Abstract

The drive for higher performance in optical fiber systems has renewed interest in coherent detection. We review detection methods, including noncoherent, differentially coherent, and coherent detection, as well as a hybrid method. We compare modulation methods encoding information in various degrees of freedom (DOF). Polarization-multiplexed quadrature-amplitude modulation maximizes spectral efficiency and power efficiency, by utilizing all four available DOF, the two field quadratures in the two polarizations. Dual-polarization homodyne or heterodyne downconversion are linear processes that can fully recover the received signal field in these four DOF. When downconverted signals are sampled at the Nyquist rate, compensation of transmission impairments can be performed using digital signal processing (DSP). Linear impairments, including chromatic dispersion and polarization-mode dispersion, can be compensated quasi-exactly using finite impulse response filters. Some nonlinear impairments, such as intra-channel four-wave mixing and nonlinear phase noise, can be compensated partially. Carrier phase recovery can be performed using feedforward methods, even when phase-locked loops may fail due to delay constraints. DSP-based compensation enables a receiver to adapt to time-varying impairments, and facilitates use of advanced forward-error-correction codes. We discuss both single- and multi-carrier system implementations. For a given modulation format, using coherent detection, they offer fundamentally the same spectral efficiency and power efficiency, but may differ in practice, because of different impairments and implementation details. With anticipated advances in analog-to-digital converters and integrated circuit technology, DSP-based coherent receivers at bit rates up to 100 Gbit/s should become practical within the next few years.

© 2008 Optical Society of America

Full Article  |  PDF Article

Corrections

Ezra Ip, Alan P. Lau, Daniel J. Barros, and Joseph M. Kahn, "Coherent detection in optical fiber systems: erratum," Opt. Express 16, 21943-21943 (2008)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-16-26-21943

