Abstract

In this paper, we investigate the use of nonlinear distortion of the electrical post-detection signal in order to design simple, yet very effective, maximum likelihood sequence detection (MLSD) receivers for optical communications with direct photo-detection. This distortion enables the use of standard Euclidean branch metrics in the Viterbi algorithm which implements MLSD. Our results suggest that the nonlinear characteristic can be optimized with respect to the uncompensated chromatic dispersion and other relevant system parameters, such as the extinction ratio. The proposed schemes with optimized distortion exhibit the same performance of more sophisticated MLSD schemes, still guaranteeing more efficient Viterbi algorithm implementation.

© 2007 Optical Society of America

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References

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  1. O. E. Agazzi, M. R. Hueda, H. S. Carrer, and D. E. Crivelli, “Maximum-Likelihood Sequence Estimation in Dispersive Optical Channels,” J. Lightwave Technol. 23, 749–763 (2005).
    [Crossref]
  2. M. Franceschini, G. Ferrari, R. Raheli, and G. Bongiorni, “Fundamental limits of electronic dispersion compensation in optical communications with direct photodetection,” IEE Electron. Lett. 42, 874–875 (2006).
    [Crossref]
  3. G. Agrawal, Fiber-Optic Communications Systems (John Wiley & Sons, New York, NY, USA, 2002).
    [Crossref]
  4. J. G. Proakis, Digital Communications, 4th Edition. (McGraw-Hill, New York, NY, USA, 2001).
  5. S. Benedetto, E. Biglieri, and V. Castellani, Digital Transmission Theory (Prentice-Hall, Englewood Cliffs, NJ, 1987).
  6. G. D. Forney, “The Viterbi Algorithm,” Proc. IEEE61, 268–278 (1973).
    [Crossref]
  7. T. Foggi, E. Forestieri, G. Colavolpe, and G. Prati, “Maximum likelihood sequence detection with closed-form metrics in OOK optical systems impaired by GVD and PMD,” J. Lightwave Technol. 24, 3073–3087 (2006).
    [Crossref]
  8. G. Bosco and P. Poggiolini, “Long-distance effectiveness of MLSE IMDD receivers,” IEEE Photon. Technol. Lett. 18, 1037–1039 (2006).
    [Crossref]
  9. D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9, 505–513 (1991).
    [Crossref]
  10. E. Forestieri, “Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and post-detection filtering,” J. Lightwave Technol. 18, 1493–1503 (2000).
    [Crossref]
  11. M. R. Hueda, D. E. Crivelli, and H. S. Carrer, “Performance of MLSE-based receivers in lightwave systems with nonlinear dispersion and amplified spontaneous emission noise,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), pp. 299–303 (Dallas, TX, USA, 2004).
  12. A. Prat, J. M. Napoli, M. Gene, P. Omella, V. Poggiolini, and Curri, “Square root strategy: a novel method to linearize an optical communication system with electronic equalizers,” in Proc. European Conf. on Optical Commun. (ECOC), vol. 3, pp. 713–714 (Glasgow, Scotland, 2005).
  13. G. J. Foschini, L. J. Greenstein, and G. Vanucci, “Noncoherent detection of coherent lightwave signals corrupted by phase noise,” IEEE Trans. Commun. 36, 306–314 (1988).
    [Crossref]
  14. L. G. Kazovsky and O. K. Tonguz, “ASK and FSK coherent lightwave systems: a simplified approximate analysis,” J. Lightwave Technol. 8, 338–352 (1990).
    [Crossref]
  15. O. K. Tonguz and L. G. Kazovsky, “Theory of Direct Detection Lightwave Receivers using Optical Amplifiers,” J. Lightwave Technol. 9, 174–181 (1991).
    [Crossref]
  16. O. K. Tonguz and R. E. Wagner, “Equivalence between Preamplified Direct Detection and Heterodyne Receivers,” IEEE Photon. Technol. Lett. 3, 835–837 (1991).
    [Crossref]

2006 (3)

M. Franceschini, G. Ferrari, R. Raheli, and G. Bongiorni, “Fundamental limits of electronic dispersion compensation in optical communications with direct photodetection,” IEE Electron. Lett. 42, 874–875 (2006).
[Crossref]

T. Foggi, E. Forestieri, G. Colavolpe, and G. Prati, “Maximum likelihood sequence detection with closed-form metrics in OOK optical systems impaired by GVD and PMD,” J. Lightwave Technol. 24, 3073–3087 (2006).
[Crossref]

G. Bosco and P. Poggiolini, “Long-distance effectiveness of MLSE IMDD receivers,” IEEE Photon. Technol. Lett. 18, 1037–1039 (2006).
[Crossref]

