www-g.eng.cam.ac.uk/photonic_commsPhotonic Communications Research
Extension of Statistical Multimode Fiber Channel Model to Electronic Dispersion
Compensation
J. D. Ingham, R. V. Penty and I. H. WhiteUniversity of Cambridge, Department of Engineering
Trumpington Street, Cambridge, CB2 1PZ, United [email protected]
www-g.eng.cam.ac.uk/photonic_commsPhotonic Communications Research
Talk outline
• Brief review of statistical MMF channel model
• Extension of model to EDC• Model verification for EDC
• Types of EDC studied
• Link yield as function of • EDC type• Fiber launch• Link length
• Conclusions
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Brief Review of Statistical MMF Model
see Cambridge channel modeling talk for detail
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Multimode Fiber Numerical Modeling Input:Fibre profileProfile / position of launch beam
Calculate fibre modeprofiles /group indices
Calculate overlap integrals,impulse resp.
Output:bandwidths, CPRDMD, loss
0 10 20 30 40 501.47
1.48
1.49
radial distance / µm
refra
ctiv
e in
dex
Unoptimumregion
Optimised profile
0 10 20 30
22
26
30
High-order fibre modes
Mode group
Del
ay ti
me
(ns/
km)
0
200
400
600
1000
0 5
Ban
dwid
th /
(MH
z.km
)
ExperimentTheoryOFL-experimentOFL-theory
• Laser Launch conditions determine Mode Power Distribution (MPD) amongst fiber modes
Dispersive low-order fibre modes
1.5 800
10 15 20 25Offset / µm
• Fibre bandwidth determined by propagation characteristics and the distribution of power amongst fiber modes
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Steps in the GbE statistical model
• Generate a set of representative fiber index profiles
• Calculate OFL frequency response and bandwidth
• Calculate impulse and frequency responses at beam offsets ranging across the entire fiber core radius
• Calculate DMD from assessment of the impulse responses at each offset
• Compare DMD to “worst-case” value, e.g. 5% of installed fibers have DMD > 2 ns/km for 62.5-µm MMF at 1300 nm
• Convert to set of “worst-case” fibers by scaling frequency responses according to ratio of DMD to “worst-case” DMD
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Statistical MMF Bandwidth Simulations
• 81 fiber profiles chosen
• DMD scaled to 2ns/km for each profile (worst case 5% population)
• Bandwidths calculated using mode profile and group indices
• Statistical scaling allows yield calculation
M. Webster, L. Raddatz, I. H. White, D. G. Cunningham, “A statistical analysis of conditioned launch for Gigabit Ethernet links using multimode fiber,” Journal of Lightwave Technology, vol. 17, no. 9, pp. 1532-1541, 1999
www-g.eng.cam.ac.uk/photonic_commsPhotonic Communications Research
Initial results for 10GbE EDC
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• At GbE, the statistical model is used to extract MMF bandwidths.
• In an unequalized link, there is a strong inverse correlation between ISI penalty and bandwidth
• With EDC, knowledge of the bandwidth is not sufficient - the entire MMF link frequency response determines link performance
• Use calculated frequency response to determine link response to PRBS
• Noise can also be incorporated into the BER calculation determine BERs and penalties
• Easy to add different EDCs in the Rx (time or frequency domain)
Considerations relating to the extension of model to EDC
-10
-8
-6
-4
-2
0
0 1 2 3 4 5 6frequency, GHz
rela
tive
resp
onse
/ dB
EDC uses power in passband
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Steps in the extended model
BER
MMF frequency responseextracted from GbE modeland scaled to desired linklength – includes chromaticdispersion
f
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0
2
4
6
8
10
12
14
16
18
x 10-4
time / ns
optic
al p
ower
/ W
0 0.010.020.030.040.050.060.070.080.09-0.50
0.51
1.5
time / ns
EDC Penalties
Laser output modeled byPRBS waveform which islow-pass filtered to ensureappropriate rise and fall times
PINTIA thermal noisemodeled in conjunctionwith low-pass filter.Other noise sources, e.g. RIN,accounted for at this point
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Inclusion of Noise into System Model• Important consideration due to the potential for noise
enhancement effects in some EDC architectures• Noise sources considered: receiver thermal noise & RIN
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
90
100850-nm 10-Gb/s MMF link without EDC
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
90
100
link length / m
perc
enta
ge o
f wor
st-c
ase
links
w
ith p
enal
ty b
elow
4 d
B
850-nm 10-Gb/s MMF link without EDC
No RINNo EDC
RIN of -130 dB / Hz
• Additional penalties due to RIN found to be in line with 10 GbE spreadsheet calculations
link length / m
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Types of EDC
Decision-feedback equalizer (DFE)Feedforward equalizer (FFE)For each of the two EDC types, we have considered:• Unconstrained-complexity equalization to determine upper bounds on performance • Constrained-complexity equalization to determine what may be realistically expected of an implementation.