References

  • View by:
  • |
  • |
  • |

  1. C.E. Shannon, "A mathematical theory of communication," Bell. Syst. Tech. J. 27, 379−423 (1948).
  2. J. M. Geist, "Capacity and cutoff rate for dense M-ary PSK constellations," in MILCOM 1990, (Monterey, CA, USA, 1990), pp. 768−770.
  3. K.-P. Ho, "Exact evaluation of the capacity for intensity-modulated direct-detection channels with optical amplifier noises," IEEE Photon. Technol. Lett. 17, 858−860 (2005).
    [CrossRef]
  4. P.P. Mitra and J.B. Stark, "Nonlinear limits to the information capacity of optical fiber communications," Nature 411, 1027-1030 (2001).
    [CrossRef] [PubMed]
  5. J. M. Kahn and K.-P. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM Systems," J. Sel. Top. Quantum Electron. 10, 259-271 (2004).
    [CrossRef]
  6. V. Jungnickel, A. Forck, T. Haustein, S. Schiffermuller, C. Helmolt, F. Luhn, M. Pollock, C. Juchems, M. Lampe, S. Eichnger, W. Zirwas, E. Schulz, "1 Gbit/s MIMO-OFDM transmission experiments," in Proceedings of IEEE Conference on Vehicular Technol. (Institute of Electrical and Electronics Engineers, Dallas, 2005), pp. 861-866.
  7. K. Kikuchi, "Coherent detection of phase-shift keying signals using digital carrier-phase estimation," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2006), Paper OTuI4.
  8. T. Pfau, S. Hoffmann, R. Peveling, S. Bhandard, S. Ibrahim, O. Adamczyk, M. Porrmann, R. Noé and Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).
    [CrossRef]
  9. A. Leven, N. Kaneda, U.-V. Koc and Y.-K. Chen, "Coherent receivers for practical optical communication systems," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2007), Paper OThK4.
  10. S. J. Savory, G. Gavioli, R. I. Killey, P. Bayvel, "Transmission of 42.8 Gbit/s polarization multiplexed NRZ-QPSK over 6400 km of standard fiber with no optical dispersion compensation," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2007), Paper OTuA1.
  11. K. Sekine, N. Kikuchi, S. Sasaki, S. Hayase, C. Hasegawa and T. Sugawara, "40 Gbit/s, 16-ary (4 bit/symbol) optical modulation/demodulation scheme," Electron. Lett. 41, 430-432, (2005).
    [CrossRef]
  12. J. Hongo, K. Kasai, M. Yoshida and M. Nakazawa, "1-Gsymbol/s 64-QAM coherent optical transmission over 150 km," IEEE Photon. Technol. Lett. 19, 638-640 (2007).
    [CrossRef]
  13. 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]
  14. M. Nazarathy and E. Simony, "Multichip differential phase encoded optical transmission," IEEE Photon. Technol. Lett. 17, 1133-1135 (2005).
    [CrossRef]
  15. D. Divsalar and M. Simon, "Multiple-symbol differential detection of MPSK," IEEE Trans. Commun. 38, 300-308 (1990).
    [CrossRef]
  16. S. Benedetto and P. Poggiolini, "Theory of polarization shift keying modulation," IEEE Trans. Commun. 40, 708−721 (1992).
    [CrossRef]
  17. S. Betti, F. Curti, G. de Marchis and E. Iannone, "Multilevel coherent optical system based on Stokes parameters modulation," J. Lightwave Technol. 8, 1127−1136 (1990).
    [CrossRef]
  18. E. Ip and J. M. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightwave Technol.,  25, 2675-2692 (2007).
    [CrossRef]
  19. E. Ip and J.M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightwave Technol. 25, 2033-2043 (2007).
    [CrossRef]
  20. E. Ip and J.M. Kahn, "Carrier synchronization for 3- and 4-bit-per-symbol optical transmission," J. Lightwave Technol. 23, 4110-4124 (2005).
    [CrossRef]
  21. S. Tsukamoto, K. Katoh and K. Kikuchi, "Coherent demodulation of optical multilevel phase-shift-keying signals using homodyne detection and digital signal processing," IEEE Photon. Technol. Lett. 18, 1131-1133 (2006).
    [CrossRef]
  22. G. P. Agrawal, Fiber-Optic Communiation Systems, 3rd ed. (Wiley, New York, 2002).
    [CrossRef]
  23. J. R. Barry and J.M. Kahn, "Carrier synchronization for homodyne and heterodyne detection of optical quadriphase-shift keying," J. Lightwave Technol. 10, 1939-1951 (1992).
    [CrossRef]
  24. R. Noé, "Phase noise-tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedforward carrier recovery," J. Lightwave Technol. 23, 802−808 (2005).
    [CrossRef]
  25. J. Rebola and A. Cartaxo, "Optimization of level spacing in quaternary optical communication systems," Proc. SPIE 4087, 49−59 (2000).