2005 (1)

2000 (1)

1991 (3)

D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9, 505–513 (1991).
[Crossref]

O. K. Tonguz and L. G. Kazovsky, “Theory of Direct Detection Lightwave Receivers using Optical Amplifiers,” J. Lightwave Technol. 9, 174–181 (1991).
[Crossref]

O. K. Tonguz and R. E. Wagner, “Equivalence between Preamplified Direct Detection and Heterodyne Receivers,” IEEE Photon. Technol. Lett. 3, 835–837 (1991).
[Crossref]

1990 (1)

L. G. Kazovsky and O. K. Tonguz, “ASK and FSK coherent lightwave systems: a simplified approximate analysis,” J. Lightwave Technol. 8, 338–352 (1990).
[Crossref]

1988 (1)

G. J. Foschini, L. J. Greenstein, and G. Vanucci, “Noncoherent detection of coherent lightwave signals corrupted by phase noise,” IEEE Trans. Commun. 36, 306–314 (1988).
[Crossref]

Agazzi, O. E.

Agrawal, G.

G. Agrawal, Fiber-Optic Communications Systems (John Wiley & Sons, New York, NY, USA, 2002).
[Crossref]

Benedetto, S.

S. Benedetto, E. Biglieri, and V. Castellani, Digital Transmission Theory (Prentice-Hall, Englewood Cliffs, NJ, 1987).

Biglieri, E.

S. Benedetto, E. Biglieri, and V. Castellani, Digital Transmission Theory (Prentice-Hall, Englewood Cliffs, NJ, 1987).

Bongiorni, G.

M. Franceschini, G. Ferrari, R. Raheli, and G. Bongiorni, “Fundamental limits of electronic dispersion compensation in optical communications with direct photodetection,” IEE Electron. Lett. 42, 874–875 (2006).
[Crossref]

Bosco, G.

G. Bosco and P. Poggiolini, “Long-distance effectiveness of MLSE IMDD receivers,” IEEE Photon. Technol. Lett. 18, 1037–1039 (2006).
[Crossref]

Carrer, H. S.

O. E. Agazzi, M. R. Hueda, H. S. Carrer, and D. E. Crivelli, “Maximum-Likelihood Sequence Estimation in Dispersive Optical Channels,” J. Lightwave Technol. 23, 749–763 (2005).
[Crossref]

M. R. Hueda, D. E. Crivelli, and H. S. Carrer, “Performance of MLSE-based receivers in lightwave systems with nonlinear dispersion and amplified spontaneous emission noise,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), pp. 299–303 (Dallas, TX, USA, 2004).

Castellani, V.

S. Benedetto, E. Biglieri, and V. Castellani, Digital Transmission Theory (Prentice-Hall, Englewood Cliffs, NJ, 1987).

Colavolpe, G.

Crivelli, D. E.

O. E. Agazzi, M. R. Hueda, H. S. Carrer, and D. E. Crivelli, “Maximum-Likelihood Sequence Estimation in Dispersive Optical Channels,” J. Lightwave Technol. 23, 749–763 (2005).
[Crossref]

M. R. Hueda, D. E. Crivelli, and H. S. Carrer, “Performance of MLSE-based receivers in lightwave systems with nonlinear dispersion and amplified spontaneous emission noise,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), pp. 299–303 (Dallas, TX, USA, 2004).

Curri,

A. Prat, J. M. Napoli, M. Gene, P. Omella, V. Poggiolini, and Curri, “Square root strategy: a novel method to linearize an optical communication system with electronic equalizers,” in Proc. European Conf. on Optical Commun. (ECOC), vol. 3, pp. 713–714 (Glasgow, Scotland, 2005).

Ferrari, G.

M. Franceschini, G. Ferrari, R. Raheli, and G. Bongiorni, “Fundamental limits of electronic dispersion compensation in optical communications with direct photodetection,” IEE Electron. Lett. 42, 874–875 (2006).
[Crossref]

Foggi, T.

Forestieri, E.

Forney, G. D.

G. D. Forney, “The Viterbi Algorithm,” Proc. IEEE61, 268–278 (1973).
[Crossref]

Foschini, G. J.

G. J. Foschini, L. J. Greenstein, and G. Vanucci, “Noncoherent detection of coherent lightwave signals corrupted by phase noise,” IEEE Trans. Commun. 36, 306–314 (1988).
[Crossref]

Franceschini, M.

M. Franceschini, G. Ferrari, R. Raheli, and G. Bongiorni, “Fundamental limits of electronic dispersion compensation in optical communications with direct photodetection,” IEE Electron. Lett. 42, 874–875 (2006).
[Crossref]

Gene, M.

