Abstract

A Stokes-space modulation format classification (MFC) technique is proposed for coherent optical receivers by using a non-iterative clustering algorithm. In the clustering algorithm, two simple parameters are calculated to help find the density peaks of the data points in Stokes space and no iteration is required. Correct MFC can be realized in numerical simulations among PM-QPSK, PM-8QAM, PM-16QAM, PM-32QAM and PM-64QAM signals within practical optical signal-to-noise ratio (OSNR) ranges. The performance of the proposed MFC algorithm is also compared with those of other schemes based on clustering algorithms. The simulation results show that good classification performance can be achieved using the proposed MFC scheme with moderate time complexity. Proof-of-concept experiments are finally implemented to demonstrate MFC among PM-QPSK/16QAM/64QAM signals, which confirm the feasibility of our proposed MFC scheme.

© 2017 Optical Society of America

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References

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  1. W. Wei, C. Wang, and J. Yu, “Cognitive optical networks: Key drivers, enabling techniques, and adaptive bandwidth services,” IEEE Commun. Mag. 50(1), 106–113 (2012).
    [Crossref]
  2. K. Roberts and C. Laperle, “Flexible transceivers,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (online) (Optical Society of America, 2012), paper We.3.A.3.
    [Crossref]
  3. O. A. Dobre, A. Abdi, Y. Bar-Ness, and W. Su, “Survey of automatic modulation classification techniques: classical approaches and new trends,” IET Commun. 1(2), 137–156 (2007).
    [Crossref]
  4. E. Ip, A. P. T. Lau, D. J. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16(2), 753–791 (2008).
    [Crossref] [PubMed]
  5. N. G. Gonzalez, D. Zibar, and I. T. Monroy, “Cognitive digital receiver for burst mode phase modulated radio over fiber links,” in 36th European Conference and Exhibition on Optical Communication,Torino, 2010, pp.1–3.
    [Crossref]
  6. F. N. Khan, Y. Zhou, A. P. Lau, and C. Lu, “Modulation format identification in heterogeneous fiber-optic networks using artificial neural networks,” Opt. Express 20(11), 12422–12431 (2012).
    [Crossref] [PubMed]
  7. 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.
    [Crossref]
  8. R. Borkowski, D. Zibar, A. Caballero, V. Arlunno, and I. T. Monroy, “Optical modulation format recognition in stokes space for digital coherent receivers,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTh3B.3.
    [Crossref]
  9. R. Boada, R. Borkowski, and I. T. Monroy, “Clustering algorithms for Stokes space modulation format recognition,” Opt. Express 23(12), 15521–15531 (2015).
    [Crossref] [PubMed]
  10. P. Isautier, J. Pan, and S. Ralph, “Robust autonomous software-defined coherent optical receiver,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper W1G.7.
    [Crossref]
  11. P. Isautier, J. Pan, R. DeSalvo, and S. E. Ralph, “Stokes space-based modulation format recognition for autonomous optical receivers,” J. Lightwave Technol. 33(24), 5157–5163 (2015).
    [Crossref]
  12. T. Bo, J. Tang, and C. Chan, “Blind modulation format recognition for software-defined optical networks using image processing techniques,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2016), paper Th2A.31.
    [Crossref]
  13. P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16QAM,” J. Lightwave Technol. 28(4), 547–556 (2010).
    [Crossref]
  14. C. Xie and G. Raybon, “Digital PLL based frequency offset compensation and carrier phase estimation for 16QAM coherent optical communication systems,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (online) (Optical Society of America, 2012), paper Mo.1.A.2.
    [Crossref]
  15. T. Pfau, S. Hoffmann, and R. No’e, “Hardware-efficient coherent digital receiver concept with feed forward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(5), 989–999 (2009).
    [Crossref]
  16. A. Rodriguez and A. Laio, “Clustering by fast search and find of density peaks,” Science 344(6191), 1492–1496 (2014).
    [Crossref] [PubMed]
  17. I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
    [Crossref]
  18. T. Tanimura, S. Oda, T. Tanaka, T. Hoshida, Z. Tao, and J. C. Rasmussen, “A simple digital skew compensator for coherent receiver” in 2009 35th European Conference on Optical Communication, Vienna, 2009, pp. 1–2.
  19. R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
    [Crossref]
  20. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
    [Crossref] [PubMed]
  21. F. Gardner, “A BPSK/QPSK timing-error detector for sampled receivers,” IEEE Trans. Commun. 34(5), 423–429 (1986).
    [Crossref]
  22. D. Godard, “Pass band timing recovery in an all-digital modem receiver,” IEEE Trans. Commun. 26(5), 517–523 (1978).
    [Crossref]
  23. B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
    [Crossref] [PubMed]
  24. M. Chagnon, M. Osman, X. Xu, Q. Zhuge, and D. V. Plant, “Blind, fast and SOP independent polarization recovery for square dual polarization-MQAM formats and optical coherent receivers,” Opt. Express 20(25), 27847–27865 (2012).
    [Crossref] [PubMed]
  25. C. M. Bishop, Pattern Recognition and Machine Learning (Information Science and Statistics, 2006).
  26. A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. B 31, 1–38 (1999).
    [Crossref]
  27. J. L. Bentlet, “Multidimensional binary search trees used for associative searching,” Commun. ACM 18(9), 509–517 (1975).
    [Crossref]
  28. G. Bosco, M. Visintin, P. Poggiolini, and F. Forghieri, “A novel update algorithm in stokes space for adaptive equalization in coherent receivers,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper Th3E.6.
    [Crossref]

