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PAM-N Tutorial Material
802.3bj 100 Gb/s Backplane and Copper Cable Task Force
IEEE 802.3 Interim Session
Newport Beach, CA
24-25 January 2012
Chris Cole
Ilya Lyubomirsky
26-27 January 2012 2
Outline
■ Introduction
■ Objectives
■ PAM-N Ideal Channel Simulations
■ PAM-N Optimum Receiver Analysis
■ PAM-N Realizable Receiver Simulations
■ Summary
■ References
26-27 January 2012 3
Introduction
■ 25Gb/s modulation alternatives are being debated in 802.3bj
■ Higher order modulation will be required in future standards to support bandwidth and density growth
■ It is critical that there is a broad understanding of PAM-N (amplitude) and more generally QAM (amplitude and phase) modulation to enable informed debate about technology choices for present and future standards
26-27 January 2012 4
Objectives
■ Develop PAM-N modulation tutorial material
■ Solicit PAM-N modulation tutorial contributions
■ Develop PAM-N performance understanding from:
● Ideal channel models
● Fundamental theory
■ Compare PAM-2 (NRZ) & PAM-4 performance
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Matlab Model 1: Raised Cosine Channel
PAM
Symbols
Raised
Cosine Filter
Eye
Diagram
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PAM-N Eye Diagrams
40 ps
63.4 ps
80 ps
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PAM-N Horizontal Eye Opening
0
10
20
30
40
50
60
5 10 15 20 25
Ho
rizo
nta
l Eye
Op
enin
g (p
s)
Raised Cosine Filter Cutoff Frequency (GHz)
25 Gb/s NRZ
25 Gb/s PAM-4
25 Gb/s PAM-3
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Matlab Model 2: Exponential Loss Channel
PAM
Symbols
Cu Channel
Model
Eye
Diagram
3-Tap
DFE
Channel Model
0 5 10 15 20 25 30 35 40 45 50-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
Square
Am
plitu
de
Rect
Pulse
■ Ideal Linear Phase Channel
■ 20dB loss @12.5GHz
■ FFE equalizer not included to gain PAM-N performance understanding from DFE only equalizer output
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PAM-N Eye Diagrams after DFE
Addition of FFE equalizer will significantly increase the vertical eye opening
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PAM-N Eye Opening
(fNY = 12.5 GHz)
Horizontal and vertical eye openings defined as “inner eye opening”
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PAM-N Eye Diagram Observations
■ PAM-N has zero ISI at the ideal sampling point with a raised cosine channel response
■ For an ideal Nyquist channel, PAM-4 has twice the horizontal eye opening versus NRZ
■ In practice ideal sampling never happens; performance is limited by horizontal eye closure due to ISI
■ Horizontal eye closure rate with increasing channel loss is faster for PAM-4 than NRZ; ~15dB crossover w/ 3-Tap DFE
■ For an ideal Nyquist channel, PAM-4 has better immunity to interferers, like suck-outs and crosstalk, from FPAM-4_Nyquist
to FNRZ_Nyquist
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NRZ better PAM-4 better Equal
frequency
12.5 GHz
(~3mm stub)
6.25 GHz
(~6mm stub)
Interference
Immunity
26-27 January 2012
PAM
Symbols
Salz
SNRIdeal
DFEs(t)
P
h(t)
N0/2
w(t)
Model Assumptions:
1. Ideal DFE (infinite taps)
2. Matched filter W(t) using ideal FFE (infinite taps)
3. DFE decision errors ignored (i.e. SNR is high enough)
4. Noise is AWGN
5. Nyquist pulse shaping TX filter S(t)
6. Exponential loss channel modeled as H(f) = exp(- f)
Baud rate = 1/T
Salz Model
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Analytical solution for normalized Mean Square Error
(MSE) at output of DFE (Salz SNR bound):
= P*T/(N0/2) = TX SNR
Tde
T
eSNR0
1ln
Salz Model, cont.
PAM
Symbols
Salz
SNRIdeal
DFEs(t)
P
h(t)
N0/2
w(t)
Baud rate = 1/T
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26-27 January 2012
In the limit of high TX SNR, Taylor series expansion can be
used to obtain a remarkably simple formula for Salz SNR:
The effective SNR at DFE output is approximately the TX
SNR decreased by ½ the IL (channel insertion loss) in dB at
the Nyquist frequency.
fNY = 1 / 2T
)(2
1NYfdBdB ILSNR
Salz Model, cont.
