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Bit Error Rate Metrology and Analysis

Bit Error Rate Metrology and Analysis. Prof. Patrice Mégret Service d’Electromagnétisme et de Télécommunications Faculté Polytechnique de Mons Patrice.megret@fpms.ac.be. Outline. What is BER and why to measure it? Theoretical bit-error-rate  Statistics of measured bit-error-rate BER

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Bit Error Rate Metrology and Analysis

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  1. Bit Error Rate Metrology and Analysis Prof. Patrice Mégret Service d’Electromagnétisme et de Télécommunications Faculté Polytechnique de Mons Patrice.megret@fpms.ac.be

  2. Outline • What is BER and why to measure it? • Theoretical bit-error-rate  • Statistics of measured bit-error-rate BER • Principle of bit-error-rate meters: measurement of k/n • Characteristics of the sources and fibers used in the case studies • Case study 1: optical link without dispersion • Case study 2: optical link with dispersion • Case study 3: optical link with reflection • Case study 4: effect of wander • Alternative method 1: eye diagram analysis • Alternative method 2: variable threshold technique • Conclusions

  3. Outline • What is BER and why to measure it? • Theoretical bit-error-rate  • Statistics of measured bit-error-rate BER • Principle of bit-error-rate meters: measurement of k/n • Characteristics of the sources and fibers used in the case studies • Case study 1: optical link without dispersion • Case study 2: optical link with dispersion • Case study 3: optical link with reflection • Case study 4: effect of wander • Alternative method 1: eye diagram analysis • Alternative method 2: variable threshold technique • Conclusions

  4. The main goal of bit-error-rate metrology is to measure BER versus signal amplitude • It is important to measure the BER floor • It is also interesting to appreciate the ‘bursty’ nature of errors • If BERas > BERspecs one has to redesign the link • Where should we place the measuring time and how long should it be ?

  5. Typical example of BER metrology • How to chose the point on the x-axis? • How long should be each measurement? • What is the precision of each measurement? • What is the statistical distribution of the errors? • Can we reduce the measuring time? • How can measure this curve?

  6. experimental Sensitivity @ 10-9 Sensitivity @ 10-12 Receiver sensitivity is the minimum average power needed for a given BER

  7. Power penalty is the increase of the minimum average power to obtain a given BER Power penalty for a given BER: Difference (in dB) between sensitivities of different configurations Example 1 (cf. figure) - configuration 1: idealcase - configuration 2: real case Example 2 - configuration 1: experimental link with a given set of parameters - configuration 2: same link with one modified parameter ideal experimental Penalty @ 10-9  2 dB

  8. Outline • What is BER and why to measure it? • Theoretical bit-error-rate  • Statistics of measured bit-error-rate BER • Principle of bit-error-rate meters: measurement of k/n • Characteristics of the sources and fibers used in the case studies • Case study 1: optical link without dispersion • Case study 2: optical link with dispersion • Case study 3: optical link with reflection • Case study 4: effect of wander • Alternative method 1: eye diagram analysis • Alternative method 2: variable threshold technique • Conclusions

  9. p(v/'1') µ 1 P['1'/'0'] v(t) E P['0'/'1'] µ 0 t p(v/'0') d Bit-error-rate is the probability of wrong detecting a symbol The fluctuating signal v(t) is received by the receiver decision circuit and sampled at decision time td in order to regenerate the signal. The noise corrupts the signal and the sampled value v varies around an average value 1 if a '1' has been transmitted and 0 if a '0' has been transmitted. The decision circuit compares this sampled value v with the decision threshold E and regenerates a '1' if v>E and a '0' if v<E. Theoretical bit-error-rate  :  is thus a deterministic variable depending on the various link parameters and can be computed by using classical telecommunication theory

  10. T=1/B 1 E 0 td Choice of E and td have a great impact on the bit-error-rate To get the best performances, the decision threshold E and the decision time td should be chosen at the center of the eye diagram.

