Modulator: a crucial part of any communication systems

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Fourier Transform and Communication Systems 116 Introductory concepts in communications Modulator: a crucial part of any communication systems 117

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

1 Fourier Transform and Communication Systems 116 Introductory concepts in communications Modulator: a crucial part of any communication systems 117 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 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)

2 Frequency-Shift Property of Suppose we have a signal whose content is concentrated at. Multiply this signal by a complex-exponential signal: The product is Frequency-Shift Property: Multiplying by a complexexponential signal of frequency shifts the frequency content of the original signal by. The original content at will now occur at If, the original content is shifted to the right by. 118 If, the original content is shifted to the left by. Modulation Property of Multiplying by a complex-exponential signal of frequency shifts the frequency content of the original signal by : 119 What about multiplication by a cosine? Recall that Therefore,.

3 Important Properties of x y t xytd xtyd Convolution Properties: Shifting Properties: Modulation: x y X Y x y X Y j ft t f g t e G j fct e g t G f fc Note that the magnitude of this is simply 120 g t t G f G f f f f c c c Practice Problems (Another Revisit) t f t f t t f 121

4 Simple Modulation: Freq. Domain Message (modulating signal) f t c Modulator 122 g t t G f G f f f f c c c c c c xt mt ft M f f M f f M f fc M f f c Simple Modulation: Time Domain 123

5 Simple Modulation Message (modulating signal) f t Modulator c 124 Fourier Transform and Communication Systems So, which frequencies do we actually use? Radio-frequency spectrum 125

com/ebchecked/topic-art/585825/3697/commercially-exploited-bands-of-the-radio-frequency-spectrum]

6 Electromagnetic Spectrum 3 MHz 3 GHz 100 m 10 cm [Gosling, 1999, Fig 1.1 and 1.2] c f Wavelength Frequency 126 [ Radio-frequency spectrum Commercially exploited bands 127 c f Wavelength Frequency Note that the freq. bands are given in decades; the VHF band has 10 times as much frequency space as the HF band.

128 Analog (Old) terrestrial TV in BKK VHF.(Low Band) Channel Picture Bandwidth.. Carrier. Audio Carrier. 2 47-54 48.25 53.75 3 54-61 55.25 60.75 4 61-68 62.25 67.75 VHF.(Hight Band) Channel.

7 128 Analog (Old) terrestrial TV in BKK VHF.(Low Band) Channel Picture Bandwidth.. Carrier. Audio Carrier VHF.(Hight Band) Channel. Bandwidth. Picture Carrier. Audio Carrier UHF.(Band 4) Channel. Bandwidth. Picture Carrier. Audio Carrier ( ) UHF.(Band 5) Channel Picture Bandwidth.. Carrier. Audio Carrier Terrestrial TV in BKK VHF.(Low Band) Channel Picture Bandwidth.. Carrier. Audio Carrier VHF.(Hight Band) Channel. Bandwidth. Picture Carrier. Audio Carrier UHF.(Band 4) Channel. ( ) Bandwidth. Picture Carrier. Audio Carrier MUX 1 MUX 2 MUX 3 MUX 4 MUX 5 UHF.(Band 5) Channel Picture Bandwidth.. Carrier. Audio Carrier

130 Announced on September 12, 2017. Released on November 3, 2017.

(850, 900, 1700/2100, 1900, 2100 MHz) GSM/EDGE (850, 900, 1800, 1900 MHz) Additionally, only in models A1865 TD-SCDMA 1900 (F), 2000 (A) CDMA EV-DO Rev.

8 130 Announced on September 12, Released on November 3, Cellular Support in iphone X FDD-LTE (Bands 1, 2, 3, 4, 5, 7, 8, 12, 13, 17, 18, 19, 20, 25, 26, 28, 29, 30, 66) TD-LTE (Bands 34, 38, 39, 40, 41) UMTS/HSPA+/DC-HSDPA (850, 900, 1700/2100, 1900, 2100 MHz) GSM/EDGE (850, 900, 1800, 1900 MHz) Additionally, only in models A1865 TD-SCDMA 1900 (F), 2000 (A) CDMA EV-DO Rev. A (800, 1900, 2100 MHz) Model A FDD and TDD LTE frequency bands FDD LTE frequency band allocations TDD LTE frequency band allocations [

9 Operating bands specified for LTE in 3GPP below 1 GHz 132 [Dahlman, Parkvall, and Skold, 2016] Operating bands specified for LTE in 3GPP above 1 GHz 133 [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.

