Post on 18-Apr-2022
transcript
Digital Modulations
Nathalie Thomas
IRIT/ENSEEIHTNathalie.Thomas@enseeiht.fr
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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
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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
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(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
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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
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Transmission channel modeling
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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)
Transmission channel modeling
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
Transmission channel modeling
Transmission channel modeling
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
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SNRdB = 10 log Puseful signal
Pnoise
Impact of an AWGN channel : noise effect
Transmission channel modeling
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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
Transmission channel modeling
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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.
Transmission channel modeling
hc(t)
n(t)
x(t) y(t)
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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
Transmission channel modeling
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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
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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
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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
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Transmitter
Digitization
Transmission channel
Analog signal
Corrupted analog signal
Receiver
Received Binary information: 0 1 0 1 0 1 1 1 1 1
Analog signal : sound, image …
Basic digital transmission channel
Binary information to transmit: 0 1 1 0 0 1 0 1 1 0
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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
Transmission channel
Analog signal
Corrupted analog signal
Receiver
Received Binary information: 0 1 1 0 0 1 0 1 1 0
BASIC
CHANNEL
Analog signal : sound, image …
Basic digital transmission channel
Binary information to transmit: 0 1 1 0 0 1 0 1 1 0
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Basic digital transmission channel
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t
V
- V
Example :
t
V
- V
SNR = 10 dB :
t
V
- V
SNR = 0 dB :
Analog signal:
Corrupted analog signal:
Transmitter
Digitization
Transmission channel
Analog signal
Corrupted analog signal
Receiver
Received binary information: 0 1 0 1 0 1 1 1 1 1
Binary information to transmit: 0 1 1 0 0 1 0 1 1 0
SNR
BER = 0.0784
BER = 2.38 10-6
Analo Signal : sound, image …
BER
BASIC
CHANNEL
Transmitter
Digitization
Transmission channel
Analog signal
Corrupted analog signal
Receiver
Received Binary information: 0 1 1 0 0 1 0 1 1 0
BASIC
CHANNEL
Analog signal : sound, image …
Basic digital transmission channel
Binary information to transmit: 0 1 1 0 0 1 0 1 1 0
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.
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Transmitter
Digitization
Transmission channel
Analog signal
Corrupted analog signal
Receiver
Received Binary information: 0 1 1 0 0 1 0 1 1 0
BASIC
CHANNEL
Analog signal : sound, image …
Basic digital transmission channel
Binary information to transmit: 0 1 1 0 0 1 0 1 1 0
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.
Price to pay: occupied bandwidth is larger for
digital transmissions.
But source coding will help on this point !
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Example : fixed phone digitizationBanalog = 3.1 kHz
Bdigital 64 kHz (Fe=8kHz, nb=8 bits) ~
Transmission channel
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
Received Binary information: 0 1 0 1 0 1 1 …
Basic digital transmission channel
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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
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Transmitter
Digitization
Transmission channel
Analog signal
Corrupted analog signal
Receiver
Received Binary information: 0 1 1 0 0 1 0 1 1 0
BASIC
CHANNEL
Analog signal : sound, image …
Basic digital transmission channel
Binary information to transmit: 0 1 1 0 0 1 0 1 1 0Transmission 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.
Of course there is a price to pay: occupied
bandwidth is larger for digital transmissions.
But source coding will help on this point !
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Transmitter
Digitization
Transmission channel
Analog signal
Corrupted analog signal
Receiver
Received Binary information: 0 1 1 0 0 1 0 1 1 0
BASIC
CHANNEL
Analog signal : sound, image …
Basic digital transmission channel
Binary information to transmit: 0 1 1 0 0 1 0 1 1 0Transmission 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.
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.
But source coding will help on this point !
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Transmission channel
Analog signal
BASIC
CHANNEL
Channel coding
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
Channel decoding
Physical layer
Received Binary information: 0 1 0 1 0 1 1 …
Basic digital transmission channel
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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
Transmission channel
Modulation
Demodulation
Analog signal
Corrupted 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
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Transmission channel
BASIC
CHANNEL
Channel coding
Source codingT
R
A
N
S
M
I
T
T
E
R
Physical layer
Modulation
Binary information to transmit: 0 1 1 0 0 1 0 …
Analog signal
Source decoding
R
E
C
E
I
V
E
R
Demodulation
Channel decoding
Physical layer
Received Binary information: 0 1 0 1 0 1 1 …
Basic digital transmission channel
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Analog signal
Disturbed 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
Transmission channel
0 0 0 1 1 1 1 1 1 0 0 0
SNR=0 dB
BER=2/4
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Transmission channel
Analog signal
WHOLE
BASIC
CHANNEL
Channel coding
Source codingT
R
A
N
S
M
I
T
T
E
R
Physical layer
Modulation
Binary information to transmit: 0 1 1 0 0 1 0 …
Corrupted analog signal
Source decoding
R
E
C
E
I
V
E
R
Demodulation
Channel decoding
Received Binary information: 0 1 0 1 0 1 1 …
Basic digital transmission channel
Synchronization
DAC
ADC
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!! Need for synchronization !!