  11. Under the gaussian approximation,  depends on the means and variances and on E and td

  12. When the same amount of errors occurs on the ones and the zeroes,  is a very simple function of Q • The means i(td) and variances i(td) are characteristics of the link properties (noises) whereas the sampling time td and the decision threshold E are receiver dependent. • In order to compute the bit-error-rate for any E and td, one has to know the means and variances. • The bit-error-rate is minimum at the two pdfs intersection • In general, one assumes the same probabilities of error on ones and zeroes,  optimum is E-independent:

  13. BER can be quickly estimated from Q

  14. 1 2 1 1 1 Cascade of links

  15. Outline • What is BER and why to measure it? • Theoretical bit-error-rate  • Statistics of measured bit-error-rate BER • Principle of bit-error-rate meters: measurement of k/n • Characteristics of the sources and fibers used in the case studies • Case study 1: optical link without dispersion • Case study 2: optical link with dispersion • Case study 3: optical link with reflection • Case study 4: effect of wander • Alternative method 1: eye diagram analysis • Alternative method 2: variable threshold technique • Conclusions

  16. 1 0 0 1 1 1* 1 1 1 0 0 1 1 0 1 1 BER is the main quality measure of digital links Measured bit-error-rate BER : BER is the measured bit-error-rate and is defined by the ratio of the number of errors k to the number of transmitted bits n during a measuring time Tn. B is the bit rate equal to 1/T if T is the bit period. BER is thus a random variable depending on the experimental setup BER is the main quality measure of digital links and represents the probability of wrong detecting a bit at the receiver end.

  17. There are 5 (+1) important parameters • BER = measured bit-error-rate = k/n on the measuring time Tn • EFS (Error-Free Seconds) = percentage or probability of one-second measurement intervals that are error free • ES (Error Seconds) = percentage or probability of one-second measurement intervals that are in error (ES = 1 - EFS) • %T1 = percentage of time T1 that the measured BER does not exceed a given threshold value • EFB (Error-Fee Block) = percentage or probability of data blocks that are error free These parameters all attempt to characterize the same performance characteristics but yield different results for the same link and measurement interval Tn. With EFS and %T1, one can appreciate the ‘bursty’ nature of the errors

  18.  stationary errors statisticallyindependent Bernoulli process the errored bits k have a binomial distribution k is a binomial random variable

  19. BER is binomial random variable with the same distribution as k BER is unbiased and consistent estimator of  BER is thus also a random binomial variable

  20. The time interval between two consecutive errors follows a geometric law In average, there is one error each T/=1/B seconds. In order words, B is the mean number of errors in one second.

  21. The binomial law is difficult to compute when n is large (n!)

  22. The convergence towards the Poisson law is quick and does not depend on BER • To use the Poisson law in practice, it is necessary to chose Tn such that n>50 whatever BER is (<0.1 is always realized in good links !):

  23. This graph summarizes the convergence time towards a Poisson law

  24. The convergence towards the normal law is slow and depends on BER • To use the normal law in practice, it is necessary to chose Tn such that n>5, i.e. k>5 (<0.5 is always realized in good links !)

  25. This graph summarizes the convergence time towards the normal law

  26. When the errors are independent, the link between the various indicators is simple

  27. EFS helps to see the ‘bursty’ nature of the errors

  28. %T1 helps to specify quality objectives

  29. BER+A BER BER-A BER measuring times can be very long • to compute the measuring time Tn , the binomial law is approximated by a gaussian one (n > 5 and  < 0.5): • the measurement precision is y% if the confidence interval length (2A) is less than 2yBER/100 ==> • Physically, confidence interval represents the interval around BER which has a probability 1- of containing the true value 

  30. BER measuring times can be very long • This table assumes a stationary process which means that there is no error burst • k errors =k/(B.BER) • IC are confidence intervals based on gaussian statistics (=5%) • At 2.5 Gbit/s these times are decreased by a factor of 2.5

  31. BER measuring times are inversely proportional to the bit rate • This table assumes a stationary process which means that there is no error burst • k errors =k/(B.BER) • IC are confidence intervals based on gaussian statistics (=5%)

  32. This graph summarizes the time to have 5 errors

  33. This graph summarizes the time to have 10 errors

  34. This graph summarizes the time to have 384 errors y = 10%  = 5%

  35. Outline • What is BER and why to measure it? • Theoretical bit-error-rate  • Statistics of measured bit-error-rate BER • Principle of bit-error-rate meters: measurement of k/n • Characteristics of the sources and fibers used in the case studies • Case study 1: optical link without dispersion • Case study 2: optical link with dispersion • Case study 3: optical link with reflection • Case study 4: effect of wander • Alternative method 1: eye diagram analysis • Alternative method 2: variable threshold technique • Conclusions

