Research in PRML for High Speed Optical Communications

Romain Rousseau

Tutor: Zaki Ahmed

Master of Science (MSc)Communication Engineering and Signal Processing

Department of Communication and Electronic Engineering

University of Plymouth, Faculty of TechnologySeptember 2007

Research in PRML for High Speed Optical Communications

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2 Picture taken at Science Museum, London (UK)

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Extracted from: Introduction to Fibre Optics and Optical Networks (2007) Available http://www.engineeringlab.com/fiberoptics.html#demo

1. Backgrounda) ISIb) PRML technology

2. Projecta) Realisationb) Results

3. Conclusiona) Future works

Outline

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1.a) ISI from Fibre optics

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1.a) InterSymbol Interference

eEEzti ))((

0

eHHzti ))((

0

HE 00 and

f 2

)(

signal pulse of a bit

Respectively amplitude of electric and magnetic fieldsAngular frequency

Propagation constant

2.405 22

12

2

1

2

nnnkV

Normalised Frequency

Refractive Index Difference

n

nn

1

21

6


7

From a polarisation point of view :

Fast axis: Mode propagation along the x-axis has the smaller effective mode index

Slow axis: Mode propagation along the y-axis has the smaller effective mode index

x

y

Birefringence-Polarization Mode Dispersion effects

yxFB

BL

2

yxFB 2

Modal birefringence Beat length

Lz yx Phase birefringence :


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Total Dispersion or Chromatic Dispersion

velocity of the light becomes wavelength dependent v

cn )(


9


10

Fibre will have material dispersion if 02

2

dnd

Material dispersion

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2

dnd

cDm

n1 Is the core refractive index

Material Dispersion

kmpsnm //


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“A waveguide is a device such as coaxial cable or glass fibre, designed to confine and direct the propagation of electromagnetic waves. In optical fibers the confinement is achieved by having a region with a larger refractive index” Österberg Ulf L

Waveguide Dispersion

fibre will have waveguide dispersion if 02

2

dd

is constant propagation

waveguide dispersion

2

221

Vd

VbdVcnn

Dw

kmpsnm //


12

kmnmps

Vd

VbdVcnn

d

ndc

DDD wmT //in 2

221

2

2

kmnsinDL T /

)/(2.0

(max) sbitB

rms pulse broadening

data rate limitation

total dispersion parameter

Total Dispersion


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Line Coding

Line coding consists of modulating binary data in order to map symbols into specific waveform, before sending them to the receiver.

3 points that need to be opposed when you want to choose your line coding:

i. The coded spectrum goes to zero at the frequency approaches 0 (DC energy can not be transmitted)

ii. A clock can be recovered from the coded data stream (necessary for synchronous systems and detection)

iii. They can detect errors or even correct errors


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Different modulations for data sequence 010111001

Line Coding


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Non Return to Zero (NRZ) format also known as NRZ-OOK (On Off Keying). This modulation is composed of two “sub-modulation”

• Unipolar NRZ: values interpreted by the photodiode is +v for a logical ‘1’ and 0v for a logical ‘0’.• Polar NRZ: values interpreted by the photodiode is +v for a logical ‘1’ and –v for a logical ‘0’.

Line Coding

NRZ format needs all the bandwidth to transmit information Can not be used for synchronous systems because


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Return to Zero (RZ) format is composed of two “sub-modulation”

•Unipolar RZ: values interpreted by the photodiode for a logical ‘1’ is

+v for and 0v for next In the case of a logical ‘0’, current

delivered by photodiode is a 0v for a full period of

•Polar RZ: values interpreted by the photodiode for a logical ‘1’ is the

same than Unipolar RZ logical ‘1’. For a logical ‘0’, voltage is –v for a

period of and then 0v for next

Line Coding

2T b

2T b

2T b

2T b

T b

Both RZ format require 2 times bandwidth than a NRZ format.RZ format increases lifetime of laser. RZ Polar format enables to extract timing for synchronous-systems.


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Line Coding

Summary

1.b) PRML Technology

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PRML is a combination of a PR target (created with an equalizer) associated to a Maximum Likelihood Sequence Decoder (MLSD).