10 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; ;.) Blocks of spectrum are now commonly assigned through spectral auctions to the highest bidder [

11 Thailand Freq. Allocations 136 [ ] 137 [ nbtc.go.th/spectrum_management//.aspx ]

12 National Table of Frequency Allocation 138 [ nbtc.go.th/spectrum_management/â Â n / µ µ Îµ ºÉ ªµ ÉÂ n µ.aspx ] Thailand Freq. Allocations Chart 139

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

13 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. 140 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 141

Nov 2015: Thailand 1800MHz Auction 40bn baht 15 MHz (UL)

Auction 76bn baht 10 MHz (UL) + 10 MHz (DL) 3.

14 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 ( 2.5) (15 years) (18 years) 142 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 ( 3) Nov years Dec years (forfeit) 143

15 Digital TV License Auction in 2012 Channels for variety TV in high definition (HD) and standard definition (SD) 144 [ ] Digital TV License Auction in 2012 News and children's/family channels 145 [ ]

Radio-frequency resources are not fully utilized There exists a large number of frequency bands that have considerable, and sometimes periodic, idle time intervals.

16 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. 146 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. 147

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

selfinterests.) For more than half a century, game theory has led to revolutionary changes in economics.

148 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.

17 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 selfinterests.) 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. 148 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. 149 [ [

18 150 Fourier Transform and Communication Systems Demodulation 151

19 Message (modulating signal) DSB-SC Channel f t Modulator c f t c LPF Demodulator 152 Key equation: LPF mt fct fct xt vt mt In the time domain 153 Note the oscillation at twice the carrier frequency

Properties: Modulation: x y X Y x y X Y j ft t f g t e G j fct e g t

20 Scaling and Suppressing Frequency Components 154 Important Properties of :A Revisit x y t xytd xtyd Convolution Properties: Shifting Properties: Modulation: x y X Y x y X Y j ft t f g t e G j fct e g t G f fc Note that the magnitude of this is simply 155 g t t G f G f f f f c c c

21 Filter Property of x y t xytd xtyd Convolution Properties: Time Domain View: Filter xt x ht x y X Y x y X Y Frequency Domain View: Filter X f X f H f DSB-SC [Demo_DSBSC_Sound_ReadWAV.m] 157

22 DSB-SC (Zoomed in time) Note how the baseband signal becomes the envelope of the modulated signal. Note the delay caused by the LPF. 158 (Zoomed in time) 159

23 In the time domain we expect 160 Note the oscillation at twice the carrier frequency In the time domain When the sampling rate is not fast enough, 161

24 The problem with sampling rate This is the plot of when we don t connect the dots 162 The problem with sampling rate 163

25 BW Inefficiency in Our System (1) Conjugate symmetry property of Fourier transform: Recall If. is real-valued, then 164 Bandwidth The bandwidth (BW) of a signal is usually calculated from the differences between two frequencies (called the bandwidth limits). Absolute bandwidth: Use the highest frequency and the lowest frequency in the positive-f part of the signal s nonzero magnitude spectrum. Half-power bandwidth (3-dB bandwidth): Use the frequencies where the signal power starts to decrease by 3 db (1/2). Null-to-null bandwidth: Use the signal spectrum s first set of zero crossings. Occupied bandwidth: Consider the frequency range in which X% (for example, 99%) of the energy is contained in the signal s bandwidth. 165

26 BW Inefficiency (2) Message bandwidth and the transmitted signal bandwidth The DSB spectrum has two sidebands: the upper sideband (USB) and the lower sideband (LSB), both containing complete information about the base-band signal m(t). As a result, DSB signals occupy twice the bandwidth required for the baseband. 166 Fourier Transform and Communication Systems Quadrature Amplitude Modulation (QAM) 167

27 QAM Send two messages over the same bandwidth of 2B Hz. m t v t H f LP m t f t c f t c f t c x t ht y t f t c m t v t H f m LP t 168 A more general formula: g t t G f G f f f f c c c j j gt fct Gf fce Gf fce 169

28 QAM Demodulation When, B f c x t fct m t x t fct m t 170 c m t ft c m t fct ft c m t ft c m t fct ft c m t f t m t f t v t x t f t c c m t fc t c m t m t f t Complex form of QAM x t m t fct m t fct j fct mte where. 171 : complex envelope or complex baseband signal : in-phase component : quadrature(-phase) component

29 QAM vs. DSB-SC Key Equations DSB-SC Key Equation LPF mt fct fct x t mt QAM Key Equation LPF j ft c j ft c mt e e x t mt 172 Derivation of the QAM Key Equation (1) Recall that. Find and simplify the Fourier transform of. Find and simplify the Fourier transform of. 173

30 Derivation of the QAM Key Equation (2) LPF j ft c j ft c mt e e x t mt 174

ECS 455 Chapter 1 Introduction

ECS 455 Chapter 1 Introduction 1.3 Spectrum Allocation 1 Dr.Prapun prapun.com/ecs455 Office Hours: BKD, 6th floor of Sirindhralai building Tuesday 14:20-15:20 Wednesday 14:20-15:20 Friday 9:15-10:15 Electromagnetic