Abstract

We present a new method for analyzing eye diagrams that always provides a unique solution by making use of a robust, least-median-of-squares (LMS) location estimator. In contrast to commonly used histogram techniques, the LMS procedure is insensitive to outliers and data distributions. Our motivation for developing this algorithm is to create an independent, benchmark method that is both amenable to a thorough uncertainty analysis and can function as a comparison tool since no standardized industry algorithms currently exist. Utilizing this technique, we calculate the fundamental parameters of an eye diagram, namely the one and zero levels, and the time and amplitude crossings. With these parameters determined, we can derive various performance metrics, such as extinction ratio and root-mean-square jitter, and perform eye-mask alignment. In addition to describing our algorithm in detail, we compare results computed with this method to those of a commercial oscilloscope, and obtain excellent agreement. Finally, we suggest new definitions of eye height and eye width that are more robust than those that are commonly used.

© 2008 IEEE

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References

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  1. D. Derickson, Fiber Optic Test and Measurement (Prentice-Hall, 1998).
  2. P. Andersson, K. Akermark, "Accurate optical extinction ratio measurements," IEEE Photon. Technol. Lett. 6, 1356-1358 (1994).
  3. T. Clement, P. Hale, D. Williams, C. Wang, A. Dienstfrey, D. Keenan, "Calibration of sampling oscilloscopes with high-speed photodiodes," IEEE Trans. Instrum. Meas 54, 3173-3181 (2006).
  4. M. Hart, C. Duff, S. Hinch, "Firmware measurement algorithms for the HP83480 digital communications analyzer," Hewlett-Packard J. (1996).
  5. W. Finke, Algorithm for Finding the Eye Crossing Level of a Multilevel Signal U.S. patent 6,614,434 B1 (2003).
  6. IEEE Standard on Transitions, Pulses, and Related Waveforms IEEE Std. 181-2003Institute of Electrical and Electronics Engineers (2003).
  7. P. Rousseeuw, A. Leroy, Robust Regression and Outlier Detection (Wiley, 2004).
  8. J. A. Hartigan, Clustering Algorithms (Wiley, 1975).
  9. P. D. Hale, C. M. Wang, "Measurement of pulse parameters and propagation of uncertainty," IEEE Trans. Instrum. Meas. .
  10. J. Gowar, Optical Communication Systems (Prentice-Hall, 1984).
  11. OFSTP-4A: Optical Eye Pattern Measurement Procedure, Telecommunications Industries of America/Electronics Industries of America (TIA/EIA) Standard (1997).
  12. IEC 61280-2-2: Fibre Optic Communication Subsystem Test Procedures—Part 2-2: Digital Systems—Optical Eye Pattern, Waveform, and Extinction Ratio Measurement, International Electrotechnical Commission (2005).
  13. GR-253-CORE: Synchronous Optical Network (SONET) Transport Systems: Common Generic Criteria, Telcordia Technologies (1999).
  14. CSMA/CD Access Method and Physical Layer Specifications—Amendment: Media Access Parameters, Physical Layers, and Management Parameters for 10 Gb/s Operation IEEE Std. 802.3aeInstitute of Electrical and Electronics Engineers (2002).
  15. ITU-T Recommendation G.957: Optical Interfaces for Equipments and Systems Relating to the Synchronous Digital Hierarchy, Telecommunication Standardization Sector of International Telecommunications Union (ITU-T) (2006).
  16. J. M. Chambers, W. S. Cleveland, B. Kleiner, P. A. Tukey, Graphical Methods for Data Analysis (Wadsworth, 1983).
  17. R Development Core Team 2003 R: A Language and Environment for Statistical Computing R Foundation for Statistical ComputingViennaAustria 3-900051-00-3 http://www.R-project.org.

2006 (1)

T. Clement, P. Hale, D. Williams, C. Wang, A. Dienstfrey, D. Keenan, "Calibration of sampling oscilloscopes with high-speed photodiodes," IEEE Trans. Instrum. Meas 54, 3173-3181 (2006).

1996 (1)

M. Hart, C. Duff, S. Hinch, "Firmware measurement algorithms for the HP83480 digital communications analyzer," Hewlett-Packard J. (1996).

1994 (1)

P. Andersson, K. Akermark, "Accurate optical extinction ratio measurements," IEEE Photon. Technol. Lett. 6, 1356-1358 (1994).

Hewlett-Packard J. (1)

M. Hart, C. Duff, S. Hinch, "Firmware measurement algorithms for the HP83480 digital communications analyzer," Hewlett-Packard J. (1996).

IEEE Trans. Instrum. Meas (1)

T. Clement, P. Hale, D. Williams, C. Wang, A. Dienstfrey, D. Keenan, "Calibration of sampling oscilloscopes with high-speed photodiodes," IEEE Trans. Instrum. Meas 54, 3173-3181 (2006).

IEEE Photon. Technol. Lett. (1)

P. Andersson, K. Akermark, "Accurate optical extinction ratio measurements," IEEE Photon. Technol. Lett. 6, 1356-1358 (1994).

IEEE Trans. Instrum. Meas. (1)

P. D. Hale, C. M. Wang, "Measurement of pulse parameters and propagation of uncertainty," IEEE Trans. Instrum. Meas. .

Other (13)

J. Gowar, Optical Communication Systems (Prentice-Hall, 1984).

OFSTP-4A: Optical Eye Pattern Measurement Procedure, Telecommunications Industries of America/Electronics Industries of America (TIA/EIA) Standard (1997).

IEC 61280-2-2: Fibre Optic Communication Subsystem Test Procedures—Part 2-2: Digital Systems—Optical Eye Pattern, Waveform, and Extinction Ratio Measurement, International Electrotechnical Commission (2005).

GR-253-CORE: Synchronous Optical Network (SONET) Transport Systems: Common Generic Criteria, Telcordia Technologies (1999).

CSMA/CD Access Method and Physical Layer Specifications—Amendment: Media Access Parameters, Physical Layers, and Management Parameters for 10 Gb/s Operation IEEE Std. 802.3aeInstitute of Electrical and Electronics Engineers (2002).

ITU-T Recommendation G.957: Optical Interfaces for Equipments and Systems Relating to the Synchronous Digital Hierarchy, Telecommunication Standardization Sector of International Telecommunications Union (ITU-T) (2006).

J. M. Chambers, W. S. Cleveland, B. Kleiner, P. A. Tukey, Graphical Methods for Data Analysis (Wadsworth, 1983).

R Development Core Team 2003 R: A Language and Environment for Statistical Computing R Foundation for Statistical ComputingViennaAustria 3-900051-00-3 http://www.R-project.org.

D. Derickson, Fiber Optic Test and Measurement (Prentice-Hall, 1998).

W. Finke, Algorithm for Finding the Eye Crossing Level of a Multilevel Signal U.S. patent 6,614,434 B1 (2003).

IEEE Standard on Transitions, Pulses, and Related Waveforms IEEE Std. 181-2003Institute of Electrical and Electronics Engineers (2003).

P. Rousseeuw, A. Leroy, Robust Regression and Outlier Detection (Wiley, 2004).

J. A. Hartigan, Clustering Algorithms (Wiley, 1975).

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