  36. CLK Di Do D.U.T Error analyzer Data generator CLK The BER measurement is realized by comparing the received sequence with the emitted one Di x x x 1 0 0 1 1 0 1 1 x x x x x x x x x x x D0 x x x x x x x 1 0 0 1 1 1 1 1 x x x x x x x • The error analyzer compares bit by bit the digital received sequence D0 with an image of the one emitted Di • In general, there is no connection between the data generator and the error receiver • It is clear that a synchronization mechanism should occur in the error analyzer in order to compute BER • In general, the clock signal should be provided to the error analyzer

  37. Data or pattern generator Codes (AMI, NRZ, RZ, …) Bit rates (normalized or not) Added errors (10-n, one, …) Choice of the length of the PRBS 2n-1, n=7, 10, 15, 23, 31 Type of signals (ELC, TTL, …) Zero substitution Phase jitter ... Error analyzer Codes (AMI, NRZ, RZ, …) Bit rates (normalized or not) Choice of the length of the PRBS 2n-1, n=7, 10, 15, 23, 31 Type of measurements (bit, code, on ones, on zeroes, G821, G826, …) Choice of the measuring time (absolute time, number of errors, ….) E and td (fixed, automatic, …) … The main parameters are the code, the sequence, the bit rate, the decision threshold and the decision time

  38. Laser Source 1300 or 1550 nm Transmitter 100 Mbit/s  3 Gbit/s Receiver Erreur detection O-E Converter Attenuator Powermeter Bit-error-rate measurements need expensive equipment

  39. The temporal analysis allows to estimate to error statistics

  40. Typical example of stationary results

  41. Error distribution is Poissonian

  42. Outline • What is BER and why to measure it? • Theoretical bit-error-rate  • Statistics of measured bit-error-rate BER • Principle of bit-error-rate meters: measurement of k/n • Characteristics of the sources and fibers used in the case studies • Case study 1: optical link without dispersion • Case study 2: optical link with dispersion • Case study 3: optical link with reflection • Case study 4: effect of wander • Alternative method 1: eye diagram analysis • Alternative method 2: variable threshold technique • Conclusions

  43. mean=1551.24 nm pic=1551.40 nm =0.95238 nm (118.65 GHz) =4.7875 nm =1.67 nm Fabry-Perot lasers are multi-longitudinal mode sources • mean=1316.59 nm • pic=1317.54 nm • =0.78947 nm (136.53 GHz) • =2.943 nm • =1.42 nm

  44. pic=1550.20 nm =2.175 nm Offset=-0.175 nm SMSR=40.89 dB DFB lasers are mono-longitudinal mode (monochromatic) sources • pic=1309.90 nm • =2.537 nm • Offset=0.381 nm • SMSR=42.83 dB

  45. 0=1309.87 nm S0=0.0865 ps/nm2km 0=1544.79 nm S0=0.0615 ps/nm2km Dispersion is around 17 ps/km.nm in C-SMF fiber @ 1550 nm and around -16 ps/km.nm in DS-SMF @ 1310 nm

  46. Outline • What is BER and why to measure it? • Theoretical bit-error-rate  • Statistics of measured bit-error-rate BER • Principle of bit-error-rate meters: measurement of k/n • Characteristics of the sources and fibers used in the case studies • Case study 1: optical link without dispersion • Case study 2: optical link with dispersion • Case study 3: optical link with reflection • Case study 4: effect of wander • Alternative method 1: eye diagram analysis • Alternative method 2: variable threshold technique • Conclusions

  47. PC + GPIB interface Nat. Inst. + Logiciel 'BER' Powermeter Anritsu ML910B Clock generator HP70311A Clock out fiber Data generator HP70841B Clock IN 10 % Optical source Attenuator HA1 Fittel Data Out 90% Clock out Clock out Trigger IN Tektronix CSA 803 Oscilloscope Data IN Power Splitter Optical Receiver Clock IN Error detector HP70842B Data IN The following results have been obtained by this set-up

  48. When there is no dispersion, no significant difference is observed between FP and DFB lasers • 25 km dispersion shifted fiber • STM 4 622.08 Mbit/s • Low cost 1550 nm receiver(BCP 51R 1550)

  49. The error number k linearly increases with time for FP laser without dispersion • -27 dBm • Tn= 1 h • t = 30 s • similar results for the other powers

  50. The error distribution follows a Neyman type II distribution for FP laser without dispersion • -27 dBm • Tn= 1 h • t = 30 s • similar results for the other powers

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