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ICT Elementary for Embedded SystemsSignal/Electronic Fundamental

Fourier Transform and Communication Systems

Asst. Prof. Dr. Prapun Suksompongprapun@siit.tu.ac.th

Me?

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Ph.D. from Cornell University, USA In Electrical and Computer Engineering Minor: Mathematics (Probability Theory) Ph.D. Research: Neuro-Information Theory Current Research:

Wireless Communications 2009 and 2013 SIIT Best Teaching Awards 2011 SIIT Research Award 2013 TU Outstanding Young Researcher Award

prapun.com

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Course Organization

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Course Website:http://www2.siit.tu.ac.th/prapun/ICTES/index.html

Lectures: July 27, 2015 9:00-10:20; 10:40-12:00 13:30-14:50; 15:10-16:30

Textbook: Modern Digital and Analog Communication Systems

By B.P. Lathi and Zhi Ding 4nd Edition

ISBN 978-0-471-27214-4

Library Call No. TK5101 L333 2009

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More references

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Principles of Communications By Rodger E. Ziemer and William H. Tranter 6th International student edition ISBN 978-0-470-39878-4 Library Call No. TK5105 Z54 2010 Student Companion Site: http://bit.ly/mN18kQ

Communication Systems: An Introduction to Signals and Noise in Electrical Communication By A. Bruce Carlson and Paul B. Crilly 5th International edition Call No. TK5102.5 C3 2010 ISBN: 978-007-126332-0

More references

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J. G. Proakis and M. Salehi, Communication Systems Engineering, 2nd Edition, Prentice Hall, 2002. ISBN: 0-13-095007-6

S.S. Haykin, Communication Systems, 4th Edition, John Wiley & Sons, 2001. Call Number: TK5101 H38 2001.

More references

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prapun.com

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Fourier Transform and Communication Systems

First Concept: Signal

Signal (Waveform)

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Microphone

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Microphones are a type of transducer.

They convert acoustical energy (sound waves) into electrical energy (the audio signal).

Dynamic microphones

[http://www.totalvenue.com.au/articles/microphones/microphones.html]

Dynamic Microphone

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11 [http://www.bespokenart.com/modern_art_prints/print8big.jpg]

Sound Wave Necklace

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From Berlin-based designer David Bizer

Translate a short audio clip into its visual wave pattern Each portion of the pattern is represented by a thin wafer of

plastic, metal or wood.

“The Vibe”

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3D printed iPhone cases which you can fully customize with your favorite waveform.

Signal (Waveform)

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“I Love You” Waveform

Audio Waveform Jewelry

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By Sakurako Shimizu (Japanese artist/designer in NY)

A line of jewelry that integrates audio waveforms into the pieces via laser etching

The “Bell” sound bracelet.

The “I do” rings

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17

Fourier Transform and Communication Systems

From time domain to frequency domain

LED Audio Spectrum Analyzer

18 [http://www.instructables.com/id/100-LED-10-band-Audio-Spectrum-atmega32-MSGEQ7-wit/]

Fourier transform ( )

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The Fourier transform is a frequency domain representation of the original signal.

The term Fourier transform refers to both the frequency domain representation and the corresponding mathematical operation ( ).

0 0 01 1cos 22 2

f t f f f f

t ff0-f0

12

12

The (Fundamental) Frequencies of Musical Instruments

20 [http://www.psbspeakers.com/articles/The-Frequencies-of-Music]

Note frequency

Fourier transform: Example

21

cos13 cos 3

15 cos 5

f

12

12

16

16

110

110t

t

Practice Problems

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Euler’s Formula

23

cos sinje j

1cos Re21sin Im2

jA jA jA

jA jA jA

A e e e

A e e ej

Complex exponential

2

2

cos( ) cos( )

cos sin( )2

2sin( )co

2cos 1 cos 2

2sin 1 coss( ) sin(2 )

sin cos

1cos( )cos( ) cos( ) cos( )

2

2

x x

x x

x x xd x xdx

x y x y x

x x

x x

y

(product-to-sum formula)

The Most Beautiful Equation

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Euler’s identity (Euler’s equation)

[http://www.scientificamerican.com/article/equations-are-art-inside-a-mathematicians-brain/]

Relate the three fundamental constants e, and i.

Fact: When mathematicians describe equations as beautiful, they are not lying. Brain scans show that their minds respond to beautiful equations in the same way other people respond to great paintings or masterful music.

