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Appendix
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Objectives
To be able to understand the modulation concepts.
To be able in an example to calculate the unavailability objective
due to the equipment failures. To be able to understand the general concepts of the
M.21xx series and the differences between G.821/826and M.21xx recommendations.
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Table of Contents
Switch to notes view! Page
1 Refresh on modulation concepts 7Modulation Concepts 8
BB Transmission 10Bandwidth Formula 11Modulated Signal Spectrum 122-PSK 174-PSK 2016-QAM 2216-TCM 27Performances Versus Noise 30Exercise 31Main Modulation Types Characteristics 32Thermal Noise (C/N versus BER) 33Comparison of Different Mod. Schemes 37Roll-off calculation example 39Blank Page 40
2 Equipment unavailability 41Introduction 43Unavailability objective 44Unavailability of a non-protected section (1+0) 47Unavailability of a protected section (1+1) 50
3 M.21xx-series Recommendations 51End of Module 54
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Table of Contents [cont.]
Switch to notes view!
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1 Refresh on modulation concepts
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1 Refresh on modulation concepts
Modulation Concepts
Why modulation?
Modulation is necessary to occupy RF narrow bandwidth!
Without modulation (BB transmission) the occupied bandwidth is:
where: f b = bit rate
= roll-off factor
( )12
fBw b +=
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1 Refresh on modulation concepts
BB Transmission [cont.]
Ideal Transmission Channel
Att. = constant
Rx
Att.
f
f0
0
Tx
-
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1 Refresh on modulation concepts
BB Transmission
Real Transmission Channel
Att. = Kost.Att.
f0
Tx Att. =
fc
Rx
32fc
t
2fc
1
Att. = Kost.Att.
f0
Att. =
fc t
1T =
2 13
T TT T
2 13
1fb
T =
fb = Bit rate frequency
1=
1fb
2
2fc
2fc
2fc 2=
fbfc
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1 Refresh on modulation concepts
Bandwidth Formula
= 1.0
= 1.0
= 0.3
= 0.1
0 < < 1
R(f)
-fC
0.1
r(t)
C
-2fC
0.3
+fC +2fC
a
Antisymmetrical Freq. Responce
ac
Roll Off = =
R(f)
Ideal Freq. Responce
-T-2T-3T-4T 0 +T +2T +3T +4T
Bw = Bw = f b
Bw = (1+ )
fb
2
fb
2
-fc +fc
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1 Refresh on modulation concepts
Modulated Signal Spectrum
V
f
MOD
70 MHz
LO
IF
f0
Bw = 2fc
fc 70+fc
f0
7070-fc
B
2fc
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1 Refresh on modulation concepts
2-PSK [cont.]
2 PSK Modulator
2 PSK Demodulator
DIFF.
DEC.
100111
Data
L.O.
IF
IF signal
BTF
1 0
B A
DIFF.
ENC.
100111
Data
L.O.
IF
IF signal
PostConversion
Filter
2 PSKMixer
BTF
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1 Refresh on modulation concepts
2-PSK [cont.]
2-PSK Waveforms - Modulator
DATA IN
1 1 0 1 0 1 1 0 0
CARRIER
IF OUTPUT
+V
-V
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1 Refresh on modulation concepts
2-PSK [cont.]
2-PSK Waveforms - Demodulator
DATA OUT
1 1 0 1 0 1 1 0 0
CARRIER
IF INPUT
DEMODULATED SIGNAL
-V
+V
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1 Refresh on modulation concepts
2-PSK [cont.]
Absolute Coding Differential Coding
0 = B 0 = No change in the phase of the carrier
1 = A 1 = 180 change in the phase of the carrier
BA1 0
A A
1
B
0
A
1
B
1
B
0
A
1
Switch
A A B B A B B A
0 1 0 1 1 0 1
B A B B A B B A
1 1 0 1 1 0 1
RX
ON
TX B
0
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1 Refresh on modulation concepts
2-PSK
BTF Binary Transversal Filter (digital filter)
IN
H(f)
T5
IN
XA10
T5
XA5
T5
XA2
T5
XA5
A10
X
OUT
A
A/10
A/5T/5
A/2T/5
A/5T/5
A/10T/5
fN-fN-2fN
=1
0.4
0
fN(1+ ) 2f N
OUT
H(t)
1W
-1
2W-
12W
+1W
+
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1 Refresh on modulation concepts
4-PSK [cont.]
