MLSE Channel Estimation MLSE Channel Estimation MLSE Channel - PowerPoint PPT Presentation

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

Non- -Parametric Parametric: : Canonical Histogram Method Canonical Histogram Method – – HM HM Non Non-Parametric: Canonical Histogram Method – HM = ⋅ 2 x y a x r d OFE ADC MLSE (AGC) E ye a n d A DC th re sh o ld s Non-parametric Method y Determine detected bit pattern d Associate observed quantized amplitude r Count observed amplitudes r for pattern d into a histogram N(d, r) t Metrics for given d and r is ~ log N(d, r) A m p litu d e d istrib u tio n a n d A DC th re sh o ld s = d 000 Histogram based channel model No parameters are estimated. But a Pros full amplitude histogram needs to be = Simple – just counting events d 111 „measured“ for each bit pattern. Robust – insensitive to model mismatch -1 0 1 2 3 4 5 6 7 8 r Cons A m p litu d e Histo g ra m s fo r 3 -b it A DC Canonical metrics Data collection time ~ ADC resolution Metrics for given r is the logarithm of the observed relative frequency value. Number of counters ~ ADC resolution Possibly more sensitive to error propagation? (decision errors translate into metrics errors) Non- -Parametric Parametric Non r 0 1 2 3 4 5 6 7 OFC 2008 JThA60 2

Parametric: Square : Square Root Method Root Method – – SQRT SQRT Parametric Parametric: Square Root Method – SQRT = ⋅ z = 2 x y a x r y d √ OFE ADC MLSE (AGC) y: signal dependent noise The electrical signal has more Eye and mean values Eye and mean values z noise on ones than on zeros. y z: signal independent noise The sqrt‘ed electrical signal has roughly Gaussian noise and roughly Parametric Method signal independent noise. Take square-root z of signal y Determine detected bit pattern d t t Determine mean z-amplitude m(d) for pattern d Amplitude distribution and ADC thresholds Metrics for given d and z is ~ ( z - m(d) ) ² Amplitude distribution and ADC thresholds Pros Mean based channel model Simple – just one parameter per PDF y y Only the mean value for each bit pattern needs Fast – mean value can be estimated quickly to be estimated when signal independent noise is postulated (i.e. when the red PDFs are used) Robust – decision errors do not corrupt PDF shape Model PDFs Model PDFs Cons Model mismatch penalties are possible DC coupling Euclidean metrics Metrics for given z is then the Euclidean distance from the mean sqrt‘ed signal. Note : The square root operation can also be applied implicitly by a non-uniform ADC, z y or explicitly after the uniform ADC, the latter with minor performance degradation Parametric Parametric OFC 2008 JThA60 3

Possible Problems of Problems of Parametric Estimation Parametric Estimation Possible Possible Problems of Parametric Estimation Method-Independent Problems Some problems are specific for a parametric approach. ISI Overload Channel Memory exceeds State Memory All can lead to „wrong metrics“. In short: Quantization Amplitude differences become invisible Model Mismatch Unrealistic Noise Model → wrong PDF shape When noise model does not sufficiently accurately model the „true“ noise PDF, metrics errors are introduced. ISI Overload → wrong PDF shape and parameters Note : Noise PDF for coarse state Using a model density instead of the mixture density. is a mixture density (i.e. a convex Model PDF vs. true PDF Model metrics vs. true log-likelihoods combination of several PDFs) Model Mismatch under ISI overload Resulting Log-Likelihood (Metric) 6 2 real 10 0.8 0 model Model PDF 10 5 True PDF 0.7 Means real 4 model 0.6 0.5 3 -5 10 0.4 2 0.3 1 0.2 Model Metrics 0.1 True Log-Likelihoods 0 -12 10 0.0 -12 10 Neglected Effects → wrong PDF shape or parameters E.g. imperfect clock (here: sinusoidal jitter) Quantization → wrong PDF parameters Mean quantized ≠ true mean Model Mismatch under Sinusoidal Jitter Resulting Log-Likelihood (Metric) 1.0 0 Model PDF 10 Jitter PDF 0.9 True PDF 0.8 Histogram mean versus true mean 0.7 9 true mean histogram mean 0.6 8 ADC thresholds 0.5 7 0.4 6 0.3 5 0.2 Model Metrics 4 0.1 True Log-Likelihoods 3 1500 ps/nm 0.6UI NRZ 0.0 -12 10 2 1 PDF vs PMF Note : Jitter impact on PDF depends on 0 0.7 0 1 2 3 4 5 6 7 8 9 slope and is therefore pattern-dependent: 0.6 • Strong impact on edges. 0.5 • Little impact on rails Using PDF values → 0.4 wrong PMF value 0.3 Computing PDF is easy, but PMF is hard. 0.2 „Wrong Wrong“ “ Metrics Metrics? ? „ 0.1 OFC 2008 JThA60 4 0.0 1 2 3 4 5

Channel Estimation Methods for MLSE MLSE Metrics Metrics Channel Estimation Methods for Channel Estimation Methods for MLSE Metrics MLSE needs metrics. Number of states in Trellis impacts performance Channel observer associates delayed OFE AGC ADC MLSE inputs (quantized waveform samples) and outputs (bit sequences, patterns) τ Quantizer resolution impacts performance Channel estimator uses the CR Metrics Channel channel observations to estimate Computer Observer a channel model Sampling clock jitter impacts performance Metrics are computed Channel from the channel model Estimator Parametric Parametric Non- -parametric parametric Non There are two approaches of channel estimation There are two approaches of channel estimation Estimate parameters (e.g. μ , σ ) of Estimate probabilities , i.e. values of Probability Density Function (PDF) to Gaussian PDFs Probablity Mass Function (PMF) Gaussian Histograms compute log-likelihood metrics channel observations 1.0 1.0 0.9 estimate 0.9 0.8 histograms 0.8 parameters μ 0.7 0.7 0.6 0.6 compute PDF 0.5 0.5 0.4 0.4 compute PMF σ 0.3 0.3 0.2 0.2 0.1 metrics 0.1 0.0 0.0 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 Any performance difference? ? Any performance difference OFC 2008 JThA60 5

Abstract and Problem Statement Abstract and Problem Statement Abstract and Problem Statement Abstract Abstract We compare the performance of MLSE-based receivers with parametric and non- We compare the performance of MLSE-based receivers with parametric and non- parametric channel estimation methods and characterize their sensitivity against parametric channel estimation methods and characterize their sensitivity against quantization, sampling jitter, and intersymbol interference (ISI) overload (1) quantization, sampling jitter, and intersymbol interference (ISI) overload (1) Non-Parametric Likelihoods are estimated directly MLSE needs branch metrics (1) ISI Overload: The physical (from observed relative frequencies) channel memory exceeds the Branch metrics are log-likelihoods state memory of the MLSE Parametric Likelihoods are estimated indirectly Two approaches to estimate likelihoods from observations: (parameters of a probabilistic model are estimated from observations) Problem Statement Problem Statement Do parametric models suffer from effects not covered in the model? Do parametric models suffer from effects not covered in the model? Are there relevant “model mismatch” penalties ? Are there relevant “model mismatch” penalties ? Simulation Approach Simulation Approach Histogram Method “ HM ” a practice-proven canonical method of non-parametric channel estimation SQRT method “ SQRT ” a particularly efficient example of a parametric method Compare ultimately and practically achievable performance of HM and of SQRT. Compare ultimately and practically achievable performance of HM and of SQRT. OFC 2008 JThA60 6