csc535 communication networks i chapter 3a: data transmission fundamentals dr. cheer-sun yang

CSC535 Communication Networks I

Chapter 3a:Data Transmission Fundamentals

Dr. Cheer-Sun Yang

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Fundamental of CommunicationsFourier Series Approximation(section 3.3)Nyquist Theorem(section 3.4)Shannon’s Theorem(section 3.4)Line Encoding (section 3.5)Modulation and Demodulation (section

3.6)

Copyrighted by McGraw Hill (Leon-Garca and Widjaja) Communication Networks

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Receiver

Communication channel

Transmitter

Figure 3.5

A Transmission System

....0110101 ....0110101

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Transmission System ComponentsTransmitterReceiverMedium (physical link)

Guided mediume.g. twisted pair, optical fiber

Unguided mediume.g. air, water, vacuum

Channel (Logical Link)

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Channel TypesDirect link

No intermediate devices

Point-to-point Direct link Only 2 devices share link

Multi-point More than two devices share the link

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Signal ClassificationsContinuous signal

Amplitude changes in a smooth way over time

Discrete signalAmplitude maintains a constant level then changes

to another constant level

Periodic signalPattern repeated over time

Aperiodic signalPattern not repeated over time

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Continuous & Discrete Signals

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PeriodicSignals

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Properties of a Periodic SignalAmplitude (A)

maximum strength of signal unit: volts

Frequency (f) Rate of change of signal Hertz (Hz) or cycles per second Period = time for one repetition (T) T = 1/f

Phase () Relative position in time

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Varying Sine Waves

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WavelengthDistance occupied by one cycleDistance between two points of

corresponding phase in two consecutive cycles

Represented by the symbol Assuming signal velocity v

= vT f = v c = 3*108 ms-1 (speed of light in free space)

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Characterizations of Communication ChannelsTime Domain Characterization -

represents the amplitude s(t) changes of a channel at different time

Frequency Domain Characterization - represents the amplitude s(f) of frequencies of a signal

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Time Domain ConceptsTime domain characterization of a

communication channel reflects the “capability” of carrying an input signal to a long distance.

The propagation speed of a signal over a channel is reflected by the impulse response at the receiver end.


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Channel

t0t

h(t)

td

Figure 3.17

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Time Domain Concepts(cont’d)A very narrow pulse s(t) is applied to the

channel at time t = 0.The pulse appears at the other end of a

channel as an impulse response, h(t).Ideally, we hope that h(t) = s(t - td).But, it is impossible to achieve this in real

systems.

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Fourier Transform

Jean B. Fourier found that any periodic function can be expressed as an infinite sum of sine function.

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0 /2sin/2cos2

1)(

ni

ni PitbPitaats

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We can addsines together to make new functions...

g2(t)=1/3sin(2( 3f )t)

g1(t)=sin(2f t)

g3(t)= g1(t) + g2(t)

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Addition of FrequencyComponents


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1 0 0 0 0 0 0 1

. . . . . .

t

1 ms

Figure 3.15


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- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

0

0.125 0.2

5

0.375 0.5

0.625 0.7

5

0.875

1

- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

0

0.125 0.2

5

0.375 0.5

0.625 0.7

5

0.875

1

- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

0

0.125 0.2

5

0.375 0.5

0.625 0.7

5

0.875

1

( b ) 2 H a r m o n i c s

( c ) 4 H a r m o n i c s

( a ) 1 H a r m o n i c

Figure 3.16

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Frequency Domain ConceptsSignal usually made up of many

frequenciesComponents are sine wavesCan be shown (Fourier analysis) that

any signal is made up of component sine waves

Can plot frequency domain functions


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Channel

t t

Aincos 2ft Aoutcos (2ft + (f))

Aout

AinA(f) =

Figure 3.13

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FrequencyDomain

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Signal with DC Component

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Spectrum & BandwidthSpectrum

range of frequencies contained in signal

Absolute bandwidth width of spectrum

Effective bandwidth Often just bandwidth Narrow band of frequencies containing most of the

energy

DC Component Component of zero frequency What is the frequency of a function f(t) = 5?

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Analog and Digital Data TransmissionData

Entities that convey meaning

Signals Electric or electromagnetic representations of

data

Transmission Communication of data by propagation and

processing of signals

From now on, we can assume that a bit stream can be transmitted via a physical link using pulses or sine waves.


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communication channel

d meters

0110101... 0110101...