4-PSK Modulator1 0
DIFFER.
ENCODER
IF
PostConvertion
Filter
2 PSKMixer
BTF
L.O.
90
L.O.
90
BTF
0010111
2 PSKMixer
SP
L.O.
RFBranching
Filter
Bw=fb (1+ ) Bw= f s (1+ )
fs
0
1
2 PSK f s = fb
4 PSK f s =fb2
22
8 PSK =3
23
16 PSK =4
24
B (10) A (00)
C(11) D (01)
fsfb
fsfb
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1 Refresh on modulation concepts
4-PSK [cont.]
Differential Coding
B B
00
B
B
D
B
C
C
D
B
D
Switch
D
11 10 01 11 01 01
ON
= No change
01 = -90 changeTX C
A
A (00)
10 01 11 01 0100
RX B B B C BC10 = +90 change
11 = -180 change
001001110101.........
D (01)
B (10)
C (11)
- +
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1 Refresh on modulation concepts
4-PSK
4-PSK Demodulator
2 PSKMixer
BTF
L.O.
90
L.O.
90
BTF
2 PSK
Mixer
P
S
IF DIFFER.
DECODER
Y1
X1
Y1
X1DecisionCircuit
DecisionCircuit
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1 Refresh on modulation concepts
16-QAM [cont.]
16-QAM Modulator
11
10
01
00
0100 1110
Vy
Vx
Y1
X1
Y2
X2
Y
X
1 1 +3V
1 0 +1V
0 1 -1V
0 0 -3V
BTF
L.O.
90
L.O.
90
BTF
S
P
IFDIFFER.
ENCODER
X2 X2
2RX1 X1
Y2
Y1
X2
X1
Y2
Y1
FEC
X2
X1
Y2
Y1
2R
Y2
2R
Y2
Y1 Y1
2R
X2
X1
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1 Refresh on modulation concepts
16-QAM
16-QAM Demodulator
BTF
L.O.
90
L.O.
90
BTF
P
S
IF DIFFER.
DECODER
X2X2
DecisionCircuit
DecisionCircuit
X2
X1X1X1
Y2Y2Y2
Y1Y1Y1
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1 Refresh on modulation concepts
16-TCM [cont.]
16-TCM Modulator
BTF
L.O.
90
L.O.
90
BTF
S
P
IF
DIFFER.
CONVOL.
X2 X2
2RX1 X1
Y2
Y1
X2
X1
Y2
Y1
MAPPING
X2
X1
Y2
Y1
2R
Y2
2R
Y2
Y1 Y1
2R
X2
X1
+
ENCODER
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1 Refresh on modulation concepts
16-TCM [cont.]
16-TCM Demodulator
BTF
L.O.
90
L.O.
90
BTF
P
S
IF
DIFFER.DECODER
X2X2
DecisionCircuit
DecisionCircuit
X2
X1X1X1
Y2Y2Y2
Y1Y1Y1
VITERBIDECODER
+
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1 Refresh on modulation concepts
16-TCM [cont.]
TCM Principles - State Diagram (Example with 8-TCM)
SP
ab
S0S1
c
CONVOLUTIONAL ENCODER
S0 S1
0 0
b c0 / 0
S0 S1
0 1S0 S1
1 1
b c0 / 1
S0 S1
1 0
b c1 / 0
b c1 / 1
b c1 / 0
b c0 / 0
b c0 / 1
b c1 / 1
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1 Refresh on modulation concepts
16-TCM [cont.]