(Continuous-Time) Fourier Transform

25

2 2j ft j ftg t G f e df G f g t e dt

Time Domain Frequency Domain

Complex exponential: 2 cos 2 sin 2j fte ft j ft

0g G f df

0G g t dt

Capital letter is used to represent corresponding signal in the frequency domain.

7 Equations

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that changed the world

… and still rule everyday life

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7 Equations

Fourier Transform Pairs (1)

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2 2j ft j ftg t G f e df G f g t e dt

Time Domain Frequency Domain

00

2j tf fe f

t ff0-f0

12

12

0cos 2 tf 0 01 12 2

f ff f

ff0

1

Delta function (f)

29

(Dirac) delta function or (unit) impulse function

Usually depicted as a vertical arrow at the origin

Not a true function Undefined at f = 0

Intuitively we may visualize (f) as an infinitely tall, infinitely narrow rectangular pulse of unit area

f

1

2

2

f

1

→ 0Area = 1

Delta function (f)

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(Dirac) delta function or (unit) impulse function

Usually depicted as a vertical arrow at the origin

Not a true function Undefined at f = 0

Intuitively we may visualize (f) as an infinitely tall, infinitely narrow rectangular pulse of unit area

f

2

2

f→ 0

Area = A

Practice Problems (A Revisit)

31

Practice Problems (More)

32

2

cos 200 cos 400

cos 200

cos 200 cos 400

t t

t

t t

Fourier Transform Pairs (2)

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2 2j ft j ftg t G f e df G f g t e dt

Time Domain Frequency Domain

sinsinc( ) xxx

-0.2172

0.1284

-0.0913

Practice Problems

34

t

1

1-1

t

1

2-2

f

f

Fourier Transform Pairs (3)

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2 2j ft j ftg t G f e df G f g t e dt

Time Domain Frequency Domain

More realistic signal…

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0 5 10 15 20 25-1

-0.5

0

0.5

1

Seconds

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 104

0

0.05

0.1

0.15

0.2

Frequency [Hz]

Mag

nitu

de

plotspec.m

plotspec.m

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% plotspec(x,Ts) plots the spectrum of the signal x% Ts = time (in seconds) between adjacent samples in x

function plotspec(x,Ts)N=length(x); % length of the signal xt=Ts*(0:(N-1)); % define a time vector ssf=((-N/2):(N/2-1))/(Ts*N); % frequency vectorfx=Ts*fft(x(1:N)); % do DFT/FFTfxs=fftshift(fx); % shift it for plottingsubplot(2,1,1); set(plot(t,x),'LineWidth',1.5); % plot the waveformxlabel('Seconds'); % label the axessubplot(2,1,2); set(plot(ssf,abs(fxs)),'LineWidth',1.5); % plot magnitude spectrumxlabel('Frequency [Hz]'); ylabel('Magnitude') % label the axes

38

Fourier Transform and Communication Systems

Introductory concepts in communications…

Modulator: a crucial part for any communication

systems

Modulation

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The term baseband is used to designate the band of frequencies of the signal delivered by the source.

Modulation is a process that causes a shift in the range of frequencies in a signal.

Motivation

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 104

0

0.05

0.1

0.15

0.2

Frequency [Hz]

Mag

nitu

de

Frequency-Division Multiplexing (FDM) and Frequency-Division Multiple Access(FDMA)

Reasonable antenna size for effective radiation of power over a radio link

Communication channel matching (avoiding frequencies that suffer from large attenuation/distortion)

An Important Property of

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Important Properties of

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*x y X Y*x y X Y

Convolution Properties:

Modulation:

* ( ) ( ) ( ) ( ) ( )x y t x y t d x t y d

Shifting Properties: 0

02 tj fg t e Gt f

00

2j tfe g t G f f

1 1cos 22 2c c cf f fg t t G f G f

Note that the magnitude of this is simply

Practice Problems (Another Revisit)

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2

cos 200

cos 200

cos 200 cos 400

t

t

t t

Simple Modulation

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×

2 cos 2 cf t

Modulator

Message(modulating signal)

1 1cos 22 2c c cf f fg t t G f G f

cos 222 22

2c c cx t m t f t M f f M f f

1 12 2c cM f f M f f

Simple Modulation

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×

2 cos 2 cf t

Modulator

Message(modulating signal)

1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005-1

-0.5

0

0.5

1

Seconds

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 104

0

0.05

0.1

0.15

0.2

Frequency [Hz]

Mag

nitu

de

1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005-1

-0.5

0

0.5

1

Seconds

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 104

0

0.05

0.1

0.15

0.2

Frequency [Hz]

Mag

nitu

de

Simple Modulation: Time Domain

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46

Fourier Transform and Communication Systems

So, … which frequencies do we actually use?

