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OFC 2008 JThA60

MLSE Channel Estimation Parametric or Non-Parametric? MLSE Channel Estimation MLSE Channel Estimation Parametric or Non Parametric or Non-

• Parametric?

Parametric?

Optical Fiber Communication Conference 2008

Parametric versus Non-Parametric Branch Metrics for Parametric versus Non-Parametric Branch Metrics for MLSE–based Receivers w ith ADC and Clock Recovery MLSE–based Receivers w ith ADC and Clock Recovery

Stefan Langenbach (1), Gabriella Bosco (2), Pierluigi Poggiolini (2), Theo Kupfer (1) 1) CoreOptics, Nordostpark 12-14, D-90411 Nürnberg, Germany – {stefan,theo}@coreoptics.com 2) Politecnico di Torino, Corso Duca Abruzzi 24, Torino, Italy – {gabriella.bosco,pierluigi.poggiolini}@polito.it

Part of this work was sponsored by the EU Integrated Project NOBEL II, WP5

OFC 2008 JThA60 2

Non-Parametric: Canonical Histogram Method – HM Non Non-

• Parametric

Parametric: : Canonical Histogram Method Canonical Histogram Method – – HM HM

Non Non-

• Parametric

Parametric MLSE ADC

2

x a y ⋅ =

OFE (AGC)

r d x

Non-parametric Method Determine detected bit pattern d Associate observed quantized amplitude r Count observed amplitudes r for pattern d into a histogram N(d, r) Metrics for given d and r is ~ log N(d, r)

• 1

1 2 3 4 5 6 7 8 A m p litu d e d istrib u tio n a n d A DC th re sh o ld s 1 2 3 4 5 6 7 A m p litu d e Histo g ra m s fo r 3 -b it A DC E ye a n d A DC th re sh o ld s

Pros Simple – just counting events Robust – insensitive to model mismatch Cons Data collection time ~ ADC resolution Number of counters ~ ADC resolution Possibly more sensitive to error propagation? (decision errors translate into metrics errors) Canonical metrics Metrics for given r is the logarithm of the observed relative frequency value.

000 = d 111 = d

r y t

Histogram based channel model No parameters are estimated. But a full amplitude histogram needs to be „measured“ for each bit pattern.

r

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y z =

Parametric: Square Root Method – SQRT Parametric Parametric: Square : Square Root Method Root Method – – SQRT SQRT

Parametric Method Take square-root z of signal y Determine detected bit pattern d Determine mean z-amplitude m(d) for pattern d Metrics for given d and z is ~ ( z - m(d) ) ²

MLSE

√

Parametric Parametric ADC

2

x a y ⋅ =

OFE (AGC)

r d

z: signal independent noise The sqrt‘ed electrical signal has roughly Gaussian noise and roughly signal independent noise. Euclidean metrics Metrics for given z is then the Euclidean distance from the mean sqrt‘ed signal. Pros Simple – just one parameter per PDF Fast – mean value can be estimated quickly Robust – decision errors do not corrupt PDF shape Cons Model mismatch penalties are possible DC coupling

x

y: signal dependent noise The electrical signal has more noise on ones than on zeros.

y

y

Note: The square root operation can also be applied implicitly by a non-uniform ADC,

• r explicitly after the uniform ADC, the latter

with minor performance degradation

y z t y z t

Mean based channel model Only the mean value for each bit pattern needs to be estimated when signal independent noise is postulated (i.e. when the red PDFs are used)

OFC 2008 JThA60 4

Some problems are specific for a parametric approach. All can lead to „wrong metrics“. In short:

Model Mismatch

Possible Problems of Parametric Estimation Possible Possible Problems of Problems of Parametric Estimation Parametric Estimation

Method-Independent Problems

ISI Overload Channel Memory exceeds State Memory Quantization Amplitude differences become invisible

1500 ps/nm 0.6UI NRZ

Neglected Effects → wrong PDF shape or parameters E.g. imperfect clock (here: sinusoidal jitter)

„ „Wrong Wrong“ “ Metrics Metrics? ?

Using PDF values → wrong PMF value Computing PDF is easy, but PMF is hard.

Note: Noise PDF for coarse state is a mixture density (i.e. a convex combination of several PDFs)

Unrealistic Noise Model → wrong PDF shape When noise model does not sufficiently accurately model the „true“ noise PDF, metrics errors are introduced.

