From Quantum Physics to Digital Communication: Single

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

THANK YOU

Karim kasanContact : karim.kasan@centralesupelec.fr

Haïfa FarèsContact : haifa.fares@centralesupelec.fr