from quantum physics to digital communication: single
TRANSCRIPT
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Presented by: Karim Kasan, Haïfa Farès, Christian Glattli and Yves Louët
11.06.2019, Rennes
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From Quantum Physics to Digital Communication:Single Sideband Frequency Shift Keying
SSB-FSK using Leviton pulses
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▪ Basically, Single side-band (SSB) signals are obtained by post-modulationtreatment:
2
INTRODUCTION
fc
A half side-band suppression
fc
fc
or
Double side-band signal
Single side-band signals
▪ Pass-band filtering▪ Hilbert transform▪ …
Is it possible to directly generate SSB signals ?
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OUTLINES
1. Levitons from quantum physics
2. SSB-FSK modulation using Levitons
▪ Single Sideband property
▪ Orthogonality property
3. SSB-FSK receivers
▪ Full Viterbi receiver
▪ Low-complexity Viterbi receiver
4.Conclusions & Perspectives
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LEVITONS FROM QUANTUM PHYSICS
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LEVITONS FROM QUANTUM PHYSICS
D. Christian Glattli, SPEC, CEA-Saclay Leonid Levitov, MIT, Boston
J. Dubois et al, Nature 502, 659 (2013)
T. Jullien et al., Nature 514, 603 (2014)
ERC Advanced Grant MeQuaNo 2008-2014ERC Proof of Concept C-Levitonics 2015-2017
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Simple
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LEVITONS FROM QUANTUM PHYSICS
IDEA: resolve the current to an individual charge (single electron source)
)( tV
)()(2
tVh
etI =
Or:
𝐼(𝑡)𝑑𝑡 =𝑛𝑒
𝑒𝑉(𝑡)𝑑𝑡 =𝑛ℎ
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LEVITONS FROM QUANTUM PHYSICS
Or: )( tV
)()(2
tVh
etI =
𝐼(𝑡)𝑑𝑡 =𝑛𝑒
𝑒𝑉(𝑡)𝑑𝑡 =𝑛ℎ
𝑁𝑒 +𝑁ℎ > 𝑛!
2 1 1
Unwanted excitations
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LEVITONS FROM QUANTUM PHYSICS
Or: )( tV
)()(2
tVh
etI =
𝐼(𝑡)𝑑𝑡 =𝑛𝑒
𝑒𝑉(𝑡)𝑑𝑡 =𝑛ℎ
Lorentzian pulses
provide clean injection
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EF
hole
)(~f
el.
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LEVITONS FROM QUANTUM PHYSICS
EF
)(~f
el.
hole Electron energy spectrum becomes SSBEnergy Domain
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SSB-FSK MODULATION USING LEVITONS
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- 9 -
LEVITON FOR DIGITAL COMMUNICATION
( )
==
+
==
t
bb
b
LTtLTdg
LTtwt
w
dt
dtg
0
0
22
0
,2)(
,0,2
)(
Lorentzian pulse
Correcting factor
=
+
=
−
w
LTdt
wt
w b
LT
LT
b
b
2arctan
2
2
22/
2/
22
bk
cos( )
s(t)
sin( )
*
Lorentzian pulse
SSB-FSK modulator
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LORENTZIAN PULSE IN TIME
Large Lorentzians (w) causes more ISI
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FREQUENCY DOMAIN
Losing SSB property for rational modulation index
Antipodal coding is not allowed
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SINGULARITIES OF THE MODULATED SIGNAL
GMSK SSB-FSK
• Antipodal coding • No antipodal coding
➔To get one side of the spectrum
