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EE140 Introduction to
Communication Systems
Lecture 8
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Instructor: Prof. Xiliang Luo
ShanghaiTech University, Spring 2018
Architecture of a (Digital) Communication System
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Source A/Dconverter
Sourceencoder
Channelencoder Modulator
Channel
DetectorChanneldecoder
Sourcedecoder
D/Aconverter
User
Transmitter
Receiver
Absent ifsource isdigital
Noise
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Contents
• Analog Modulation
– Amplitude modulation
– Pulse modulation
– Angle modulation (phase/frequency)
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Bandpass Noise (Lecture 6)
• Canonical form of a band-pass noise process
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n(t)nw(t) Bandpass filter h(t)
)tfsin()t(n)tfcos()t(n)t( cscc ππ 22n
Low-pass noise process
In-phase component Quadrature component
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Representation of Bandpass Signals
• Baseband equivalent model of passband signal
– Suggested reading: Chap. 4.1.1, J. Proakis, M. Salehi, Digital Communications, 5th Edition, McGraw-Hill, 2007
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tfj
cc
ce)t(jQ)t(IRe
)tfsin()t(Q)tfcos()t(I)t(s~)t(jQ)t(Is(t)
π
ππ2
22
DSB-SC Spectrum
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)ff(M)ff(MA)f(S cc 2
1
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SSB• Advantage: SSB
modulation is efficient because it requires no more bandwidth than that of the original signal and only half that of the corresponding DSB signal.
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VSB Modulation• Frequency domain graphic interpretation
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Contents
• Analog Modulation
– Amplitude modulation
– Pulse modulation
– Angle modulation (phase/frequency)
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Analog Pulse Modulation
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Pulse-Amplitude Modulation (PAM)
Pulse-Width Modulation (PWM)
Pulse-Position Modulation (PPM)
Modulating Signal
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Analog Pulse Modulation (cont’d)• PAM: constant-width, uniformly spaced pulses
whose amplitude is proportional to the values of at the sampling instants.
• PWM: constant-amplitude pulses whose width is proportional to the values of the input at the sampling instants.
• PPM: constant-width, constant-amplitude pulses whose position is proportional to the values of the input at the sampling instants.
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Analog Pulse Modulation (cont’d)• Remarks
– PWM is a popular choice where the remote proportional control of a position or a position rate is desired.
– Disadvantages of PWM include the necessity for detection of both pulse edges and a relatively large guard time is needed.
– Only the trailing edges of the PWM waveforms contain the modulating information. PPM conveys only the timing marks of the trailing edges.
– PAM and PWM are “self-clocking” (the waveform presents clock timing), while the use of PPM requires a method of regenerating clock timing.
– PWM and PPM are nonlinear, Fourier analysis cannot be used directly.
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Pulse-code Modulation (PCM)
• Quantization: the sampled analog signal is quantized into a number of discrete levels.
• Digitization: assign a digit to each level (one-to-one mapping) so that the waveform is reduced to a set of digits at the successive sample times.
• Code: the digits are expressed in a coded form. Binary code (i.e. a code using only two possible pulse levels) is the most popular choice.
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(3-bit code) Representations of PCM code
(8 levels)
PCM (cont’d)• Advantages of PCM systems
– In long-distance communications, PCM signals can be completely regenerated (noise-free) at intermediate repeater stations because all the information is contained in the code. The effects of noise do not accumulate and only the transmission noise between adjacent repeaters need be concerned.
– Modulating and demodulating circuitry is all digital, thus affording high reliability and stability.
– Signals may be stored and time scaled efficiently.– Efficient codes can be utilized to reduce unnecessary
repetition (redundancy) in message. (source coding)– Appropriate coding can reduce the effects of noise and
interference. (channel coding)
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Contents
• Analog Modulation
– Amplitude modulation
– Pulse modulation
– Angle modulation (phase/frequency)
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Analog Modulation• Characteristics that can be modified in the carrier
– Amplitude
– Frequency
– Phase
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Amplitude modulation
Angle modulation
AMPM
)t(t)t(fcos)t(A)t(C θπ 2
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Angle Modulation• Either phase or frequency of the carrier is varied
according to the message signal• General form
– time-varying phase– Instantaneous frequency
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)]t(tfcos[A)t(s c θπ 2
)t(θ
dt
)t(d)t(f
θ
PM and FM• Phase modulation
– Overall output
• Frequency modulation
– Overall output
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constant a is and deviation phase is where pp K),t(mK)t( θ
)]t(mKtfcos[A)t(s pc π2
constant a is and deviation frequency is where ff K),t(mKdt
)t(d
θ
]d)(mKtfcos[A)t(st
fc 0
0
2 θττπ
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PM and FM: Graphic Interpretation
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AM and PM• Amplitude modulation (AM) is linear
–
• Angle modulation (PM and FM) is nonlinear
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m(t))t(dm
)t(ds of tindependen is
tfcos)t(mA)t(s cπ2
23
22
22
3
1
2
11
2
32
322
2
tfsin!
