Abstract

Stokes space modulation format recognition (Stokes MFR) is a blind method enabling digital coherent receivers to infer modulation format information directly from a received polarization-division-multiplexed signal. A crucial part of the Stokes MFR is a clustering algorithm, which largely influences the performance of the detection process, particularly at low signal-to-noise ratios. This paper reports on an extensive study of six different clustering algorithms: k-means, expectation maximization, density-based DBSCAN and OPTICS, spectral clustering and maximum likelihood clustering, used for discriminating between dual polarization: BPSK, QPSK, 8-PSK, 8-QAM, and 16-QAM. We determine essential performance metrics for each clustering algorithm and modulation format under test: minimum required signal-to-noise ratio, detection accuracy and algorithm complexity.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  3. N. Guerrero Gonzalez, D. Zibar, and I. Tafur Monroy, “Cognitive digital receiver for burst mode phase modulated radio over fiber links,” in 36th European Conference and Exhibition on Optical Communication (IEEE, 2010), pp. 1–3.
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  6. J. Liu, Z. Dong, K. P. Zhong, A. P. T. Lau, C. Lu, and Y. Lu, “Modulation Format Identification Based on Received Signal Power Distributions for Digital Coherent Receivers,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper Th4D.3.
  7. E. J. Adles, M. L. Dennis, W. R. Johnson, T. P. McKenna, C. R. Menyuk, J. E. Sluz, R. M. Sova, M. G. Taylor, and R. A. Venkat, “Blind Optical Modulation Format Identification From Physical Layer Characteristics,” J. Lightwave Technol. 32(8), 1501–1509 (2014).
    [Crossref]
  8. R. Borkowski, D. Zibar, A. Caballero, V. Arlunno, and I. T. Monroy, “Stokes Space-Based Optical Modulation Format Recognition for Digital Coherent Receivers,” IEEE Photon. Technol. Lett. 25(21), 2129–2132 (2013).
    [Crossref]
  9. P. Isautier, A. Stark, J. Pan, K. Mehta, and S. E. Ralph, “Autonomous Software-Defined Coherent Optical Receivers Performing Modulation Format Recognition in Stokes-Space,” in 39th European Conference and Exhibition on Optical Communication (IEEE, 2013), pp. 1–3.
    [Crossref]
  10. G. Bosco, M. Visintin, P. Poggiolini, A. Nespola, M. Huchard, and F. Forghieri, “Experimental Demonstration of a Novel Update Algorithm in Stokes Space for Adaptive Equalization in Coherent Receivers,” in 2014 European Conference on Optical Communication (IEEE, 2014), pp. 1–3.
    [Crossref]
  11. B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
    [Crossref] [PubMed]
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    [Crossref]
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  15. M. Ester, H. P. Kriegel, J. Sander, and X. Xu, “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise,” in Second International Conference on Knowledge Discovery and Data Mining (1996), pp. 226–231.
  16. M. Ankerst, M. M. Breunig, H.-P. Kriegel, and J. Sander, “OPTICS: ordering points to identify the clustering structure,” SIGMOD Rec. 28(2), 49–60 (1999).
    [Crossref]
  17. A. Y. Ng, M. I. Jordan, and Y. Weiss, “On spectral clustering: Analysis and an algorithm,” in Advances in Neural Information Processing Systems (2001), pp. 849–856.
  18. P. J. Rousseeuw, “Silhouettes: A graphical aid to the interpretation and validation of cluster analysis,” J. Comput. Appl. Math. 20, 53–65 (1987).
    [Crossref]
  19. P. Poggiolini, Sistemi Numerici di Trasmissione Ottica Basati sulla Modulazione di Polarizzazione (Ph.D. thesis, Politecnico di Torino, Facoltà di Ingegneria, Dipartimento di Elettronica: Italy) (1993).