2015 (2)

2014 (1)

A. Rodriguez and A. Laio, “Clustering by fast search and find of density peaks,” Science 344(6191), 1492–1496 (2014).
[Crossref] [PubMed]

2012 (3)

2010 (2)

2009 (2)

2008 (3)

2007 (1)

O. A. Dobre, A. Abdi, Y. Bar-Ness, and W. Su, “Survey of automatic modulation classification techniques: classical approaches and new trends,” IET Commun. 1(2), 137–156 (2007).
[Crossref]

1999 (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 31, 1–38 (1999).
[Crossref]

1986 (1)

F. Gardner, “A BPSK/QPSK timing-error detector for sampled receivers,” IEEE Trans. Commun. 34(5), 423–429 (1986).
[Crossref]

1978 (1)

D. Godard, “Pass band timing recovery in an all-digital modem receiver,” IEEE Trans. Commun. 26(5), 517–523 (1978).
[Crossref]

1975 (1)

J. L. Bentlet, “Multidimensional binary search trees used for associative searching,” Commun. ACM 18(9), 509–517 (1975).
[Crossref]

Abdi, A.

O. A. Dobre, A. Abdi, Y. Bar-Ness, and W. Su, “Survey of automatic modulation classification techniques: classical approaches and new trends,” IET Commun. 1(2), 137–156 (2007).
[Crossref]

Bar-Ness, Y.

O. A. Dobre, A. Abdi, Y. Bar-Ness, and W. Su, “Survey of automatic modulation classification techniques: classical approaches and new trends,” IET Commun. 1(2), 137–156 (2007).
[Crossref]

Barros, D. J.

Bentlet, J. L.

J. L. Bentlet, “Multidimensional binary search trees used for associative searching,” Commun. ACM 18(9), 509–517 (1975).
[Crossref]

Boada, R.

Borkowski, R.

Buhl, L. L.

Chagnon, M.

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 31, 1–38 (1999).
[Crossref]

DeSalvo, R.

Dobre, O. A.

O. A. Dobre, A. Abdi, Y. Bar-Ness, and W. Su, “Survey of automatic modulation classification techniques: classical approaches and new trends,” IET Commun. 1(2), 137–156 (2007).
[Crossref]

Doerr, C. R.

Fatadin, I.

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

Gardner, F.

F. Gardner, “A BPSK/QPSK timing-error detector for sampled receivers,” IEEE Trans. Commun. 34(5), 423–429 (1986).
[Crossref]

Gnauck, A. H.

Godard, D.

D. Godard, “Pass band timing recovery in an all-digital modem receiver,” IEEE Trans. Commun. 26(5), 517–523 (1978).
[Crossref]

Gonzalez, N. G.

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

Hoffmann, S.

Ip, E.

Isautier, P.

Ishihara, K.

Ives, D.

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

Kahn, J. M.

Khan, F. N.

Kobayashi, T.

Kudo, R.

Laio, A.