)t(tfcos
!
)t(tfsin)t(tfcosA
)t(!
j)t(!
)t(j A eRe
eA eRe)t(tfcosA)t(s
cccc
tfj
)t(jtfjc
c
c
πθ
πθ
πθπ
θθθ
θπ
π
θπ
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“Linear” Angle Modulation• Nonlinear angle modulation: the sidebands arising
in angle modulation do not obey the principle of superposition.
• However, if , the high-order terms in can be ignored
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1)t(θ
tfsin)t(tfcosA)t(s cc πθπ 22
Approximately linear!
Narrowband FM (NBFM)• Narrowband FM (NBFM) – sinusoidal modulating
signal
• Given
– where is the peak frequency deviation, and is the modulation index
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]d)(mKtfcos[A)t(st
fc 0
0
2 θττπ 0 and 2 0 θtfcosa)t(m mπ
tfsintfsinf
ftfsin
f
aKd)(mK)t( mm
mm
m
ft
f πβπππ
ττθ 22220
Δ
fΔ β
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NBFM (Cont’d)• If (i.e. ), the narrowband FM
signal is given by
• Compared with DSB-LC (AM)
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1)t(θ10 β
tfjtfjtfj
cmc
mmc eeAeRe
tfsintfsinAtfcosA)t(s
πππ ββ
ππβπ
222
221
2 2 2
tfjtfjtfj
cmc
mmc em
em
AeRe
tftfmAtfcosA)t(s
πππ
πππ
222
221
2cos 2cos 2
Narrowband PM (NBPM)• Narrowband PM (NBPM) – sinusoidal modulating
signal
• Given
• If , s(t) is approximately linear.• DSB-LC(AM), NBPM and NBFM are examples of
linear modulation. • If the modulating signal bandwidth is , the
narrowband angle-modulated signal will have a bandwidth of .
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)]t(mKtfcos[A)t(s pc π2
0 and 2 0 θtfcosa)t(m mπ
tfcostfcosaK)t(mK)t( mmpp πβπθ 22
10 β
mf
mf2
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Wideband FM• If modulation index is NOT small, the spectral
density of a general angle-modulated signal cannot be obtained by Fourier transform.
• Wideband FM
– Modulation index
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]d)(mKtfcos[A)t(st
fc 0
0
2 θττπ
tfsinjtfj
mcmm
fc
mc eAeRe
tfsintfcosAtfsinf
KtfcosA)t(s
πβπ
πβπππ
π
22
2222
2
m
f
m f
K
f
f
πβ
2
Δ
Wideband FM• is a periodic function of time with a
fundamental frequency of . Its Fourier series representation is
– Bessel functions of the first kind
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tfsinj me πβ 2
2
2
2222 1 where
T
T
tnfjtfsinjn
n
tnjn
tfsinj dteeT
FeFe mmmm ππβωππβ ,
)(JF nn β
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Spectra of FM Signal• Total average power in an FM signal is a constant.
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constant mf constant fΔ
Bandwidth of FM Signals• Bandwidth of FM signals, theoretically unlimited.
• Significant sideband– For large : diminish rapidly for . Assume there
are significant sidebands, .– For small : only and have significant
magnitude. Assume , .
• Carson’s rule:– An approximation of the bandwidth.
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mfnW 2β )(Jn β βn
fffnW mm Δ 2 2 2 ββnβ )(J β0 )(J β1
mfW 21n
β 1 2 2 mm fffW Δ
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Example• A 10 MHz carrier is frequency-modulated by a sinusoidal signal
such that the peak frequency deviation is 50 kHz. Determine the approximate bandwidth of the FM signal (a) 500 kHz; (b) 500 Hz; (c) 10 kHz.
