Abstract

This paper thoroughly investigates the maximum-likelihood sequence detection (MLSD) receiver for the optical ON-OFF keying (OOK) channel in the presence of both polarization mode dispersion and group velocity dispersion (GVD). A reliable method is provided for computing the relevant performance for any possible value of the system parameters, with no constraint on the sampling rate. With one sample per bit time, a practically exact expression of the statistics of the received samples is found, and therefore the performance of a synchronous MLSD receiver is evaluated and compared with that of other electronic techniques such as combined feedforward and decision-feedback equalizers (FFE and DFE). It is also shown that the ultimate performance of electronic processing can be obtained by sampling the received signal at twice the bit rate. An approximate accurate closed-form expression of the receiver metrics is also identified, allowing for the implementation of a practically optimal MLSD receiver.

© 2006 IEEE

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  1. G. J. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers", J. Lightw. Technol., vol. 9, no. 11, pp. 1439-1456, Nov. 1991.
  2. E. Forestieri, G. Colavolpe and G. Prati, "Novel MSE adaptive control of optical PMD compensator", J. Lightw. Technol., vol. 20, no. 12, pp. 1997-2003, Dec. 2002.
  3. M. Secondini, E. Forestieri and G. Prati, "PLC optical equalizer for chromatic and polarization-mode dispersion compensation based on MSE control", IEEE Photon. Technol. Lett., vol. 16, no. 4, pp. 1173-1175, Apr. 2004.
  4. F. Buchali and H. Bulow, "Adaptive PMD compensation by electrical and optical techniques", J. Lightw. Technol., vol. 22, no. 4, pp. 1116-1126, Apr. 2004.
  5. J. H. Winters and R. D. Gitlin, "Electrical signal processing techniques in long-haul fiber-optic systems", IEEE Trans. Commun., vol. 38, no. 9, pp. 1439-1453, Sep. 1990.
  6. J. H. Winters and S. Kasturia, "Adaptive nonlinear cancellation for high-speed fiber-optic systems", J. Lightw. Technol., vol. 10, no. 7, pp. 971-977, Jul. 1992.
  7. H. Bulow and G. Thielecke, "Electronic PMD mitigation-From linear equalization to maximum-likelihood detection", in Proc. OFC, vol. 3, 2001, pp. WDD34-1-WDD34-3.
  8. H. F. Haunstein, W. Sauer-Greff, A. Dittrich, K. Sticht and R. Urbansky, "Principles for electronic equalization of polarization-mode dispersion", J. Lightw. Technol., vol. 22, no. 4, pp. 1169-1182, Apr. 2004.
  9. G. D. Forney Jr., "The Viterbi algorithm", Proc. IEEE, vol. 61, no. 3, pp. 268-278, Mar. 1973.
  10. J. G. Proakis, Digital Communications, 3rd ed. New York: McGraw-Hill, 1996.
  11. P. S. Henry, "Error-rate performance of optical amplifiers", presented at the Optical Fiber Communication (OFC), Houston, TX, Paper THK3, Feb. 1989.
  12. D. Marcuse, "Derivation of analytical expression for the bit-error probability in lightwave systems with optical amplifiers", J. Lightw. Technol., vol. 8, no. 12, pp. 1816-1823, Dec. 1990.
  13. P. A. Humblet and M. Azizoglu, "On the bit error rate of lightwavex systems with optical amplifiers", J. Lightw. Technol., vol. 9, no. 11, pp. 1576-1582, Nov. 1991.
  14. Y. Cai, J. M. Morris, T. Adali and C. R. Menyuk, "On turbo code decoder performance in optical-fiber communication systems with dominating ASE noise", J. Lightw. Technol., vol. 21, no. 3, pp. 727-734, Mar. 2003.
  15. O. E. Agazzi, M. R. Hueda, H. S. Carrer and D. E. Crivelli, "Maximum-likelihood sequence estimation in dispersive optical channels", J. Lightw. Technol., vol. 23, no. 2, pp. 749-763, Feb. 2005.
  16. A. J. Weiss, "On the performance of electrical equalization in optical fiber transmission systems", IEEE Photon. Technol. Lett., vol. 15, no. 9, pp. 1225-1227, Sep. 2003.
  17. H. Meyr, M. Oerder and A. Polydoros, "On sampling rate, analog prefiltering and sufficient statistics for digital receivers", IEEE Trans. Commun., vol. 42, no. 12, pp. 3208-3214, Dec. 1994.
  18. A. Farbert, et al. "Performance of a 10.7 Gb/s receiver with digital equaliser using maximum likelihood sequence estimation", presented at the Eur. Conf. Optical Communication (ECOC), Stockholm, Sweden,Paper Th4.1.5, 2004.
  19. E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre-and postdetection filtering", J. Lightw. Technol., vol. 18, no. 11, pp. 1493-1503, Nov. 2000.
  20. T. Foggi, G. Colavolpe, E. Forestieri and G. Prati, "Adaptive electronic processing in optical PMD-impaired systems," in Optical Networks and Technology, K.-I. Kitayama, F. Masetti-Placci, and G. Prati, Eds. New York: Springer-Verlag, 2004, pp. 499-506.
  21. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. San Diego, CA: Academic, 2001.
  22. A. F. Elrefaie, R. E. Wagner, D. A. Atlas and D. G. Daut, "Chromatic dispersion limitations in coherent lightwave transmission systems", J. Lightw. Technol., vol. 6, no. 5, pp. 704-709, May 1988.
  23. E. Forestieri and L. Vincetti, "Exact evaluation of the Jones matrix of a fiber in the presence of polarization mode dispersion of any order", J. Lightw. Technol., vol. 19, no. 12, pp. 1898-1909, Dec. 2001.
  24. E. Forestieri and G. Prati, "Exact analytical evaluation of second-order PMD impact on the outage probability for a compensated system", J. Lightw. Technol., vol. 22, no. 4, pp. 988-996, Apr. 2004.
  25. H. Kogelnik, L. E. Nelson, J. P. Gordon and R. M. Jopson, "Jones matrix for second-order polarization mode dispersion", Opt. Lett., vol. 25, no. 1, pp. 19-21, 2000.
  26. C. W. Helstrom, "Approximate evaluation of detection probabilities in radar and optical communications", IEEE Trans. Aerosp. Electron. Syst., vol. AES-14, no. 7, pp. 630-640, Jul. 1978.
  27. B. Chan and J. Conradi, "On the non-Gaussian noise in erbium-doped fiber amplifiers", J. Lightw. Technol., vol. 15, no. 4, pp. 680-687, Apr. 1997.
  28. M. V. Eyuboglu and S. U. Qureshi, "Reduced-state sequence estimation with set partitioning and decision feedback", IEEE Trans. Commun., vol. 36, no. 1, pp. 13-20, Jan. 1988.
  29. G. Ferrari, G. Colavolpe and R. Raheli, Detection Algorithms for Wireless Communications, Hoboken, NJ: Wiley, 2004.
  30. L. R. Bahl, J. Cocke, F. Jelinek and J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate", IEEE Trans. Inf. Theory, vol. IT-20, no. 2, pp. 284-287, Mar. 1974.
  31. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, New York: Dover, 1972.
  32. R. Holzlöhner and C. R. Menyuk, "Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems", Opt. Lett., vol. 28, no. 20, pp. 1894-1896, Oct. 2003.

