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Journal of Lightwave Technology

Journal of Lightwave Technology


  • Vol. 27, Iss. 22 — Nov. 15, 2009
  • pp: 5115–5126

Power-Efficient Modulation Formats in Coherent Transmission Systems

Erik Agrell and Magnus Karlsson

Journal of Lightwave Technology, Vol. 27, Issue 22, pp. 5115-5126 (2009)

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Coherent optical transmission systems have a four-dimensional (4–D) signal space (two quadratures in two polarizations). These four dimensions can be used to create modulation formats that have a better power efficiency (higher sensitivity) than the conventional binary phase shift keying/quadrature phase shift keying (BPSK/QPSK) signals. Several examples are given, with some emphasis on a 24-level format and an 8-level format, including descriptions of how they can be realized and expressions for their symbol and bit error probabilities. These formats are, respectively, an extension and a subset of the commonly used 16-level dual-polarization QPSK format. Sphere packing simulations in 2, 3, and 4 dimensions, up to 32 levels, are used to verify their optimality. The numerical results, as the number of levels increases, are shown to agree with lattice-theoretical results. Finally, we point out that the use of these constellations will lead to improved fundamental sensitivity limits for optical communication systems, and they may also be relevant as a way of reducing power demands and/or nonlinear influence.

© 2009 IEEE

Erik Agrell and Magnus Karlsson, "Power-Efficient Modulation Formats in Coherent Transmission Systems," J. Lightwave Technol. 27, 5115-5126 (2009)

