Optical Code Design for Multi-Wavelength-OOC Optical CDMA system Claire GOURSAUD Mikaël MORELLE

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Apr 21, 2023

Optical Code Design for Optical Code Design for Multi-Wavelength-OOC Multi-Wavelength-OOC Optical CDMA systemOptical CDMA system

Claire GOURSAUD

Mikaël MORELLEAnne JULIEN-VERGONJANNE

Christelle AUPETIT-BERTHELEMOTJean-Pierre CANCESJean-Michel DUMASPhilippe GUIGNARD

XLIM Dpt-C²S² UMR CNRS 6172ENSIL - University of LIMOGES

FRANCE

[email protected]

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Apr 21, 2023

MotivationsMotivations

Optical CDMA: Optical Code Division Multiple Access

Spread Spectrum technique

Inspired from radio communications (mobile phone …)

Multiple Access method: users one common resource

Allocation to each user a specific code

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– D=155Mbit/s up to 1 Gbit/s per user– Passive Optical Networks 30 users– BER (Bit Error Rate) < 10-9

Possible solution : O-CDMA

Alternative to TDMA and WDMA techniques

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O-CDMA

Coherent Incoherent

All optical system

Partially optical system

Unipolar codes (1D or 2D)

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For low cost : electronic devices

Data

DemuxCDMA

Decoding

Mux

Electrical part –Reception

Electrical part – Emission Optical part

(laser)

CDMAcoding

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electronic devices:electronic devices:

Limited bandwidth B Short code length F (for high data rate D)

Performances degraded due to


•MAI (Multiple Access Interference)•Beat noise•Thermal noise

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OutlineOutline

• 2D-OCDMA system– 2 Dimensional coding method– 2D DS-OCDMA

• Conventional Correlation Receiver (CCR)– Structure– Performance analysis

• Parallel Interference Cancellation receiver (PIC)– Structure– Performance analysis

• Design of 2D codes

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OutlineOutline





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2 Dimensional coding method2 Dimensional coding method

• MWOOC : Multi-Wavelength Optical Orthogonal Codes

• (L,F,W,λa,λc)– L : number of wavelengths– F : code length– W : code weight

– λa : auto correlation value

– λc : cross correlation value

Wavelength interference L

t

D F(L,F) low

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New Construction MWOOC (LxF,W,1,1)

- Any value of L : W L F- Any value of W

LLmin min = W : MWOOC (= W : MWOOC (LxF,W=L,1,1) )

High flexibility

11S-S.Lee and S-W.Seo, “New construction of Multiwavelength Optical Orthogonal Codes”, IEEE Trans. on comm., vol. 50, n°12, pp. 2003-2008, dec. 2002.

– 11MWOOC(LxF,W=λc+2,1, λc) : impose W=3

10G.C.Yang, W.C.Kwong, “Performance Comparison of Multiwavelength CDMA and WDMA + CDMA for Fiber-Optic Networks”, IEEE Trans. on comm., vol.45, n°11, pp. 1426-1434, nov. 1997.

– 10MWOOC (FxF,W,1,1) : impose L=F

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1D OOC code

Fmin max( W(W-1)+1, 30 – L)30 users

[a0, a1, …, aw-1] : an OOC(F, W=L, 1, 1) position vectorF : Prime Number

{ [ i, j*ai ] }{ [ i, a0 ], [ i, a1 ], …, [ i, aw-1 ] }With i [0, L-1], j [0, F-1]

Cardinality : NMWOOC = F + L

)1(

1WWFNooc

F Code matrices L Code matrices

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Example: MWOOC(5x23,5,1,1)

OOC(23,5,1,1): (0, 1, 3, 8, 14){ [ 0, j*0 ] ; [ 1, j*1 ] ; [ 2, j*3 ] ;[ 3, j*8 ] ; [ 4, j*14 ] } j [0, 22]{ [ i, 0] ; [ i, 1] ; [ i, 3] ;[ i, 8] ; [i, 14] } i [0, 4],

NMWOOC(5x23,5,1,1) = 28


j=3

i=211111 11111

t

t

1

1

1

1

1

1

1

1

1

1

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00...01

10...00

...............