TCM Principles - Mapping (Example with 8-TCM)
1
0
7
65
4
3
2
a
0 1 2 3 4 5 6
0 0 0 0 1 1 1
b 0 0 1 1 0 0 1
0 1 0 1 0 1 0c
7
1
1
1
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1 Refresh on modulation concepts
16-TCM
TCM Principles - Trellis Diagram (Example with 8-TCM)
04
0
4
0
4
0b=0
T0 T1 T2 T3
3
7
b=1
b=0
1
5
2
6
5
1
b=1
37
2
6
62
04
1
5
37
0
0 1
1 0
1 1
S0 S1
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1 Refresh on modulation concepts
Performances Versus Noise [cont.]
2-PSK
C
A
= Carrier
N = Noise B
Threshold
1 1
CN
C+N
Errors depend of the distance between two points.
We have "ERROR" if N > C N > 1
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1 Refresh on modulation concepts
Performances Versus Noise [cont.]
4-PSK
2 PSK and 4 PSK have the same performance versus noise, but for this reason is never used2 PSK due to its double bandwidth
B A
C D
1
1
Two DifferentThreshold
2
2= 0.7
2
If the Noise (N) is:
you have error
N > 0.7
ModulationType
2 PSK
4 PSK
ErrorCondition
N > 1
N > 0.7
Bandwidth
BW
BW
2(-3dB)
SymbolFreq. (fs)
fb
fb
2
Noise Power (N) = Amplitde x Bandwidth
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1 Refresh on modulation concepts
Performances Versus Noise
DEMODULATOR
IF data
DETECTOR
ERROR
10-6
S
N= 13.5 dB
10-6
4 PSK
S
N= 18.6 dB
10-6
8PSK
SN = 20.5 dB10-6
16 QAM
SN = 26.5 dB10-6
64 QAM
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1 Refresh on modulation concepts
Main Modulation Types Characteristics
4 PSK
0
8 PSK
0
16 QAM
2.5
64 QAM
3.7
Modulation type
Position of Vectorial modulationstates (levels) at equal peakpower (Cmax)
Peak-to-Mean power ratio (dB)
R/2 R/3 R/4 R/6Nyquist Bandwidth (Bny)Symbol frequency (S)(R = Binary information capacity)
2 3 4 6Modulation efficiency (bit/sec/Hz)
(Theoretical)
S/N (dB)(Theoretical at BER = 10-6)
13.5 18.6 20.5 26.5
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1 Refresh on modulation concepts
Thermal Noise (C/N versus BER)
1 1 0 (normalized)2 PSK
v C/N (20log v/)Mod.
1 0.70 +3.1 dB4 PSK
1 0.38 +8.4 dB8 PSK
1 0. 19 +14.2 dB16 PSK
0.7 0.23 +9.7 dB16 QAM
0.6 0.10 +15.6 dB64 QAM
0.6 0.047 +22.1 dB256 QAM
16 QAM
Phase level
decisionthreshold
I
v
Q
v
Q8 PSK
I
= noise voltage
v = carrier peak voltage
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1 Refresh on modulation concepts
Comparison of Different Mod. Schemes [cont.]
Bit/s
(Hz)6
4
2
10 15 20 25 W (dB)
2 2
4
8
4
8
16
16
BER = 10-6QAM
FSK
64
32
16 QAM 16 PSK
PSK
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1 Refresh on modulation concepts
Comparison of Different Mod. Schemes [cont.]
10-10
5 W(dB)
10-9
10 15 20 25
10-8
10-7
10-6
10-5
10-4
10-3
10-2
16QAM16PSK
2PSK4PSK
8PSK32PSK
64QAM
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1 Refresh on modulation concepts
Comparison of Different Mod. Schemes [cont.]
Comparison of different modulation schemes
(Theoretical WandS/N values at 10-6 BER; calculated values may have slightly different assumptions)
a) Basic modulation scheme
(1) As an example, error
correction with redundancy (r)
of 6.7% is used for calculation
in this Table.