• Solution: – (a)
• Carson’s rule gives:
– (b)
• Carson’s rule gives:
– (c) . Check Bessel function table, we have
• Carson’s rule gives:
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1100500
50 .
f
f
m
Δβ MHzfB m 12
MHz.)(fB m 1112 β
1100500
50000
mf
fΔβ kHzfB 100 2 Δ
kHz)(fB m 10112 β
51050
kHz)(fB m 12012 β
kHznfB m 1602 8n
Wideband PM• Wideband PM:
– Instantaneous phase:
– Peak phase deviation:
– Instantaneous frequency:
– Peak frequency deviation:
• Wideband PM – sinusoidal modulating signal– Let and
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])t(mKtfcos[A)t(s pc 02 θπ
02 θπθ )t(mKtf)t( pc
)t(mKmax p θΔ
)t(mdt
dKmaxf pΔ
)t(mdt
dKf)t(
dt
d)t(f pc θ
tfcosa)t(m mπ2 00 θ
tfcosjtfjmpc
mc eAeRetfcosKatfcosA)t(s πβπππ 222 2
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Generation of Wideband FM Signals• Direct method: vary the carrier frequency directly
with the modulating signal by using the voltage-controlled oscillator (VCO).– The oscillation frequency of a simple tuned electronic
oscillator is given by , where L: inductance; C: capacitance.
– For very small variations (i.e. ), the square-root relationship can be approximated by a linear term.
• Requirement of direct method:– The long-term frequency stability is not as good as the
crystal-stabilized oscillators so that frequency stabilization is needed.
– The percentage frequency deviation that can be attained in this method is quite small. (say 0.2 in theory)
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)t(m
LC/f π210
cff Δ
Generation of Wideband FM Signals (Cont’d)
• Indirect method: Armstrong indirect FM transmitter– produce a narrowband FM signal. – use frequency multiplier to increase the value of β.
• Frequency multiplier is a nonlinear device designed to multiply the frequencies of the input signal by a given factor, say .
• Frequency converter is often used to control the value of the carrier frequency. It translates the spectrum of a signal by a given amount but does not alter its spectral content.
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lawnth Frequency multiplier Frequency converter
mf mnf
cn 1 cn
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Generation of Wideband FM Signals (Cont’d)
• Indirect method: Armstrong indirect FM transmitter
– As a result of the multiplication and heterodyne operations, it is difficult in this system to maintain the correct magnitude of carrier to sidebands, and thus it could not be used for an information signal with DC content.
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Demodulation of Wideband FM Signals• Demodulation: to provide an output signal whose
amplitude is linearly proportional to the instantaneous frequency of the input FM signal.
• Direct method: use frequency discriminator – Frequency discriminator is the system that has a linear
frequency-to-voltage transfer characteristic. – Ideal differentiator has a linear amplitude versus frequency
characteristic and therefore is a frequency discriminator.Input:
Output:
– If , the modulating signal can then be detected by an envelope detector.
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]d)(mktfcos[A)t(st
fc 00 2 θττπ
00
2 ]2[ θττ d)(mKtπfsin)t(mKπfA)t(sdt
d t
fcfc
cf f)t(mK π2
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Demodulation of Wideband FM Signals (Cont’d)
• Examples of frequency discriminator
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Demodulation of Wideband FM Signals (Cont’d)
• Indirect method: use phase-locked loop (PLL)
– Phase comparator detects the timing difference between the two periodic signals (with the same fundamental frequency) and produces an output voltage that is proportional to this difference.
– Loop filter controls the dynamic response of the PLL. We have
– Voltage-controlled oscillator (VCO) generates a constant-amplitude periodic waveform whose instantaneous frequency is proportional to the input voltage, i.e., .
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Phasecomparator)(tsi
Loopfilter
Voltage-controlledoscillator (VCO)
)(tso
)(tsc
)(ts f
)t(h)t(s)t(s co
)t(sKf)t(s ofcf π2
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Demodulation of Wideband FM Signals (Cont’d)
• Indirect method: output of PLL
– Assume and the phase comparator output is then
– If is small and we have .37
)]t(tfcos[A)t(s ici νπ 21 )],t(tfsin[A)t(s fcf νπ 22
)]t()t(sin[AA
)]t(tfsin[A)]t(tfcos[A)t(s
if
LPfcicc
νν
νπνπ
21
21
2
1
2 2
)t()t( if νν )]t()t([k)t(s ifcc νν
Phasecomparator)(tsi
Loopfilter
Voltage-controlledoscillator (VCO)
)(tso
)(tsc
)(ts f
Demodulation of Wideband FM Signals (Cont’d)
• Indirect method: output of PLL
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)t(h)]t()t(sin[kk)t(h)t(sk)t(sk)t(dt
difcfcfoff ννν
Phasecomparator)(tsi
Loopfilter
Voltage-controlledoscillator (VCO)
)(tso
)(tsc
)(ts f
0 )t(kk)t(kk)t(dt
dicffcff ννν
1
)t(h
x)xsin(No PLL loop
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Demodulation of Wideband FM Signals (Cont’d)
• Indirect method: output of PLL (with loop)
– Output voltage is proportional to the instantaneous frequency (referred to the carrier) of the input wideband FM signal.