A. Prat, J. M. Napoli, M. Gene, P. Omella, V. Poggiolini, and Curri, “Square root strategy: a novel method to linearize an optical communication system with electronic equalizers,” in Proc. European Conf. on Optical Commun. (ECOC), vol. 3, pp. 713–714 (Glasgow, Scotland, 2005).

Greenstein, L. J.

G. J. Foschini, L. J. Greenstein, and G. Vanucci, “Noncoherent detection of coherent lightwave signals corrupted by phase noise,” IEEE Trans. Commun. 36, 306–314 (1988).
[Crossref]

Hueda, M. R.

O. E. Agazzi, M. R. Hueda, H. S. Carrer, and D. E. Crivelli, “Maximum-Likelihood Sequence Estimation in Dispersive Optical Channels,” J. Lightwave Technol. 23, 749–763 (2005).
[Crossref]

M. R. Hueda, D. E. Crivelli, and H. S. Carrer, “Performance of MLSE-based receivers in lightwave systems with nonlinear dispersion and amplified spontaneous emission noise,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), pp. 299–303 (Dallas, TX, USA, 2004).

Kazovsky, L. G.

O. K. Tonguz and L. G. Kazovsky, “Theory of Direct Detection Lightwave Receivers using Optical Amplifiers,” J. Lightwave Technol. 9, 174–181 (1991).
[Crossref]

L. G. Kazovsky and O. K. Tonguz, “ASK and FSK coherent lightwave systems: a simplified approximate analysis,” J. Lightwave Technol. 8, 338–352 (1990).
[Crossref]

Marcuse, D.

D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9, 505–513 (1991).
[Crossref]

Napoli, J. M.

A. Prat, J. M. Napoli, M. Gene, P. Omella, V. Poggiolini, and Curri, “Square root strategy: a novel method to linearize an optical communication system with electronic equalizers,” in Proc. European Conf. on Optical Commun. (ECOC), vol. 3, pp. 713–714 (Glasgow, Scotland, 2005).

Omella, P.

A. Prat, J. M. Napoli, M. Gene, P. Omella, V. Poggiolini, and Curri, “Square root strategy: a novel method to linearize an optical communication system with electronic equalizers,” in Proc. European Conf. on Optical Commun. (ECOC), vol. 3, pp. 713–714 (Glasgow, Scotland, 2005).

Poggiolini, P.

G. Bosco and P. Poggiolini, “Long-distance effectiveness of MLSE IMDD receivers,” IEEE Photon. Technol. Lett. 18, 1037–1039 (2006).
[Crossref]

Poggiolini, V.

A. Prat, J. M. Napoli, M. Gene, P. Omella, V. Poggiolini, and Curri, “Square root strategy: a novel method to linearize an optical communication system with electronic equalizers,” in Proc. European Conf. on Optical Commun. (ECOC), vol. 3, pp. 713–714 (Glasgow, Scotland, 2005).

Prat, A.

A. Prat, J. M. Napoli, M. Gene, P. Omella, V. Poggiolini, and Curri, “Square root strategy: a novel method to linearize an optical communication system with electronic equalizers,” in Proc. European Conf. on Optical Commun. (ECOC), vol. 3, pp. 713–714 (Glasgow, Scotland, 2005).

Prati, G.

Proakis, J. G.

J. G. Proakis, Digital Communications, 4th Edition. (McGraw-Hill, New York, NY, USA, 2001).

Raheli, R.

M. Franceschini, G. Ferrari, R. Raheli, and G. Bongiorni, “Fundamental limits of electronic dispersion compensation in optical communications with direct photodetection,” IEE Electron. Lett. 42, 874–875 (2006).
[Crossref]

Tonguz, O. K.

O. K. Tonguz and R. E. Wagner, “Equivalence between Preamplified Direct Detection and Heterodyne Receivers,” IEEE Photon. Technol. Lett. 3, 835–837 (1991).
[Crossref]

O. K. Tonguz and L. G. Kazovsky, “Theory of Direct Detection Lightwave Receivers using Optical Amplifiers,” J. Lightwave Technol. 9, 174–181 (1991).
[Crossref]

L. G. Kazovsky and O. K. Tonguz, “ASK and FSK coherent lightwave systems: a simplified approximate analysis,” J. Lightwave Technol. 8, 338–352 (1990).
[Crossref]

Vanucci, G.

G. J. Foschini, L. J. Greenstein, and G. Vanucci, “Noncoherent detection of coherent lightwave signals corrupted by phase noise,” IEEE Trans. Commun. 36, 306–314 (1988).
[Crossref]

Wagner, R. E.