Radio-frequency spectrum

Electromagnetic Spectrum

47

[Gosling , 1999, Fig 1.1 and 1.2]

c f Wavelength

Frequency

83 10 m/s

Radio-frequency spectrum

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Commercially exploited bands

c f Wavelength

Frequency

83 10 m/s

[http://www.britannica.com/EBchecked/topic-art/585825/3697/Commercially-exploited-bands-of-the-radio-frequency-spectrum]

Note that the freq. bands are given in decades; the VHF band has 10 times as much frequency space as the HF band.

Cellular Support in iPhone 6

49

LTE on iPhones (sold in Thailand)

50 [http://www.apple.com/iphone/LTE/]

More LTE bands help you benefit from the growing number of roaming agreements around the world

Upto 150Mbps download speed.

FDD and TDD LTE frequency bands

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TDD LTE frequency band allocationsFDD LTE frequency band allocations

[http://www.radio-electronics.com/info/cellulartelecomms/lte-long-term-evolution/lte-frequency-spectrum.php]

Analog (Old) terrestrial TV in BKK

52

Channel.

Bandwidth.Picture Carrier.

Audio Carrier.

2 47 - 54 48.25 53.753 54 - 61 55.25 60.754 61 - 68 62.25 67.75

Channel.

Bandwidth.Picture Carrier.

Audio Carrier.

5 174 - 181 175.25 180.756 181 - 188 182.25 187.757 188 - 195 189.25 194.758 195 - 202 196.25 201.759 202 - 209 203.25 208.75

10 209 - 216 210.25 215.7511 216 - 223 217.25 222.7512 223 - 230 224.25 229.75

Channel.

Bandwidth.Picture Carrier.

Audio Carrier.

26 510 - 518 511.25 516.7527 518 - 526 519.25 524.7528 526 - 534 527.25 532.7529 534 - 542 535.25 540.7530 542 - 550 543.25 548.7531 550 - 558 551.25 556.7532 558 - 566 559.25 564.7533 566 - 574 567.25 562.7534 574 - 582 575.25 580.75

ความถ ีส่ญัญาณโทรทศัน์ VHF.(Low Band)

ความถ ีส่ญัญาณโทรทศัน์ VHF.(Hight Band)

ความถ ีส่ญัญาณโทรทศัน์ UHF.(Band 4)

Channel.

Bandwidth.Picture Carrier.

Audio Carrier.

35 582 - 590 583.25 588.7536 590 - 598 591.25 596.7537 598 - 606 599.25 604.7538 606 - 614 607.25 612.7539 614 - 622 615.25 620.7540 622 - 630 623.25 628.7541 630 - 638 631.25 636.7542 638 - 646 639.25 644.7543 646 - 654 647.25 652.7544 654 - 662 655.25 660.7545 662 - 670 663.25 668.7546 670 - 678 671.25 676.7547 678 - 686 679.25 684.7548 686 - 694 687.25 692.7549 694 - 702 695.25 700.7550 702 - 710 703.25 708.7551 710 - 718 711.25 716.7552 718 - 726 719.25 724.7553 726 - 734 727.25 732.7554 734 - 742 735.25 740.7555 742 - 750 743.25 748.7556 750 - 758 751.25 756.7557 758 - 766 759.25 764.7558 766 - 774 767.25 772.7559 774 - 782 775.25 780.7560 782 - 790 783.25 788.75

ความถ ีส่ญัญาณโทรทศัน์ UHF.(Band 5)

(โทรทศัน์ภาคพื้นดนิ)

Terrestrial TV in BKK

53

Channel.

Bandwidth.Picture Carrier.

Audio Carrier.

2 47 - 54 48.25 53.753 54 - 61 55.25 60.754 61 - 68 62.25 67.75

Channel.

Bandwidth.Picture Carrier.

Audio Carrier.

5 174 - 181 175.25 180.756 181 - 188 182.25 187.757 188 - 195 189.25 194.758 195 - 202 196.25 201.759 202 - 209 203.25 208.75

10 209 - 216 210.25 215.7511 216 - 223 217.25 222.7512 223 - 230 224.25 229.75

Channel.

Bandwidth.Picture Carrier.

Audio Carrier.