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In 1962 Adam Lender presents PR targets in his paper “The Duobinary Technique for High-Speed Data Transmission” [5]

It was first introduced in magnetic recording system by Kobayashi and Tang, two researchers of IBM, in 1970

Recently, many scientists have proved that duobinary signalling allows high bandwidth frequency and is a very efficient way to counter dispersion effects of fibre optics

PR targets require less power and complexity than other Multi level schemes.The aim of duobinary signalling is to accept and to transform ISI into a specific pattern. Then the receiver is built depending on this pattern and it makes use of the nature of the ISI instead of cancelling it.


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In 1966 Kretzmer shorted Partial response channels in different class specifying the “partial response polynomial” H(D), where D is a delay

For a minimum bandwidth system must have in H(D), but for k>>0 number of levels is increase so error performance is degraded

)1( D K

factor reduces low-frequency component in spectrum needed)1( D


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The characteristic polynomial of widely used channel is a composition of )1( D K)1( D

DDDDH 2111

This partial response is called Modified Duobinary or PR Class IV (PR4)

For channel models are usually referred to as “extended Class-4” models

and denoted by 41PREn

2k

22


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Basically an equalizer analyses channel distortions by receiving a specific impulse response. Differences between original pulse and received pulse by equaliser correspond to the channel deformations

By adjusting parameters {Cn} of equalizer we can correct attenuations

Preset Equalizer


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N

Nnnout ntChCtEq )( Ch(t) is channel’s pulse response

Preset Equalizer

Output of equalizer

0

1

2

1

0

22)2(

20

2

2)2(

220

1

1

01

TCh

TTNCh

TTCh

TTCh

TTNCh

TTCh

TTCh

CN

C

CC

C N

Example for a EPR4 target (sequence number 1,2,1) and =T


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Convolutional codes are codes with memory which means that the output depends on previous inputs.

The code rate of convolutional codes is a ratio between numbers of input symbols k over numbers of output symbols n. PR code rate considered as 1-rate.

The length of input block K is often called constraint length.

Maximum Likelihood Sequence Decoder

PR4 system is non-recursive convolutional code.

Recursive convolutional codes which have both feed forward and feedback nodes.Non-recursive convolutional codes which have only feed forward nodes


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Maximum Likelihood Sequence Decoder

Trellis Creation:


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Most famous MLSD: Viterbi Algorithm

Decoding Process:

1.Estimate the new path metric, by adding the path metric with the survivor path from state k-1 respectively for each states available on the trellis.2.For each path, select the survivor path with the best metric.3.Store the survivor path and metric for each vertex at time k, increment k and repeat the three steps above until end of data.4.Choose the minimum value from all possible vertexes and trace back from end to first state and output the bit information using the path matrix saved.


2.a) Investigations

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2.a) My Realisation

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Single mode fibre link

1st block: Attenuation generated with a 7th order elliptic Low Pass filter using a normalised cutoff frequency of 0.21. The ripple in the passband is 0.3 dB and 50dB for stopband.2nd block:Preset equalizer with EPR4 and E3PR4 targets.3rd block: AWGN noise. It gives details about strength of system especially the decoder part. 4th block: Detector which consists of a Soft Input Hard Output (SIHO) Viterbi Algorithm

2.a) My Realisation

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1st Block: Low Pass Filter

On the left, this is the pulse used to estimate the coefficient for equalizer On the right is a typical attenuation for single mode fibre

2.a) My Realisation

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0

0

2/1

1

2/1

0

0

222

22

2

2

1

0

1

2

1

TCh

TNCh

TNCh

TCh

CN

C

C

C

C

C

C N

2nd Block: Equalizer

EPR4

E3PR4

0

0

6/1

3/2

1

3/2

6/1

0

0

222

22

2

3

2

1

0

1

2

3

1

TCh

TNTCh

TNTCh

TCh

CN

C

C

C

C

C

C

C

C N

2.a) My Realisation

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2nd Block: Equalizer

2.a) My Realisation

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3rd Block: AWGN noise

AWGN noise is to observe the strength of our system especially the decoder part.

