ICT Elementary for Embedded Systems and Commu v7.pdf · 5th International edition ... S.S. Haykin,...

ICT Elementary for Embedded SystemsSignal/Electronic Fundamental

Fourier Transform and Communication Systems

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

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

General Information

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

Lectures: July 20, 2017 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

Website

prapun.com

Website

More references

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

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.

Another Reference (in Thai)

หนังสอื หลกัการไฟฟ้าสือ่สาร เลม่นีก้ลา่วถงึ ทฤษฎกีารแปลงฟูเรยีร ์(Fourier transform) ระบบเชงิเสน้ สหสมัพนัธ ์(Correlation) ความหนาแน่นสเปกตรมั (Spectral density) การมอดเูลตเชงิแอมพลจิดู (amplitude modulation) การมอดเูลตเชงิมุม (angle modulation) กระบวนการสุม่ (random process) สญัญาณรบกวน (noise) ทฤษฎกีารชกัตวัอย่าง (sampling theory) การมอดเูลตโดยใชพ้ลัส ์(pulse modulation) การสง่ผ่านพลัสเ์บสแบนด ์(baseband pulse transmission) การมอดเูลตแบนดพ์าส (digital passband transmission) และทฤษฎขีา่วสาร (information)

หนังสอืเลม่นีเ้ป็นผลจากความรว่มมอืทางวชิาการของคณาจารย ์จากหลายสถาบนัการศกึษาทีม่ชี ือ่เสยีงของประเทศหลายแห่ง

[http://www.chulabook.com/description.asp?barcode=9789740327707]

รศ. ดร. ลญัฉกร วฒุสิทิธกิลุกจิ และคณะ, หลกัการไฟฟ้าสือ่สาร, พมิพค์ร ัง้ที ่2,สาํนักพมิพแ์ห่งจฬุาลงกรณ ์มหาวทิยาลยั, 2554. ISBN: 978-974-03-2770-7

From time domain to frequency domain

Signal (Waveform)

10[https://www.youtube.com/watch?v=cq7hXp7xUn8]

Signal in the time domain (audio)

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

Sound as Vibration

12 [https://www.youtube.com/watch?v=LH0PD_dX5Z4]

Microphone

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

LED Audio Spectrum Analyzer

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

Fourier transform ( )

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

The (Fundamental) Frequencies of Musical Instruments

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

Note frequency

A440 on Different Instruments

18 [https://www.youtube.com/watch?v=9iGjo2cd69s][http://www.philvarner.com/2015/01/27/why-does-a-tuning-fork-sound-different-than-a-piano-even-if-theyre-playing-the-same-note/]

[GarageBand]

“Same” timbre of a tuning fork (“pure” tone)

Any physical instrument is not only going to play the fundamental but also harmonics. These harmonics are frequencies in the sound that are integer multiples of the fundamental tone.

Ex.1: A440 on a Cathedral Organ

19[http://www.philvarner.com/2015/01/27/why-does-a-tuning-fork-sound-different-than-a-piano-even-if-theyre-playing-the-same-note/]

Left track

Right track

Ex.2: A440 on a Grand Piano

Left track

Right track

[http://www.philvarner.com/2015/01/27/why-does-a-tuning-fork-sound-different-than-a-piano-even-if-theyre-playing-the-same-note/]

Tone Dialing

Most modern telephones use a dialing system known as Touch-Tone. Dual-tone multifrequency (DTMF) system.

Use pairs of audio (voice-frequency) tones to create signals representing the numbers to be dialed.

First developed in the Bell System in the United States, and became known under the trademark Touch-Tone for use in push-button telephones starting in 1963. Replace the use of rotary dial.

Standardized by ITU-T Recommendation Q.23. Also known in the UK as MF4.

[Apr, 1964]

Dial Tone

North American and UK: A continuous mix of 350 Hz and 440 Hz These two frequencies

correspond to the standard concert pitch of A440, and approximately an “F”.