26 510 - 518 511.25 516.7527 518 - 526 519.25 524.7528 526 - 534 527.25 532.7529 534 - 542 535.25 540.7530 542 - 550 543.25 548.7531 550 - 558 551.25 556.7532 558 - 566 559.25 564.7533 566 - 574 567.25 562.7534 574 - 582 575.25 580.75

ความถ ีส่ญัญาณโทรทศัน์ VHF.(Low Band)

ความถ ีส่ญัญาณโทรทศัน์ VHF.(Hight Band)

ความถ ีส่ญัญาณโทรทศัน์ UHF.(Band 4)

Channel.

Bandwidth.Picture Carrier.

Audio Carrier.

35 582 - 590 583.25 588.7536 590 - 598 591.25 596.7537 598 - 606 599.25 604.7538 606 - 614 607.25 612.7539 614 - 622 615.25 620.7540 622 - 630 623.25 628.7541 630 - 638 631.25 636.7542 638 - 646 639.25 644.7543 646 - 654 647.25 652.7544 654 - 662 655.25 660.7545 662 - 670 663.25 668.7546 670 - 678 671.25 676.7547 678 - 686 679.25 684.7548 686 - 694 687.25 692.7549 694 - 702 695.25 700.7550 702 - 710 703.25 708.7551 710 - 718 711.25 716.7552 718 - 726 719.25 724.7553 726 - 734 727.25 732.7554 734 - 742 735.25 740.7555 742 - 750 743.25 748.7556 750 - 758 751.25 756.7557 758 - 766 759.25 764.7558 766 - 774 767.25 772.7559 774 - 782 775.25 780.7560 782 - 790 783.25 788.75

ความถ ีส่ญัญาณโทรทศัน์ UHF.(Band 5)

(โทรทศัน์ภาคพื้นดนิ)

MUX 1

MUX 2

MUX 3

MUX 4

MUX 5

Lower limits on radio use

54

Efficiency of an antenna in radiating radio energy is dependent on its length expressed as a fraction of wavelength. Too low frequency = too large antenna

Ex. The “Sanguine” submarine communication system 30 Hz (10,000 km wavelength) Designed (but never built) for the US Navy Base antenna: 24 km square mesh of wires. 10MW RF input Radiate only 147 W

All the remainder of the power dissipates as heat.

[Gosling, 1999, p 11]

Upper limits on radio use

55

Atmospheric absorption Atmospheric

Opacity/Transparency Quasi-optical propagation

Short wavelength = Deep shadows behind obscuring objects = Unreliable coverage.

Increased absorption by building and structural materials

[Gosling , 1999, Fig 1.3]

14 dB/km @ 60 GHz

Make commu. very dependent on weather conditions

Spectrum Allocation

56

Spectral resource is limited. Most countries have government agencies responsible for

allocating and controlling the use of the radio spectrum. Commercial spectral allocation is governed

globally by the International Telecommunications Union (ITU) ITU Radiocommunication Sector (ITU-R) is responsible for radio

communication. in the U.S. by the Federal Communications Commission (FCC) in Europe by the European Telecommunications Standards Institute

(ETSI) in Thailand by the National Broadcasting and Telecommunications

Commission (NBTC; คณะกรรมการกจิการกระจายเสยีง กจิการโทรทศัน์และกจิการโทรคมนาคมแห่งชาต ิ; กสทช.)

Blocks of spectrum are now commonly assigned through spectral auctions to the highest bidder.

57[http://www.ntia.doc.gov/page/2011/united-states-frequency-allocation-chart]2011

Thailand Freq. Allocations Chart

58http://www.ntc.or.th/uploadfiles/freq_chart_thai.htm

Spectrum Allocation (Final Words)

59

Spectrum is a scarce resource. “Radio spectrum will be the first of our finite resources to run

out, long before oil, gas or mineral deposits.”

Spectrum is allocated in “chunks” in frequency domain. “Chunks” are licensed to (cellular/wireless) operators.

Within a single cellular operator, the chunk is further divided into many channels. Each channel has its own band of frequency.

Mobile networks based on different standards may use the same “frequency chunk”. For example, AMPS, D-AMPS, N-AMPS and IS-95 all use the

800 MHz “frequency chunk”. This is achieved by the use of different channels.

Oct 2012: Thailand 2.1GHz Auction

60

4.5bn baht per license (freq chunk) 1 license (chunk) = 5 MHz (UL) 5 MHz (DL)

450 million baht per MHz 30 million baht per MHz per year

Digital TV License Auction in 2012

61[ http://hilight.kapook.com/view/95367 ]

Channels for variety TV in high definition (HD) and standard definition (SD)

Digital TV License Auction in 2012

62 [ http://hilight.kapook.com/view/95408 ]