• 12

• 12

• 12

• 5

Note: Jitter impact on PDF depends on slope and is therefore pattern-dependent:

• Strong impact on edges.
• Little impact on rails

ISI Overload → wrong PDF shape and parameters Using a model density instead of the mixture density. Quantization → wrong PDF parameters Mean quantized ≠ true mean

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1 2 3 4 5 6 7 8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Gaussian Histograms

Channel Estimation Methods for MLSE Metrics Channel Estimation Methods for Channel Estimation Methods for MLSE MLSE Metrics Metrics

Any performance difference Any performance difference? ? Parametric Parametric Non Non-

• parametric

parametric

metrics histograms estimate parameters compute PDF compute PMF channel observations

1 2 3 4 5 6 7 8 9 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Gaussian PDFs

μ σ

OFE AGC ADC MLSE Channel Observer Metrics Computer

τ

CR Channel Estimator

MLSE needs metrics. Metrics are computed from the channel model Channel estimator uses the channel observations to estimate a channel model Channel observer associates delayed inputs (quantized waveform samples) and outputs (bit sequences, patterns) Sampling clock jitter impacts performance Quantizer resolution impacts performance Number of states in Trellis impacts performance

There are two approaches of channel estimation There are two approaches of channel estimation

Estimate parameters (e.g. μ, σ) of Probability Density Function (PDF) to compute log-likelihood metrics Estimate probabilities, i.e. values of Probablity Mass Function (PMF)

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Abstract and Problem Statement Abstract and Problem Statement Abstract and Problem Statement

MLSE needs branch metrics Branch metrics are log-likelihoods Two approaches to estimate likelihoods from observations: Non-Parametric Likelihoods are estimated directly (from observed relative frequencies) Parametric Likelihoods are estimated indirectly (parameters of a probabilistic model are estimated from observations)

We compare the performance of MLSE-based receivers with parametric and non- parametric channel estimation methods and characterize their sensitivity against quantization, sampling jitter, and intersymbol interference (ISI) overload (1) We compare the performance of MLSE-based receivers with parametric and non- parametric channel estimation methods and characterize their sensitivity against quantization, sampling jitter, and intersymbol interference (ISI) overload (1) Do parametric models suffer from effects not covered in the model?

Are there relevant “model mismatch” penalties ?

Do parametric models suffer from effects not covered in the model?

Are there relevant “model mismatch” penalties ?

Histogram Method “HM” a practice-proven canonical method of non-parametric channel estimation SQRT method “SQRT” a particularly efficient example of a parametric method

Problem Statement Problem Statement Abstract Abstract Simulation Approach Simulation Approach

(1) ISI Overload: The physical channel memory exceeds the state memory of the MLSE

Compare ultimately and practically achievable performance of HM and of SQRT. Compare ultimately and practically achievable performance of HM and of SQRT.

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Results and Conclusions Results Results and and Conclusions Conclusions

We compared ultimately and practically achievable performance We assumed that SQRT suffers more from “quantization” and “model mismatch” We found such penalties but they are not very significant The HM channel estimator has practical performance advantage for 3-bit ADC The SQRT channel estimator has speed & complexity advantages for N-bit ADC For further study: Model mismatch penalties at lower BER? We compared ultimately and practically achievable performance We assumed that SQRT suffers more from “quantization” and “model mismatch” We found such penalties but they are not very significant The HM channel estimator has practical performance advantage for 3-bit ADC The SQRT channel estimator has speed & complexity advantages for N-bit ADC For further study: Model mismatch penalties at lower BER?

penalty is not very relevant – achieves the same dispersion limit (e.g. 5000 ps/nm at 15 dB)

slightly worse, but ... Practical Performance?

not for relevant jitter magnitudes

no Jitter Penalty?

significant only for 3-bit ADC

yes, but ... Quantization Penalty?

• nly at low dispersion and for PMD –

and outside of useable operation range

yes, but ... Model Mismatch Penalty?

without complexity limitations, i.e. for unlimited ADC resolution and unlimited number of states

identical Ultimate Performance?