@ -12dBm

Most of Europe: constant single tone (425 Hz)

0.05 0.06 0.07 0.08 0.09 0.1 0.11-1

Seconds

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

Frequency [Hz]

Encoding

Each number corresponds to a mix of two audio frequencies associated with each row and column of the corresponding pushbutton.

Most telephones use a standard keypad with 12 buttons or switches for the numbers 0 through 9 and the special symbols * and #.

Four additional keys for special applications.

The “1” tone

0.156 0.158 0.16 0.162 0.164 0.166 0.168 0.17 0.172 0.174 0.176-1

Seconds

-2000 -1500 -1000 -500 0 500 1000 1500 20000

Frequency [Hz]

Fourier transform: Example

cos13 cos 3

15 cos 5

Practice Problems

Sir Isaac Newton

Our modern understanding of light and color begins with Isaac Newton (1642-1726) and a series of experiments that he publishes in 1672.

He refracts white light with a prism, resolving it into its component colors.

[https://www.britannica.com/biography/Isaac-Newton/images-videos/Sir-Isaac-Newton-dispersing-sunlight-through-a-prism-for-a/153369][http://www.webexhibits.org/colorart/bh.html]

Sir Isaac Newton

[http://sirisaacne.weebly.com/accomplishments.html]

A triangular prism, dispersing light

30 [http://www.astromia.com/astronomia/newtonluz.htm]

A triangular prism, dispersing light

31[https://en.wikipedia.org/wiki/Prism#/media/File:Light_dispersion_conceptual_waves.gif]

Waves shown to illustrate the differing wavelengths of light.

Electromagnetic Spectrum

[Gosling , 1999, Fig 1.1 and 1.2]

3 MHz 3 GHz

100 m 10 cm

c f Wavelength

Frequency

83 10 m/s

Continuous Spectrum vs. Line Spectra

Continuous spectrum of an incandescent lamp

Discrete spectrum lines of a fluorescent lamp

(Discrete)

Line spectra

Remember those flame experiments from your high school chemistry class?

Line spectra

CD Tracks as Diffraction Gratings

The tracks of a compact disc can act as a diffraction grating, producing a separation of the colors of white light.

[http://3.14.by/en/read/cd-dvd-microscope]

CD Tracks as Diffraction Gratings

Sunshine

Compact Fluorescent Lamp

CF vs LED

Spectral Power Distribution

Plot of the relativepower emitted bythe light source ateach wavelengthover the visiblespectrum.

Spectral Power Distribution

Mathematically speaking…

Euler’s Formula

cos sinj je

[https://www.youtube.com/watch?v=N321EcSzNas]

15 April 1707 – 18 September 1783

a Swiss mathematician, physicist, astronomer, logician and engineer

Made important and influential discoveries in many branches of mathematics

Complex exponential function

Sinusoids

Euler's number

The Most Beautiful Equation

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.

Euler’s Formula on the Complex Plane

unit circle

(real axis)

(imaginary axis)

Euler’s Formula on the Complex Plane

unit circle

(real axis)

(imaginary axis)

Rotating Vector in a Complex Plane

cos sin2

je jt ft

50 [http://bl.ocks.org/jinroh/7524988]

Euler’s Formula

cos sinje j

1cos Re21sin Im2

jA jA jA

A e e e

A e e ej

Complex exponential

Euler’s Formula

cos sinje j

1cos Re21sin Im2

jA jA jA

A e e e

A e e ej

Complex exponential

cos( ) cos( )

cos sin( )2

2sin( )co

2cos 1 cos 2

2sin 1 coss( ) sin(2 )

sin cos

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

x x xd x xdx

x y x y x

(product-to-sum formula)

(Continuous-Time) Fourier Transform

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

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

The relationship on the left is simply a decomposition of the signal into a linear combination of (potentially infinitely many) components at different frequencies.