News and children's/family channels

63

Fourier Transform and Communication Systems

Demodulation

DSB-SC

64

× ×Channel

2 cos 2 cf t

y

2 cos 2 cf t

vLPF

Modulator Demodulator

Message(modulating signal)

22

2 cos 2 2 cos 2c c

x t

v t

m t f t f t

LPF m t

Key equation:

Scaling and Suppressing Frequency Components

65

Important Properties of

66

*x y X Y*x y X Y

Convolution Properties:

Modulation:

* ( ) ( ) ( ) ( ) ( )x y t x y t d x t y d

Shifting Properties: 0

02 tj fg t e Gt f

00

2j tfe g t G f f

1 1cos 22 2c c cf f fg t t G f G f

Note that the magnitude of this is simply

Filter Property of

*x y X Y*x y X Y

Convolution Properties: * ( ) ( ) ( ) ( ) ( )x y t x y t d x t y d

Filter x t x h tFilter X f X f H f

Time Domain View: Frequency Domain View:

DSB-SC

68

0 5 10 15 20 25-1

-0.5

0

0.5

1

Seconds

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 104

0

0.05

0.1

0.15

0.2

Frequency [Hz]

Mag

nitu

de

0 5 10 15 20 25-2

-1

0

1

2

Seconds

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 104

0

0.05

0.1

0.15

0.2

Frequency [Hz]

Mag

nitu

de0 5 10 15 20 25

-2

-1

0

1

2

Seconds

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 104

0

0.05

0.1

0.15

0.2

Frequency [Hz]

Mag

nitu

de

0 5 10 15 20 25-2

-1

0

1

2

Seconds

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 104

0

0.05

0.1

0.15

0.2

Frequency [Hz]

Mag

nitu

de

/ 2

/2

[Demo_DSBSC_Sound_ReadWAV.m]

DSB-SC (Zoomed in time)

69

1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005-1

-0.5

0

0.5

1

Seconds

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 104

0

0.05

0.1

0.15

0.2

Frequency [Hz]

Mag

nitu

de

1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005-1

-0.5

0

0.5

1

Seconds

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 104

0

0.05

0.1

0.15

0.2

Frequency [Hz]

Mag

nitu

de1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005

-2

-1

0

1

Seconds

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 104

0

0.05

0.1

0.15

0.2

Frequency [Hz]

Mag

nitu

de

1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005-1

-0.5

0

0.5

1

Seconds

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 104

0

0.05

0.1

0.15

0.2

Frequency [Hz]

Mag

nitu

de

Note how the high-frequency content is riding on top of the original baseband signal.

Note how the baseband signal becomes the envelope of

the modulated signal x .

Note the delay caused by the LPF.

70

Fourier Transform and Communication Systems

Radio Quiet Zone

Electromagnetic silence in a town where wireless signals are forbidden

71

13,000 sq miles (33,000 sq km) National Radio Quiet Zone Green Bank, West Virginia Wi-Fi, cellphones, Bluetooth, AM radio are banned under state law.

Residents are allowed to use land-line phones and wired internet The only way anyone just passing through can reach the rest of the world is

by using the pay phone on the side of a road in town Only diesel vehicles are allowed on-site, because a gasoline-powered

engine’s spark plugs give off interfering radiation. The cafeteria’s microwave is kept in a shielded cage. The Interference Protection Group was formed to hunt down rogue

signals.

National Radio Quiet Zone: Video

72 [https://www.youtube.com/watch?v=iTVLJeRQS5c]

Robert C. Byrd radio telescope

73

Green Bank is the site of the gigantic Robert C. Byrd radio telescope. In recent years, the telescopes have been used to track NASA’s

Cassini probe to Saturn’s moon and to examine Mercury’s molten core.

So sensitive that it can pick up the energy equivalent of a single snowflake hitting the ground.

Even a basic AM radio transmission is enough to overpower faint readings from outer space.

Unforeseen newcomers

74

Diane Schou

She believed the cell-phone tower near her home in Iowa is the source of her illness. Symptoms range from acute headaches,

skin burning, muscle twitching and chronic pain.

She spent months living in a Faraday cage (shielded cage), a wood-framed box with metal meshing that blocked out cell signals.

EM Radiation Refugees

75 [ https://www.youtube.com/watch?v=N8SelMsICrE ]

Unforeseen newcomers

76

Electrosensitivity Formally, Electromagnetic Hypersensitivity (EHS)

Or Idiopathic environmental intolerance attributed to electromagnetic fields (IEI-EMF)

5%? of Americans. (Estimates vary widely.) Claim that exposure to electromagnetic fields (EMF) (typically created by

mobile phones, wi-fi and other electronic equipment) makes them physically ill.