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26-27 January 2012
Salz Model NRZ & PAM-4 Comparison
■ PAM-4 fNY = ½ NRZ fNY
■ PAM-4 IL = ½ NRZ IL
■ Theoretical NRZ SNR in dB at equal TX SNR:
NRZ SNR = ¼ PAM-4 SNR (4x PAM-4 advantage)
■ To achieve the same BER:
NRZ SNR = PAM-4 SNR - 7dB (7dB NRZ advantage)
■ Therefore PAM-4 is better than NRZ for:
IL > 28dB (i.e. NRZ is better for IL < 28dB)
15
)(2
1NYfdBdB ILSNR
26-27 January 2012
Salz Model NRZ & PAM-4 Comparison
16
10
12
14
16
18
20
22
24
26
18 20 22 24 26 28 30 32 34 36 38
SN
R (
dB
)
IL at NRZ Nyquist (dB)
NRZ
PAM4
7 dB crossover
at IL = 28 dB
= 30 dB
GFEC = FEC coding gain in dB
■ 2*GFEC for NRZ
■ 4*GFEC for PAM-4
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Matlab Model 3: FFE+DFE RX w/ 28dB IL
Use of T/2 FFE with
higher number of taps will
increase the horizontal
eye opening.
17
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Matlab Model 4: FFE+DFE RX w/ 30dB IL
Use of T/2 FFE with
higher number of taps will
increase the horizontal
eye opening.
18
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Matlab Model 5: FFE+DFE RX w/ 35dB IL
19
Use of T/2 FFE with
higher number of taps will
increase the horizontal
eye opening.
26-27 January 2012
Salz RX & FFE+DFE RX Comparison
20
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
20 25 30 35 40
BE
R
IL at NRZ Nyquist (dB)
NRZ Salz Bound
PAM-4 Salz Bound
NRZ Simulation
PAM-4 Simulation
= 26 dB
SalzPAM SNRerfcBER10
1
8
34
SalzNRZ SNRerfcBER2
1
2
1
(fNY = 12.5 GHz)
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Summary Results
■ Salz Model over an exponential loss channel shows better PAM-4 versus NRZ performance for:
■ IL12.5GHz > 28dB (i.e. NRZ is better for IL12.5GHz < 28dB)
■ IL12.5GHz > 32dB (for moderate FFE+DFE RX Model)
■ For IL ~ 30dB, small implementation differences can shift the crossover, explaining conflicting Task Force results
■ Salz Model does not include random jitter and timing errors
■ PAM-N differences in sensitivity to timing jitter and errors may substantially change the IL crossover value
The timing penalty will be quantified in future work
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26-27 January 2012
References
■ J. Salz, “Optimum Mean-Square Decision Feedback Equalization,” BSTJ, Vol. 52, No. 8, pp. 1341-1370, April 1973.
■ B.L. Kaspar, “Equalization of Multimode Optical Fiber Systems”, BSTJ, Vol. 61, No. 7, pp.1367-1388, Sept. 1982.
■ G. Thompson, “How 1000BASE-T Works”, P802.3ab 1000BASE-T Task Force, Nov. 1997, http://www.ieee802.org/3/ab/public/nov97/geoff1.pdf
■ C. Mick, et al., “A Tutorial Presentation”, P802.3ab 1000BASE-T Task Force, March 1998, http://www.ieee802.org/3/tutorial/march98/mick_170398.pdf
■ Abler, et al., “PAM-4 versus NRZ Signaling: Basic Theory”, P802.3 Backplane Ethernet Task Force, July 2004, http://www.ieee802.org/3/ap/public/jul04/abler_01_0704.pdf
■ D.G. Kam et al., “Multi-level Signaling in High Density, High Speed Electrical Links”, DesignCon 2008.
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References
■ D.G. Kam et al. "Is 25 Gb/s On-Board Signaling Viable?," IEEE Trans. Advanced Packaging, vol. 32, no 2, May 2009, pp. 328-344.
■ W. Bliss, “Sensitivity to Timing Error Jitter for NRZ and PAM-4”, P802.3bj Backplane and Copper Cable Task Force, Nov. 2011, http://www.ieee802.org/3/bj/public/nov11/bliss_01a_1111.pdf
■ Q. Gua, et al., “20-Gb/s Single-Feeder WDM-PON Using Partial-Response Maximum Likelihood Equalizer”, IEEE Photonics Technology Letters, Vol. 23, No. 23, Dec. 2011, pp. 1802-1804
■ References without url are available for download at:
site: ftp://ftp.finisar.com/
username: ieee
password: ieee8023
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