Other (32)

G. J. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers", J. Lightw. Technol., vol. 9, no. 11, pp. 1439-1456, Nov. 1991.

E. Forestieri, G. Colavolpe and G. Prati, "Novel MSE adaptive control of optical PMD compensator", J. Lightw. Technol., vol. 20, no. 12, pp. 1997-2003, Dec. 2002.

M. Secondini, E. Forestieri and G. Prati, "PLC optical equalizer for chromatic and polarization-mode dispersion compensation based on MSE control", IEEE Photon. Technol. Lett., vol. 16, no. 4, pp. 1173-1175, Apr. 2004.

F. Buchali and H. Bulow, "Adaptive PMD compensation by electrical and optical techniques", J. Lightw. Technol., vol. 22, no. 4, pp. 1116-1126, Apr. 2004.

J. H. Winters and R. D. Gitlin, "Electrical signal processing techniques in long-haul fiber-optic systems", IEEE Trans. Commun., vol. 38, no. 9, pp. 1439-1453, Sep. 1990.

J. H. Winters and S. Kasturia, "Adaptive nonlinear cancellation for high-speed fiber-optic systems", J. Lightw. Technol., vol. 10, no. 7, pp. 971-977, Jul. 1992.

H. Bulow and G. Thielecke, "Electronic PMD mitigation-From linear equalization to maximum-likelihood detection", in Proc. OFC, vol. 3, 2001, pp. WDD34-1-WDD34-3.

H. F. Haunstein, W. Sauer-Greff, A. Dittrich, K. Sticht and R. Urbansky, "Principles for electronic equalization of polarization-mode dispersion", J. Lightw. Technol., vol. 22, no. 4, pp. 1169-1182, Apr. 2004.