O. K. Tonguz and R. E. Wagner, “Equivalence between Preamplified Direct Detection and Heterodyne Receivers,” IEEE Photon. Technol. Lett. 3, 835–837 (1991).
[Crossref]

IEE Electron. Lett. (1)

M. Franceschini, G. Ferrari, R. Raheli, and G. Bongiorni, “Fundamental limits of electronic dispersion compensation in optical communications with direct photodetection,” IEE Electron. Lett. 42, 874–875 (2006).
[Crossref]

IEEE Photon. Technol. Lett. (2)

O. K. Tonguz and R. E. Wagner, “Equivalence between Preamplified Direct Detection and Heterodyne Receivers,” IEEE Photon. Technol. Lett. 3, 835–837 (1991).
[Crossref]

G. Bosco and P. Poggiolini, “Long-distance effectiveness of MLSE IMDD receivers,” IEEE Photon. Technol. Lett. 18, 1037–1039 (2006).
[Crossref]

IEEE Trans. Commun. (1)

G. J. Foschini, L. J. Greenstein, and G. Vanucci, “Noncoherent detection of coherent lightwave signals corrupted by phase noise,” IEEE Trans. Commun. 36, 306–314 (1988).
[Crossref]

J. Lightwave Technol. (6)

L. G. Kazovsky and O. K. Tonguz, “ASK and FSK coherent lightwave systems: a simplified approximate analysis,” J. Lightwave Technol. 8, 338–352 (1990).
[Crossref]

O. K. Tonguz and L. G. Kazovsky, “Theory of Direct Detection Lightwave Receivers using Optical Amplifiers,” J. Lightwave Technol. 9, 174–181 (1991).
[Crossref]

D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9, 505–513 (1991).
[Crossref]

E. Forestieri, “Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and post-detection filtering,” J. Lightwave Technol. 18, 1493–1503 (2000).
[Crossref]

O. E. Agazzi, M. R. Hueda, H. S. Carrer, and D. E. Crivelli, “Maximum-Likelihood Sequence Estimation in Dispersive Optical Channels,” J. Lightwave Technol. 23, 749–763 (2005).
[Crossref]

T. Foggi, E. Forestieri, G. Colavolpe, and G. Prati, “Maximum likelihood sequence detection with closed-form metrics in OOK optical systems impaired by GVD and PMD,” J. Lightwave Technol. 24, 3073–3087 (2006).
[Crossref]

Other (6)

G. Agrawal, Fiber-Optic Communications Systems (John Wiley & Sons, New York, NY, USA, 2002).
[Crossref]

J. G. Proakis, Digital Communications, 4th Edition. (McGraw-Hill, New York, NY, USA, 2001).

S. Benedetto, E. Biglieri, and V. Castellani, Digital Transmission Theory (Prentice-Hall, Englewood Cliffs, NJ, 1987).

G. D. Forney, “The Viterbi Algorithm,” Proc. IEEE61, 268–278 (1973).
[Crossref]

M. R. Hueda, D. E. Crivelli, and H. S. Carrer, “Performance of MLSE-based receivers in lightwave systems with nonlinear dispersion and amplified spontaneous emission noise,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), pp. 299–303 (Dallas, TX, USA, 2004).

A. Prat, J. M. Napoli, M. Gene, P. Omella, V. Poggiolini, and Curri, “Square root strategy: a novel method to linearize an optical communication system with electronic equalizers,” in Proc. European Conf. on Optical Commun. (ECOC), vol. 3, pp. 713–714 (Glasgow, Scotland, 2005).

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Figures (4)

Fig. 1.
Fig. 1.

Scheme of a receiver front-end with the proposed nonlinear processing block after the postdetection filter.

Fig. 2.
Fig. 2.

Comparison between exact PDFs and Gaussian approximations (Euclidean metrics). Two data sequences, corresponding to high (all “0” pattern) and low (all “1” pattern) levels, and two values of α, namely 1/2 and 1/3, are considered.

Fig. 3.
Fig. 3.

OSNR, as a function of the nonlinearity exponent α, at a BER equal to 10-3. CD values equal to 0 ps/nm, 1700 ps/nm, and 2550 ps/nm are considered. For comparison, the performance of the receiver with accurate branch metrics is also shown (horizontal lines).

Fig. 4.
Fig. 4.

OSNR, as a function of the CD, at BER equal to 10-3. The behavior of the OSNR is analyzed for α=1/2, α=1/3, and optimized value of α. For comparison, the OSNR required by a VA with accurate metrics is also shown.

Equations (3)

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a ̂ = argmax a    log p ( r a )
log p ( r a ) i log p ( r i a )
r out ( t ) = r in ( t ) α

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