1st
accesspoint
2nd
accesspoint
3rd
accesspoint
Baseband signal :Spectrum around frequency 0
0
ISM band
tV
-V
Binary information to transmit:
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
Transmission channel
Analog signal
Corrupted analog signal
Receiver
Received Binary information:
0 1 0 1 0 1 1 …
BASIC
CHANNEL
Performance criteria
Binary information to transmit:
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
BER = <1Number of erroneous bits
Number of transmitted bits
- Needed SNR at the receiver input => needed
transmitted power.
Two main transmission channel performance criteria
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Transmission channel
Analog signal
WHOLE
BASIC
CHANNEL
Channel coding
Source codingT
R
A
N
S
M
I
T
T
E
R
Physical layer
Modulation
Binary information to transmit: 0 1 1 0 0 1 0 …
Corrupted analog signal
Source decoding
R
E
C
E
I
V
E
R
Demodulation
Channel decoding
Physical layer
Received Binary information: 0 1 0 1 0 1 1 …
Basic digital transmission channel
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
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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
BER = <1Number of erroneous bits
Number of transmitted bits
- Needed SNR at the receiver input => needed
transmitted power.
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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
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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 ?
Baseband signal :Spectrum around frequency 0
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
Occupiedbandwidth B ?
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
M-ary SymbolsShaping filter
h(t)Mapping
Baseband Modulation
x(t)
Occupiedbandwidth B ?
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
Baseband Digital ModulationSome spectrum examples
→ Biphase or Manchester (Ethernet waveform : IEEE802.3)
x(t)
h(t)
TS
+1
-1t
2/TS4/TS …-4/TS -2/TS
f
-13dB
… 47
Baseband Digital ModulationSome spectrum examples
→ 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
M-ary SymbolsShaping filter
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
Baseband Digital DemodulationJoint optimization with the modulation
→ 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
Baseband Digital DemodulationJoint optimization with the modulation
→ 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
Baseband Digital DemodulationJoint optimization with the modulation
→ Example of Nyquist filter : raised cosine filter
53
Baseband Digital DemodulationJoint optimization with the modulation
→ Example of Nyquist filter : raised cosine filter
Some typical values: α=0.22 (UMTS), α=0.35 (DVB-S), α=0.15 (DVB-C) 54
Baseband Digital DemodulationJoint optimization with the modulation
→ Example of Nyquist filter : raised cosine filter
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
Baseband Digital DemodulationJoint optimization with the modulation
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
Baseband signal :Spectrum around frequency 0
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
Linear Carrier Frequency ModulationComplex envelop
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
Linear Carrier Frequency ModulationComplex envelop
h (t)
Complex envelop associated to x(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
Linear Carrier Frequency ModulationComplex envelop
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 envelop associated to x(t):
Complex symbols
Bits Mapping
Complex baseband modulationFrequency
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
Linear Carrier Frequency ModulationExamples
→ 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
Linear Carrier Frequency ModulationExamples
→ Two-dimensionnal linear modulations : M-PSK
and are linked
Example : 8-PSK (DVB-S2)
x(t)
I(t) Q(t)
Zoom
72
Linear Carrier Frequency ModulationExamples
→ 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
Linear Carrier Frequency ModulationExamples
→ 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
Complex baseband modulationFrequency
transposition
Complex envelop
associated to :
Linear Carrier Frequency ModulationReceiver
LPF
LPF
j
Bits Receiver filter
hr(t)Mapping-1
Baseband Demodulation
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
Baseband Demodulation
Frequency
transposition
(Bande Be)
Complex envelop
associated to :
Downconversion
jBits
h (t)
Symboles complexes
Bits Mapping
Baseband modulation
Receiver
filter
hr(t)Demapping Decisions
SamplingBand
Pass
filter
78
Low
pass
Low
pass
Linear Carrier Frequency ModulationEquivalent lowpass channel: construction
Baseband Demodulation
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
Linear Carrier Frequency ModulationEquivalent lowpass channel: construction
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
Linear Carrier Frequency ModulationEquivalent lowpass channel: construction
f
Equivalent
low pass channel
Equivalent
low pass channel
81
Linear Carrier Frequency ModulationEquivalent lowpass channel: construction
h (t)
Symboles complexes
Bits Mapping
Baseband modulationFrequency
transposition
Downconversion
jBits
Receiver
filter
hr(t)Demapping Decisions
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
hr(t)Demapping Decisions
Sampling
Matched
filtering
Fullfill Nyquist criterion on:
Equivalent
low pass channel
Baseband modulation
Baseband Demodulation
(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
Satellite Digital Video Broadcasting : DVB-SCouche physique
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
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
Reed Solomon
RS(204,188, t=8)
Forney Convolutionnal
Interleaving
Inner
code
Convolutional
code
(7,1/2)
A digital TV transmission must
be « Quasi Error Free » (QEF) :
TEB < 10-10
Satellite Digital Video Broadcasting : DVB-SCouche physique
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
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
Reed Solomon
RS(204,188, t=8)
Forney Convolutionnal
InterleavingQPSK SRRCF
α = 0.35
Inner
code
Convolutional
code
(7,1/2)
To RF
Satellite
Channel
Satellite Digital Video Broadcasting : DVB-SCouche physique
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