Figure 3.10

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Transmission SpeedAlso known as bit rate with the unit of

bits/sec.We need to measure how fast a signal can

be transmitted by a transmitter: transmission speed

We also are interested in how fast a signal can be propagated through a physical link: propagation speed

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DataAnalog

Continuous values within some interval e.g. sound, video

Digital Discrete values e.g. text, integers

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SignalsMeans by which data are propagatedAnalog

Continuously variable Various media

wire, fiber optic, space

Speech bandwidth 100Hz to 7kHz Telephone bandwidth 300Hz to 3400Hz Video bandwidth 4MHz

Digital Use two DC components

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Data and SignalsUsually use digital signals for digital data

and analog signals for analog dataCan use analog signal to carry digital data

Modem

Can use digital signal to carry analog data Compact Disc audio

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Analog SignalsDigital computers are incompatible with

analog transmission media such as phone lines.

How can one use analog signals to represent digital data bits?

We need to convert digital data to analog signal at the sender side and convert analog data back to digital data at the receiver side.

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Acoustic Spectrum (Analog)

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Analog Signals Carrying Analog and Digital Data

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Digital Signals Carrying Analog and Digital Data

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Analog TransmissionAnalog signal transmitted without regard

to contentMay be analog or digital dataAttenuated over distance Use amplifiers to boost signalAlso amplifies noise

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Digital TransmissionConcerned with contentIntegrity endangered by noise,

attenuation etc.Repeaters usedRepeater receives signalExtracts bit patternRetransmitsAttenuation is overcomeNoise is not amplified

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Advantages of Digital TransmissionDigital technology

Low cost LSI/VLSI technology

Data integrity Longer distances over lower quality lines

Capacity utilization High bandwidth links economical High degree of multiplexing easier with digital techniques

Security & Privacy Encryption

Integration Can treat analog and digital data similarly


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(a) Analog transmission: all details must be reproduced accurately

Sent

Sent

Received

Received

• e.g digital telephone, CD Audio

(b) Digital transmission: only discrete levels need to be reproduced

• e.g. AM, FM, TV transmission

Figure 3.6

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Transmission ImpairmentsSignal received may differ from signal

transmittedAnalog - degradation of signal qualityDigital - bit errorsCaused by

Attenuation and attenuation distortion Delay distortion Noise

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AttenuationSignal strength falls off with distanceDepends on mediumReceived signal strength:

must be enough to be detected must be sufficiently higher than noise to be

received without error

Attenuation is an increasing function of frequency


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AmplifierEqualizer

TimingRecovery

Decision Circuit.& SignalRegenerator

Figure 3.9

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Delay DistortionOnly in guided mediaPropagation velocity varies with frequency

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Noise (1)Additional signals inserted between

transmitter and receiverThermal

Due to thermal agitation of electrons Uniformly distributed White noise

Intermodulation Signals that are the sum and difference of

original frequencies sharing a medium

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Noise (2)Crosstalk

A signal from one line is picked up by another

Impulse Irregular pulses or spikes e.g. External electromagnetic interference Short duration High amplitude


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Source Repeater DestinationRepeater

Transmission segment

Figure 3.7


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Attenuated & distorted signal +

noise

EqualizerRecovered signal

+residual noise

Repeater

Amp.

Figure 3.8

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Channel CapacityData rate

In bits per second Rate at which data can be communicated

Bandwidth In cycles per second of Hertz Constrained by transmitter and medium


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f0 W

A(f)

(a) Lowpass and idealized lowpass channel

(b) Maximum pulse transmission rate is 2W pulses/second

0 Wf

A(f)1

Channel

tt

Figure 3.11

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Bandwidth RevisitedA transmission channel can be characterized

by the signals within a certain frequency ranges.

If a channel allows low frequency signals to pass, it is called a low-pass channel.

If a channel allows high frequency signals to pass, it is called a high-pass channel.

The bandwidth of a channel is defined as the range of fequencies that is passed by a channel.

First major theorem: Nyquist’s Result

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Bit Rate and BandwidthFirst major theorem: Nyquist’s ResultThe bit rate at which pulses can be

transmitted over a channel is proportional to the bandwidth.

In essence, if a channel has a bandwidth W, the narrowest pulse that can be transmitted over the channel has width = 1/2W seconds.

Thus the fastest rate at which pulses can be transmitted into the channel is given by the Nyquist rate: rmax = 2W pulses/second.