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  1. T. Pfau, S. Hoffmann, R. Peveling, S. Ibrahim, O. Adamczyk, M. Porrmann, S. Bhandare, R. Noé, Y. Achiam, "Synchronous QPSK transmission at 1.6 Gbit/s with standard DFB lasers and real-time digital receiver," Electron. Lett. 42, 1175-1176 (2006).
  2. A. Leven, N. Kaneda, U. Koc, Y. Chen, "Coherent receivers for practical optical communication systems," Proc. Opt. Fiber Commun. Nat. Fiber Opt. Eng. Conf. (OFC/NFOEC) (2007).
  3. A. Leven, N. Kaneda, Y.-K. Chen, "A real-time CMA-based 10 Gb/s polarization demultiplexing coherent receiver implemented in an FPGA," Proc. Opt. Fiber Commun./Nat. Fiber Opt. Eng. Conf. (OFC/NFOEC) (2008).
  4. H. Sun, K. Wu, K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Exp. 16, 873-879 (2008).
  5. D. Ly-Gagnon, K. Katoh, K. Kikuchi, "Unrepeatered optical transmission of 20 Gbit/s quadrature phase-shift keying signals over 210 km using homodyne phase-diversity receiver and digital signal processing," Electron. Lett. 41, 206-207 (2005).
  6. G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, S. Bigo, "Transmission of 40 Gb/s QPSK with coherent detection over ultra-long distance improved by nonlinearity mitigation," Proc. Eur. Conf. Opt. Commun. (ECOC) (2006) pp. 35-36.
  7. S. Tsukamoto, D. Ly-Gagnon, K. Katoh, K. Kikuchi, "Coherent demodulation of 40-Gbit/s polarization-multiplexed QPSK signals with 16-GHz spacing after 200-km transmission," Proc. Opt. Fiber Commun. Nat. Fiber Opt. Eng. Conf. (OFC/NFOEC) (2005).
  8. G. Charlet, M. Salsi, J. Renaudier, O. Pardo, H. Mardoyan, S. Bigo, "Performance comparison of singly-polarised and polarisation-multiplexed coherent transmission at 10 Gbauds under linear impairments," Electron. Lett. 43, 1109-1111 (2007).
  9. J. Renaudier, G. Charlet, M. Salsi, O. Pardo, H. Mardoyan, P. Tran, S. Bigo, "Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver," J. Lightw. Technol. 26, 36-42 (2008).
  10. G. Jacobsen, Noise in Digital Optical Transmission Systems (Artech House, 1994).
  11. L. Kazovsky, S. Benedetto, A. Willner, Optical Fiber Communication Systems (Artech House, 1996).
  12. J. Kahn, K.-P. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM systems," IEEE J. Sel. Topics Quantum Electron. 10, 259-272 (2004).
  13. K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer-Verlag, 2005).
  14. E. Ip, A. Lau, D. Barros, J. Kahn, "Coherent detection in optical fiber systems," Opt. Exp. 16, 753-791 (2008) (erratum, vol. 16, no. p. 26, p. 21943, 2008).
  15. D. Saha, T. Birdsall, "Quadrature-quadrature phase-shift keying," IEEE Trans. Commun. 37, 437-448 (1989).
  16. G. Welti, J. Lee, "Digital transmission with coherent four-dimensional modulation," IEEE Trans. Inf. Theory IT-20, 497-502 (1974).
  17. L. Zetterberg, H. Brändström, "Codes for combined phase and amplitude modulated signals in a four-dimensional space," IEEE Trans. Commun. COM-25, 943-950 (1977).
  18. G. Taricco, E. Biglieri, V. Castellani, "Applicability of four-dimensional modulations to digital satellites: A simulation study," Proc. IEEE Global Telecommun. Conf. (GLOBECOM) (1993) pp. 28-34.
  19. S. Betti, F. Curti, G. De Marchis, E. Iannone, "Exploiting fibre optics transmission capacity: 4-quadrature multilevel signalling," Electron. Lett. 26, 992-993 (1990).
  20. S. Betti, F. Curti, G. D. Marchis, and E. Iannone, "A novel multilevel coherent optical system: 4-quadrature signaling," J. Lightw. Technol. 9, 514-523 (1991).
  21. S. Betti, G. De Marchis, E. Iannone, P. Lazzaro, "Homodyne optical coherent systems based on polarization modulation," J. Lightw. Technol. 9, 1314-1320 (1991).
  22. R. Cusani, E. Iannone, A. Salonico, M. Todaro, "An efficient multilevel coherent optical system: M-4Q-QAM," J. Lightw. Technol. 10, 777-786 (1992).
  23. M. Karlsson, E. Agrell, "Which is the most power-efficient modulation format in optical links?," Opt. Exp., 1713 pp. 10814-10819 (2009) http://www.opticsexpress.org/abstract.cfm?URI=oe-17-13-10814.
  24. S. Benedetto, P. Poggiolini, "Theory of polarization shift keying modulation," IEEE Trans. Commun. 40, 708-721 (1992).
  25. S. Benedetto, A. Djupsjöbacka, B. Lagerström, R. Paoletti, P. Poggiolini, G. Mijic, "Multilevel polarization modulation using a specifically designed LiNbO$_3$ device," IEEE Photon. Technol. Lett. 6, 949-951 (1994).
  26. H. Zhao, E. Agrell, M. Karlsson, "Unequal bit error probability in coherent QPSK fiber-optic systems using phase modulator based transmitters," Eur. Trans. Telecommun. 19, 895-906 (2007).
  27. H. Zhao, M. Karlsson, E. Agrell, "Transmitter comparison and unequal bit error probabilities in coherent QPSK systems," Proc. Opt. Fiber Commun. Nat. Fiber Opt. Eng. Conf. (OFC/NFOEC) (2007).
  28. H. Zhao, E. Agrell, M. Karlsson, "Intersymbol interference in DQPSK fiber-optic systems," Eur. Trans. Telecommun. .
  29. K. Kikuchi, S. Tsukamoto, "Evaluation of sensitivity of the digital coherent receiver," J. Lightw. Technol. 26, 1817-1822 (2008).
  30. S. Benedetto, E. Biglieri, Principles of Digital Transmission: With Wireless Applications (Kluwer, 1999).
  31. J. Proakis, Digital Communications (McGraw-Hill, 2001).
  32. H. Bülow, "Polarization QAM modulation (POL-QAM) for coherent detection schemes," Proc. Opt. Fiber Commun. Nat. Fiber Opt. Eng. Conf. (OFC/NFOEC) (2009).
  33. J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer-Verlag, 1999).
  34. O. Musin, "The kissing number in four dimensions," Ann. Math. 168, 1-32 (2008).
  35. N. J. A. Sloane, R. H. Hardin, T. S. Duff, J. H. Conway, (1997)"Minimal-energy clusters, library of 3-d clusters, library of 4-d clusters," http://www.research.att.com/~njas/cluster/.
  36. R. L. Graham, N. J. A. Sloane, "Penny-packing and two-dimensional codes," Discrete Comput. Geom. 5, 1-11 (1990).
  37. M. Simon, S. Hinedi, W. Lindsey, Digital Communication Techniques: Signal Design and Detection (Prentice-Hall, 1995).
  38. L. Xiao, X. Dong, "New analytical expressions for orthogonal, biorthogonal, and transorthogonal signaling in Nakagami fading channels with diversity reception," IEEE Trans. Wireless Commun. 4, 1418-1424 (2005).
  39. M. K. Simon, R. Annavajjala, "On the optimality of bit detection of certain digital modulations," IEEE Trans. Commun. 53, 299-307 (2005).
  40. G. Foschini, R. Gitlin, S. Weinstein, "Optimization of two-dimensional signal constellations in the presence of Gaussian noise," IEEE Trans. Commun. COM-22, 28-38 (1974).
  41. N. J. A. Sloane, R. H. Hardin, T. S. Duff, J. H. Conway, "Minimal-energy clusters of hard spheres," Discrete Comput. Geom. 14, 237-259 (1995).
  42. J.-E. Porath, T. Aulin, "Design of multidimensional signal constellations," Inst. Electr. Eng. Proc.-Commun. 150, 317-323 (2003).
  43. J. R. Pierce, "Comparison of three-phase modulation with two-phase and four-phase modulation," IEEE Trans. Commun. COM-28, 1098-1099 (1980).
  44. N. Ekanayake, T. Tjhung, "On ternary phase-shift keyed signaling," IEEE Trans. Inf. Theory IT-28, 658-660 (1982).
  45. J. P. Gordon, L. R. Walker, W. H. Louisell, "Quantum statistics of masers and attenuators," Phys. Rev. 130, 806-812 (1963).
  46. J. R. Pierce, "Optical channels: Practical limits with photon counting," IEEE Trans. Commun. 26, 1819-1821 (1978).

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