– The PLL demodulates the input wideband FM signal!
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ττνν d)(sk)t()t(t
offi 0
)t(dt
d
k)t(s i
fo ν
1
Signal-to-noise Ratio (SNR) in FM Reception
• Input signal and input noise of the FM detector
• Output signal of the FM detector
• For convenience, assume• Output noise of the FM detector
– Unmodulated carrier with additive bandpass noise
where and
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2 2 200
/AS]d)(fktfcos[A)t(s i
t
fc θττπ
)t(fk)t(dt
d)t()t(s fcco ωθωω
)t(fkS)t(fk)t(s fofo22
)]t(tcos[)t(r
tsin)t(ntcos)t(ntcosA)t(ntcosA
c
cscccc
γω
ωωωω
)t(n)t(n)t(nNtfsin)t(ntfcos)t(n)t(n scicscc222 22 ππ
22 )]t(n[)]t(nA[)t(r sc .)t(nA
)t(ntan)t(
c
s 1
γ
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SNR in FM Reception (cont’d)• Output noise of the FM detector
– Assume the noise is small, i.e. , we have
– Output noise: .
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A)t(n&)t(n sc
A
)t(n
A
)t(ntan
)t(nA
)t(ntan)t( ss
c
s
11γ
)t(ndt
d
A)t(
dt
d)t(n so
1 γ
Power Spectral Density / Mean Power of Noise
• Input noise of the FM detector
Bandwidth:
• Quadrature noise component
Bandwidth:
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Hzwatts)(Sn 2ηω
π
η
πω
2
2 2 2 WW
)(S)t(nN ni mnW ω 2
0 2W2W
)(snS
)t(ns
ηωωω LPcncnn )ω(S)ω(S)(Ss
π
η
πω
2
2
2 22 WW
)(S)t(nsns
mnW ω 2
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Power Spectral Density / Mean Power of Noise
• Output noise of the FM detector
– where is the frequency response of the time differentiator (recall
• The discriminator output is limited by a low-pass filter (LPF) with a cutoff frequency of , the bandwidth of output noise is .
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)t(no
2
2
2
22
2
1
A)(S
A)(H)(S
A)(S
sso nnn
ηωω
ωωωω
ωω j)(H
)(Fj)t(fdt
dFT ωω
mω
mω
2
3
0
22
2
3
2
1
Ad
Ad)(S)t(nN m
noo
mm
mo π
ωηωω
π
ηωω
π
ωω
ω
SNR in FM Reception (cont’d)• Signal-to-noise ratios (SNR) in FM reception
– For wideband FM, the output signal-to-noise ratio increases as the square of the bandwidth, which is proportional to .
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W
A
N
SSNR
i
ii
2
η
π
3
222
3
m
f
o
oo
)t(fKA
N
SSNR
ωη
π
fK
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SNR in PM Reception• Input signal of the PM detector
• Output signal of the PM detector
• For convenience, assume • Input noise of the PM detector
• Output noise of the PM detector
– Assume the noise is small,
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2 20 AS])t(fKtcos[A)t(s ipc θω
)t(fkt)t()t(s pco 0θωθ
)t(fkS)t(fk)t(s popo22
)t(n
π
η
πωηω
2
2 2 2 2 WW
)(S)t(nNHzwatts)(S nin
)t(no
)t(nA)t(ntan)t()t(n cso 1γ
.A
)t(n)t( sγ
222
22
22
1
AA)t(nN
A)(S
A)(S mm
oonn so π
ωη
π
ωηηωω
SNR in PM Reception (cont’d)• Signal-to-noise ratios (SNR) in PM reception
• For sinusoidal modulating signal, i.e. , we have
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W
A
N
SSNR
i
ii
2
η
π
m
p
o
oo
)t(fkA
N
SSNR
ωη
π
222
mmm
p
o
o A)(AakA
N
S
ωη
βπ
ωη
θπ
ωη
π
2
2
2
2222222
Δ
i
i
o
o
N
Sn
N
S 2β
tωcosa)t(m m
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SNR in PM Reception (cont’d)• Compared to the AM signal with 100% modulation,
we have
– Conclusion: the output SNR can be made much higher in PM than in DSB-LC (AM) by increasing the modulation index .
– Assumption: (1) ; (2) .– Expense: an increase in also increases the signal
bandwidth.
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AMo
o
AMi
c
PMo
o
N
S
N
S
N
S
22 ββ
β
A)t(n&)t(n sc 1ββ
Comparison of CW Modulation Systems
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Thanks for your kind attention!
Questions?
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