2014 (3)

2013 (2)

R. Borkowski, D. Zibar, A. Caballero, V. Arlunno, and I. T. Monroy, “Stokes Space-Based Optical Modulation Format Recognition for Digital Coherent Receivers,” IEEE Photon. Technol. Lett. 25(21), 2129–2132 (2013).
[Crossref]

N. J. Muga and A. N. Pinto, “Digital PDL Compensation in 3D Stokes Space,” J. Lightwave Technol. 31(13), 2122–2130 (2013).
[Crossref]

2012 (1)

2010 (1)

1999 (1)

M. Ankerst, M. M. Breunig, H.-P. Kriegel, and J. Sander, “OPTICS: ordering points to identify the clustering structure,” SIGMOD Rec. 28(2), 49–60 (1999).
[Crossref]

1987 (1)

P. J. Rousseeuw, “Silhouettes: A graphical aid to the interpretation and validation of cluster analysis,” J. Comput. Appl. Math. 20, 53–65 (1987).
[Crossref]

1977 (1)

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum Likelihood from Incomplete Data via the EM Algorithm,” J. R. Stat. Soc., B 39, 1–38 (1977).

Adles, E. J.

Aguado, J. C.

Ankerst, M.

M. Ankerst, M. M. Breunig, H.-P. Kriegel, and J. Sander, “OPTICS: ordering points to identify the clustering structure,” SIGMOD Rec. 28(2), 49–60 (1999).
[Crossref]

Arlunno, V.

R. Borkowski, D. Zibar, A. Caballero, V. Arlunno, and I. T. Monroy, “Stokes Space-Based Optical Modulation Format Recognition for Digital Coherent Receivers,” IEEE Photon. Technol. Lett. 25(21), 2129–2132 (2013).
[Crossref]

Borkowski, R.

R. Borkowski, D. Zibar, and I. Tafur Monroy, “Anatomy of a digital coherent receiver,” IEICE Trans. Commun. E 97.B(8), 1528–1536 (2014).
[Crossref]

A. Caballero, R. Borkowski, I. de Miguel, R. J. Duran, J. C. Aguado, N. Fernandez, T. Jimenez, I. Rodriguez, D. Sanchez, R. M. Lorenzo, D. Klonidis, E. Palkopoulou, N. P. Diamantopoulos, I. Tomkos, D. Siracusa, A. Francescon, E. Salvadori, Y. Ye, J. L. Vizcaino, F. Pittala, A. Tymecki, and I. T. Monroy, “Cognitive, Heterogeneous and Reconfigurable Optical Networks: The CHRON Project,” J. Lightwave Technol. 32(13), 2308–2323 (2014).
[Crossref]

R. Borkowski, D. Zibar, A. Caballero, V. Arlunno, and I. T. Monroy, “Stokes Space-Based Optical Modulation Format Recognition for Digital Coherent Receivers,” IEEE Photon. Technol. Lett. 25(21), 2129–2132 (2013).
[Crossref]

Breunig, M. M.

M. Ankerst, M. M. Breunig, H.-P. Kriegel, and J. Sander, “OPTICS: ordering points to identify the clustering structure,” SIGMOD Rec. 28(2), 49–60 (1999).
[Crossref]

Caballero, A.

de Miguel, I.

Dempster, A. P.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum Likelihood from Incomplete Data via the EM Algorithm,” J. R. Stat. Soc., B 39, 1–38 (1977).

Dennis, M. L.

Diamantopoulos, N. P.

Duran, R. J.

Ester, M.

M. Ester, H. P. Kriegel, J. Sander, and X. Xu, “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise,” in Second International Conference on Knowledge Discovery and Data Mining (1996), pp. 226–231.

Fernandez, N.

Francescon, A.

Jimenez, T.

Johnson, W. R.

Khan, F. N.

Klonidis, D.

Kriegel, H. P.

M. Ester, H. P. Kriegel, J. Sander, and X. Xu, “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise,” in Second International Conference on Knowledge Discovery and Data Mining (1996), pp. 226–231.