A. Rodriguez and A. Laio, “Clustering by fast search and find of density peaks,” Science 344(6191), 1492–1496 (2014).
[Crossref] [PubMed]

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 31, 1–38 (1999).
[Crossref]

Lau, A. P.

Lau, A. P. T.

Lu, C.

Magarini, M.

Marshall, T.

Miyamoto, Y.

Monroy, I. T.

R. Boada, R. Borkowski, and I. T. Monroy, “Clustering algorithms for Stokes space modulation format recognition,” Opt. Express 23(12), 15521–15531 (2015).
[Crossref] [PubMed]

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

Nebendahl, B.

No’e, R.

Osman, M.

Pan, J.

Pfau, T.

Plant, D. V.

Ralph, S. E.

Rodriguez, A.

A. Rodriguez and A. Laio, “Clustering by fast search and find of density peaks,” Science 344(6191), 1492–1496 (2014).
[Crossref] [PubMed]

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 31, 1–38 (1999).
[Crossref]

Sano, A.

Savory, S. J.

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
[Crossref] [PubMed]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

Su, W.

O. A. Dobre, A. Abdi, Y. Bar-Ness, and W. Su, “Survey of automatic modulation classification techniques: classical approaches and new trends,” IET Commun. 1(2), 137–156 (2007).
[Crossref]

Szafraniec, B.

Takatori, Y.

Wang, C.

W. Wei, C. Wang, and J. Yu, “Cognitive optical networks: Key drivers, enabling techniques, and adaptive bandwidth services,” IEEE Commun. Mag. 50(1), 106–113 (2012).
[Crossref]

Wei, W.

W. Wei, C. Wang, and J. Yu, “Cognitive optical networks: Key drivers, enabling techniques, and adaptive bandwidth services,” IEEE Commun. Mag. 50(1), 106–113 (2012).
[Crossref]

Winzer, P. J.

Xu, X.

Yu, J.

W. Wei, C. Wang, and J. Yu, “Cognitive optical networks: Key drivers, enabling techniques, and adaptive bandwidth services,” IEEE Commun. Mag. 50(1), 106–113 (2012).
[Crossref]

Zhou, Y.

Zhuge, Q.

Zibar, D.

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

Commun. ACM (1)

J. L. Bentlet, “Multidimensional binary search trees used for associative searching,” Commun. ACM 18(9), 509–517 (1975).
[Crossref]

IEEE Commun. Mag. (1)

W. Wei, C. Wang, and J. Yu, “Cognitive optical networks: Key drivers, enabling techniques, and adaptive bandwidth services,” IEEE Commun. Mag. 50(1), 106–113 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (1)

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photonics Technol. Lett. 20(20), 1733–1735 (2008).
[Crossref]

IEEE Trans. Commun. (2)

F. Gardner, “A BPSK/QPSK timing-error detector for sampled receivers,” IEEE Trans. Commun. 34(5), 423–429 (1986).
[Crossref]

D. Godard, “Pass band timing recovery in an all-digital modem receiver,” IEEE Trans. Commun. 26(5), 517–523 (1978).
[Crossref]

IET Commun. (1)

O. A. Dobre, A. Abdi, Y. Bar-Ness, and W. Su, “Survey of automatic modulation classification techniques: classical approaches and new trends,” IET Commun. 1(2), 137–156 (2007).
[Crossref]

J. Lightwave Technol. (4)

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 31, 1–38 (1999).
[Crossref]

Opt. Express (6)

Science (1)

A. Rodriguez and A. Laio, “Clustering by fast search and find of density peaks,” Science 344(6191), 1492–1496 (2014).
[Crossref] [PubMed]

Other (10)

T. Tanimura, S. Oda, T. Tanaka, T. Hoshida, Z. Tao, and J. C. Rasmussen, “A simple digital skew compensator for coherent receiver” in 2009 35th European Conference on Optical Communication, Vienna, 2009, pp. 1–2.

