1

Gennum and the Gennum logo are trademarks of the Gennum Corporation.

PAM-8 and PAM-16 Optical Receivers for 2km 100G Links with a 4dB loss budget.

Presenter: Francois Tremblay

Contributor: Alan Tipper10th March 2012

2

Basics of PAM-M

• Modulate the Optical Tx with M level pulse Amplitude Modulation (PAM)

• 2 bits/symbol for PAM-4

• 3bits/symbol for PAM-8

• 4 bits/symbol for PAM-16

3

Rx Error Probability Calculation (1)

∫∞

2/),0(

1

ddvN

Mσ ∫

∞

2/),0(

1

ddvN

Mσ

Normalised PDF of PAM-8 Received Signal

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6 7 8

Normalised Input Current

No

rmali

sed

Pro

bab

ilit

y

Den

sit

y

∫∞

2/),0(

2

ddvN

MσFor levels 1 to M-2 the error probability is:

For levels 0 and M-1 the error probability is: ∫∞

2/),0(

1

ddvN

Mσ

)22

(1

),0(1

22/ σ

σd

erfcM

MdvN

M

M

d

−=

−∫

∞

Hence the total error probability is:

d

N(mean, standard deviation) is the standard Gaussian PDF

RMS noise = σσσσ

4

Rx Error Probability Calculation (2)

1

2

1

1

−+

−>=<

ME

Esd

)1

1

)1(2(

1

+

−

−

><−=

E

E

M

serfc

M

MPE

σ

Now we can express d in terms of the mean electrical signal and the optical extinction ratio as follows:

So we can relate the symbol error rate to the mean signal to RMS noise ratio as follows:

Where <s> is the mean signal, σ the rms noise and E the linear extinction ratio:

Assumptions: Data is gray coded to make BER equal to symbol error rate / (no bits per symbol)levels are equally spacedNoise is independent of signal

)1

1

)1(2(

)(log

1

2 +

−

−

><−=

E

E

M

serfc

MM

MBER

σ

5

Time Domain Numerical Model

• To investigate the effect of non linearity and other pulse distortions it is necessary to do a symbol by symbol numerical model. This has been implemented in a Matlab-Simulink like environment (Python/SciPy)

• A long data pattern is sampled at eye centre using a CDR triggered off the zero crossings of the PAM input signal. The M-1 slicing thresholds are distributed evenly between the measured Max and Min voltages of the data signal.

• The vector distances between each sample and the M-1 thresholds are calculated and then the probability of crossing the adjacent thresholds due to added Gaussian noise is computed. The error probability is then averaged over the pattern length

6

Numerical Model: Comparison of near Ideal Eye with Closed Form Expression for Error rate

SER Numerical Sim vs Ideal Theory

1E-12

1E-11

1E-10

1E-09

1E-08

1E-07

1E-06

1E-05

0.0001

0.001

0.01

0.1

1

0 10 20 30 40 50 60 70

SNR

SE

R Theory

Num Model

))1(2

(1

−

><−=

M

serfc

M

MPE

σ

Linear

5dB

7

Rx Dynamic Range Comparison For different PAM Schemes

Error rate vs OMA for various PAM Schemes

Based upon existing 25Gb/s TIAs

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

-30.00 -25.00 -20.00 -15.00 -10.00 -5.00 0.00 5.00

OMA dBm

Err

or

rate

PAM-8

PAM-4

PAM-16

PAM-2

Typical Rx overload

9dB range for PAM-8 + FEC

8dB Tx ER, -149dB/Hz RIN

PAM-16 has

insufficient

Dynamic rangeLimited by Tx RIN

& Detector overload

PAM-8 has

sufficient

Dynamic range for

4dB path loss

+ impairments

8

PAM-8 THD Penalty from Symmetrical Compression(Calculated at 10-5 BER sensitivity)

penalty dB

-1

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7

THD %

SN

R P

en

alt

y d

Bpenalty dB

1dB optical /2dB

Elec penalty

at 2.9% THD

2.7% THD

9

-1

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7

THD %

SN

R P

en

alt

y d

B

PAM-8

PAM-16

PAM-8 vs PAM-16 Simulated THD Penalty

1dB optical /2dB

Elec penalty

at 1.9% THD for

PAM-16, 2.9%

for PAM-8

OIF 5% THD Spec for100G Coherent RXUsing balanced linear TIAs

PAM-8 and PAM-16 Receivers will need strict linearity specificationsPAM-16s small dynamic range will be further eroded by linearity constraints

10

PAM-8 Slice Threshold Optimization for Improved THD Tolerance

(and numerous other impairments)