G. D. Forney Jr., "The Viterbi algorithm", Proc. IEEE, vol. 61, no. 3, pp. 268-278, Mar. 1973.

J. G. Proakis, Digital Communications, 3rd ed. New York: McGraw-Hill, 1996.

P. S. Henry, "Error-rate performance of optical amplifiers", presented at the Optical Fiber Communication (OFC), Houston, TX, Paper THK3, Feb. 1989.

D. Marcuse, "Derivation of analytical expression for the bit-error probability in lightwave systems with optical amplifiers", J. Lightw. Technol., vol. 8, no. 12, pp. 1816-1823, Dec. 1990.

P. A. Humblet and M. Azizoglu, "On the bit error rate of lightwavex systems with optical amplifiers", J. Lightw. Technol., vol. 9, no. 11, pp. 1576-1582, Nov. 1991.

Y. Cai, J. M. Morris, T. Adali and C. R. Menyuk, "On turbo code decoder performance in optical-fiber communication systems with dominating ASE noise", J. Lightw. Technol., vol. 21, no. 3, pp. 727-734, Mar. 2003.

O. E. Agazzi, M. R. Hueda, H. S. Carrer and D. E. Crivelli, "Maximum-likelihood sequence estimation in dispersive optical channels", J. Lightw. Technol., vol. 23, no. 2, pp. 749-763, Feb. 2005.

A. J. Weiss, "On the performance of electrical equalization in optical fiber transmission systems", IEEE Photon. Technol. Lett., vol. 15, no. 9, pp. 1225-1227, Sep. 2003.

H. Meyr, M. Oerder and A. Polydoros, "On sampling rate, analog prefiltering and sufficient statistics for digital receivers", IEEE Trans. Commun., vol. 42, no. 12, pp. 3208-3214, Dec. 1994.

A. Farbert, et al. "Performance of a 10.7 Gb/s receiver with digital equaliser using maximum likelihood sequence estimation", presented at the Eur. Conf. Optical Communication (ECOC), Stockholm, Sweden,Paper Th4.1.5, 2004.

E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre-and postdetection filtering", J. Lightw. Technol., vol. 18, no. 11, pp. 1493-1503, Nov. 2000.

T. Foggi, G. Colavolpe, E. Forestieri and G. Prati, "Adaptive electronic processing in optical PMD-impaired systems," in Optical Networks and Technology, K.-I. Kitayama, F. Masetti-Placci, and G. Prati, Eds. New York: Springer-Verlag, 2004, pp. 499-506.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. San Diego, CA: Academic, 2001.

A. F. Elrefaie, R. E. Wagner, D. A. Atlas and D. G. Daut, "Chromatic dispersion limitations in coherent lightwave transmission systems", J. Lightw. Technol., vol. 6, no. 5, pp. 704-709, May 1988.

E. Forestieri and L. Vincetti, "Exact evaluation of the Jones matrix of a fiber in the presence of polarization mode dispersion of any order", J. Lightw. Technol., vol. 19, no. 12, pp. 1898-1909, Dec. 2001.

E. Forestieri and G. Prati, "Exact analytical evaluation of second-order PMD impact on the outage probability for a compensated system", J. Lightw. Technol., vol. 22, no. 4, pp. 988-996, Apr. 2004.

H. Kogelnik, L. E. Nelson, J. P. Gordon and R. M. Jopson, "Jones matrix for second-order polarization mode dispersion", Opt. Lett., vol. 25, no. 1, pp. 19-21, 2000.

C. W. Helstrom, "Approximate evaluation of detection probabilities in radar and optical communications", IEEE Trans. Aerosp. Electron. Syst., vol. AES-14, no. 7, pp. 630-640, Jul. 1978.

B. Chan and J. Conradi, "On the non-Gaussian noise in erbium-doped fiber amplifiers", J. Lightw. Technol., vol. 15, no. 4, pp. 680-687, Apr. 1997.

M. V. Eyuboglu and S. U. Qureshi, "Reduced-state sequence estimation with set partitioning and decision feedback", IEEE Trans. Commun., vol. 36, no. 1, pp. 13-20, Jan. 1988.

G. Ferrari, G. Colavolpe and R. Raheli, Detection Algorithms for Wireless Communications, Hoboken, NJ: Wiley, 2004.

L. R. Bahl, J. Cocke, F. Jelinek and J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate", IEEE Trans. Inf. Theory, vol. IT-20, no. 2, pp. 284-287, Mar. 1974.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, New York: Dover, 1972.

R. Holzlöhner and C. R. Menyuk, "Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems", Opt. Lett., vol. 28, no. 20, pp. 1894-1896, Oct. 2003.

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