Analog Transmission of Digital Data: ASK, FSK, PSK, QAM

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1 Analog Transmission of Digital Data: ASK, FSK, PSK, QAM Required reading: Forouzan 5. Garia 3.7 CSE 33, Fall 6 Instrutor: N. Vlaji

2 Why Do We Need Digital-to-Analog Conversion?! ) The transmission medium is bandpass, and/or ) Multiple users need to share the medium.

3 Modulation of Digital Data 3 Modulation proess of onverting digital data or a low-pass analog signal to band-pass (higher-frequeny) analog signal Digital-to-analog modulation. Analog-to-analog modulation. Carrier Signal aka arrier frequeny or modulated signal - high frequeny signal that ats as a basis for the information signal information signal is alled modulating signal bandpass hannel freq

based on the information in a digital signal sinewave is defined by three harateristis (amplitude, frequeny, and

4 Modulation of Digital Data (ont.) 4 Digital-to-Analog Modulation proess of hanging one of the harateristis of an analog signal (typially a sinewave) based on the information in a digital signal sinewave is defined by three harateristis (amplitude, frequeny, and phase) digital data (binary and ) an be represented by varying any of the three appliation: transmission of digital data over telephone wire (modem) or over wireless medium Types of Digital-to-Analog Modulation

5 Modulation of Digital Data: ASK 5 ASK strength of the arrier signal is varied to represent binary or both frequeny and phase remain onstant while the amplitude hanges ommonly, one of the amplitudes is zero s(t) = A A os(πf os(πf t), t), binary binary =, Aos(πft), binary binary Is this piture, from the textbook, entirely orret?! +A -A demodulation: only the presene or absene of a sinusoid in a given time interval needs to be determined advantage: simpliity disadvantage: ASK is very suseptible to noise interferene noise usually (only) affets the amplitude, therefore ASK is the modulation tehnique most affeted by noise appliation: ASK is used to transmit digital data over optial fiber

6 6

7 Modulation of Digital Data: ASK (ont.) 7 Example [ ASK ] v d (t) v (t) v ASK (t) v d (f) v (f) f How does the frequeny spetrum of v ASK (t) look like!?

8 Modulation of Digital Data: ASK (ont.) 8 ASK-Modulated Signal: Frequeny Spetrum osa osb = + Carrier signal: ( os(a -B) + os(a B) ) v (t) = os(πft) = os(ω t), where πf =ω v d (f) v (f) Digital signal: (unipolar!!!) Modulated signal: (t) = A + osωt os3ωt + os5ω t... π 3π 5π v d v ASK (t) = v (t) v d (t) = = osωt + osωt os3ωt + π 3π = osωt + osωt osωt - osω π 3π = osωt + π 3π 5π [ os( ω ω ) t + os( ω + ω ) t] os5ωt... = t os3ω t +... = [ os( ω 3ω ) t + os( ω + 3ω ) t] ω d_max ω ω ω -ω d_max ω ω +ω d_max ω

9 appliation: modems, aller-id,... (low speed and noisy environments where auray is preferred over speed) Modulation of Digital Data: FSK 9 FSK frequeny of the arrier signal is varied to represent binary or both peak amplitude and phase remain onstant during eah bit interval s(t) = Aos(πft), Aos(πft), binary binary +A f <f -A demodulation: demodulator must be able to determine whih of two possible frequenies is present at a given time advantage: FSK is less suseptible to errors than ASK reeiver is looking for speifi frequeny hanges over a number of intervals, so voltage (noise) spikes an be ignored disadvantage: FSK spetrum is x ASK spetrum

10 Modulation of Digital Data: FSK (ont.) Example [ FSK ] v d (t) v (t) v (t) v FSK (t) v d (t)*v (t) [-v d (t)]*v (t) ω d_max ω ω ω ω ω ω -ω ω d_max ω +ω d_max

11 Modulation of Digital Data: FSK (ont.) FSK-Modulated Signal: Frequeny Spetrum Digital signal: v d (t) - modulated with ω, and v '(t) d = - v d (t) - modulated with ω Modulated signal: v FSK (t) = osω t v = osωt + + osωt =... = osωt + π 3π osωt π + 3π d (t) + osω π π t ( v osω t 3π osω t + 3π (t)) = os3ω t + 5π os3ω t 5π [ os( ω ω ) t + os( ω + ω ) t] [ os( ω 3ω ) t + os( ω + 3ω ) t] [ os( ω ω ) t + os( ω + ω ) t] os5ωt... + os5ωt... = [ os( ω 3ω ) t + os( ω + 3ω ) t] d - -

Modulation of Digital Data: PSK PSK phase of the arrier signal is varied to represent binary or peak amplitude and frequeny remain onstant during eah bit interval example: binary is represented with

