cours transmissions numeriques nathalie thomas anglais

Digital Modulations

Nathalie Thomas

IRIT/[email protected]

1

2

Telecommunication network

From the binary information to be transmitted, the physical layer has to create a signal

able to cross the « best way » the physical link (propagation channel) between the

transmitter and the receiver.

« Physical » layer

« Network » layers

Vers toujours plus de débit...

Some examples of telecommunication systems

WiFi

IEEE802.112Mbps

IEEE802.11b11 Mbps

802.11a et g54 Mbps

802.11n450 Mbps

ADSL, 8Mbps

V90, 56kbps

VDSL, 52Mbps

FTTH, 1Gbps

V23(Minitel), 1,2kps

Fixed Phone Ethernet

10 Gigabit

Ethernet

10 Gbps

Ethernet

10 Mbps

Fast

Ethernet

100 Mbps

Gigabit

Ethernet

1 Gbps

DVB-S

40 Mbps1994

DVB-S2

52 Mbps2005

DVB-S2X

70 Mbps2014

Netcomgroup-blog,fr

Altos 20102G (GSM)

9,6kbps

2,5G (EDGE)

115kbps

3G (UMTS)

384 kbps

3G+ (HSDPA)

42 Mbps

4G (LTE Adv.)

1Gbps

Mobile phoneSatellite broadcasting

Internet of things

→ Low cost (service < 10 $ a year, terminals

< 10 $),

→ Low consumption

→ Low rates (a few kbps)

→ Long range (> 10 km)

Some examples of telecommunication systems

Digital Modulations : Introduction

→ Transmission channel→ Components of the digital communication channel→ Performance criteria

5

xDSL

Optical Fiber

Cable TV

Transmission channel: « wired » transmissions

Power Line Communications

Copper

Fiber

Coaxial6

TNT

(DVB-T and T2)

2G, 3G, 4G

(GSM, UMTS, LTE)

WiFi

Transmission channel: « wireless » transmissions

7

(ISM and UNII bands around 2.4 or 5 GHz

(propagation autour de 470-862 MHz : bande UHF)(ISM bands 876-959 MHz and 1.71-1.88 GHz)

Internet of Things (IoT)

(ISM band 868-870 MHz)

In the desert

To broadcast television

To speak with the planes

To give Internet to white spots

Off shore

In the mountains

Transmission channel: « wireless » satellite transmissions

8

Propagation in bands L : 1.4-1.6 GHz, C : 4-6GHz, Ku : 10.7-12.45 GHz

and Ka : 20-30 GHz

- Attenuation: absorption, scattering due to atmospheric gases, to clouds, to rain, skin effect for cooper (Increase with increasing frequency),

- One or several paths between the transmitter and the receiver => flat fading or frequency selective channel

- Fixed or Mobile transmission => stationnary or non stationnary channel

- Limited allocated bandwidth

- Noise :→ External noise = other signals received in addition to the useful communication

signal:‒ natural sources: atmosphere (lightning, thunder), Earth, sky (Sun, Milky Way)‒ artificial sources: human activity, interferences with other users

→ Internal Noise = Electronic devices/components inside the receiver: amplifiers, antennas, etc.

Distorsions introduced by the transmission channel

9

Transmission channel modeling

10

hc(t)

n(t)

x(t) y(t)

y(t) = α x(t - τ) + n(t)

Noise, assumed to be additive,

white and Gaussian

Attenuation and delayintroduced by the channel

x(t)

y(t)

(α , τ) , n(t)Line of Sight

(LOS)

|Hc(f)|

fArg(Hc(f))

f

Example of AWGN channel(Additive White Gaussian Noise)


hc(t)

n(t)

x(t) y(t)

- Noise modeling

→ White, with PSD = N0/2 whatever is the frequency, and N0=k(Te+Ti) • k = Bolztmann constant• Te = external noise temperature• Ti = internal noise temperature

→ Gaussian, with power σ2

→ Additive,

→ Added upstream of the receiver, considering then ideal components,

→ A degradation measurement : the signal to noise ratio (SNR)

SNRdB = 10 log Puseful signal

Pnoise

hc(t)

n(t)

x(t) y(t)

Impact of an AWGN channel : Attenuation effect on a DVB-S transmission



hc(t)

n(t)

x(t) y(t)

NRZ-type transmitted signal Noisy signal, SNRdB = 10 dB Noisy signal, SNRdB = 0 dB

Examples :

Transmitted image

100 200 300 400 500

100

200

300

400

500

Received image

100 200 300 400 500

100

200

300

400

500

Received image

100 200 300 400 500

100

200

300

400

500

Received image, SNRdB = 10 dBTransmitted image Received image, SNRdB = 0 dB

BER = 0.0784BER = 2.38 10-6

13

SNRdB = 10 log Puseful signal

Pnoise

Impact of an AWGN channel : noise effect


14

hc(t)

n(t)

x(t) y(t)

y(t) = α x(t - τ) + n(t)