SQRT SQRT Method Method compared to compared to Histogram Histogram Method Method (@ BER 10 (@ BER 10-

• 3

3)

) in a Nutshell in a Nutshell Conclusions Conclusions

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Simulation Setups Simulation Setups Simulation Setups

for unconstrained complexity for CD, PMD, Jitter

infinite

11.8 dB Extinction Ratio SSMF (D=16 ps/nm), linear propagation 2 samples per bit, self-training, varied number of states gain optimized(1) roughly, best sampling phase, varied quantizer resolution NRZ @ 10.7 Gbit/s Format AGC / ADC

PRBS-18 (218 bits, 20 samples/bit)

DeBruijn-15 (219 bits, 32 samples/bit) Data MLSE

5-pole Bessel (7.5 GHz)

4-pole Bessel (7.5 GHz)

• El. Filter

SuperGauss 2nd Order (35 GHz)

Flat Top (40GHz)

• Opt. filter

Fiber

5-pole Bessel (7.5 GHz)

0.3 UI rise-time erfc shaped + 1-pole Bessel (10.7 GHz) Shaping Filter

Setup 2 „Good Tx“ Setup 1 „Bad Tx“

Setups Setups

Electrical filter Fiber (linear)

+

ASE noise Optical filter SQRT MLSE HM MLSE

(·)²

Tx Photo Diode Transmitter parameters varied

References References References

Non-parametric Channel Estimation

suggested early for MLSE usage in non-linear channel

• W. Sauer-Greff et al., "Modified Volterra Series and State Model Approach …”, Proc. IEEE Sig Proc 99, 19-23
• H. F. Haunstein et al., “Design of near optimum electrical equalizers for optical transmission …”, OFC 2001, WAA 4-1

implemented in real systems, e.g.

• A. Färbert et al., “Performance of a 10.7 Gb/s Receiver with Digital Equalizer using …”, ECOC 2004, Th4.1.5

(many) experimental data available, e.g.

J.P. Elbers et al., „Measurement of the dispersion tolerance of optical duobinary ...“, OFC 2005, OThJ4

• S. Chandrasekhar et al., “Chirp-managed laser and MLSE-RX ...”, PTL, Vol. 18, No. 14, 1560-1562, 2006
• S. Chandrasekhar et al., “Performance of MLSE Receiver ...”, PTL, Vol. 18, No. 23, 2448-2450, 2006
• J. M. Gené et al., “Joint PMD and Chromatic Dispersion Compensation Using an MLSE”, ECOC 2006 , We2.5.2
• I. L. L. Polo et al., “Comparison of Maximum Likelihood Sequence Estimation equalizer ...”, ECOC 2006, We2.5.3
• J. D. Downie et al., “Experimental Measurements of the Effectiveness of MLSE ...”, OFC 2007, OMG4
• C. Xie et. al., ”Performance Evaluation of Electronic Equalizers for Dynamic PMD ...”, OFC 2007, OTuA7

Parametric Channel Estimation

studied since long (for perfomance analysis), e.g.

• P. A. Humblet, M. Azizoglu, “On the Bit Error Rate …”, JLT 9/11 p.1577 (3), 1991 (and predecessors)
• A. Weiss, “On the Performance of Electrical Equalization in Optical Fiber Transmission Systems”, PTL, Vol. 15, 1225-1227, 2003

well covered in recent MLSE literature, e.g.

• D. E. Crivelli et al., “On the Performance of Reduced-State Viterbi Receivers …”, ECOC 2004, We4.P.083
• N. Alic et al., “Signal statistics and maximum likelihood sequence estimation …”, Optics Express, Vol.13, No. 12, 4568-4578, 2005
• G. Bosco et al., “Long-Distance Effectiveness of MLSE IMDD Receivers”, PTL, vol. 18, pp.1037-1039, 2006
• T. Freckmann, J. Speidel, “Viterbi Equalizer with Analytically Calculated Branch Metrics …”PTL, Vol. 18, 277-279, 2006
• T. Foggi et al., “Maximum-likelihood sequence detection with closed-form metrics …”, JLT, Vol. 24, No. 8, 3073-3087, 2006
• P. Poggiolini et al., ”Branch Metrics for Effective Long-Haul MLSE'', ECOC 2006, We2.5
• M. R. Hueda et al., “Parametric Estimation of IM/DD Optical Channels …”, JLT, Vol. 25, No. 3, 957-975, 2007

(some) experimental data from offline simulations, e.g.

• P. Poggiolini et al., “1,040 km uncompensated IMDD transmission …”, ECOC 2006, post-deadline Th4.4.6

References References

(1) For HM, gain was not optimized. Mean rectified

value was maintained at a constant level.