• Modulation index h = 0.5• Modulation index is integer• Phase increment is
• Limited complexity for optimal detector
• Long phase response then
high complexity for optimal
detector
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SINGLE SIDEBAND PROPERTY
b
cT
f10
=
1=h
=L
2=
20dB
The power exponentialdecay is
proportional to the Lorentzian width w
Tradeoff for w value
bTw 37.0=
Spikes
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SINGLE SIDEBAND PROPERTY
b
cT
f10
=
1=h
=L
bTw 37.0=
( ) 295.0=
Suppression of spectral lines
Slight loss in the other half-band
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LORENTZIAN TRUNCATION IMPACT
L SSB-PSK GMSK (BT = 0.25)
L = BW = 1
BW = 0.86 L = 12 BW = 1.0801
L = 4 BW = 1.2637
L = 2 BW = 1.5332
BW = Spectral occupancy in terms of 1/Tb
(99 % of the transmitted signal power for w/Tb = 0.37)
We need to truncate as little as possible (L --)
Long Lorentzians causes more ISI (L ++)
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▪ Using and SSB-FSK signals, the orthogonality property becomes
for
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ORTHOGONALITY PROPERTY
( )
( )h
hthj
hjwt
jwt
jwt
etu ~
1~
)(~
~
2
1
2
1)(
0
−
+=
−=
−
▪ Let define the set of the orthonormal wave-functions, using the non-truncated Levitonic pulse
▪ The set of for all integer verifies the orthogonal property )(~ tuh h
~
'~
,~
'~~ )()(
2
1hhhh
dttutu
=+
−
'~
,~
0
'~
*~ )()(
2
1hhhh
dtdt
dtsts
=
+
−
)(~ tsh
)('
~ tsh
kbhh =~
)(0 t
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SSB-FSK RECEIVERS
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FULL VITERBI RECEIVER (NON CODED CASE)
▪ The Viterbi algorithm performsMaximum likelihood detection (optimal detection)
▪ It finds a path through the trellis with the largest metric (maximum correlation)
▪ Viterbi Receiver complexity: SN = 2^(L-1) (state number)
o L = 4 ➔ Bw = 1.25/Tb and SN = 8 (Figure)
o L = 5 ➔ Bw = 1.19/Tb and SN = 16
o L = 12 ➔ Bw = 1.06/Tb BUT SN = 2048
▪ Need a low-complexity sub-optimal receiver
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PAM DECOMPOSITION
Pseudo-Symbols:
𝛼1,𝑛 = 𝑗𝑎~
𝑛
𝛼2,𝑛 = −𝑎~
𝑛𝑎~
𝑛−1
𝛼2,𝑛 = −𝑎~
𝑛𝑎~
𝑛−2
▪ Rewriting the SSB-CPM signal:
▪ PAM decomposition of ൯𝑠1(𝑡, 𝑎~
𝑠𝑏 𝑡, 𝑎 = 𝑒𝑗ℎ 𝑘=−∞
+∞)𝑎𝑘𝜑(𝑡−𝑘𝑇
= 𝑒ቇ𝑗2𝜋ℎ
𝑘=−∞
+∞𝑎𝑘~𝜑0~(𝑡−𝑘𝑇
ቁ𝑠1(𝑡,𝑎~
𝑒ቇ𝑗2𝜋ℎ
𝑘=−∞
+∞𝜑0~(𝑡−𝑘𝑇
)𝑠2(𝑡
൯𝑠1(𝑡, 𝑎~
≈
𝑛
𝐽𝑛ℎ0(𝑡 − 𝑛𝑇) + 𝐽𝑛𝛼1,𝑛ℎ1(𝑡 − 𝑛𝑇)
൧+𝐽𝑛𝛼2,𝑛ℎ2(𝑡 − 𝑛𝑇) + 𝐽𝑛𝛼3,𝑛ℎ3(𝑡 − 𝑛𝑇)
Information dependent signal Deterministic signal
[1] X. Huang et al., « The PAM Decomposition of CPM Signals with Integer Modulation Index »,
IEEE Trans. Comm., vol 51, no 4, 2003.
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PAM DECOMPOSITION
SSB-FSK
L 12 6 4
NMSE *(10^-2) 1.53 0.41 0.1
h1
h2
h0
h3
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LOW-COMPLEXITY VITERBI RECEIVER
1- Extracting the noisy information-dependent component of the SSB-FSK signal
2- Matched Filtering
3- Computing Branch metrics 𝜆𝑎𝑛−2𝑎𝑛−1𝑎𝑛 for the simplified Viterbi receiver
4- Computing cumulative branch metric
5- Trace Back process
𝑟1(𝑡) =𝑟(𝑡)
𝑠2(𝑡)
𝑦𝑘(𝑛) = න𝑛𝑇
(𝑛+𝐿𝑘)𝑇
𝑟1(𝑡 − 𝑛𝑇)ℎ𝑘(𝑡)𝑑𝑡 , 𝑘 = 0,1,2,3.