00...10

01...00

...

1,

1,1

1,2

1,1

1,

FL

FL

F

F

FL

d

d

d

d

C

bi1(t){0,1}

NFLC ,

biN(t)

2 Dimensional Emission scheme2 Dimensional Emission scheme

74...31

31...06

...............

18...27

63...41

Electrical part Optical part

λL

Mul

tiW

avel

engt

h la

ser

rL,F(t)

r1,F(t)

WavelengthMUX

RL,F(t)λ1

DS-OCDMA : Direct Sequence OCDMA

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OutlineOutline





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Conventional Correlation Receiver Conventional Correlation Receiver (CCR)(CCR)

RL,F(t)Wavelength

DEMUX

Optical to Electrical Converter (OEC)

r1,F(t)

rL,F(t)O / E

O / E 74...31

tbi1ˆ

00...011, FLd

01...001,1 Fd

63...41

Tb

0

CCR #1

S

Tb

0

Errors occur only when = 0 tbi1

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iNiN

SiECCR LF

W

LF

W

i

NP

1221

21

2

1

2

1

Conventional Correlation Receiver Conventional Correlation Receiver (CCR)(CCR)

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OutlineOutline





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Parallel Interference CancellationParallel Interference Cancellation (PIC) Receiver (PIC) Receiver

)1(ˆib

CCR #1RL,F(t)

CCR # 2

CCR # i

CCR # N

-

+

2,FLC

)2(ˆib

)(ˆ kib

)(ˆ Nib

kFLC ,

NFLC ,

Errors occur only when = 1 tbi1

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Parallel Interference Cancellation Parallel Interference Cancellation (PIC) Receiver(PIC) Receiver

1

1

1

1

111

1

1

2

2122

1

1 )1()(2

1 N

SN

NN

SWN

NNNI

NI

NNN

NN

N

EPIC

T F

PPCCP

nNnN

Sn

nNI LF

W

LF

WC

F

WP

T

11

1

2

1

221..

C.Goursaud, et al., “Improvement of Parallel Interference Cancellation technique with hard limiter for DS-CDMA systems”, IEEE GLOBECOM 2005, St-Louis, MO, USA, 28 Nov – 2 Dec, 2005. Session Photonic Technologies PT06.

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OutlineOutline





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CCR: MWOOC(12x137,12,1,1)

PIC: MWOOC(6x43,6,1,1)

2D code design2D code design

B = F.D = 21 GHz

B = F.D = 6.5 GHz

D = 155 Mbit/s

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2D code design2D code design

SNR [15, 25] dB: Noise dominates

SNR [25, 30] dB: MAI dominates

SNR [30, 40] dB :

CCR(12x137,12) has better performancedue to the high weight

PIC(6x43,6) has better performancedue to the PIC efficiency to remove MAI

Performance in the noiseless case

BER = 10-9: CCR SNRmin= 30 dB

PIC SNRmin= 28 dB F

L = W

SNR

MWOOC + PIC:

AWGN noise perturbation

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ConclusionConclusion

New construction of Multi-Wavelength Optical Orthogonal Code

High flexibility

Short temporal code length

Minimal number of wavelength equal to the weight

Optimal Code Design

without noise

SNR require with

AWGN

Conventional Correlation Receiver MWOOC(12x137,12,1,1) 30 dB

Parallel Interference Cancellation receiver MWOOC(6x43,6,1,1) 28 dB

BER 10-9 N = 30 D 155 Mbit/s

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Thank you for your attentionThank you for your attention

Documents

Optical Code Design for Multi-Wavelength-OOC Optical CDMA system Claire GOURSAUD Mikaël MORELLE