Noise, assumed to be additive,

white and Gaussian

Attenuation and delayintroduced by the channel

-BW BW

|Hc(f)|

f

Arg(Hc(f))

f-BW BW

Example of AWGN with limited bandwidth


15

hc(t)

n(t)

x(t) y(t)

Example of frequency selective channel (stationnary)

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.510

-4

10-2

100

102

Normalized frequency

Channel transfer function: |Hc(f)|

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-4

-2

0

2

4

Normalized frequency

Channel phase response: Arg(Hc(f))

|Hc(f)|

Arg(Hc(f))

0 2 4 6 8 10 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9Channel Impulse responsehc(t)

Bc : The channel coherence bandwidth Bc is a statistical measurement of the range of frequencies over which the channel can be considered "flat", or in other words the approximate maximum bandwidth over which two frequencies of a signal are likely to experience comparable amplitude fading.


hc(t)

n(t)

x(t) y(t)

16

Impact of a frequency selective channel: signal distorsion

Transmitted image

100 200 300 400 500

100

200

300

400

500

0 0.5 110

-20

10-10

100

1010

PSD of the transmitted image (SRRC shaping)

Received image

100 200 300 400 500

100

200

300

400

500

0 0.5 110

-20

10-10

100

1010

PSD of the received image


17

hc(t)

n(t)

x(t) y(t)

Example of non stationnary frequency selective channel

→ Multi paths => frequency selectivity if needed bandwidth B > coherence bandwidthof the channel Bc

→ Mobility => Doppler effect => signal spectrum spreading => time selectivity

(2) The coherence time is the time duration over which the channel impulse response is considered to be not varying

→ Doppler spread:

→ Coherence time Tc(2):

The channel is stationnary on duration T if T>Tc

18

Wireless transmission channel => frequencies regulation

- Depending on the countries : regulatory agencies or a ministries

Examples :

→ In France : ARCEP (Autorité de Régulation des Communications Electroniques), ANRT (Agence

Nationale de Régulation des Fréquences), CSA (Conseil Supérieur de l’Audiovisuel)

→ In the United States of America : FCC (Federal Communications Commission)

→ In Japan: MIC (Ministry of Internal Affairs and Communications )

- Collaborations between states:

Examples :

→ ORECE : Organe des Régulateurs Européens des Communications Electroniques in Europ,

→ NARUC : National Association of Regulatory Utility Commissioners (regulators of individual states) in

the United States,

→ ARTAC : Association des Régulateurs de Télécommunications de l’Afrique Centrale, in Africa,

- International Telecommunication Union (ITU)→ Chargée de la réglementation et de la planification des télécommunications dans le monde

→ 193 états membres et 700 membres associés du secteur des TIC.

→ Instance au sein de laquelle les Etats et le secteur privé se coordonnent

- Unlicensed bandwidth→ industrial, scientific and medical (ISM) : (902-928 MHz, 2.400-2.4835 GHz)

→ Unlicensed National Information Infrastructure (UNII) : 5 .15-5.25 GHz, 5 .25-5.35 GHz

→ UNII-3/ISM : 5.725-5.850 GHz

19

Shared transmission channel: Multiplexing methods

Example 1 : Time Division Multiplexing Example 2 : Frequency Division Multiplexing

Time DivisionMultiple Access

Service 1Service 2Service 3

Service 3

Service 2

Service 1

TDMA FDMA

Se

rvic

e 1

Se

rvic

e 1

Se

rvic

e 2

Se

rvic

e 3

Se

rvic

e 2

Se

rvic

e 3

Service 1

CDMA

Service 2Service 3

Service 3Service 2Service 1

Example 3 : code division

multiplexing

Frequency Division

Multiple Access

Code Division

Multiple Access

MF-TDMA

MC-CDMA

Transmitter

Digitization

Transmission channel

Analog signal

Corrupted analog signal

Receiver

Received Binary information: 0 1 0 1 0 1 1 …

BASIC

CHANNEL

Analog signal : sound, image …

Basic digital transmission channel

Binary information to transmit: 0 1 1 0 0 1 0 1 1 0

20

Transmitter

Digitization


Analog signal


Receiver

Received Binary information: 0 1 0 1 0 1 1 1 1 1




21

Example DVB : BER<10-10, Rb 30 à 40 Mbps ~

BER =Number of erroneus bits

Nunber of transmitted bits

Bit rate: Rb

Number of transmitted bits

per second

Bit Error rate (BER) :