System Variants W
(dB)
S/N
(dB)
Nyquist
Bandwidth (bn)
FSK 2-state FSK with discriminator detection 13.4 13.4 B
3-state FSK (duo-binary) 15.9 15.9 B
4-state FSK 20.1 23.1 B/2
PSK 2-state PSK with coherent detection 10.5 10.5 B
4-state PSK with coherent detection 10.5 13.5 B/2
8-state PSK with coherent detection 14.0 18.8 B/3
16-state PSK with coherent detection 18.4 24.4 B/4
QAM 16-QAM with coherent detection 17.0 20.5 B/4
32-QAM with coherent detection 18.9 23.5 B/5
64-QAM with coherent detection 22.5 26.5 B/6
128-QAM with coherent detection 24.3 29.5 B/7
256-QAM with coherent detection 27.8 32.6 B/8
512-QAM with coherent detection 28.9 35.5 B/9
Basic modulation schemes with FEC
QAM 16-QAM with coherent detection 13.9 17.6 B/4*(1+r)
with 32-QAM with coherent detection 15.6 20.6 B/5*(1+r)
block 64-QAM with coherent detection 19.4 23.8 B/6*(1+r)
codes(1)
128-QAM with coherent detection 21.1 26.7 B/7*(1+r)
256-QAM with coherent detection 24.7 29.8 B/8*(1+r)
512-QAM with coherent detection 25.8 23.4 B/9*(1+r)
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Comparison of Different Mod. Schemes
B) Coded modulation scheme
System Variants W
(dB)
S/N
(dB)
Nyquist
Bandwidth (bn)(1)
BCM(2)
16 BCM - 8D (QAM. One step partition) 15.3 18.5 B/3.75
80 BCM - 8D (QAM. One step partition) 23.5 28.4 B/6
88 BCM - 6D (QAM. One step partition) 23.8 28.8 B/6
96 BCM - 4D (QAM. One step partition) 24.4 29.0 B/6
128 BCM - 8D (QAM. One step partition) 23.6 28.2 B/6
TCM(3)
16 TCM - 2D 12.1 14.3 B/3
32 TCM - 2D 13.9 17.6 B/4
64 TCM - 4D 18.3 21.9 B/5.5
128 TCM - 2D 19.0 23.6 B/6
128 TCM - 4D 20.0 24.9 B/6.5
512 TCM - 2D 23.8 29.8 B/8
512 TCM - 4D 24.8 31.1 B/8.5
MLCM(4)
32-MLCM - 2D (QAM) 14.1 18.3 B/4.5
64-MLCM - 2D (QAM) 18.1 21.7 B/5.5
128-MLCM - 2D (QAM) 19.6 24.5 B/6.5
(1) The bit rate B does not include code redundancy.(2) The block code length is half the number of the BCM signal dimensions.(3) The performances depend upon the implemented decoding algorithm.
In this example, an optimum number is used.(4) In this example, convolutional code is used for lower 2 levels and block codes are used for the third level to
give overall redundancies as those of 4D-TCM. Specially redundancies on the two convolutional codedlevels are 3/2, 8/7 and 24/23 on the block coded third level.
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1 Refresh on modulation concepts
Roll-off calculation example [cont.]
Example 1Available bandwidth = 40 MHzTransmitted stream = 34 Mbit/s
Modulation type = 2 PSK Roll-off = ?
BW = fb (1+K)40 = 34 (1+ K)a = 40/34-1 = 0.05
RELATIONSHIP BETWEEN fb and fs AS FUNCTION OF THE MODULATION TYPE
2 PSK fs = fb fb = 34 Mbit/s fs = 34 MHz4 PSK fs = fb/2 fb = 34 Mbit/s fs = 17 MHz
8 PSK fs = fb/3 fb = 34 Mbit/s fs = 11.3 MHz16 QAM fs = fb/4 fb = 34 Mbit/s fs = 8.5 MHz
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1 Refresh on modulation concepts
Roll-off calculation example
Example 2Available bandwidth = 20 MHzTransmitted stream = 140 Mbit/s
Modulation type = ?
BW = fb/nn = fb/BW = 140/20 = 7
27 = 128 128 QAM with K = 028 = 256 256 QAM with K = 1
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2 Equipment unavailability
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2 Equipment unavailability
Introduction [cont.]
Unavailability = Part of the time in which the link is out of order.