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Baud Rate vs. Bit RateTransmission speed can be measured in

bits per second(bps).Technically, transmission is rated in baud,

the number of changes in the signal per second that the hardware generates.

Using RS-232 standard to communicate, bit rate rate = baud rate.

In general, bit rate rate = N * baud rate, where N is the number of signals in a string.

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Baud Rate vs. Bit Rate Sender sends the bit string, by b1 b2 … bn. The transmitter alternately analyzes each string

and transmits a signal component uniquely determined by the bit values. Once the component is sent, the transmitter gets another bit string and repeats this process.

The different signal components make up the actual transmitted signal. The frequency with which the components change is the baud rate.

At the receiving end, the process is reversed.The receiver alternately samples the incoming signal and generates a bit string.

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Baud Rate vs. Bit RateConsequently, the bit rate depends on

two things: the frequency with which a component can change (baud rate) and N, the number of bits in the string. That is why the formula:

bit rate = N * baud rate

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Nyquist Sampling Theorem Due to Harry Nyquist (1920) Nyquist showed that if F is the maximum

frequency the medium can transmit, the receiver can completely reconstruct by sampling it 2ƒ times per second on a perfectly noiseless channel.

In other words, the receiver can reconstruct the signal by sampling it at intervals of 1/(2f) second.

For example, if the max frequency is 4000 Hz, the receiver needs to sample the signal 8000 times per second or using 2ƒ as the baud rate.

Bit rate = 2ƒ * N.


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+A

-A0 T 2T 3T 4T 5T

1 1 1 10 0

Transmitter Filter

Comm. Channel

Receiver Filter Receiver

r(t)

Received signal

t

Figure 3.19

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Data Rate and Bandwidth It looks like that one can increase the

bandwidth W of a channel to achieve a higher bit rate r without considering the actual characteristics of a transmission link.

In fact, any transmission system has a limited band of frequencies. For example, a channel can use +5V as bit 1, -5V as bit 0; a channel may also be able to use +5V as ‘11’, +3V as ‘10’, -3V as ‘01’, and -5V as ‘00’. We are actually dividing the frequency range of F(=1/T) for representing 2 bits into that for representing 4 bits.

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Data Rate and Bandwidth

Question: Can we keep increasing the

bandwith or dividing the bandwidth to increase the bit rate?


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4 signal levels 8 signal levels

typical noise

Figure 3.22

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Data Rate and Bandwidth In fact, any transmission system has a limited

band of frequencies. We cannot increase the bandwidth indefinitely. Signals can be impaired.

We cannot keep dividing the total frequency range into smaller ranges since the receiver will become harder to distinguish one frequency from another.

This also limits the data rate a channel can achieve.

This leads to the second major result: Shannon’s Theorem

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Any Limit on Bit Rate?

The formula that Bit rate = 2ƒ * N seems to imply that there is no upper bound for the data rate given the maximum frequency. Unfortunately, this is not true for two reasons.

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How about real hardware?

First, if we used amplitude to represent data bits, each time we separate the amplitude into smaller ranges to represent more data bits, the receiver must be more sophisticated (and more expensive) to be able to detect smaller differences. If the differences become too small, we eventually exceed the ability of a deviec to detect them.

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How about real hardware?

Second, many channels are actually subject to noise.

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Limitation on Real Hardware

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Signal-to-Noise Ratio

Electrical engineers uses S/N to indicate the quality of sound. The higher the ration is, the better the quality is.

B = log 10 (S/N) bels, where B is the quality rate.

S/N is known as the signal-to-noise ratio.Quality of sound is measured in decibles

(abbreviated dB) or bels (1 dB = 0.1 Bel).

If B=2.5 bels, then S = ___________N?


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signal noise signal + noise

signal noise signal + noise

HighSNR

LowSNR

SNR = Average Signal Power

Average Noise Power

SNR (dB) = 10 log10 SNR

t t t

t t t

Figure 3.12

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Shannon’s TheoremBit rate = Bandwidth * log 2 (1+S/N) bps.According to this result, a bit rate around

35,000 bps is an upper limit for conventional modems.

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Example of Shannon’s TheoremBandwidth = 3000 Hz, Quality rate = 35 dB or 3.5 bels, What is the bit rate?Please work with your neighbors now.Hint: You must find S/N first.

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Reading MaterialDon’t read sections 3.2 and 3.3 now. You

may get confused.

csc535 communication networks i chapter 3a: data transmission fundamentals dr. cheer-sun yang

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