0 1 1 0 0 1 0 1 1 0

0 1 0 1 0 1 1 1 1 1

BER = 4/10 <1

The BER measures the quality

of the digital transmission

BASIC

CHANNEL

Transmitter

Digitization


Analog signal


Receiver


BASIC

CHANNEL




22


23

t

V

- V

Example :

t

V

- V

SNR = 10 dB :

t

V

- V

SNR = 0 dB :

Analog signal:

Corrupted analog signal:

Transmitter

Digitization


Analog signal


Receiver

Received binary information: 0 1 0 1 0 1 1 1 1 1


SNR

BER = 0.0784

BER = 2.38 10-6

Analo Signal : sound, image …

BER

BASIC

CHANNEL

Transmitter

Digitization


Analog signal


Receiver


BASIC

CHANNEL




Transmission quality is improved:

Quality criterion is the Bit Error Rate (BER) which

can be very low even with corrupted received

analog signals. Of course BER is a function of SNR.

24

Transmitter

Digitization


Analog signal


Receiver


BASIC

CHANNEL




Transmission quality is improved:




Price to pay: occupied bandwidth is larger for

digital transmissions.

But source coding will help on this point !

25

Example : fixed phone digitizationBanalog = 3.1 kHz

Bdigital 64 kHz (Fe=8kHz, nb=8 bits) ~


Analog signal

BASIC

CHANNEL

Source codingT

R

A

N

S

M

I

T

T

E

R

Physical layer

Binary information to transmit: 0 1 1 0 0 1 0 …

Disturbed analog signal

Analog signal

Source decoding

R

E

C

E

I

V

E

R

Physical layer



26

Message to transmit: EMMENE MOI A LA MER

E M Espace A N I O R L

4/19 4/19 4/19 2/19 1/19 1/19 1/19 1/19 1/19

0000 0001 0010 0011 0100 0101 0110 0111 1000

Natural binary coding:

9 different characters = > 4 bits per character (24=16)

19x4 = 76 bits to be sent, example with 2G transmission (9,6 kbps) : 0,79 ms

Smarter code (Huffman) :

12x2+3x4+4x5 = 56 bits to be sent, example with 2G transmission (9,6 kbps) : 0,58 ms

E M Espace A N I O R L

4/19 4/19 4/19 2/19 1/19 1/19 1/19 1/19 1/19

01 10 11 0000 0011 00100 00101 00010 00011

Gain : 26,32 %

Example of source coding : Huffman coding

27

Transmitter

Digitization


Analog signal


Receiver


BASIC

CHANNEL



Binary information to transmit: 0 1 1 0 0 1 0 1 1 0Transmission quality is improved:




Of course there is a price to pay: occupied

bandwidth is larger for digital transmissions.


28

Transmitter

Digitization


Analog signal


Receiver


BASIC

CHANNEL



Binary information to transmit: 0 1 1 0 0 1 0 1 1 0Transmission quality is improved:




New functions (digital functions) can be used in

the transmission channel, like channel coding

allowing to obtain the same BER with a lower

transmitted power.

Of course there is a price to pay: occupied

bandwidth is larger for digital transmissions.


29


Analog signal

BASIC

CHANNEL

Channel coding

Source codingT

R

A

N

S

M

I

T

T

E

R

Physical layer



Analog signal

Source decoding

R

E

C

E

I

V

E

R

Channel decoding

Physical layer



30

R

E

C

E

I

V

E

R

Physical layer

T

R

A

N

S

M

I

T

T

E

R

Physical layer

Example of channel codingBinary information to transmit:

0 1 1 0

Channel coding

Coded Binary information:

0 0 0 1 1 1 1 1 1 0 0 0


Modulation

Demodulation

Analog signal


Decoded Binary information:

0 0 1 1

Channel decoding

Corrupted coded binary information:

0 0 1 1 0 0 1 1 1 1 1 1

Adding redundancy

Coding rate = 1/3

Correction ability: 1 error

Detection ability: 2 errors

31


BASIC

CHANNEL

Channel coding

Source codingT

R

A

N

S

M

I

T

T

E

R

Physical layer

Modulation


Analog signal

Source decoding

R

E

C

E

I

V

E

R

Demodulation

Channel decoding

Physical layer



32

Analog signal


T

R

A

N

S

M

I

T

T

E

R

Physical layer

Binary information to transmit:

0 1 1 0

Channel coding

Coded Binary information:

0 0 0 1 1 1 1 1 1 0 0 0

Baseband

Modulation

Analog signal

Example of Modulation

Digital signal

tV

-V

( Frequency

Transposition )

D

I

G

I

T

A

L

M

O

D

U

L

A

T

I

O

N

Digital to Analog Convertor

Modulation

Example : NRZ signal

R

E

C

E

I

V

E

R

Physical layer

Retrieved binary information:

0 0 1 1

Channel decoding

Corrupted coded Binary information:

0 0 1 1 0 0 1 1 1 1 1 1

Baseband

Demodulation

Corrupted Analog signal

Corrupted Digital signal

tV

-V

( Down

conversion)

D

I

G

I

T

A

L

D

E

M

O

D

U

L

A

T

I

O

N

Analog To Digital Concvertor

Demodulation


0 0 0 1 1 1 1 1 1 0 0 0

SNR=0 dB

BER=2/4

33


Analog signal

WHOLE

BASIC

CHANNEL

Channel coding

Source codingT

R

A

N

S

M

I

T

T

E

R

Physical layer

Modulation



Source decoding

R

E

C

E

I

V

E

R

Demodulation

Channel decoding



Synchronization

DAC

ADC

34

!! Need for synchronization !!

1st

accesspoint

2nd

accesspoint

3rd

accesspoint

Baseband signal :Spectrum around frequency 0

0

ISM band

tV

-V


0 1 1 0

Signal:

Ts : symbol duration

Time 0

- On the clock

- On the carrier for carrier-modulated transmissions

Carrier-modulated signal :Spectrum around a given carrier frequency

Carrier frequencyerror

WiFi example(IEEE802.11 b et g) :

Down conversion before baseband demodulation35

Transmitter


Analog signal


Receiver

Received Binary information:

0 1 0 1 0 1 1 …

BASIC

CHANNEL

Performance criteria


0 1 1 0 0 1 0 1 1 0- Transmit a given bit rate Rb = Number of bits to be transmitted

per second.

- Achieve a given Bit ErrorRate

Channel transmission isdesigned to: It will cost in terms of:

- Needed bandwidth in the transmission

channel.

- Needed SNR at the receiver input => needed

transmitted power.

BER = <1Number of erroneous bits

Number of transmitted bits36

Performance criteria

Channel transmission isdesigned to:

It will cost in terms of:

- Needed bandwidth Bin the transmission

channel

Spectral Efficiency: needed bandwidth B to transmit wanted Rb

Power Efficiency: needed SNR per bit at the receiver input to

achieve wanted BER

- Transmit a given bit rate Rb = Number of bits to be transmitted

per second.

- Achieve a given Bit Error Rate




transmitted power.

Two main transmission channel performance criteria

37


Analog signal

WHOLE

BASIC

CHANNEL

Channel coding

Source codingT

R

A

N

S

M

I

T

T

E

R

Physical layer

Modulation



Source decoding

R

E

C

E

I

V

E

R

Demodulation

Channel decoding

Physical layer



Synchronization

DAC

ADC

Bit rate Rb

Needed transmission bandwidth B

Needed SNR

Bit Error Rate (BER)

Spectral Efficiency: needed bandwidth B to transmit

wanted Rb

Power Efficiency: needed SNR per bit at the receiver

input to achieve wanted BER

38

Channel transmission is designed to: It will cost in terms of:

- Needed bandwidth Bin the transmission

channel

- Transmit a given bit rate Rb = Number of bits to

be transmitted per second.

- Achieve a given Bit Error Rate




transmitted power.

39

Rb SNRB

Exemple du DVB-S : diffusion de contenu multi-média par satellite

Quasi Error Free (QEF) transmission:

TEB < 10 -10

Basic digital transmission channel: example

Baseband Modulator/demodulator:joint optimization

→ Signal generation, Spectral efficiency→ Inter Symbol Interference(ISI), Nyquist criterion→Matched filtering, → BER computation, Power efficiency

40

Binary information:

0 1 1 0 0 1 0 1 1 0Baseband

Modulation

Baseband Digital Modulation/Demodulation

x(t) Retrieved

binary information:

0 1 0 1 0 1 1 1 1 1

Baseband

Demodulation

Transmission

channel

hc(t)

n(t)

r(t)

Bit rate Rb =1/Tb

BER

SNR per bit: Eb/N0 ?

Occupiedbandwidth B ?


0

Sx(f)

Performance criteria:

→ Spectral Efficiency: Needed bandwidth B to transmit wanted bit rate Rb

→ Power Efficiency: Needed SNR per bit at the receiver input to achieve wanted Bit Error Rate (BER)

→ Robustness to non linearities ; Signal with constant envelop ?41

→ Elementary coding with independent symbols

→ Coding using a level :→Unipolar NRZ :

→Polar NRZ :

→ Coding with an edge→Biphase :

→ Bloc coding with independent symbols

→ Coding using a level :→Several level NRZ :

1 0 1 0 1 1 0 0 1 1

Ts

t

+V

0

t

+V0

-V

t

+V

0-V

Baseband Digital ModulationSome signal examples

Ts=2Tb

t

+3V

0-V

+V

-3V 42

Binary information:

0 1 1 0 0 1 0 1 1 0Baseband

Modulation

Bit rate Rb =1/Tb

Example (NRZ, M=4):

t

-3-1

+1+3

…

h (t)

t

+1

sT

200 250 300 350-4

-2

0

2

Bit Rate (bits/s)Symbol rate

(symbols/s or bauds)

Baseband Digital ModulationGeneral model

Binary information

0 1 1 0 0 1 0 1 1 0

M-ary SymbolsShaping filter

h(t)Mapping

Baseband Modulation

x(t)

Symbol rate = number of transmitted

symbols per seconds:

M=number of possible symbols


sT 43

Baseband Digital ModulationExample on Matlab

Generation of a polar NRZ

%Symbol duration in number of samples

Ts=4;

%Number of generated bits

nb_bits=100;

%Bit generation

bits=randint(1,nb_bits);

%Symbol generation : 0->-1, 1->1

Symboles=2*bits-1;

%Weighted Dirac delta function series

Suite_diracs=kron(Symboles, [1 zeros(1,Ts-1)]);

%Shaping filter impulse response (for NRZ)

h=ones(1,Ts)

%Shaping filtering

y=filter(h,1,Suite_diracs);

%Signal display

plot(y);

axis([0 nb_bits-1 -1.5 1.5]);

44

Binary information:

0 1 1 0 0 1 0 1 1 0Baseband

Modulation

Bit rate Rb =1/Tb

Baseband Digital ModulationGeneral model

Binary information

0 1 1 0 0 1 0 1 1 0


h(t)Mapping

Baseband Modulation

x(t)


where : ; ;

Cyclostationnary

signal

f

Example (NRZ, M=4):

Baseband Pulse Amplitude Modulation : M-PAM = Linear Modulation, spectrum around frequency 0

45

Baseband Digital ModulationSome spectrum examples

→ Two level NRZ (GPS waveform)

x(t)

TS

h (t)

+1

t

1/TS 2/TS 3/TS …

-13dB-18dB

f 46


→ Biphase or Manchester (Ethernet waveform : IEEE802.3)

x(t)

h(t)

TS

+1

-1t

2/TS4/TS …-4/TS -2/TS

f

-13dB

… 47


→ Square root raised cosine shaping (DVB-C, DVB-S waveform)

x(t)

TS

h(t)

- TSt

48

Baseband Digital ModulationSpectral efficiency

→ Bandwidth definition:

▪Definition 1 : frequency bandwidth B concentrating x % of the signal energy (typical values : 95 à 99 %)

▪ Definition 2 : frequency bandwidth beyond which the minimum rejection is of x dB(typical values: 20 à 30 dB)

→ Spectral Efficiency (bits/s/Hz):

- x dB

B

49

M-ary symbols

Baseband Digital DemodulationJoint optimization with the modulation

Binary

information

0 1 1 0 0 1


h(t)Mapping

Baseband Modulation

x(t)

Retrieved

Binary

information

0 1 0 1 0 1

Receiver filter

hr(t)Mapping-1

Baseband Demodulation

r(t)Decisions

Sampling

Transmission

channelhc(t)

n(t)

Decisions

ISI at sampling instants

Noise(filtered and sampled)

Interest term

(Inter Symbol Interference)50


→ Interference visualization at the sampler input : example

t0 2TS

t

TS

-Ts

0

Ts

TS

Ts

Interference (ISI)on the following symbol

Instants where ISI=0

-1 +1 -1 -1 +1 +1 -1

On the signal :

Eye diagram

TFavec

→ Interference suppression at t0+mTs : Nyquist criterion

▪ Time domain expression:

▪ Frequency domain expression:

51


→ Interference suppression at t0+mTs : frequency domain Nyquist criterion

▪ Example

▪ Nyquist bandwidth

f

……

f

……

⇒ Maximum symbol rate without interferencesat time sampling instants : 52

Nyquist Bandwidth


→ Example of Nyquist filter : raised cosine filter

53



Some typical values: α=0.22 (UMTS), α=0.35 (DVB-S), α=0.15 (DVB-C) 54



t0 t0 t0

αe = αr= 1

Some eyediagrams without noise (on 2Ts)

Without noise, different roll off at the

transmitter and receiver :

αe = αr= 0.35 αe = αr= 0

ISI

55


Decisions

ISI at sampling instants

Noise(filtered and sampled)

Interest term

(Inter Symbol Interference)

→ Interference suppression at t0+mTs: Nyquist criterion

Maximize ⬄ Maximize

Matched FilterTF-1

→ SNR maximisation at t0+mTs: matched filter (to the received waveform)

Filtered and sampled noise:

wm, variance σ2

Interest term

( Cauchy-Schwarz inequality: , equality for )

for

56

Baseband Digital DemodulationDecision block

→ Decision rule: Maximum A Posteriori

Binary case:

Nyquist criterion is fulfilled :

(Threshold detector or slicer)

4-ary case:

for equally likely symbols

57

Baseband Digital M-PAM TransmissionPerformance

→ Symbol Error Rate (SER)Matched filtering

▪ Binary case:

▪ M-ary case:

Obtained for a M-PAM modulation (Baseband), in a Nyquist channel, with matched

filtering

One erroneous symbol = 2 erroneous bits

One erroneous symbol = 1 erroneous bit

« Natural » mapping: GRAY Mapping

P1>P2

Matched filtering

→ Bit Error Rate (BER): Mapping optimization

D

Example for V=1, N0=10-3 V2/Hz, Rb=1kbps:

58

Baseband Digital M-PAM Transmission

→ BER = f(Eb/N0) for M-PAM transmission

Obtained results for a M-ary baseband modulation (PAM), in a Nyquist channel,

with matched filtering and Gray mapping

BER0

Power efficiency Spectral efficiency

Power efficiency

59

Linear Carrier Frequency Modulations:

→ One or two dimensional modulations, → Complex envelop, → Equivalent lowpass channel,→ Performance

The complex envelop associated to the transmitted signal linearly depends on the message

60

Baseband

Modulation

Linear Carrier Frequency ModulationOne-dimensionnal


0

Frequency

transposition

Coherent demodulation

Down conversion

LPF

Carrier-modulated signal:Spectrum around a carrier frequency fp

fp

M-ASK (Amplitude Shift Keying)

Binary

information:

0 1 1 0 0

Baseband

Demodulation

Retrieved

Binary

information:

0 0 1 0 1

Frequency

transposition

Down

conversion

61

Linear Carrier Frequency ModulationOne-dimensionnal

M-ASK (Amplitude Shift Keying)

Example : 4-ASK, rectangular shaping

fp-fp

f

Signal modulated on fp :

f62

Baseband

Modulation

Linear Carrier Frequency ModulationTwo-dimensionnal

Frequency

transposition

Binary

information:

0 1 1 0 0 Baseband

Modulation

+

-

Baseband

Demodulation

Downconversion

Binary

information:

0 1 1 0 0 Baseband

Deodulation

LPF

LPF

Coherent demodulation

Orthogonal signals63

Baseband

Modulation

Linear Carrier Frequency ModulationComplex envelop

Binary

information:

0 1 1 0 0 Baseband

Modulation

I(t)

In Phase Component

Q(t)

Quadrature Component

Complex envelop associated to x(t)

Frequency

transposition

+

-

64

Baseband

Modulation


Frequency

transposition

Binary

information:

0 1 1 0 0 Baseband

Modulation

+

-

h (t)

Complex envelop associated to x(t):

Complex symbols

Bits Mapping

Complex baseband modulationFrequency

transposition

65


h (t)


Complex symbols

Bits Mapping

Complex message generation with a baseband modulatorFrequency

transposition

→ The PSD of the carrier-modulated signal:

is obtained from the PSD of its associated complex envelop (known baseband spectrum):

→ But also :

Re-use the results obtained for

baseband modulations

66


BitsComplex Baseband

modulation

Frequency

transposition

Downconversion

LPF

LPF

j

Use lower sampling frequencies

for digital implementationsEquivalent

complex lowpass channel

Complex Baseband

DemodulationBits

67

Linear Carrier Frequency ModulationTwo main classes of two-dimensionnal modulations

h (t)


Complex symbols

Bits Mapping


transposition

→ ak and bk:: M-ary independent symbols {+/- 1, +/- 3, …, +/- ( M-1)}

square M-QAM (Quadrature Amplitude Modulation)

→

M-PSK (Phase Shift Keying)

68

Linear Carrier Frequency ModulationConstellation

ak

bk

0 1 3 5 7 …… -7 -5 -3 -1

1

3

5

7

...

-7

-5

-3

-1

...

ak

bk

Representation of possible dks in the (ak, bk) plane = modulation « constellation »

QAM Constellations

Power efficient

(DVB-C, DVB-T, xDSL)

PSK Constellations

Robust to non linearities

(DVB-S)

Hybrid modulations : APSK

(DVB-S2, DVB-S2X)

69

Linear Carrier Frequency ModulationExamples

→ Two-dimensionnal linear modulations : M-QAM

Independent and

Example : 4-QAM or QPSK (DVB-S)

I(t) Q(t)

x(t)

70


→ Two-dimensionnal linear modulations : M-QAM

Independent and

Example : 16-QAM (DVB-C)

x(t)

* *0111

*0110

0101

*0100

+1 +3

*0010

*0011

*0000

*0001

-3 -1*

1110

*1111

*

1101

*1100

-1

-3

+3

+1

*1010

*1011

*1000

*1001

ak

bk

I(t) Q(t)