12 Modulation of Digital Data: PSK PSK phase of the arrier signal is varied to represent binary or peak amplitude and frequeny remain onstant during eah bit interval example: binary is represented with a phase of º, while binary is represented with a phase of 8º=πrad PSK is equivalent to multiplying the arrier signal by + when the information is, and by - when the information is -PSK, or Binary PSK, sine only different phases are used. Aos(πft), s(t) = Aos(πft + π), Aos(πft), s(t) = - Aos(πft), binary binary binary binary +A -A demodulation: demodulator must be able to determine the phase of reeived sinusoid with respet to some referene phase advantage: PSK is less suseptible to errors than ASK, while it requires/oupies the same bandwidth as ASK more effiient use of bandwidth (higher data-rate) are possible, ompared to FSK!!! disadvantage: more omplex signal detetion / reovery proess, than in ASK and FSK

13 Modulation of Digital Data: PSK (ont.) 3 Example [ PSK ] v d (t) v (t) v PSK (t) ω d_max ω ω ω -ω d_max ω ω +ω d_max ω

14 Modulation of Digital Data: PSK (ont.) 4 PSK Detetion / Reovery multiply the reeived / modulated signal os A = + ( os A) ± Aos(πf resulting signal Aos t) by *os(πf t) (π f t) = A + [ os(4πf t) ], binary - Aos (π ft) = A + [ os(4πf t) ], binary by removing the osillatory part with a low-pass filter, the original baseband signal (i.e. the original binary sequene) an be easily determined A k = A, for binary A k = -A, for binary

15 Modulation of Digital Data: PSK (ont.) 5 Information sender Baseband Signal Modulated Signal x(t) +A -A T T 3T 4T 5T 6T +A -A T T 3T 4T 5T 6T A os(πft) A { + os(4πft)} -A os(πft) -A { + os(4πft)} Signal shifted above / below zero level. reeiver After multipliation at reeiver x(t) os(πf t) +A -A T T 3T 4T 5T 6T Baseband signal disernable after smoothing +A -A T T 3T 4T 5T 6T

16 Modulation of Digital Data: PSK (ont.) 6 Fats from Modulation Theory If then Baseband signal x(t) oupies bandwidth W / W / B Data rate = *W / = B [bps] f Modulated signal x(t)os(πf t) oupies bandwidth W Hz f -B W f f +B f If bandpass hannel has bandwidth W [Hz], then baseband hannel has W / [Hz] available, so modulation system supports C = *(W /) = W [pulses/seond] reall Nyqyist Law: baseband transmission system of bandwidth W [Hz] an theoretially support W pulses/se How an we reover the fator in supported data-rate!?

17 Modulation of Digital Data: PSK (ont.) 7 Example [ data rate of ASK signal ] We have an available bandwidth of khz whih spans from 3 khz. What are the arrier frequeny and the bit rate if we modulated our data by using ASK? khz 3 khz B=5kHz arrier signal = middle of the bandwidth = 5 khz bandwidth of digital signal B = 5 khz digital data rate = * B = kbps

18 Modulation of Digital Data: PSK (ont.) 8 Example [ data rate of ASK signal ] Assumptions are the same as in the previous example (-3 khz Available, for ASK modulated signal), but the line is full-duplex. khz 3 khz uplink downlink bandwidth for uplink = bandwidth for downlink = 5 khz arrier for uplink = 5 khz arrier for downlink = 75 khz bandwidth of digital signal = 5 khz digital data rate = * B = 5 kbps

19 Modulation of Digital Data: PSK (ont.) 9 Example [ data rate of FSK signal ] Find the minimum bandwidth for FSK signal transmitting at bps using half-duplex mode, and the arriers are separated by 3 Hz???? Hz 3 Hz overall bandwidth = band. dig. sig band dig. sig. band. dig. sig. = C / = Hz overall bandwidth = 5 Hz

20 Modulation of Digital Data: PSK (ont.) QPSK = 4-PSK PSK that uses phase shifts of 9º=π/ rad 4 different signals are generated, eah representing bits Aos(πft), π Aos(πft + ), s(t) = Aos(πft + π), 3π Aos(πft + ), binary binary binary binary advantage: higher data rate than in PSK ( bits per bit interval), while bandwidth oupany remains the same 4-PSK an easily be extended to 8-PSK, i.e. n-psk however, higher rate PSK shemes are limited by the ability of equipment to distinguish small differenes in phase

21 Signal Constellation Constellation Diagram used to represents possible symbols that may be seleted by a given modulation sheme as points in -D plane X-axis is related to in-phase arrier: os(ω t) the projetion of the point on the X-axis defines the peak amplitude of the in-phase omponent Y-axis is related to the quadrature arrier: sin(ω t) the projetion of the point on the Y-axis defines the peak amplitude of the quadrature omponent the length of the line that onnets the point to the origin is the peak amplitude of the signal element (ombination of X and Y omponents) the angle the line makes with the X-axis is the phase of the signal element

22 Signal Constellation (ont.) Example [ signal onstellation of QPSK ] s(t) = Aos(πft), π Aos(πft + ), Aos(πft + π), 3π Aos(πft + ), binary binary binary binary - Asin(πft) - Aos(πft) Asin(πf t) A -A A -A

23 Signal Constellation (ont.) 3 Example [ other types of modulations ]

Chapter 3 Digital Transmission Fundamentals

Chapter 3 Digital Transmission Fundamentals Modems and Digital Modulation CSE 33, Winter Instrutor: Foroohar Foroozan Modulation of Digital Data Modulation of Digital Data Modulation proess of onverting