From the decomposition point of view, the value of at a particular frequency is simply the weight (scaling/coefficient) which tells how much component there is in .

By the orthogonality among complex exponential functions, the value of at a particular frequency can be calculated by the formula above.

This coefficient considered as a function of frequency is the Fourier transform of our signal.

7 Equations

that changed the world

… and still rule everyday life

7 Equations

Time Domain Frequency Domain

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

direct transform

inverse transform

Signals in this form is “easy” to work with under LTI system.

0g G f df

0G g t dt

Delta function (f)

(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

→ 0f

Area = 1

smaller f

Area = 1 Area = 1

(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 A(f) as an infinitely tall, infinitely narrow rectangular pulse of area A

f→ 0

Area = A

smaller f

Area = A Area = A

Fourier Transform Pairs (1)

2j tf fe f

t ff0-f0

0cos 2 tf 0 01 12 2

f ff f

Practice Problems (A Revisit)

Practice Problems (More)

cos 200 cos 400

cos 200

cos 200 cos 400

Fourier Transform of Symbolic Expression in MATLAB

function G = fourierf(g)syms fG = simplify(subs(fourier(g),'w',2*pi*f));end

>> syms t; g = exp(1j*2*pi*5*t);>> G = fourierf(g)G =dirac(f - 5)

>> syms t; g = cos(2*pi*5*t);>> G = fourierf(g)G =dirac(f - 5)/2 + dirac(f + 5)/2>> pretty(G)

dirac(f - 5) dirac(f + 5) ------------ + ------------

>> syms t f0; g = cos(2*pi*f0*t);>> G = fourierf(g)G =dirac(f + f0)/2 + dirac(f - f0)/2>> pretty(G)

dirac(f + f0) dirac(f - f0) ------------- + -------------

sinsinc( ) xxx

-0.2172

0.1284

-0.0913

sinc function

sincsin

sinc function

-0.2172

0.1284

-0.0913

sincsin

Zero crossings are at all non-zero integer multiples of π because sin = 0.

Sinusoidal oscillations of period 2π

As → 0, we have . Using L'Hospital's Rule, we set sinc 0 1.

sinc function

Main lobe(null to null)

sinc function

-0.2172

0.1284

-0.0913

sincsin 1

Amplitude of sin decreases

continuously as .

Fourier Transform of Symbolic Rectangular Function in MATLAB

>> syms a t>> g = rectangularPulse(-a,a,t)g =rectangularPulse(-a, a, t)>> G = fourierf(g)G =sin(2*pi*a*f)/(pi*f)

2 sinc 2

Practice Problems

Normalized sinc function

sinc sin

Its zero crossings are at non-zero integer values of its argument.

-0.2172

0.1284

-0.0913

More realistic signal…

0 5 10 15 20 25-1

Seconds

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

Frequency [Hz]

plotspect.m

% plotspec(x,t) plots the spectrum of the signal x% whose values are sampled at time (in seconds) specified in t function plotspect(x,t)N=length(x); % length of the signal xTs = t(2)-t(1); % find the sampling intervalssf=((-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

Phone/Cellphone (Muffled) Audio

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

PILOT'S ALPHABET

International Radiotelephony Spelling Alphabet.

Pilots use it so that essential letter combinations can be easily understood by individuals transmitting and receiving voice messages.

VoLTE Audio

VoLTE Audio: AMR-WB

iPhone 5 supports HD Voice

in the form of AMR-WB over 3G (UMTS)

In Thailand, dtac is the first mobile operator and the only one that provides HD Voice via 3G network.

