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Chapter 3 – Data Transmission: Chapter 3 – Data Transmission: Concepts and Terminology Concepts and Terminology

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TransmissionTransmission TerminologyTerminology

data transmission occurs between a transmitter & receiver via some medium

guided medium eg. twisted pair, coaxial cable, optical fiber

unguided / wireless medium eg. air, water, vacuum

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TransmissionTransmission TerminologyTerminology

direct 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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TransmissionTransmission TerminologyTerminology

Simplex transmission one direction

• eg. television

Half-duplex transmission either direction, but only one way at a time

• eg. police radio (walkie-talkie: push-to-talk and release-to-listen)

Full-duplex transmission both directions at the same time

• eg. telephone

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Time domain concepts of signalsTime domain concepts of signals

time domain concepts analog signal

• various in a smooth way over time digital signal

• maintains a constant level then changes to another constant level

periodic signal• pattern repeated over time

aperiodic signal• pattern not repeated over time

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Analog and digital signalsAnalog and digital signals

Periodic signalsPeriodic signals

The signal period T is the inverse of signal frequency f :

The signal s(t) is periodic if:

The signal amplitude is denoted by A

ttsTts )()(

)(

)(sec

1

HzHertzinf

sondsinT

fT

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Sine waveSine wave

Mathematically, the sine wave is given by :

Three parameters :1. Peak amplitude (A)

maximum strength of signal usually measured in volts

2. Frequency ( f ) rate of change of signal measured in Hertz (Hz) or cycles per second period = time for one repetition ( T ) T = 1/f

3. Phase ( ) relative position in time

)2sin()( ftAts

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Varying Sine Waves)2sin()( ftAts

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Wavelength (λ)

is the distance occupied by one cycle assuming signal velocity v, then = vT or equivalently f = v, since T=1/f for the special case when v=c

c = 3*108 m/s (speed of light in free space) c=λf

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Frequency Domain Concepts

signal are made up of many frequencies components are sine waves Fourier analysis can shown that any signal

is made up of component sine waves Fourier series of a square wave with

amplitudes A and –A :

oddkk k

kftAts

,1

)2sin(4)(

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Fourier Transform

Mathematical tool that relates the frequency-domain description of the signal to its time-domain description

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Time-domain vs frequency-domain

Figure 3.5a: frequency domain function for the signal of Figure 3.4c.

Time-domain vs frequency-domain

Time-domain

Frequency- domain

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Spectrum and bandwidth

Spectrum range of frequencies contained in signal

Absolute bandwidth width of spectrum

effective bandwidth often just bandwidth narrow band of frequencies containing most energy

DC Component component of zero frequency

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Acoustic Spectrum

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Analog and digital data transmission

data – entities that convey meaning

signals & signalling– electric or electromagnetic representations of

data, physically propagates along medium

transmission– communication of data by propagation and

processing of signals

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Audio Signals

freq range 20Hz-20kHz (speech 100Hz-7kHz) easily converted into electromagnetic signals varying volume converted to varying voltage can limit frequency range for voice channel to

300-3400Hz

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Digital Data

as generated by computers etc. has two dc components bandwidth depends on data rate

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Analog Signals

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Digital signals

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Advantages and disadvantages of digital signals

cheaper less susceptible to noise but greater attenuation digital now preferred choice

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Transmission Impairments

signal received may differ from signal transmitted causing: analog - degradation of signal quality digital - bit errors

most significant impairments are attenuation and attenuation distortion delay distortion noise

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Attenuation

where signal strength falls off with distancedepends on mediumreceived signal strength must be:

strong enough to be detectedsufficiently higher than noise to receive without error

so increase strength using amplifiers/repeatersis also an increasing function of frequencyso equalize attenuation across band of

frequencies used

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Delay distortion

propagation velocity varies with frequency hence various frequency components

arrive at different times particularly critical for digital data since parts of one bit spill over into others causing intersymbol interference

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Noise

Additional unwanted signals inserted between transmitter and receiver Thermal

due to thermal agitation of electrons uniformly distributed white noise

Interference from other users in a multi-user environment (e.g., mobile environment)

KelvinsinTempratureT

KJtconssBoltzmannk

bandwidthofHzperwattsindensitypowernoiseN

HzWkTN

/1038.1tan'

1

)/(

23

0

0

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Noise

crosstalk a signal from one line is picked up by another

impulse irregular pulses or spikes

• eg. external electromagnetic interference short duration high amplitude a minor annoyance for analog signals but a major source of error in digital data

• a noise spike could corrupt many bits

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Noise: example0

1

+5V

-5V

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Data-rate

Data rate: is the rate, in bits per second (bps), at which data can be communicated

kbpsmTdurationbit

RRatedatab

50sec02.0

111

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Spectrum, bandwidth and Data-rate

Spectrum of a signal: is the range of frequencies that it contains

Absolute bandwidth: is the width of the spectrum Effective bandwidth: is a relatively narrow band that contains

most signal energy Any transmission system has a limited bandwidth Square wave have infinite components and hence infinite

bandwidth, but most energy in first few components Limited bandwidth increases distortion Limited bandwidth also limit the data rate that can be carried

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Bandwidth

KHzBBandwidththen

KHzfAssume

fffBBandwidth

2

,1

213

KHzBeffectivethen

mXAssumeX

lobemainofwidthBEffective

BAbsolute

1

sec,1

1

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Data-rate and bandwidth

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Channel Capacity

Channel Capacity: max possible rate at which data can be transmitted over a given communication path, under given conditions