    [CrossRef]
  26. J. J. Bussgang and M. Leiter, "Error rate approximations for differential phase-shift keying." IEEE Trans. Commun. Systems 12, 18-27 (1964).
    [CrossRef]
  27. J. G. Proakis, "Probabilities of error for adaptive reception of M-phase signals," IEEE Trans. Commun. Tech. 16, 71-81 (1968).
    [CrossRef]
  28. S. Benedetto and P. Poggiolini, "Multilevel polarization shift keying: optimum receiver structure and performance evaluation," IEEE Trans. Commun. 42, 1174-1186 (1994).
    [CrossRef]
  29. J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, New York, 2001).
  30. M. Suzuki and N. Edagawa, "Dispersion-managed high-capacity ultra-long-haul transmission," J. Lightwave Technol. 21, 916−929 (2003).
    [CrossRef]
  31. E. Forestieri and G. Prati, "Exact analytical evaluation of second-order PMD impact on the outage probability for a compensated system," J. Lightwave Technol. 22, 988−996 (2004).
    [CrossRef]
  32. C. D. Poole, R. W. Tkach, A. R. Chraplyvy and D. A. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).
    [CrossRef]
  33. H. Bülow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Küppers and W. Weiershausen, "Measurement of the maximum speed of PMD fluctuation in installed field fiber," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, San Diego, 1999), Paper OWE4.
  34. C. D. Poole, "Statistical treatment of polarization dispersion in single-mode fiber," Opt. Lett. 13, 687-689 (1988).
    [CrossRef] [PubMed]
  35. N. Gisin, J.-P. Von der Weid and J.-P. Pellaux, "Polarization mode dispersion of short and long single-mode fibers," J. Lightwave Technol. 9, 821-827 (1991).
    [CrossRef]
  36. G. J. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single-mode fibers," J. Lightwave Technol. 9, 1439-1456 (1991).
    [CrossRef]
  37. H. Bülow, "System outage probability due to first- and second-order PMD," IEEE Photon. Technol. Lett. 10, 696-698 (1998).
    [CrossRef]
  38. H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson and P. Andrekson, "A comparison between different PMD compensation techniques," J. Lightwave Technol. 20, 368-378 (2002).
    [CrossRef]
  39. F. Buchali and H. Bülow, "Adaptive PMD compensation by electrical and optical techniques," J. Lightwave Technol. 22, 1116-1126 (2004).
    [CrossRef]
  40. R. Noé, D. Sandel, M. Yoshida-Dierolf, S. Hinz, V. Mirvoda, A. Schöpflin, C. Flingener, E. Gottwald, C. Scheerer, G. Fischer, T. Weyrauch and W. Haase, "Polarization mode dispersion compensation at 10, 20, and 40 Gb/s with various optical equalizer," J. Lightwave Technol. 17, 1602-1616 (1999).
    [CrossRef]
  41. S. Lee, R. Khosravani, J. Peng, V. Grubsky, D. S. Starodubov, A. E. Willner and J. Feinberg, "Adjustable compensation of polarization mode dispersion using a high-birefringence nonlinearly chirped fiber Bragg grating," IEEE Photon. Technol. Lett. 11, 1277-1279 (1999).
    [CrossRef]
  42. T. Saida, K. Takiguchi, S. Kuwahara, Y. Kisaka, Y. Miyamoto, Y. Hashizume, T. Shibata and K. Okamoto, "Planar lightwave circuit polarization-mode dispersion compensator," IEEE Photon. Technol. Lett. 14, 507-509 (2002).
    [CrossRef]
  43. J. Wang and J. M. Kahn, "Performance of electrical equalizers in optical amplified OOK and DPSK systems," IEEE Photon. Technol. Lett. 16, 1397-1399 (2004).
    [CrossRef]
  44. C. Vinegoni, M. Karlsson, M. Petersson and H. Sunnerud, "The statistics of polarization-dependent loss in a recirculating loop," J. Lightwave Technol. 22, 968−976 (2004).
    [CrossRef]
  45. A. H. Gnauck, P. J. Winzer and S. Chandrasekhar, "Hybrid 10/40-G transmission on a 50-GHz Grid through 2800 km of SSMF and seven optical add-drops," IEEE Photon. Technol. Lett. 17, 2203−2205 (2005).
    [CrossRef]
  46. G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19, 969−971 (2007).
    [CrossRef]
  47. N. Amitay and J. Salz, "Linear Equalization Theory in Digital Data Transmission over Dually Polarized Fading Radio Channels," Bell. Syst. Tech. J. 63, 2215-2259 (1984).
  48. J. Salz, "Digital transmission over cross-coupled linear channels," AT&T Tech. J. 64, 1147-1159 (1985).
  49. H. Meyr, M. Moeneclaey and S. Fechtel, Digital Communication Receivers. (John Wiley, New York, 1997).
