PAM-N Tutorial Material · 2012. 1. 26. · 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

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

[email protected]

[email protected]

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”

26-27 January 2012

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

11

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

12

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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

13

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.

14

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

26-27 January 2012

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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Use of T/2 FFE with



eye opening.

18

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19

Use of T/2 FFE with



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)

26-27 January 2012

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

21

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.

22

http://www.ieee802.org/3/ab/public/nov97/geoff1.pdf

http://www.ieee802.org/3/tutorial/march98/mick_170398.pdf

http://www.ieee802.org/3/ap/public/jul04/abler_01_0704.pdf

26-27 January 2012

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

23

http://www.ieee802.org/3/bj/public/nov11/bliss_01a_1111.pdf

ftp://ftp.finisar.com/

Documents

PAM-N Tutorial Material · 2012. 1. 26. · 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