• FFE is modeled by an N-tap transversal filter which tap coefficients according to the MMSE criterion. • DFE is modeled by an N-tap MMSE transversal filter followed by M bits of decision feedback
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FFE bound with next-generation MMF
0 100 200 300 400 500 6000
1
2
3
4
5
6
7
8
910
link length / m
optic
al IS
I pow
er p
enal
ty /
dB
Conventional Receiver
FFE
• 10 Gb/s at 850 nm over 50-µm 2000 MHz.km MMF• IBM (OFC 2003): 7-tap transversal filter reduced ISI penalty by 8.8 dB
from 11 dB to 2.2 dB over 600 m of next-generation fiber• Simulations agree with IBM results
P. Pepeljugoski et al. “Improved performance of 10 Gb/s multimode fiber optic links using equalization,” Proc. OFC 2003, vol. 2, pp. 472-474
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1300-nm 62.5 µm 500-MHz.km MMF – Model Parameter SetTransmitter Transmit pulse rise time 0.2 UI Laser center wavelength 1300 nm Laser RMS spectral width 0.1 nm Laser RIN -130 dB / Hz Fiber Launch Launch spot 7 µm FWHM Gaussian Offset launch conditions 20 µm +/- 3 µm Fiber Properties Fiber DMD for scaling process 2 ns/km Fiber chromatic dispersion 10 ps/(nm.km) Fiber length 30 m to 300 m Receiver Properties Photodetector responsivity 0.9 A/W TIA input-referred noise current 1.1 µA TIA bandwidth 7.5 GHz
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50 100 150 200 250 3000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
link length / m
optic
al IS
I pen
alty
/ dB
50 100 150 200 250 3000
1020304050
607080
90100
link length / mpe
rcen
tage
of w
orst
-cas
e lin
ks
with
ISI p
enal
ty b
elow
4 d
B Installed base yield / %
99
98
100
97
1300nm 10G Transmission Without EDC – Using 81 Fiber Model with 20 µm ± 3 µ m offset launch (ie 243 links)
• RH Graph shows pass% of “81 fibre” links with <4dB ISI penalty• Since these represent worst 5% of installed fibers, it is possible to extrapolate to installed fiber link failure for 4dB penalty• Installed fiber base yield (%) = (95+100-pass yield/20)• Valid for pass % > 50% (ie installed base yield >97.5%)
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IEEE 802.3z MBI field test: yields for FFE and DFE bounds
50 100 150 200 250 3000
10
20
30
40
50
60
70
80
90
100
link length / m
perc
enta
ge o
f lin
ks w
ith IS
I pe
nalty
bel
ow th
resh
old
Conventional Receiver
4dB
6dB
50 100 150 200 250 3000
10
20
30
40
50
60
70
80
90
100
perc
enta
ge o
f lin
ks w
ith IS
I pe
nalty
bel
ow th
resh
old
link length / m
4dB
6dB
DFE bound
50 100 150 200 250 3000
10
20
30
40
50
60
70
80
90
100
perc
enta
ge o
f lin
ks w
ith IS
I pe
nalty
bel
ow th
resh
old
link length / m
4dB
6dB
FFE bound
• ROFL (1.0dB)
• Calculated frequency responses scaled to lengths from 0 to 300 m
• Links failing the 500 MHz km specification are not included
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1300-nm 62.5-µm 500-MHz.km MMF - Unequalized & FFE bound
• Optical ISI power penalty vs. link length
Conventional Receiver
FFE bound
50 100 150 200 250 3000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
link length / m
optic
al IS
I pen
alty
/ dB
50 100 150 200 250 3000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
link length / m
optic
al IS
I pen
alty
/ dB
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81 fiber statistical model: yields for FFE and DFE bounds
50 100 150 200 250 3000
10
20
30
40
50
60
70
80
90
100
link length / m
perc
enta
ge o
f wor
st-c
ase
links
with
IS
I pen
alty
bel
ow 4
dB
CONVENTIONAL RECEIVER
FFE BOUND
Installed base yield / %
99
98
100
50 100 150 200 250 3000
10
20
30
40
50
60
70
80
90
100
DFE BOUND
CONVENTIONAL RECEIVER
perc
enta
ge o
f wor
st-c
ase
links
with
IS
I pen
alty
bel
ow 4
dB
link length / m
Installed base yield / %
99
98
100
• All launches offset launch and values quoted for 4dB power penalty
• Note simulations do not take error propagation in DFE into account
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50 100 150 200 250 3000
10
20
30
40
50
60
70
80
90
100FFE BOUND
9-TAP FFE
CONVENTIONAL RECEIVER
perc
enta
ge o
f wor
st-c
ase
links
with
IS
I pen
alty
bel
ow 4
dB