[https://www.dtac.co.th/en/network/hd-voice.html]

Digital Audio Watermarking

82 [http://www.sersc.org/journals/IJSIA/vol5_no2_2011/3.pdf]

Introductory concepts in communications…

Modulator: a crucial part of any communication

systems

Modulation

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

Frequency [Hz]

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

Important Properties of

*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

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)

cos 200

cos 200 cos 400

Simple Modulation: Freq. Domain

2 cos 2 cf t

Modulator

Message(modulating signal)

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: Time Domain

Simple Modulation

2 cos 2 cf t

Modulator

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

Seconds

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

Frequency [Hz]

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

Seconds

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

Frequency [Hz]

So, … which frequencies do we actually use?

Radio-frequency spectrum

Electromagnetic Spectrum

[Gosling , 1999, Fig 1.1 and 1.2]

3 MHz 3 GHz

100 m 10 cm

c f Wavelength

Frequency

83 10 m/s

Radio-frequency spectrum

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.

Analog (Old) terrestrial TV in BKK

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.

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.

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.

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

(โทรทศันภ์าคพืน้ดนิ)

Terrestrial TV in BKK

Channel.

Audio Carrier.

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

Channel.

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.

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)

Channel.

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

(โทรทศันภ์าคพืน้ดนิ)

Cellular Support in iPhone 7

FDD-LTE (Bands 1, 2, 3, 4, 5, 7, 8, 12, 13, 17, 18, 19, 20, 25, 26, 27, 28, 29, 30)

TD-LTE (Bands 38, 39, 40, 41)

UMTS/HSPA+/DC-HSDPA (850, 900, 1700/2100, 1900, 2100 MHz)

GSM/EDGE (850, 900, 1800, 1900 MHz)

http://www.apple.com/iphone-7/specs/

Model A1778Model A1784

Announced on September 7, 2016. Released on September 16, 2016.

Additionally, only in models A1660 and A1661 TD-SCDMA 1900 (F), 2000 (A) CDMA EV-DO Rev. A (800, 1900, 2100

FDD and TDD LTE frequency bands

TDD LTE frequency band allocationsFDD LTE frequency band allocations

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

1 1920 - 1980 2110 - 2170 60 190 130

2 1850 - 1910 1930 - 1990 60 80 20

3 1710 - 1785 1805 -1880 75 95 20

4 1710 - 1755 2110 - 2155 45 400 355

5 824 - 849 869 - 894 25 45 20

6 830 - 840 875 - 885 10 35 25

7 2500 - 2570 2620 - 2690 70 120 50

8 880 - 915 925 - 960 35 45 10

9 1749.9 - 1784.9 1844.9 - 1879.9 35 95 60

10 1710 - 1770 2110 - 2170 60 400 340

11 1427.9 - 1452.9 1475.9 - 1500.9 20 48 28

12 698 - 716 728 - 746 18 30 12

13 777 - 787 746 - 756 10 -31 41

14 788 - 798 758 - 768 10 -30 40

15 1900 - 1920 2600 - 2620 20 700 680

16 2010 - 2025 2585 - 2600 15 575 560

17 704 - 716 734 - 746 12 30 18

18 815 - 830 860 - 875 15 45 30

19 830 - 845 875 - 890 15 45 30

20 832 - 862 791 - 821 30 -41 71

21 1447.9 - 1462.9 1495.5 - 1510.9 15 48 33

22 3410 - 3500 3510 - 3600 90 100 10

23 2000 - 2020 2180 - 2200 20 180 160

24 1625.5 - 1660.5 1525 - 1559 34 -101.5 135.5

25 1850 - 1915 1930 - 1995 65 80 15

26 814 - 849 859 - 894 30 / 40 10

27 807 - 824 852 - 869 17 45 28

28 703 - 748 758 - 803 45 55 10

29 n/a 717 - 728 11

30 2305 - 2315 2350 - 2360 10 45 35

31 452.5 - 457.5 462.5 - 467.5 5 10 5

WIDTH OF BAND (MHZ)

DUPLEX SPACING

BAND GAP (MHZ)

LTE BAND NUMBER

UPLINK (MHZ) DOWNLINK (MHz)