C. Xie and G. Raybon, “Digital PLL based frequency offset compensation and carrier phase estimation for 16QAM coherent optical communication systems,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (online) (Optical Society of America, 2012), paper Mo.1.A.2.
[Crossref]

T. Bo, J. Tang, and C. Chan, “Blind modulation format recognition for software-defined optical networks using image processing techniques,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2016), paper Th2A.31.
[Crossref]

P. Isautier, J. Pan, and S. Ralph, “Robust autonomous software-defined coherent optical receiver,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper W1G.7.
[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.
[Crossref]

R. Borkowski, D. Zibar, A. Caballero, V. Arlunno, and I. T. Monroy, “Optical modulation format recognition in stokes space for digital coherent receivers,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTh3B.3.
[Crossref]

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

K. Roberts and C. Laperle, “Flexible transceivers,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (online) (Optical Society of America, 2012), paper We.3.A.3.
[Crossref]

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

G. Bosco, M. Visintin, P. Poggiolini, and F. Forghieri, “A novel update algorithm in stokes space for adaptive equalization in coherent receivers,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper Th3E.6.
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Block diagram of DSP architecture with proposed MFC technique designed for coherent optical receivers
Fig. 2
Fig. 2 Ideal constellations (a)-(e) in the 3-D Stokes space and (f)-(j) in the least square plane of the five modulation formats. The green plane in (a)-(e) means the least square plane.
Fig. 3
Fig. 3 (a)-(c): Schematic diagrams illustrating the minimum distances δ for three kinds of points; (d): decision graph
Fig. 4
Fig. 4 Clustering results of the LSP constellations of the five different modulation formats at relatively high OSNRs. The red points mean the cluster centers.
Fig. 5
Fig. 5 Program flow chart for the proposed MFC technique.
Fig. 6
Fig. 6 Probability of correct classification at different (a) number of symbols; (b) OSNRs. The dotted lines (same color with the corresponding data curves) denote FEC thresholds of the corresponding modulation formats.
Fig. 7
Fig. 7 (a) Probability of correct classification vs. OSNR for PM-16QAM signals. Insets: decision graphs for modified and original clustering algorithms; (b) time complexity and OSNR performance (minimum required OSNR to achieve reliability higher than 95%) comparisons between the proposed MFC algorithm and DBSCAN, ML based MFC algorithms.
Fig. 8
Fig. 8 Experimental Setup. AOM: acoustic-optic modulator; OBPF: optical band pass filter; Att.: tunable attenuator.
Fig. 9
Fig. 9 LSP constellations in Stokes space before rotation correction: (a) PM-QPSK signals at OSNR of 12 dB; (b) PM-16QAM signals at OSNR of 18 dB; (c) PM-64QAM signals at OSNR of 24 dB, and after rotation correction: (d) PM-QPSK signals at OSNR of 12 dB; (e) PM-16QAM signals at OSNR of 18 dB; (f) PM-64QAM signals at OSNR of 24 dB (The red points mean the cluster centers).
Fig. 10
Fig. 10 Measured probability of correct classification vs. (a) number of test symbols; (b) OSNR in the case of back to back; signal power launched to optical fiber after fiber transmission (c) with 4000 test symbols for the PM-QPSK and PM-16QAM signals and 10000 test symbols for the PM-64QAM signal, and (d) with 22000 test symbols PM-QPSK, PM-16QAM and PM-64QAM signals.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

S ( k ) = ( s 0 ( k ) s 1 ( k ) s 2 ( k ) s 3 ( k ) ) = ( e x ( k ) e x * ( k ) + e y ( k ) e y * ( k ) e x ( k ) e x * ( k ) e y ( k ) e y * ( k ) e y ( k ) e x * ( k ) + e x ( k ) e y * ( k ) j e y ( k ) e x * ( k ) + j e x ( k ) e y * ( k ) ) = ( a x 2 ( k ) + a y 2 ( k ) a x 2 ( k ) a y 2 ( k ) 2 a x ( k ) a y ( k ) cos Δ ϕ ( k ) 2 a x ( k ) a y ( k ) sin Δ ϕ ( k ) )
R = t h e n u m b e r o f i n a r e a Ω t h e t o t a l n u m b e r o f p o i n t s i n t h e L S P
ρ i = j χ ( d i j d c )
ψ i = var ( D i ) =   j = 1 n ( d j   D i ¯ ) 2   , d j D i
δ i =     j :   ψ j <   ψ i min ( d i j )
d i s t a n c e ( S , T ) =   i = 1 n s i   t n e a r e s t 2 ,                     s i S ,   t n e a r e s t T 4 , T 8 or T 16

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