link length / m
50 100 150 200 250 3000
10
20
30
40
50
60
70
80
90
100
DFE BOUND
(5,3)-TAP DFE
perc
enta
ge o
f wor
st-c
ase
links
with
IS
I pen
alty
bel
ow 4
dB
link length / m
CONVENTIONAL RECEIVER
Installed base yield / %
99
98
100
Installed base yield / %
99
98
100
81 fiber statistical model: yields for constrained FFE and DFE for 4dB penalty
• Constraining EDC implementation results in reduced achievable link length
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DFE BOUND
Yields for constrained FFE and DFE for 6dB penalty
50 100 150 200 250 3000
10
20
30
40
50
60
70
80
90
100
link length / m
CONVENTIONAL RECEIVER
(5,3)-TAP DFE
perc
enta
ge o
f wor
st-c
ase
links
w
ith IS
I pen
alty
bel
ow 6
dB Installed base yield / %
100
99
98
50 100 150 200 250 3000
10
20
30
40
50
60
70
80
90
100
link length / m
CONVENTIONAL RECEIVER
FFE BOUND100
99
98
perc
enta
ge o
f wor
st-c
ase
links
w
ith IS
I pen
alty
bel
ow 6
dB Installed base yield / %
9-TAP FFE
• Allowing ISI penalty to rise to 6dB allows greater link lengths
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EDC Results Summary
Yield at 300 m for 4dB ISI penalty (installed base yield)
Yield at 300 m for 6dB ISI penalty (installed base yield)
ROFL 1.0 dB MBI fibers
Unequalized 10 % 16 % FFE bound 55 % 74 % DFE bound 77 % 100 %
Offset Launch 81 fiber statistical
Unequalized 9% (-) 26% (-) FFE bound 62% (98.1%) 86% (99.3%)
N=9 tap FFE 52% (97.6%) 74% (98.7%) DFE bound 87% (99.3%) 100% (100%)
(N,M) = (5,3) tap DFE 62% (98.1%) 87% (99.4%)
• Note: MBI fibre link yield not representative of installed based yield
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Modelling Caveats
• 2 ns/km DMD for 5% worst-case is now dated – should we revisit?
• Model does not include error propagation in EDC
• Known to be a problem, particularly in DFE
• Model does not take into account any noise statistic modification in the EDC chip
• May give rise to additional penalties
• Precise implementation of EDC will cause variations in the link yields predicted
• Should look upon the yield figures calculated to date as an upper bound
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Conclusions• GbE statistical “worst-case” model reviewed and extended to
10G EDC, including noise effects• DMD scaling technique appears reasonable • General agreement with published experiments
• Extended model allows different EDC approaches to be easily investigated
• FFE and DFE implementations appear valid
• Preliminary indication of benefit of EDC for over 62.5-µm MMF at 1300 nm is achievable link length increase by a factor ~ 2 for 99% link yield
• Precise EDC yield curves will be implementation specific
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Future work• Work with the Ethernet standards body to develop a
statistical fiber model for EDC-enabled 10GbE links
• Once the model is agreed, provide a set of corner-case impulse responses for input into simulations to enable estimation of theoretical performance of different classes of EDC
• Help out in the development of a “worst-case” spreadsheet based on 10GbE spreadsheet and power-budget model for EDC-enabled links
Acknowledgment• Cambridge would like to acknowledge the advice / input of
Phyworks Ltd
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References
• M. Webster, L. Raddatz, I. H. White, D. G. Cunningham, “A statistical analysis of conditioned launch for Gigabit Ethernet links using multimode fiber,” Journal of Lightwave Technology, vol. 17, no. 9, pp. 1532-1541, 1999.
• D. G. Cunningham, W. G. Lane, Gigabit Ethernet Networking. Indianapolis, IN: Macmillan Technical Publishing, 1999.
• P. Pepeljugoski, J. Schaub, J. Tierno, J. Kash, S. Gowda, B. Wilson, H. Wu, A. Hajimiri, “Improved performance of 10 Gb/s multimode fiber optic links using equalization,” Proc. OFC 2003, vol. 2, pp. 472-474.
• E. A. Lee, D. G. Messerschmitt, Digital Communication, second edition. Norwell, MA: Kluwer Academic Publishers, 1994.
• S. Quershi, “Adaptive equalization,” IEEE Communications Magazine, March 1982, pp. 9-16.
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