Where:
MTTR = Mean Time To Repair
MTBF = Mean Time Between Failures
MTBMTTR
MTTR
U+
=
Equipment unavailability
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2 Equipment unavailability
Introduction
By supposing:
Failures statistically independent
MTTR
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2 Equipment unavailability
Unavailability objective
EQUIPMENT UNAVAILABILITY OBJECTIVE
for HRDP (L = 2500 km) is supposed to be 1/3 of the total unavailability:
Ueq. < 0.1% = 0.001
The HRDP consists of 9 switching sections (section length = 280 km approx.)
For one-direction of the link only:
Ueq.s1 < 55.10-6
4eq.
eq.s 101.19
UU
=
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2 Equipment unavailability
Unavailability of a non-protected section (1+0) [cont.]
Suppose that a radio section consists of:
1 Tx Terminal
1 Rx Terminal
5 Repeaters (egual each other)
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2 Equipment unavailability
Unavailability of a non-protected section (1+0) [cont.]
1+0 radio section: 6 hops, 5 repeater stations
Mod. Tx
PSU
Z'
Rx Dem
PSU
Mod Tx Rx Dem
PSU
Z
L = 50 km L = 50 km
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2 Equipment unavailability
Unavailability of a non-protected section (1+0)
UTx Term. = UTerm. Mod + UTx + UPSU
URep. = URx + URep. Dem + URep. Mod + UTx + UPSU
URx Term. = URx + UTerm. Dem + UPSU
Unavailability of the non-protected section (uni-directional) (points Z-Z):
US(1+0) = UTx Term + 5 URep. + URx Term
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2 Equipment unavailability
Unavailability of a protected section (1+1) [cont.]
TS = Tx part of the switching system, the failure of which causes the totalunavailability of the section.
RS = Rx part of the switching system, the failure of which causes the totalunavailability of the section.
Lp = Part of the switching system, the failure of which doesnt allow the regularoperation of the switching system.
MTBFs = Global MTBF of the switching system series part.
MTBFp = Global MTBF of the switching system parallel part.
US
US
R'
TS
R
RS
Lp
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2 Equipment unavailability
Unavailability of a protected section (1+1) [cont.]
1+1 radio section: 6 hops, 5 repeater stations
Mod. Tx
PSU
Z'
Rx Dem
PSU
Mod Tx Rx Dem
PSU
Z
L = 50 km L = 50 km
Mod. Tx
PSU
Z'
Rx Dem
PSU
Mod Tx Rx Dem
PSU
Z
R' R
LOGIC
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2 Equipment unavailability
Unavailability of a protected section (1+1)
Global unavailability of the 1+1 protected section:
The section is unavailable due to:
failures of the 2 channels
failure of the series part of the switching system
failure of a channel and of the parallel part of the switchingsystem
( ) ( ) ( ) ( )0.5$UU$UUU 01sparser2 01s11s ++= +++
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3 M.21xx-series Recommendations
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3 M.21xx-series Recommendations
General concepts [cont.]
Differences between Recommendations G.821/G.826 and the M.21xx series start with theirdifferent origins:
G-series Recommendations are from ITU-T Study Group 13 (General networkissues);
M-series are from Study Group 4 (Network Maintenance and TMN).
Main differences:
G.821/G.826 define long-term performance objectives to be met.
G.821/G.826 requirevery long test intervals (one month).
The M-series Recommendations are particularly useful when bringing-into-servicenew transmission equipment. They are intended to assure that the requirements ofthe G series are met in every case.
As a general rule, the requirements of the M-series are tougher than those of theG-series.
For practical reasons, the M.21xx-series Recommendations allow short testintervals.
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3 M.21xx-series Recommendations
General concepts [cont.]
Media independent (ITU-T)
M.2100 for PDH paths sections and transmission systems
M.2110 how to apply M.2100 and M.2101 for BIS (Bring-Into-Service)
M.2120 how to apply M.2100 and M.2101 for maintenance
M.2101 for SDH paths and multiplex section
Radio specific (ITU-R)
F.1330 for parts of international PDH and SDH paths and sections.
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