Channel capacity is a function of :data rate - in bits per second [bps]bandwidth - in Hertz [Hz]noise - on communication linkerror rate - the rate at which errors occur, reception of 1

when 0 is transmitted, and visa versa

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Nyquist Bandwidth

Consider noise free channels If rate of signal transmission is 2B then we can

carry signal with frequencies no greater than B i.e., given bandwidth B, highest signal rate is 2B

For binary signals (0,1), 2B bps need bandwidth B Hz Can increase rate by using M signal levels or M

symbols (e.g. M=4, Quaternary: 00, 01, 10,11) Nyquist formula is: So increase rate by increasing signal levels

at cost of receiver complexity limited by noise & other impairments

][log2 2 bpsMBC

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Shannon Capacity Formula

Consider relation of data rate, noise & error rate faster data rate shortens each bit so bursts of noise affects more bits given noise level, higher rates means higher errors

Signal-to-Noise Ratio (SNR):

SNR in decibles (dB):

Shannon’s channel capacity (C) in bits/s is related to the channel bandwidth (B) in Hertz and SNR by:

theoretical maximum capacity get lower in practise

powernoise

powersignalSNR

SNRSNRdB 10log10

)1(log2 SNRBC

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Nyquit bandwidth and Shannon Capacity Example: Suppose that the spectrum of a channel is

between 3MHz and 4MHz and the SNRdB=24dB. Find:

1. The channel bandwidth (B)

2. The channel capacity (C)

3. Based on Nyquist formula, how many signalling levels are required to achieve the max capacity

Solution:

1. B = 4MHz - 3MHz = 1MHz

2.

3.

MbpsSNRBC 8108)2511(log10)1(log 62

62

251

log1024 10

SNR

SNRdBSNRdB

16log102108

log2

266

2

MM

MBC

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Decibels and signal strength

It is customary to express gain or loss (attenuation) in decibels: Logarithmic unit (compressed scale) Multiplication and division reduce to addition and subtraction

The decibel power gain (GdB):

The decibel power loss (LdB):

The decibel voltage loss:

levelpoweroutputP

levelpowerinputP

P

PG

out

in

in

outdB

:

:

log10 10

out

in

in

outdB P

P

P

PL 1010 log10log10

RresistoracrossvoltagetheisVwhere

V

V

RV

RV

P

PL

out

in

out

in

out

indB 102

2

1010 log20/

/log10log10

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Decibels and signal strength

Example 1: if a signal with a power level of 10mW is inserted onto a transmission line and the measured power some distance away is 5mW, then the loss can be expressed as:

Example 2: Consider a series of transmission elements in which the input is at a power level of 4mW, the first element is a transmission line with 12dB loss, the second element is an amplifier with 35dB gain, and the third element is a transmission line with 10dB loss.

1. The net gain is -12 + 35 – 10= 13dB

2. The output power (Pout):

mWmWP

mW

PdBG

out

outdB

8.79104

4log1013

3.1

10

dBmW

mW

P

PL

out

indB 3

5

10log10log10 1010

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Decibels and signal strength

The dBW (decibel-Watt):

Example: a power of 1W is 0dBW,

a power of 1000W is 30dBW,

a power of 1mW is –30dBW

The dBm (decibel-milliWatt):

Example: a power of 1mW is 0dBm,

a power of 30dBm is 0dBW

)(log101

log10 1010 WW

dBW powerW

powerpower

mW

powerpower mW

dBm 1log10 10

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Example

Given a receiver with an effective noise temperature of 294K and a 10 MHz bandwidth. Find the thermal noise level (N0) at the receiver’s output in units of dBW?

dBW

BTkkTBW

kTBN

BandwidthB

KelvinsinTempratureT

KJconstsBoltzmannk

WkTBN

HzWkTN

dBW

9.133

707.246.228

)10(log10)294(log10)1038.1(log10

log10log10log10log101

log10

/1038.1.'

],[

]/[

71010

2310

1010101010

23

0

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The expression Eb/N0

The expression Eb/N0 : is the ratio of signal energy per bit (Eb) to noise power density per Hz (N0)

TkRSN

E

notationdecibelin

kTR

S

N

RS

N

E

TRRatedata

TempratureT

constBoltzmannkwherekTN

durationbitT

powersignalSwhereSTE

dB

dB

b

b

b

b

bb

1010100

00

0

log10log10log10

,

/

1

:

.:,

:

:,

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Example

For Binary Phase Shift Keying (BPSK) modulation, Eb/N0 = 8.4 dB is required for a bit error rate of 10-4 (one bit error out of every 10000 bits). If the effective noise temperature is 290 K (room temperature) and the data rate is 2400 bps, what received signal power level is required?

dBS

S

S

TkRSN

E

dB

dB

dB

dB

dB

b

8.161

)46.2)(10(6.228)38.3)(10(4.8

290log10)6.228(2400log104.8

log10log10log10

1010

1010100

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Eb/N0 versus SNR

We can relate Eb/N0 to the Signal-to-Noise Ratio (SNR):

efficiencyspectraltheisBCwhere

C

B

R

B

R

B

N

S

N

EN

SN

SBSNRBCcapacitychannelShannonThe

SNRRatioNoisetoSignaltheisN

Swhere

R

B

N

S

BN

RS

N

E

bandwidththeisBwhereBNNpowerNoise

N

RS

N

E

BCBCb

BC

b

b

/

1212

12

)1(log)1(log:

)(,/

/

,

/

//

0

/

22

0

0

00

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Example

Suppose we want to find the minimum Eb/N0 required to achieve a spectral efficiency C/B of 6bps/Hz

dBC

B

N

E BCb 21.105.106

11212 6/

0