Communication Theory Comm 502: Communication Theory Lecture