33 1900 - 1920 20

34 2010 - 2025 15

35 1850 - 1910 60

36 1930 - 1990 60

37 1910 - 1930 20

38 2570 - 2620 50

39 1880 - 1920 40

40 2300 - 2400 100

41 2496 - 2690 194

42 3400 - 3600 200

43 3600 - 3800 200

44 703 - 803 100

ALLOCATION (MHZ)

WIDTH OF BAND (MHZ)

LTE BAND NUMBER

Operating bands specified for LTE in 3GPP below 1 GHz

98 [Dahlman, Parkvall, and Skold, 2016]

Operating bands specified for LTE in 3GPP above 1 GHz

99 [Dahlman, Parkvall, and Skold, 2016]

Spectrum Allocation

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 กจิการโทรทศันแ์ละกจิการโทรคมนาคมแหง่ชาต ิ; กสทช.)

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

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

Thailand Freq. Allocations Chart

102http://www.ntc.or.th/uploadfiles/freq_chart_thai.htm

Spectrum Allocation

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.

Oct 2012: Thailand 2.1GHz Auction

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

Nov 2015: Thailand 1800MHz Auction

40bn baht 15 MHz (UL) + 15 MHz (DL)

1.3 billion baht per MHz 74 million baht per MHz per year

(18 years)(15 years)

( 2.5)

Dec 2015: Thailand 900MHz Auction

76bn baht 10 MHz (UL) + 10 MHz (DL)

3.8 billion baht per MHz 250 million baht per MHz per year

Dec 201515 years

Nov 201518 years

re-auction

(forfeit)

Digital TV License Auction in 2012

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

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

Digital TV License Auction in 2012

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

News and children's/family channels

Cognitive radios: Motivation

Traditional Rule: Allow predetermined licensed users the right to transmit at given frequencies. Frequency bands were sold at auction, bringing considerable revenue

to the government. Unlicensed users are regarded as “harmful interference.”

Radio-frequency resources are not fully utilized There exists a large number of frequency bands that have

considerable, and sometimes periodic, idle time intervals. For example, some TV stations do not work at night. Spectrum holes.

Cognitive radios

A revolutionary communication paradigm that can utilize the existing wireless spectrum resources more efficiently.

New Assumption: Users are intelligent and have the ability to observe, learn, and act to optimize their performance.

Game theory has been recognized as an important tool in studying, modeling, and analyzing the cognitive interaction process.

Game Theory

A branch of applied mathematics as well as of applied sciences.

A formal framework with a set of mathematical tools

To study the complex interactions analyze competition and cooperation among interdependent rational players (having individual self-interests.)

For more than half a century, game theory has led to revolutionary changes in economics. Three Nobel Prizes have been given in the economic sciences for

work primarily in game theory.

John Nash

June 13, 1928 – May 23, 2015 an American mathematician Share the 1994 Nobel Memorial Prize

in Economic Sciences with game theorists Reinhard Selten and John Harsanyi.

In 1959, Nash began showing clear signs of mental illness, and spent several years at psychiatric hospitals being treated for paranoid schizophrenia. His struggles with his illness and his

recovery became the basis for Sylvia Nasar's biography, A Beautiful Mind, as well as a film of the same name starring Russell Crowe.

[https://en.wikipedia.org/wiki/John_Forbes_Nash_Jr.#/media/File:John_Forbes_Nash,_Jr._by_Peter_Badge.jpg][https://en.wikipedia.org/wiki/A_Beautiful_Mind_(book)]

Demodulation

DSB-SC

× ×Channel

2 cos 2 cf t

Modulator Demodulator

2 cos 2 2 cos 2c c

m t f t f t

LPF m t

Key equation:

In the time domain…

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

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

2cos 2

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

Seconds

Note the oscillation at twice the carrier frequency

Scaling and Suppressing Frequency Components

Important Properties of

*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

2j tfe g t G f 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

0 5 10 15 20 25-1

Seconds

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

Frequency [Hz]