71


→ Two-dimensionnal linear modulations : M-PSK

and are linked

Example : 8-PSK (DVB-S2)

x(t)

I(t) Q(t)

Zoom

72


→ Hybrid modulations : M-APSK (DVB-S2)

16-QAM

32-APSK (4-12-16 APSK)

M-APSK

16-APSK (4-12 APSK)

ak

* *0111

*0110

0101

*0100

+1 +3

*0010

*0011

*0000

*0001

-3 -1*

1110

*1111

*

1101

*1100

-1

-3

+3

+1

*1010

*1011

*1000

*1001

73


→ Hierarchical modulations : DVB-T and T2, DVB-H, DVB-S2

Example 1 : hierarchical 16-QAM (DVB-T or H)

Internalinterleaver

Mapping

I

Q

HP

BP

* *0111

*0110

0101

*0100

+2 +4

*0010

*0011

*0000

*0001

-4 -2

*

1110

*1111

*

1101

*1100

-4

-2

+4

+2

*1010

*1011

*1000

*1001

I

Q

Example 2 : hierarchical 8-PSK (DVB-S2)

74

h (t)

Symboles complexes

Bits Mapping

→ M-ASK :

→ M-QAM :

→ M-PSK :

75

Linear Carrier Frequency ModulationTransmitter


transposition

Complex envelop

associated to :

Linear Carrier Frequency ModulationReceiver

LPF

LPF

j

Bits Receiver filter

hr(t)Mapping-1


Decisions

Sampling

Downconversion

M-ASK :

M-QAM :

M-PSK :

j

76

Downconversion

jBits

h (t)

Symboles complexes

Bits Mapping

Baseband modulation

Transmission

channelhc(t)

n(t)

Receiver

filter

hr(t)Demapping Decisions

SamplingBand

Pass

filter

Fe > 2 Fmax

Fmax = 2fp +Be

Example of used bandwidth for satellite broadcasting:

L: 1.4-1.6 GHz, C: 4-6 GHz, Ku: 10.70-12.75 GHz, Ka: 20-30 GHz.

77

Low

pass

Low

pass

Linear Carrier Frequency ModulationEquivalent lowpass channel: construction


Frequency

transposition

(Bande Be)

Complex envelop

associated to :

Downconversion

jBits

h (t)

Symboles complexes

Bits Mapping

Baseband modulation

Receiver

filter


SamplingBand

Pass

filter

78

Low

pass

Low

pass



Frequency

transposition

Fmax = Be

Lower sampling frequencies

Equivalent lowpass

channel

(Bande Be)

Complex envelop

associated to :

ffp-fp

2

ffp-fp

1

(remark: the channel is assumed to be ideal in the figure)

→ Complex envelop associated to the bandpass channel:

79


Canal de

transmissionhc(t)

n(t)

Equivalent

low pass

channel

HBPF(f)

f

N0

f2

N02

Sn(f)

-fp fp

fp-fp

2N0

ffp-fp

→ Bandpass filtering:

→ Complex envelop associated to the filtered noise:

80


f

Equivalent

low pass channel

Equivalent

low pass channel

81


h (t)

Symboles complexes

Bits Mapping

Baseband modulationFrequency

transposition

Downconversion

jBits

Receiver

filter


SamplingBand

Pass

filter

Low

pass

Low

passBaseband Demodulation

(Bande Be)

Complex envelop

associated to :

h (t)Bits Mapping

Baseband SER computations can be re-used

Symboles complexes

82

Modulation Linéaire sur fréquence porteuseChaine passe-bas équivalente

Bits

Reciever

filter


Sampling

Matched

filtering

Fullfill Nyquist criterion on:

Equivalent

low pass channel

Baseband modulation


(Bande Be)

Complex envelop

associated to :

Linear Carrier Frequency ModulationPerformance (Hypothesis : Nyquist + Matched filtering)

hr(t)h (t)Bits MappingMapping-1

⬄ two independent M- -PAM transmission channels

But !! Es = physical parameter = average symbol energy at the receiver input (M symbols dk) !!