Whether EHS is real is still debatable. Not medically recognized in the US. Sweden is the first country to recognize EHS as a disability.

Since 2007, electrosensitives started to move into Green Bank. Electrosensitives’ demands clash with locals.

They demand that local businesses uninstall fluorescent lights, and want a church to stop using wireless microphones.

[http://www.washingtonian.com/articles/people/the-town-without-wi-fi/index.php][http://boingboing.net/2015/01/05/in-west-virginia-theres-a-t.html][http://boingboing.net/2011/09/13/in-west-virginia-wi-fi-refugees-seek-shelter-from-electromagnetic-oppression.html][http://www.bbc.co.uk/news/world-us-canada-14887428]

Unforeseen newcomers

77 [ https://www.youtube.com/watch?v=GUBXY2b1OH8 ]

Unforeseen newcomers

78 [ https://www.youtube.com/watch?v=GUBXY2b1OH8 ]

79

Fourier Transform and Communication Systems

Unlicensed bands

Unlicensed bands

80

Frequency bands that are free to use according to a specific set of etiquette rules.

The purpose of these unlicensed bands is to encourage innovation and low-cost implementation.

Many extremely successful wireless systems operate in unlicensed bands, including wireless LANs, Bluetooth, and cordless phones.

Major difficulty: If many unlicensed devices in the same band are used in close

proximity, they generate much interference to each other, which can make the band unusable.

Unlicensed bands (2)

81

Unlicensed spectrum is allocated by the governing body within a given country.

Often countries try to match their frequency allocation for unlicensed use so that technology developed for that spectrum is compatible worldwide.

The following table shows the unlicensed spectrum allocations in the U.S.

(ISM = Industrial, Scientific, and Medical)

(U-NII = Unlicensed National Information Infrastructure)

900 MHz2.4 GHz5.8 GHz5 GHz5 GHz5.8 GHz

Licensed vs. Unlicensed Spectra

82

Licensed UnlicensedTypically nationwide. Over a period of a few years.From the spectrum regulatory agency.

For experimental systems and to aid development of new wireless technologies.

Bandwidth is very expensive. Very cheap to transmit on.

No hard constraints on the power transmitted within the licensed spectrum but the power is expected to decay rapidly outside.

There is a maximum power constraint over the entire spectrum.

Provide immunity from any kind of interference outside of the system itself.

Have to deal with interference.

[TseViswanath, 2005, Section 4.1]

Ex. Wi-Fi Standards

83

802.11a/b/g/n operate in the 2.4 GHz band.

802.11n optionally supporting the 5 GHz band.

The new 802.11ac standard mandates operation only in the 5 GHz band. 2.4 GHz band is susceptible to greater interference from

crowded legacy Wi-Fi devices as well as many household devices.

The 5 GHz band has relatively reduced interference and there are a greater number of nonoverlapping channels available (25non-overlapping channels in US) compared to the 2.4 GHz band (3 non-overlapping channels in the US).

2.4 GHz has > 10 Channels?

84

2.4 GHz has > 10 Channels?

85

In the US, FCC regulations permit channels 1 to 11 to be used.

Channels 10 and 11 are the only channels which are common throughout the world.

Channel 14, where available, is restricted to 802.11b operation only.

Can many networks generally operate in close proximity without interfering with each other?

[http://www.ieeeghn.org/wiki/index.php/Wireless_LAN_802.11_Wi-Fi]

The channels are spaced 5 MHz apart.

2.4 GHz Channels in Various Parts of the World

86 [Sohraby, Minoli, and Znati, 2007]

The 802.11b Spectral Mask

87

The 802.11b (and 802.11g) standards do not specify the width of a channel. Rather, they specify the center frequency of the channel and a spectral mask

for that channel. The energy radiated by the transmitter extends well beyond the 22-MHz

bandwidth of the channel (11 MHz from fc). At 11 MHz from the center of the channel, the energy must be 30 dB lower

than the maximum signal level. At 22 MHz away, the energy must be 50 dB below the maximum level.

[Maxfield and Bird, 2008]

Simulated spectrum of a filtered 1 Mbpstransmission

WiFi in the 2.4 GHz bands

88

It is common to hear that channels 1, 6 and 11 do not overlap.

It is more correct to say that, given the separation between channels 1, 6, and 11, the signal on any channel should be sufficiently attenuated to minimally interfere with a transmitter on any other channel.

Same for any two channels that are 5 or more ch.numbers away.

Tools such as Vistumbler or inSSIDer can help you visualize the WiFi landscape.

