Embed Size (px)
Citation preview
Presented by: Karim Kasan, Haïfa Farès, Christian Glattli and Yves Louët
11.06.2019, Rennes
1
From Quantum Physics to Digital Communication:Single Sideband Frequency Shift Keying
SSB-FSK using Leviton pulses
▪ 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 ?
3
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
4
LEVITONS FROM QUANTUM PHYSICS
5
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
Simple
6
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
7
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
8
LEVITONS FROM QUANTUM PHYSICS
Or: )( tV
)()(2
tVh
etI =
𝐼(𝑡)𝑑𝑡 =𝑛𝑒
𝑒𝑉(𝑡)𝑑𝑡 =𝑛ℎ
Lorentzian pulses
provide clean injection
EF
hole
)(~f
el.
9
LEVITONS FROM QUANTUM PHYSICS
EF
)(~f
el.
hole Electron energy spectrum becomes SSBEnergy Domain
10
SSB-FSK MODULATION USING LEVITONS
- 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
12
LORENTZIAN PULSE IN TIME
Large Lorentzians (w) causes more ISI
13
FREQUENCY DOMAIN
Losing SSB property for rational modulation index
Antipodal coding is not allowed
14
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
15
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
16
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
17
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 ++)
▪ Using and SSB-FSK signals, the orthogonality property becomes
for
18
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
19
SSB-FSK RECEIVERS
20
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
21
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.
22
PAM DECOMPOSITION
SSB-FSK
L 12 6 4
NMSE *(10^-2) 1.53 0.41 0.1
h1
h2
h0
h3
23
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.
24
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
25
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
26
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
27
PERFOMANCE FOR MOULATION INDEX <1
Lower Occupied BW, SSB property not affected
28
CONCLUSIONS & PERSPECTIVES
29
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
30
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
31
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.
32
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