0 5 10 15 20 25-2

Seconds

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

Frequency [Hz]

de0 5 10 15 20 25

Seconds

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

Frequency [Hz]

0 5 10 15 20 25-2

Seconds

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

Frequency [Hz]

[Demo_DSBSC_Sound_ReadWAV.m]

DSB-SC (Zoomed in time)

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

Seconds

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

Frequency [Hz]

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

Seconds

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

Frequency [Hz]

de1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005

Seconds

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

Frequency [Hz]

Note how the baseband signal becomes the envelope of

the modulated signal x .

Note the delay caused by the LPF.

1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005-2

Seconds

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

Frequency [Hz]

1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005-2

Seconds

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

Frequency [Hz]

(Zoomed in time)

1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005-2

Seconds

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

Frequency [Hz]

In the time domain… we expect

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

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

2cos 2

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

Seconds

Note the oscillation at twice the carrier frequency

In the time domain…

2cos 2

When the sampling rate is not fast enough,…

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

Seconds

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

Seconds

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

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

The problem with sampling rate

124 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5

Seconds

This is the plot of when we don’t connect the dots

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

The problem with sampling rate

125 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5

Seconds

BW Inefficiency in Our System

Conjugate symmetry property of Fourier transform:

Recall .

If is real-valued, then∗

Quadrature Amplitude Modulation (QAM)

Transmitter (modulator) Receiver (demodulator)

1v t LPH f 1m̂ t

2m t 2v t LPH f 2m̂ t

2 cos 2 cf t

2 sin 2 cf t

2 h t y t QAMx t

Channel

2 cos 2 cf t

2 sin 2 cf t

Send two messages over the same bandwidth of 2B Hz.

QAM 2cos 2 2sin 2 .

A more general formula:

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

1( )cos(2 ) ( ) ( ) .2 c

jcg t t G f e eGf fff

QAM Demodulation

When ,

2 cos 2

2 cos 2 2 cos 2

2cos 2 2 cos 2

1 cos 2 2 2

s 2 2co 2 0s 92

v t x t f t

m t f t f t

m t f t

m t f tm t f t

LPF 2 cos 2

LPF 2 sin 2

x t f t m t

Complex form of QAM

where .

: complex envelope or complex baseband signal

: in-phase component

: quadrature(-phase) component

QAM 1 2

2 cos 2 2 sin 2

2 Re ( ) ,c

x t m t f t m t f t

QAM vs. DSB-SC Key Equations

LPF m t

DSB-SC

2 cos 2 2 cos 2c c

m t f t f t

2 2Re 2 2c cj f t j f t

m t e e

LPF m t

DSB-SC Key Equation

QAM Key Equation

Derivation of the QAM Key Equation (1)

Recall that .

Find and simplify the Fourier transform of ∗ .

Find and simplify the Fourier transform of .

Derivation of the QAM Key Equation (2)

2 2Re 2 2c cj f t j f t

m t e e

LPF m t

OFDM Applications

802.11 Wi-Fi: a/g/n/ac versions DVB-T (Digital Video Broadcasting —Terrestrial)

terrestrial digital TV broadcast system used in most of the world outside North America

DMT (the standard form of ADSL - Asymmetric Digital Subscriber Line)

WiMAX, LTE (OFDMA)

Overview: Baseband OFDM Symbol

Let S = (S1, S2, …, SN) be the information vector.

One baseband OFDM modulated symbol can be expressed as

Note that:

1 2 2Re ( ) Re cos Im sinN

k kk s s

kt kts t S ST TN

1 2( ) exp , 0

1 2e1 xps

k sk s

kts t S j t TTN

ktS jTN

Some references may use different constant in the front

Some references may start with different time interval, e.g. [-Ts/2, +Ts/2]

Single-Carrier Digital Transmission

Baseband:

Passband:

s t s p t kT

1, 0,1

0, otherwise.s

t Tp t t

2Re cj f tx t s t e

-1 0 1 2 3 4 5 6 7 8 9-0.2

1.2(a)

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

Multipath Propagation

In a wireless mobile communication system, a transmitted signal propagating through the wireless channel often encounters multiple reflective paths until it reaches the receiver

We refer to this phenomenon as multipath propagation and it causes fluctuation of the amplitude and phase of the received signal.