Bits

hr(t)h (t)Bits Mapping Mapping-1 Bits

→ M-ASK

→ Squared M-QAM

→ M-PSK

83

Linear Carrier Frequency ModulationBER comparison for M-QAM and M-PSK

BER0

Power efficiency for PSK

Same spectral efficiency

PSK

QAM

84

Example of physical layer on an AWGN channel:

Satellite Digital Video Broadcasting : DVB-S (1994) and DVB-S2 (2005)

85

Mux Adaptation

and energy

dispersal

Outer

codeInterleaver Mapper

Shaping

filter

Physical

Interface

Video Coder

Audio Coder

Data Coder

Source coding and multiplexing

ES PES

Program 1

Video Coder

Audio Coder

Data Coder

ES PES

Program N

…

PCRSTC 1

PCRSTC N

Program Information

Transport Stream

Reed Solomon

RS(204,188, t=8)

Forney Convolutionnal

InterleavingQPSK SRRCF

α = 0.35

MPEG-2 System

Transport stream

generation

Inner

code

Convolutional

Code (7,1/2)

To RF

Satellite

Channel

Physical layer

86

Satellite Digital Video Broadcasting : DVB-SCouche physique

Bit

rates

Digital TV transmission

must be « Quasi Error

Free » (QEF) TEB < 10-10

Mux Adaptation

and energy

dispersal

Video Coder

Audio Coder

Data Coder

Codage source et multiplexage

ES PES

Program 1

Video Coder

Audio Coder

Data Coder

ES PES

Program N

…

PCRSTC 1

PCRSTC N

Program Information

Train transport


Scrambling

Example on an image

PSD of the

unscramble signal :

PSD of the

scramble signal :

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.510

-10

10-8

10-6

10-4

10-2

100

102

104

Fréquences normalisées

DS

P

Partie positive de la DSP du signal émis

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.510

-12

10-10

10-8

10-6

10-4

10-2

100

102

Fréquences normalisées

DS

P

Partie positive de la DSP du signal émis

Mux Adaptation

and energy

dispersal

Outer

codeInterleaver

Video Coder

Audio Coder

Data Coder


ES PES

Program 1

Video Coder

Audio Coder

Data Coder

ES PES

Program N

…

PCRSTC 1

PCRSTC N

Program Information

Train transport

Reed Solomon

RS(204,188, t=8)


Interleaving

Inner

code

Convolutional

code

(7,1/2)

A digital TV transmission must

be « Quasi Error Free » (QEF) :

TEB < 10-10


Forward Error Correction (FEC)

-4 -3 -2 -1 0 1 210

-5

10-4

10-3

10-2

10-1

100

Eb/N0 (dB)

TE

B

TEB théorique non codé

TEB simulé non codé

TEB simulé, codage convolutifTEB simulé, codes concaténés sans entrelaceur

TEB simulé, codes concaténés avec entrelaceur

Mux Adaptation

and energy

dispersal

Outer

codeInterleaver Mapper

Shaping

filter

Physical

Interface

Video Coder

Audio Coder

Data Coder


ES PES

Program 1

Video Coder

Audio Coder

Data Coder

ES PES

Program N

…

PCRSTC 1

PCRSTC N

Program Information

Train transport

Reed Solomon

RS(204,188, t=8)


InterleavingQPSK SRRCF

α = 0.35

Inner

code

Convolutional

code

(7,1/2)

To RF

Satellite

Channel


Modulation

)(1fpour

pour

pour

N

+>

+≤≤−

−+

−<

=

α

ααα

π

α

f

fffFf

f

ff

fH NNN

N

N

0

)1()1(2

sin2

1

2

1

)1(1

)(

2/1

AWGN channel

with non linearities

Satellite Digital Video BroadcastingDVB-S evolution: DVB-S2

• LDPC codes

• New modulation formats: 8PSK, hierarchical 8-PSK,

16 and 32 APSK

• A lot of possible configurations :

• QPSK, ¼, 1/3, 2/5 ; QPSK, ½ , 3/5, 2/3, ¾, 4/5, 5/6,

8/9, 9/10

• 8PSK, 3/5, 2/3, ¾, 5/6, 8/9, 9/10

• 16APSK, 2/3, ¾, 4/5, 5/6, 8/9, 9/10

• 32APSK ¾, 4/5, 5/6, 8/9, 9/10

• SRRC shaping, α=0.35, 0.25, 0.2

• CCM (Constant coding and modulation), VCM

(Variable coding and modulation) or ACM

(Adaptative coding and modulation)

Hierarchical 8PSK 90

References

→ Introduction aux communications numériques, M. Joindot, A. Glavieux, Dunod

→ Eléments de communications numériques, J.C. Bic, D. Duponteil, J.C.Imbeaux, Dunod

→ Digital Communications, J. G. Proakis, Mac Graw Hill Book Cie

→ Telecommunications system engineering, Lindsay and Simon, Prentice Hall

→ Digital communication by satellite, J.J. Spilker, Prentice Hall

→ Digital Video Broadcasting (DVB): Framing structure, channel coding and modulation for 11/12

GHz satellite services, norme ETSI EN 300 421.

→ Digital Video Broadcasting (DVB): User guidelines for the second generation system for

broadcasting, interactive services, news gathering and other broadband satellite applications (DVB-

S2), norme ETSI EN 102 376.

91

Documents

cours transmissions numeriques nathalie thomas anglais