Two setups were used

OFC 2008 JThA60 9

HM: 2, 8, 32, 64, 256 states 9 10 11 12 13 100 200 300 400 L (km) OSNR (dB) @ BER = 1e-3 3 bits 4 bits 5 bits Series3 KLSE

(c)

SQRT: 2, 8, 32, 64, 256 states 9 10 11 12 13 100 200 300 400 L (km) OSNR (dB) @ BER = 1e-3 3 bits 4 bits 5 bits unquantized KLSE

(b)

Performance with Unconstrained MLSE and ADC Performance Performance with Unconstrained with Unconstrained MLSE and ADC MLSE and ADC

SQRT Method Histogram Method

0.4 dB model mismatch penalty (with infinite Extinction Ratio) Slightly increased quantization penalty

Achievable Achievable Performance? No Performance? No difference for difference for fine ADC fine ADC

Same achievable dispersion performance „Exact Metrics“ (Karhunen Loeve Series Expansion)

SQRT versus HM penalty

0.1 0.2 0.3 0.4 0.5 100 200 300 400 L / km OSNR (dB) 3 bits 4 bits 5 bits

Setup: „Good Tx“

OFC 2008 JThA60 10

HM (16 States)

10 12 14 16 18 20 1000 2000 3000 4000 5000 6000 Chromatic Dispersion (ps/nm) OSNR (dB) @ BER = 1e-3 2 bit 3 bit 4 bit 6 bit ADC Resolution

(b) SQRT (16 States)

10 12 14 16 18 20 1000 2000 3000 4000 5000 6000 Chromatic Dispersion (ps/nm) OSNR (dB) @ BER = 1e-3 blank 3 bit 4 bit unquantized ADC Resolution

(a)

Dispersion Tolerance with 16-states MLSE and ADC Dispersion Dispersion Tolerance with Tolerance with 16 16-

• states

states MLSE and ADC MLSE and ADC

SQRT Method Histogram Method

still 0.3 dB back-to-back model mismatch penalty (at 12 dB extinction ratio) Irrelevant small model mismatch penalty under ISI overload (outside

• f useable operation range!)

0.15 dB larger quantization penalty for 3-bit ADC at medium CD

Dispersion? Relevant Dispersion? Relevant differences are small differences are small

SQRT versus HM penalty

• 0.5
• 0.3
• 0.1

0.1 0.3 0.5 1000 2000 3000 4000 5000 6000 Chromatic Dispersion (ps/nm) OSNR (dB) 3 bits 4 bits

Artifact! Penalty remains positive when HM is gain optimized

Setup: „Bad Tx“

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HM (4 States)

10 12 14 16 18 20 0.5 1 1.5 2 DGD (UI) OSNR (dB) @ BER = 1e-3 2 bit 3 bit 4 bit 6 bit ADC Resolution

(b)

1st order PMD with 4-states MLSE and ADC 1 1st

st order PMD

• rder PMD with

with 4 4-

• states

states MLSE and ADC MLSE and ADC

SQRT (4 States)

10 12 14 16 18 20 0.5 1 1.5 2

DGD (UI)

OSNR (dB) @ BER = 1e-3 blank 3 bit 4 bit unquantized ADC Resolution

(a)

SQRT Method Histogram Method

0.2 dB quantization penalty for 3-bit ADC Large but irrelevant model mismatch penalty for ISI overload (outside of useable operation range)

PMD? Relevant PMD? Relevant differences remain small differences remain small

SQRT versus HM penalty

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2

DGD (UI) OSNR (dB) 3 bits 4 bits

Setup: „Bad Tx“

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Clock Recovery with Jitter (16-states and 4-bit ADC) Clock Recovery with Clock Recovery with Jitter Jitter (16 (16-

• states

states and 4 and 4-

• bit

bit ADC) ADC)

10 11 12 13 14 0.05 0.1 0.15 0.2 Sinusoidal Peak-to-Peak Jitter (UI) OSNR (dB) @ BER = 1e-3 3000 ps/nm, HM 3000 ps/nm, SQRT blank blank 0 ps/nm, HM 0 ps/nm, SQRT

HF Jitter Specification Limit:

(a)

10 11 12 13 14 0.02 0.04 0.06 0.08 0.1 Gaussian RMS Jitter (UI) OSNR (dB) @ BER = 1e-3 3000 ps/nm, HM 3000 ps/nm, SQRT blank blank 0 ps/nm, HM 0 ps/nm, SQRT

6 σ ~ 0.15 UIpp

(b)

Sinusoidal Jitter

(Test Signal)

Gaussian Jitter

Jitter Jitter? No relevant ? No relevant difference difference

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Setup: „Bad Tx“