EE140 Introduction to Communication Systems Lecture...

3/4/2018

1

EE140 Introduction to

Communication Systems

Lecture 8

1

Instructor: Prof. Xiliang Luo

ShanghaiTech University, Spring 2018

Architecture of a (Digital) Communication System

2

Source A/Dconverter

Sourceencoder

Channelencoder Modulator

Channel

DetectorChanneldecoder

Sourcedecoder

D/Aconverter

User

Transmitter

Receiver

Absent ifsource isdigital

Noise

3/4/2018

2

Contents

• Analog Modulation

– Amplitude modulation

– Pulse modulation

– Angle modulation (phase/frequency)

3

Bandpass Noise (Lecture 6)

• Canonical form of a band-pass noise process

4

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

3/4/2018

3

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

5

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

6

)ff(M)ff(MA)f(S cc 2

1

3/4/2018

4

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.

7

VSB Modulation• Frequency domain graphic interpretation

8

3/4/2018

5

Contents





9

Analog Pulse Modulation

10

Pulse-Amplitude Modulation (PAM)

Pulse-Width Modulation (PWM)

Pulse-Position Modulation (PPM)

Modulating Signal

3/4/2018

6

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.

11

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.

12

3/4/2018

7

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.

13

(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)

14

3/4/2018

8

Contents





15

Analog Modulation• Characteristics that can be modified in the carrier

– Amplitude

– Frequency

– Phase

16

Amplitude modulation

Angle modulation

AMPM

)t(t)t(fcos)t(A)t(C θπ 2

3/4/2018

9

Angle Modulation• Either phase or frequency of the carrier is varied

according to the message signal• General form

– time-varying phase– Instantaneous frequency

17

)]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

18

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

3/4/2018

10

PM and FM: Graphic Interpretation

19

AM and PM• Amplitude modulation (AM) is linear

–

• Angle modulation (PM and FM) is nonlinear

20

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

3/4/2018

11

“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

21

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

22

]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

3/4/2018

12

NBFM (Cont’d)• If (i.e. ), the narrowband FM

signal is given by

• Compared with DSB-LC (AM)

23

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 .

24

)]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

3/4/2018

13

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

25

]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

26

tfsinj me πβ 2

2

2

2222 1 where

T

T

tnfjtfsinjn

n

tnjn

tfsinj dteeT

FeFe mmmm ππβωππβ ，

)(JF nn β

3/4/2018

14

Spectra of FM Signal• Total average power in an FM signal is a constant.

27

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.

28

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

3/4/2018

15

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)


– (c) . Check Bessel function table, we have


29

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

30

])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

3/4/2018

16

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)

31

)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.

32

lawnth Frequency multiplier Frequency converter

mf mnf

cn 1 cn

3/4/2018

17

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.

33

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.

34

]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

3/4/2018

18

Demodulation of Wideband FM Signals (Cont’d)

• Examples of frequency discriminator

35


• 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., .

36

Phasecomparator)(tsi

Loopfilter

Voltage-controlledoscillator (VCO)

)(tso

)(tsc

)(ts f

)t(h)t(s)t(s co

)t(sKf)t(s ofcf π2

3/4/2018

19


• 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


Loopfilter


)(tso

)(tsc

)(ts f


• Indirect method: output of PLL

38

)t(h)]t()t(sin[kk)t(h)t(sk)t(sk)t(dt

difcfcfoff ννν


Loopfilter


)(tso

)(tsc

)(ts f

0 )t(kk)t(kk)t(dt

dicffcff ννν

1

)t(h

x)xsin(No PLL loop

3/4/2018

20


• 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!

39

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

40

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

3/4/2018

21

SNR in FM Reception (cont’d)• Output noise of the FM detector

– Assume the noise is small, i.e. , we have

– Output noise: .

41

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:

42

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

3/4/2018

22

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 .

43

)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 .

44

W

A

N

SSNR

i

ii

2

η

π

3

222

3

m

f

o

oo

)t(fKA

N

SSNR

ωη

π

fK

3/4/2018

23

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,

45

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

46

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

3/4/2018

24

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.

47

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

48

3/4/2018

25

Thanks for your kind attention!

Questions?

49

EE140 Introduction to Communication Systems Lecture...

Documents

Transcript of EE140 Introduction to Communication Systems Lecture...