this noise can be assumed as a noise created by photodiode when converting optical impulse into electric voltage. We know that the best photodiode systems to convert data from optical to electric are avalanche photodiode, and they produce a significant noise

2.a) My Realisation

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4th Block: Viterbi Algorithm

EPR4

E3PR4

2.a) My Realisation

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EPR4

E3PR4

2.a) My Realisation

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E3PR4

2.b) Results

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2.b) Results

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Number of taps for equalizer

EPR4 = 11 taps E3PR4=17 taps

2.b) Results

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Number of taps for equalizer

EPR4 = 11 taps E3PR4=17 taps

2.b) Results

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Result of equalization

NRZ-OOK EPR4=11taps

E3PR4=17 taps

2.b) Results

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Strength of PR target

2.b) Results

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CPU time/delay created by Viterbi Algorithm

The processor used was an Intel Centrino Duo T2500@2 GHz

2.b) Results

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Global view

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2.b) Results

Issues

Ideal Coefficients {Cn}

3.a) Future works

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•MLSD is not optimised and deeper searches must be done .Bonek, et al. developed a method to simplify 16-state trellis to 8 states by considering a butterfly architecture. It reduces 47% wiring and has generalised the algorithm for n-states trellis. Farkas-Weiss and Kalet (1989) “Simulation of a Trellis Code with Duobinary Signaling” IEEE The Sixteenth Conference of Electrical & Electronics Engineers in Israel Pages:1 – 4

Ozarow and Calderbank have also proposed appropriate trellis to duobinary channel resulting in a rate ½ code. The code rate is also a part of MLSD that can be investigated for next projectsWeiss S.F. and Russell A. (????), “Simulation of a trellis code with Duobinary Signaling”, Tel-Aviv University

•PR targetGPRML provides 4.5dB gain compare to EPR4ML according to Sun’s paperSun D., Xotta A., and Abidi. A.A., (2005) “A 1 GHz CMOS Analog Front-End for a Generalized PRMLRead Channel.” IEEE Journal of Solid-State Circuits, vol. 40, no. 11, pp. 2275-2285.

•Code is essentialPR associated to serial turbo scheme (A turbo coding much interesting for data storage) and LDPC codes obtained 5dB gain compare to an uncoded PRML channel. (Song et.al.)Song H.,Liu J.,Kumar V. and Kurtas E. (2001) “Iterative soft decoded partial response channels for hybridmagneto-optical recording”, Magnetics, IEEE Transactions on, Volume 37, Issue 2 Page(s):676 – 681

Questions ???

Thanks you for your attention

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•Elijah Wu (2006), “Measuring Chromatic Dispersion of Single-Mode Optical Fibres using White Light Interferometry “, University of Auckland, MsC Thesis•Senior J. (1992), Optical Fiber Communication: Principles and Practice Prentice Hall; 2nd edition•Reeves, 2007, Optical Fibres, University of Plymouth Lecture•Lender A. (1963) “The Duobinary Technique for High-Speed Data Transmission” IEEE Transactions on Communication and Electronics, Vol. 82, pp. 214-218•Kobayashi H. and Tang D. (1970) "Application of Partial-Response Channel Coding to Magnetic Recording Systems", IBM Journal. of Res. & Dev., vol. 14, no. 4, p. 368•Bosco G. , Carena A., Curri V. and Poggiolini P. (2006) “Best Optical Filtering for Duobinary Transmission from Optical Communication Theory and Techniques“ Springer US •Lyubomirsky I. (2006) “Coherent detection for optical duobinary communication systems”, Photonics Technology Letters, IEEE, Vol 18, Issue 7 pp. 868 – 870•Kretzmer E. R. (1966) "Generalization of a Technique for Binary Data Communication,“ IEEE Transactions on Communication Technology, February 1966, pp. 67-68•Kabal, P. and Pasupathy S. (1975) "Partial-Response Signaling", IEEE Transactions On Communications, vol. Com-23, No. 9, pp. 921-934.

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2.b) Issues

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2.b) Issues

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2.b) Issues

conclusion

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Research in PRML for High Speed Optical Communications

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