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BER PERFOMANCE BENCHMARK
L SSB-PSK hGMSK (BT =
0.25)
L = 12 BW = 1.0801 1BW = 0.86
L = 4 BW = 1.2637 1
1dB
High Occupied bandwidth
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PERFOMANCE FOR MOULATION INDEX <1
h 0.8 0.85 0.9 0.95 0.98 1
𝑑_min 𝐿 = 4 2.83 2.93 2.99 3.020 3.022 1.50
𝑑_min 𝐿 = 6 2.77 2.88 2.96 3.022 3.04 1.67
𝑑_min 𝐿 = 8 2.73 2.85 2.94 3.01 3.03 1.77
𝑑_min 𝐿 = 10 2.70 2.83 2.93 2.99 3.01 1.854
L h = 1 (Occupied BW)
h = 0.98 (Occupied BW)
h = 0.9 (Occupied BW)
100 1.0003 1.0013 1.017
12 1.06 1.034 1.015
10 1.085 1.054 1.016
8 1.12 1.083 1.017
6 1.15 1.125 1.02
4 1.25 1.2 1.07
Minimum distance
Occupied BW
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PERFOMANCE FOR MOULATION INDEX <1
L SSB-PSK HGMSK (BT =
0.25)
L = 12 BW = 1.0801 1BW = 0.86
L = 6 BW = 1.02 0.9BETTER BER
Lower Occupied BW
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PERFOMANCE FOR MOULATION INDEX <1
Lower Occupied BW, SSB property not affected
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CONCLUSIONS & PERSPECTIVES
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CONCLUSIONS
- New waveform was defined with the particularity of generating directly a SSBsignal
- We explained the beginnings of this idea which are derived from quantumphysics.
- Identification of tuning parameters and study of their impact on performance interms of :
• Spectral occupancy• ISI
- Tradeoff between spectral occupancy and demodulation efficiency (ISI handling)can be concluded
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PERSPECTIVES
Study in details the effect of Modulation index, pulse length and pulse width on the symbol error performance, occupied bandwidth, and % off SSB loss
BER AND BW
- MAP detection (maximum a posteriori)
Detection and channel coding
- Laurent Decomposition for modulation index < 1- Rimoldi Decomposition
PAM decomposition for h<1
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PERSPECTIVES
Frequency offset, carrier phase and symbol timing joint estimation of SSB-CPM :- Based on Ehsan Hosseini and Erik Perrins Method (almost Finished)- Taking advantage of PAM decomposition (Not ready yet)
Synchronization
Reduced-Complexity Joint Frequency Timing and phase
Recovery for PAM Based CPM Receivers
Colavolpe, Raheli - 1997 - Reduced-complexity detection and phase synchronization of CPM signals
Timing Recovery Based on the PAM Representation of CPM
A. N. D’Andrea, A. Ginesi, and U. Mengali, “Frequency detectors for
CPM sig- nals
[1] Hosseini, E. and Perrins, E. (2013). The Cramer-Rao Bound for Training Sequence Design for Burst-Mode CPM.IEEE Transactions on Communications.
[2] G. Colavolpe, R Raheli. Reduced-complexity detection and phase synchronization of CPM signals - IEEE Journals & Magazine.
[3] E.Perrins, S.Bose, P. Wylie-Green. Timing recovery based on the PAM representation of CPM - IEEE Conference Publication.
[4] A.N. D’Andrea, A. Ginesi, U. Mengali. Frequency detectors for CPM signals - IEEE Journals & Magazine.
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PERSPECTIVES
References[1] H. Farès et al., "From Quantum Physics to Digital Communication: Single Side
Band Continuous Phase Modulation ", Comptes rendus à l'Académie de
Sciences des physiques (Elsevier), Feb. 2018.
[2] H. Farès et al., "Power Spectrum density of Single Side band CPM using
Lorentzian frequency pulses ", IEEE Wireless Comm, Letters, Dec. 2017
[3] H. Farès et al., "New Binary Single Side Band Modulation ", IEEE International
Conference on Telecom. (ICT), May 2017
[4] H. Farès et al., "Nouvelle modulation de phase a bande laterale unique ", Les
Journées Scientifiques (JS) de l’URSI, Feb. 2017
Real transmission conditions
USRP based SCEE Testbed
ALGORITHMS
APPLICATIONSIMPLEMENTATION
&VALIDATION