We call this fluctuation multipath fading.

Wireless Comm. and Multipath Fading

y t x t h t n t x t n t

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

Time0 2 4 6 8 10 12

1 0.5 0.2 0.2 0.3 0.3 0.1 0.5s s sh t t t T t T t T

2 0.5 0.2 0.7 0.3 1.5 0.1 2.3s s sh t t t T t T t T

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

The signal received consists of a number of reflected rays, each characterized by a different amount of attenuation and delay.

ISI(Intersymbol Interference)

∗ ∗

Observation and a Solution

Observation: Delay spread causes ISI

A general rule of thumb is that a delay spread of less than 5 or 10 times the symbol width will not be a significant factor for ISI.

Solution: The ISI can be mitigated by reducing the symbol rate and/or including sufficient guard times between symbols.

Multi-Carrier Transmission

Convert a serial high rate data stream on to multiple parallel low rate sub-streams.

Each sub-stream is modulated on its own sub-carrier.

Time domain perspective: Since the symbol rate on each sub-carrier is much less than the initial serial data symbol rate, the effects of delay spread, i.e. ISI, significantly decrease, reducing the complexity of the equalizer.

[Fazel and Kaiser, 2008, Fig 1-4]

Multi-Carrier Modulation

0 0 1 0

1 1 0 1

0 1 1 1

010011101011

Frequency Division Multiplexing

Frequency Domain Perspective: Even though the fast fading is frequency-selective across the entire OFDM signal band, it is effectively flat in the band of each low-speed signal.

[Myung and Goodman, 2008]

[The flatness assumption is the same one that you used in Riemann approximation of integral.]

Frequency Division Multiplexing (FDM)

To facilitate separation of the signals at the receiver, the carrier frequencies were spaced sufficiently far apart so that the signal spectra did not overlap. Empty spectral regions between the signals assured that they could be separated with readily realizable filters.

The resulting spectral efficiency was therefore quite low.

Single Carrier vs. Multi-Carrier (FDM)

Single Carrier Multi-Carrier (FDM)

Single higher rate serial scheme Parallel scheme. Each of the parallel subchannels can carry a low signaling rate, proportional to its bandwidth.

Multipath problem: Far more susceptible to inter-symbol interference (ISI) due to the short duration of its signal elements and the higher distortion produced by its wider frequency band Complicated equalization

Long duration signal elements and narrow bandwidth in sub-channels. Complexity problem: If built straightforwardly as several (N) transmitters and receivers, will be more costly to implement. BW efficiency problem: The sum of parallel signalling rates is less than can be carried by a single serial channel of that combined bandwidth because of the unused guard space between the parallel sub-carriers.

OFDM = Orthogonal frequency division multiplexing One of multi-carrier modulation (MCM) techniques Parallel data transmission (of many sequential streams) A broadband is divided into many narrow sub-channels Frequency division multiplexing (FDM)

High spectral efficiency The sub-channels are made orthogonal to each other over the

OFDM symbol duration Ts. Spacing is carefully selected.

Allow the sub-channels to overlap in the frequency domain. Sub-carriers are spaced as close as theoretically possible.

Subcarrier Spacing

Spectrum Overlap in OFDM

N separate QAM signals, at N frequencies separated by the signaling rate.

Each QAM signal carries one of the original input complex numbers.

The spectrum of each QAM signal is of the form with nulls at the center of the other sub-carriers.

1 2( e p

TjN k f

kts t S j

S k fN

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