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 digital data or a low-pass analog signal to band-pass (higher-frequeny) analog signal Digital-to-analog modulation. Analog-to-analog modulation. aka arrier frequeny - modulated signal - high frequeny signal that ats as a basis for the information signal information signal is alled modulating signal bandpass hannel freq 3
Bandpass Channels f W / f + W / Bandpass hannels pass a range of frequenies around some enter frequeny f Radio hannels, telephone & DSL modems Digital modulators embed information into waveform with frequenies passed by bandpass hannel Sinusoid of frequeny f is entered in middle of bandpass hannel Modulators embed information into a sinusoid f
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)
Amplitude Modulation 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 A s(t) = A os(πf os(πf t), t), binary, binary = binary Aos(πft), binary +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
Amplitude Modulation (Cont.) 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!? 7
Amplitude Modulation (Cont.) ASK-Modulated Signal: Frequeny Spetrum osa osb = + ( os(a -B) + os(a B) ) Carrier signal: v (t) = os(πf t) os(ω t), where πf =ω = 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] os5ω t os3ω t +... = [ os( ω 3ω ) t + os( ω + 3ω ) t] +... - t... = ω d_max ω ω ω -ω d_max ω ω +ω d_max ω 8
Frequeny Modulation FSK frequeny of the arrier signal is varied to represent binary or both peak amplitude and phase remain onstant during eah bit interval Aos(πft), s(t) = Aos(πft), binary binary f <f +A -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 appliation: over voie lines, in high-frequeny radio transmission, et. 9
Frequeny Modulation (Cont.) Example [ FSK ] v d (t) v (t) v (t) v FSK (t) ω d_max ω ω ω ω ω ω -ω ω d_max ω +ω d_max
Frequeny Modulation (Cont.) 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 osω π t ( v 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] os5ω os5ω +... + [ os( ω 3ω ) t + os( ω + 3ω ) t] +... + d - - t... + t... =
Phase Modulation PSK phase of the arrier signal is varied to represent binary or peak amplitude and frequeny remain onstant during eah bit interval -PSK, or Binary PSK, sine only different phases are used. 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 Aos(πft), s(t) = Aos(πft + π), binary binary Aos(πft), binary s(t) = - Aos(πft), binary 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 +A -A
Phase Modulation (Cont.) 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 3
Phase Modulation (Cont.) PSK Detetion / Reovery multiply the reeived / modulated signal ± Aos(πf t) by *os(πf t) os A = ( + os A) resulting signal Aos (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 4
Phase Modulation (Cont.) 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 5
Signaling rate and Transmission Bandwidth Fat from modulation theory: If Baseband signal x(t) with bandwidth B Hz then B f Modulated signal x(t)os(πf t) has bandwidth B Hz f -B f f +B f If bandpass hannel has bandwidth W Hz, Then baseband hannel has W / Hz available, so modulation system supports W / x = W pulses/seond Reall baseband transmission system of bandwidth W [Hz] an theoretially support W pulses/se
Phase Modulation (Cont.) 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 7
Quadrature Amplitude Modulation (QAM) uses two-dimensional signalling original information stream is split into two sequenes that onsist of odd and even symbols, e.g. B k and A k - - B A B A B 3 A 3 A k sequene (in-phase omponent) is modulated by os(πf t), while B k sequene (quadrature-phase omponent) is modulated by sin(πf t) omposite signal A os(π f t) + B sin(πf t) is sent through the hannel k k A k x Y i (t) = A k os(πf t) os(πf t) + Y(t) = A k os(πf t) + B k sin(πf t) B k x Y q (t) = B k sin(πf t) Transmitted Signal sin(πf t) advantage: data rate = bits per bit-interval! 8
QAM (Cont.) Example [ QAM ] B k v d (t) sin(ω t) A k os(ω t) 9
QAM (Cont.) QAM Demodulation by multiplying Y(t) by os(πft) and then low-pass filtering the resultant signal, sequene A k is obtained by multiplying Y(t) by sin(πft) and then low-pass filtering the resultant signal, sequene B k is obtained A os(πf t) + B sin(πf t) = k k Y(t) x Lowpass filter (smoother) A k os(πf t) A k os (πf t)+b k os(πf t)sin(πf t) = A k { + os(4πf t)}+b k { + sin(4πf t)} os (A) = + sin (A) = ( os(a) ) ( os(a) ) sin(a) = sin(a)os(a) x sin(πf t) Lowpass filter (smoother) B k smoothed to zero B k sin (πf t)+a k os(πf t)sin(πf t) = B k { - os(4πf t)}+a k { + sin(4πf t)} smoothed to zero
Signal Constellations 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
QAM (Cont.) QAM ont. QAM an also be seen as a ombination of ASK and PSK - Bk ( A + B ) os( f t tan ) Y(t) = Ak os(πft) + Bksin(πft) = k k π + A k 4-level QAM (-A,A) B k (A, A) A k (-A,-A) (A,-A)
QAM (Cont.) 6-level QAM the number of bits transmitted per T [se] interval an be further inreased by inreasing the number of levels used in ase of 6-level QAM, A k and B k individually an assume 4 different levels: -, -/3, /3, data rate: 4 bits/pulse 4W bits/seond - Bk ( ) tan ) k os(πft) + Bksin(πft) = Ak + B k os( ft + B k Y(t) = A π A k A k A k and B k individually an take on 4 different values; the resultant signal an take on (only) 3 different values!!! In QAM various ombinations of amplitude and phase are employed to ahieve higher digital data rates. Amplitude hanges are suseptible to noise the number of phase shifts used by a QAM system 3 is always greater than the number of amplitude shifts.