Kriegel, H.-P.

M. Ankerst, M. M. Breunig, H.-P. Kriegel, and J. Sander, “OPTICS: ordering points to identify the clustering structure,” SIGMOD Rec. 28(2), 49–60 (1999).
[Crossref]

Laird, N. M.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum Likelihood from Incomplete Data via the EM Algorithm,” J. R. Stat. Soc., B 39, 1–38 (1977).

Lau, A. P. T.

Lorenzo, R. M.

Lu, C.

Marshall, T.

McKenna, T. P.

Menyuk, C. R.

Monroy, I. T.

Muga, N. J.

Nebendahl, B.

Palkopoulou, E.

Pinto, A. N.

Pittala, F.

Rodriguez, I.

Rousseeuw, P. J.

P. J. Rousseeuw, “Silhouettes: A graphical aid to the interpretation and validation of cluster analysis,” J. Comput. Appl. Math. 20, 53–65 (1987).
[Crossref]

Rubin, D. B.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum Likelihood from Incomplete Data via the EM Algorithm,” J. R. Stat. Soc., B 39, 1–38 (1977).

Salvadori, E.

Sanchez, D.

Sander, J.

M. Ankerst, M. M. Breunig, H.-P. Kriegel, and J. Sander, “OPTICS: ordering points to identify the clustering structure,” SIGMOD Rec. 28(2), 49–60 (1999).
[Crossref]

M. Ester, H. P. Kriegel, J. Sander, and X. Xu, “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise,” in Second International Conference on Knowledge Discovery and Data Mining (1996), pp. 226–231.

Siracusa, D.

Sluz, J. E.

Sova, R. M.

Szafraniec, B.

Tafur Monroy, I.

R. Borkowski, D. Zibar, and I. Tafur Monroy, “Anatomy of a digital coherent receiver,” IEICE Trans. Commun. E 97.B(8), 1528–1536 (2014).
[Crossref]

Taylor, M. G.

Tomkos, I.

Tymecki, A.

Venkat, R. A.

Vizcaino, J. L.

Xu, X.

M. Ester, H. P. Kriegel, J. Sander, and X. Xu, “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise,” in Second International Conference on Knowledge Discovery and Data Mining (1996), pp. 226–231.

Ye, Y.

Zhou, Y.

Zibar, D.

R. Borkowski, D. Zibar, and I. Tafur Monroy, “Anatomy of a digital coherent receiver,” IEICE Trans. Commun. E 97.B(8), 1528–1536 (2014).
[Crossref]

R. Borkowski, D. Zibar, A. Caballero, V. Arlunno, and I. T. Monroy, “Stokes Space-Based Optical Modulation Format Recognition for Digital Coherent Receivers,” IEEE Photon. Technol. Lett. 25(21), 2129–2132 (2013).
[Crossref]

IEEE Photon. Technol. Lett. (1)

R. Borkowski, D. Zibar, A. Caballero, V. Arlunno, and I. T. Monroy, “Stokes Space-Based Optical Modulation Format Recognition for Digital Coherent Receivers,” IEEE Photon. Technol. Lett. 25(21), 2129–2132 (2013).
[Crossref]

IEICE Trans. Commun. (1)

R. Borkowski, D. Zibar, and I. Tafur Monroy, “Anatomy of a digital coherent receiver,” IEICE Trans. Commun. E 97.B(8), 1528–1536 (2014).
[Crossref]

J. Comput. Appl. Math. (1)

P. J. Rousseeuw, “Silhouettes: A graphical aid to the interpretation and validation of cluster analysis,” J. Comput. Appl. Math. 20, 53–65 (1987).
[Crossref]

J. Lightwave Technol. (3)

J. R. Stat. Soc., B (1)

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum Likelihood from Incomplete Data via the EM Algorithm,” J. R. Stat. Soc., B 39, 1–38 (1977).