89 [http://en.wikipedia.org/wiki/IEEE_802.11]

“ ”

802.11g Spectral Mask

90

At 11 MHz from the center, the transmitter energy level is only 20 dB below the maximum (as opposed to 35 dB for 802.11b)

At 22 MHz away, the energy is only about 30 dB below (as opposed to 50 db for 802.11b). Even as far out as 40 MHz, the energy is still only 40 dB below the maximum.

Spectral Mask Comparison

91

5 GHz Band Channels

92

Unlicensed 60 GHz Frequency Band

93

A lot of bandwidth available

Even for the smallest allocation, there is more than 3 GHz of bandwidth available, and most regions allow use of at least 7 GHz. In comparison, the 5 GHz unlicensed band has about 500 MHz

of total usable bandwidth. The 2.4 GHz band has less than 85 MHz of bandwidth in most

regions.

Worldwide spectrum availability

94

Fourier Transform and Communication Systems

Digital Communications

Elements of digital commu. sys.

95

Noise & Interferen

ce

Information Source

Destination

Channel

ReceivedSignal

TransmittedSignal

Message

Recovered Message

Source Encoder

Channel Encoder

DigitalModulator

Source Decoder

Channel Decoder

DigitalDemodulator

Transmitter

Receiver

Remove redundancy(compression)

Add systematic redundancy to combat errors introduced by the channel

Map digital sequence to analog signal

Digital Modulation/Demodulation

96

Noise & Interferen

ce

Information Source

Destination

Channel

ReceivedSignal

TransmittedSignal

Message

Recovered Message

Source Encoder

Channel Encoder

DigitalModulator

Source Decoder

Channel Decoder

DigitalDemodulator

Transmitter

Receiver

Remove redundancy(compression)

Add systematic redundancy to combat errors introduced by the channel

Map digital sequence to analog signal

101001

101001

0 1 2 3 4 5 6-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Seconds

Simple ASK: ON-OFF Keying (OOK)

97

fc = 4 HzBit rate = 1 bps

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.5

0

0.5

1

Seconds

1 0 1 0 0 1 t

tfc = 100 HzBit rate = 20 bps 0111110010011100010110000010010010111010111010000000101110001101111001100000010111110101100011011010

cos 2

101001 Digital Modulator

?

[ASK_playTones_Demo.m]

2 3 4 5

Simple “ASK”: “ON-OFF Keying”

98

Smoke signal

ASK: Higher Order Modulation

99

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-4

-2

0

2

4

Seconds

0312021222100303230103033301131301003220321210000010331113103101003320013000222121202012303311112233

00110110001001101010… Digital Modulator

?

fc = 100 HzSymbol rate = 20 symbols per secondBit rate = 40 bps

FSK

100

-1

-0.5

0

0.5

1

cos 2

M = 4 1 2 3 4, , , 3,6,9,12 [Hz]cf f f f f

00 01 10 11

cos 2 cos 2 cos 2

[FSK_playTones_Demo.m]

FSK

101

M = 4 1 2 3 4, , , 3,6,9,12 [Hz]cf f f f f

0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Seconds

[12 12 3 12 9 3 6 9 12 12] Hz

[11 11 00 11 10 00 01 10 11 11]

11110011100001101111 Digital Modulator

?

[FSK_playTones_Demo.m]

FSK

102

M = 4

[400 400 100 400 300 100 200 300 400 400]Hz

[11 11 00 11 10 00 01 10 11 11]

11110011100001101111 Digital Modulator

?

1 2 3 4, , , 100,200,300,400 [Hz]cf f f f f

0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Seconds

[FSK_playTones_Demo.m]

FSK

103

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

Seconds

-800 -600 -400 -200 0 200 400 600 8000

0.5

1

1.5

2

Frequency [Hz]

Mag

nitu

de

2×50 = 100 bits Digital Modulator

?

Rs = 5Bit rate = 10 bps

104

Fourier Transform and Communication Systems

Digital Communications:A Look in the Frequency

Domain

Spectrum of ON-OFF Keying

105

fc = 100 HzBit rate = 1 bps

0 1 2 3 4 5 6-1

-0.5

0

0.5

1

Seconds

-200 -150 -100 -50 0 50 100 150 2000

0.5

1

1.5

Frequency [Hz]

Mag

nitu

de

1 0 1 0 0 1

Five Frequencies

106

0 0.05 0.1 0.15 0.2 0.25-1

-0.5

0

0.5

1

Seconds

cos 2 cos 2 cos 2cos 2cos 2

Rate = Rs frequency-changes per second

Each tone lasts 1/Rs sec.