SNR Penalty vs THD for Optimised Decision Levels

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10

THD %

Ele

ctr

ical S

NR

Penalty d

B

uniform

optimized

Simulation using “Nelder – Mead Downhill Simplex” optimization of slice levels

For lowest SNR giving 10-5 BER. For details of the algorithm see

Nelder, J.A. and Mead, R. (1965), “A simplex method for function minimization”, The Computer Journal, 7, pp. 308-313

<1dB optical penaltyFor 5% THD possible withOptimized slice levels

As non linearity affects the outer eyes more than the inner ones we should be able

to compensate by adjusting the decision thresholds

<1dB optical penaltyFor 2.9% THD withuniform slice levels

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Simulated Optimized Decision Levels vs THD

Optimum Decision Levels vs THD

-1.14

-0.86

-0.57

-0.29

0.00

0.29

0.57

0.86

1.14

-1 0 1 2 3 4 5 6 7 8 9

THD %

Decis

ion

level/

peak d

ata

eye a

mp

litu

de

D0

D1

D2

D3

D4

D5

D6

+1.0

-1.0

8 Level Data Eye

7 Decision Thresholds

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Convergence of PAM-8 Threshold Optimization

BER Convergence

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

0 20 40 60 80 100

BER Update Sample

BE

R

BER

N-M simplex algorithm converging from an initial high BER and with 5% THD using raw BER feedback only

– this could be implemented In hardware/firmware.

13

PAM8 TX Rise Time Requirements

SNR Penalty vs TX rise time for 25GHz Rx BW

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14

Rise Time pSec 10:90

SN

R P

en

alt

y d

B

112Gb/s

103Gb/s

Need 8pSec rise/fall

For 112Gb/s operation

With PAM-8 for

0.5dB optical penalty

14

Rx Bandwidth Simulations112Gb/s Data

ISI Penalty for Different Rx Bandwidths

for 4pS & 8 pS Tx rise time (10:90)

-0.5

0

0.5

1

1.5

2

2.5

20 25 30 35 40 45 50

Rx 3dB Bandwidth GHz

Ele

ctr

ical

ISI

Pen

alt

y d

B

8pS Tr:Tf

4pS tr:tf

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Conclusions

• PAM-16 without FEC requires a high SNR that is incompatible with practical optical

receiver overload limits. With FEC the dynamic range is improved but not enough to budget for 4dB path loss and 3-4 dB of impairment margin.

• PAM-8 without FEC is similarly too restrictive on dynamic range but PAM-8 with FEC seems capable of working with a reasonable loss budget.

• PAM-8 would need to achieve <3% max THD for 1dB optical penalty and PAM-16

would need <2%. These represent challenging targets particularly given the need to operate at high peak-peak photocurrents to maintain adequate SNR.

• Adaptive threshold approaches need to be used to relieved distortion requirements to realistic 5% range.

• Operation at 112Gb/s with an 8pS rise time Tx requires Rx bandwidths of the 30-35GHz. Improvement over current 25G modulator rise times (12pS) will be necessary.

• Further work:- Model development to establish realistic budget numbers. This must include Tx

imperfections (nonlinearity, phase response) and the Rx CDR & demux plus any equalization.

- Dual PAM4 approaches

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Should we consider “dual PAM4”?

• PAM16- Simple implementation (no gearbox, simple clocking)

- Optical system does not support the approach

• PAM8- Optical system can support it but it is challenging (more power,

cost)

- Increased complexity, gearbox required, optical symbol rate is

higher than electrical bit rate (power, cost)

• “dual PAM4”- I&Q require coherent receiver

- Dual polarization requires good separation

- Dual laser may be a reasonable compromise

17

• Additional Material

18

Nonlinearity Shape used in Simulations

• The THD simulations were

done with a notional cubic nonlinearity to produce a

given THD i.e a transfer

function of the form:

3)( xxxy α−=

• Where α determines the harmonic distortion level. The THD can be calculated in a simple expression as THD=α/(4-3α) for a unit amplitude sinusoidal signal. Whilst this may be convenient for the mathematics a better description of a real hardware nonlinearity may be:

)tanh(1

)( xxy ββ

=

• In this case β determines the harmonic distortion. The THD level can be calculated numerically using a discrete fourier transform.

Cubic vs Tanh Nonlinearity

Both nonlinear transfer functions generate 3% THD

for a unit amplitude sinusoidal excitation

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5

Input

Ou

tpu

t cubic nonlin

tanh nonlin

ideal linear

Cubic Nonlinearity gives 2.3dB SNR penalty

Tanh nonlinearity gives 2.29dB SNR Penalty

The cubic nonlinearity is a good approximation to realistic hardware

nonlinearities and does not significantly affect the simulated SNR penalty