Opt. Express (2)

SIGMOD Rec. (1)

M. Ankerst, M. M. Breunig, H.-P. Kriegel, and J. Sander, “OPTICS: ordering points to identify the clustering structure,” SIGMOD Rec. 28(2), 49–60 (1999).
[Crossref]

Other (9)

A. Y. Ng, M. I. Jordan, and Y. Weiss, “On spectral clustering: Analysis and an algorithm,” in Advances in Neural Information Processing Systems (2001), pp. 849–856.

P. Poggiolini, Sistemi Numerici di Trasmissione Ottica Basati sulla Modulazione di Polarizzazione (Ph.D. thesis, Politecnico di Torino, Facoltà di Ingegneria, Dipartimento di Elettronica: Italy) (1993).

M. Ester, H. P. Kriegel, J. Sander, and X. Xu, “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise,” in Second International Conference on Knowledge Discovery and Data Mining (1996), pp. 226–231.

C. M. Bishop, Pattern Recognition and Machine Learning (Information Science and Statistics, 2006).

P. Isautier, A. Stark, K. Mehta, R. de Salvo, and S. E. Ralph, “Autonomous Software-Defined Coherent Optical Receivers,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTh3B.4.
[Crossref]

J. Liu, Z. Dong, K. P. Zhong, A. P. T. Lau, C. Lu, and Y. Lu, “Modulation Format Identification Based on Received Signal Power Distributions for Digital Coherent Receivers,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper Th4D.3.

N. Guerrero Gonzalez, D. Zibar, and I. Tafur Monroy, “Cognitive digital receiver for burst mode phase modulated radio over fiber links,” in 36th European Conference and Exhibition on Optical Communication (IEEE, 2010), pp. 1–3.
[Crossref]

P. Isautier, A. Stark, J. Pan, K. Mehta, and S. E. Ralph, “Autonomous Software-Defined Coherent Optical Receivers Performing Modulation Format Recognition in Stokes-Space,” in 39th European Conference and Exhibition on Optical Communication (IEEE, 2013), pp. 1–3.
[Crossref]

G. Bosco, M. Visintin, P. Poggiolini, A. Nespola, M. Huchard, and F. Forghieri, “Experimental Demonstration of a Novel Update Algorithm in Stokes Space for Adaptive Equalization in Coherent Receivers,” in 2014 European Conference on Optical Communication (IEEE, 2014), pp. 1–3.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Constellations of polarization-multiplexed modulation formats (top row) and their corresponding Stokes space representation in the Poincaré sphere (bottom row).
Fig. 2
Fig. 2 Visual representation of the steps for the ML-based algorithm, applied to discriminate between BPSK, QPSK and 8PSK polarization multiplexed modulation formats.
Fig. 3
Fig. 3 Setup of the simulated optical communications system. Typical stages of DSP are shown with Stokes-based modulation format recognition step highlighted in green.
Fig. 4
Fig. 4 Reliability results versus optical signal-to-noise ratio for the clustering algorithms. Average of 500 realizations. Green background represents the OSNR range higher than FEC limit for the corresponding modulation format at BER = 3.8 × 10−3 at 28 Gbaud.
Fig. 5
Fig. 5 Minimum OSNR required for recognition of modulation formats for each clustering algorithm.
Fig. 6
Fig. 6 Relative complexity, evaluated in terms of algorithm runtime, for all clustering algorithms under test.

Tables (1)

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Table 1 Algorithms’ parameters used for comparison

Equations (5)

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S=( S 0 S 1 S 2 S 3 )= 1 2 ( | x | 2 + | y | 2 | x | 2 | y | 2 2(x y ¯ ) 2(x y ¯ ) )
J= 1 N k=1 K i C k x i μ k 2 .
p( X )= k=1 K π k N( X| μ k , Σ k )
neighbourhood ε ( x i )MinPts where x i X
α= argmin θ ( i=1 N min k x i y k ( θ ) 2 )

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