Spectrum of Five Frequencies

107

cos 2 cos 2 cos 2cos 2cos 2300 Hz100 Hz 200 Hz 500 Hz400 Hz

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

Seconds

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

Frequency [Hz]

Mag

nitude

Rs = 0.5

Cos vs. Cos Pulse

108

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

-0.5

0

0.5

1

Seconds

-200 -150 -100 -50 0 50 100 150 2000

0.1

0.2

0.3

0.4

0.5

Frequency [Hz]

Mag

nitu

de

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

-0.5

0

0.5

1

Seconds

-200 -150 -100 -50 0 50 100 150 2000

0.02

0.04

0.06

0.08

0.1

Frequency [Hz]

Mag

nitu

de

cos 2 100 cos 2 100 , 0.4 0.6,0, otherwise.

0 1 2 3 4 5 6-1

-0.5

0

0.5

1

Seconds

-10 -8 -6 -4 -2 0 2 4 6 8 100

0.5

1

1.5

2

Frequency [Hz]

Mag

nitu

de

Spectrum of ON-OFF Keying

109

fc = 5 HzRs = 1

M = 2

1 0 1 0 0 1

0 1 2 3 4 5 6-1

-0.5

0

0.5

1

Seconds

-200 -150 -100 -50 0 50 100 150 2000

0.5

1

1.5

Frequency [Hz]

Mag

nitu

de

Spectrum of ON-OFF Keying

110

fc = 100 HzRs = 1

M = 2

1 0 1 0 0 1

0 1 2 3 4 5 6-1

-0.5

0

0.5

1

Seconds

-200 -150 -100 -50 0 50 100 150 2000

0.5

1

1.5

Frequency [Hz]

Mag

nitu

de

Spectrum of ON-OFF Keying

111

fc = 100 HzRs = 1

M = 2

1 0 1 0 0 1

95 96 97 98 99 100 101 102 103 104 105

0.5

1

1.5

Frequency [Hz]

Mag

nitu

de

Spectrum of Five Frequencies (1/5)

112

cos 2 cos 2 cos 2cos 2cos 2300 Hz100 Hz 200 Hz 500 Hz400 Hz

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

Seconds

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

Frequency [Hz]

Mag

nitude

Rs = 0.5

Spectrum of Five Frequencies (2/5)

113

cos 2 cos 2 cos 2cos 2cos 2300 Hz100 Hz 200 Hz 500 Hz400 Hz

Rs = 50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1

-0.5

0

0.5

1

Seconds

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

0.02

0.04

0.06

0.08

0.1

Frequency [Hz]

Mag

nitude

Spectrum of Five Frequencies (3/5)

114

cos 2 cos 2 cos 2cos 2cos 2300 Hz100 Hz 200 Hz 500 Hz400 Hz

Rs = 200 0.05 0.1 0.15 0.2 0.25

-1

-0.5

0

0.5

1

Seconds

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

0.01

0.02

0.03

Frequency [Hz]

Mag

nitude

Spectrum of Five Frequencies (4/5)

115

Rs = 500 0.02 0.04 0.06 0.08 0.1 0.12

-1

-0.5

0

0.5

1

Seconds

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

0.005

0.01

0.015

Frequency [Hz]

Mag

nitude

300 Hz100 Hz 200 Hz 500 Hz400 Hz

Spectrum of Five Frequencies (5/5)

116

cos 2 cos 2 cos 2cos 2cos 2300 Hz100 Hz 200 Hz 500 Hz400 Hz

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

Seconds

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

Frequency [Hz]

Mag

nitude

Rs = 0.595 100 1

Spectrum of FSK (1/2)

117

Freq. = [400 300 400 400 100 300 200 100 100 100] Hz

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

Seconds

-800 -600 -400 -200 0 200 400 600 8000

0.5

1

1.5

2

Frequency [Hz]

Mag

nitude

Rs = 1

M = 4

Spectrum of FSK (2/2)

118

Freq. = [100 400 500 500 100 300 300 400 400 400 400 200 300 100 100 500 200 300 500 100 100 200 500 200 200 100 200 200 100 300 100 400 100 300 400 200 300 300 100 300 400 200 500 500 500 300 200 400 200 500] Hz

Rs = 50 1 2 3 4 5 6 7 8 9 10

-1

-0.5

0

0.5

1

Seconds

-1000 -800 -600 -400 -200 0 200 400 600 800 10000

0.5

1

1.5

Frequency [Hz]

Mag

nitude

M = 5