  50. R.D. Gitlin and S. B. Weinstein, "Fractionally spaced equalization: an improved digital transversal equalizer," Bell. Syst. Tech. J. 60, 275-296 (1981).
  51. G. Ungerboeck, "Fractional tap-spacing equalizer and consequences for clock recovery in data modems," IEEE Trans. Commun. 24, 856-864 (1976).
    [CrossRef]
  52. S. Qureshi, "Adaptive equalization," Proceedings of the IEEE 73, 1349-1387 (1985).
    [CrossRef]
  53. B. Widrow and S. D. Stearns, Adaptive Signal Processing, (Prentice Hall, Englewood Cliffs, NJ, 1985).
  54. A. Oppenheim and R. Schafer, Discrete-Time Signal Processing, (Prentice Hall, Englewood Cliffs, NJ, 1989).
  55. A. Mecozzi, C. B. Clausen and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392−394 (2000).
    [CrossRef]
  56. I. Shake, H. Takara, K. Mori, S. Kawanishi and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600−1601 (1998).
    [CrossRef]
  57. R.-J. Essiambre, B. Mikkelsen and G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576−1578 (1999).
    [CrossRef]
  58. A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park and A. H. Gnauck, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445−447 (2001).
    [CrossRef]
  59. A. Striegler and B. Schmauss, "Compensation of intrachannel effects in symmetric dispersion-managed transmission systems," J. Lightwave Technol. 22, 1877−1882 (2004).
    [CrossRef]
  60. N. Alic and Y. Fainman, "Data-dependent phase coding for suppression of ghost pulses in optical fibers," IEEE Photon. Technol. Lett. 16, 1212−1214 (2004).
    [CrossRef]
  61. I.B. Djordjevic and B. Vasic, "Constrained coding techniques for suppression of intrachannel nonlinear effects in high-speed optical transmission," J. Lightwave Technol. 24, 411−419 (2006).
    [CrossRef]
  62. X. Wei and X. Liu, "Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion," Opt. Lett. 28, 2300−2302 (2003).
    [CrossRef] [PubMed]
  63. A. P. T. Lau, S. Rabbani and J. M. Kahn are preparing a manuscript to be called "On the statistics of intra-channel four-wave-mixing induced phase noise in phase modulated systems."
  64. J. P. Gordon and L.F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. 15, 1351−1353 (1990).
    [CrossRef] [PubMed]
  65. K.-P. Ho, Phase-Modulated Optical Communication Systems, (Springer, New York, 2005).
  66. K.-P. Ho, "Statistical properties of nonlinear phase noise," in Advances in Optics and Laser Research3, (Nova Science Publishers, New York, 2003).
  67. A. P. T. Lau and J. M. Kahn, "Design of inline amplifiers gain and spacing to minimize phase noise in optical transmission systems," J. Lightwave Technol. 24, 1334−1341 (2006).
    [CrossRef]
  68. A.P.T. Lau and J.M. Kahn, "Power profile optimization in phase-modulated systems in presence of nonlinear phase noise," IEEE Photon. Technol. Lett. 18, 2514−2516 (2006).
    [CrossRef]
  69. K.-P. Ho and J. M. Kahn, "Detection technique to mitigate Kerr effect phase noise," J. Lightwave Technol. 22, 779−783 (2004).
    [CrossRef]
  70. D.-S. Ly-Gagnon and K. Kikuchi, "Cancellation of nonlinear phase noise in DPSK transmission," 2004 Optoelectronics and Communications Conference and International Conference on Optical Internet (OECC/COIN2004), paper 14C3-3 (2004).
  71. X. Liu, X. Wei, R. E. Slusher and C. J. McKinstrie, "Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27, 1616−1618 (2002).
    [CrossRef]
  72. K. Kikuchi, M. Fukase and S.-Y. Kim, "Electronic post-compensation for nonlinear phase noise in a 1000-km 20-Gbit/s optical QPSK transmission system using the homodyne receiver with digital signal processing," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2007), Paper OTuA2.
  73. G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran and S. Bigo, "Transmission of 40 Gb/s QPSK with coherent detection over ultra-long distance improved by nonlinearity mitigation," in Proceedings ECOC 2006, Cannes, France, 2006, Postdeadline paper Th4.3.4.
  74. G. Zhu, L. Mollenauer and C. Xu, "Experimental demonstration of post-nonlinearity compensation in a multispan DPSK transmission," IEEE Photon. Technol. Lett. 18, 1007−1009 (2006).
    [CrossRef]
  75. K.P. Ho, "Mid-span compensation of nonlinear phase noise," Opt. Comm. 245, 391−398 (2005).
    [CrossRef]
  76. A. P. T. Lau and J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightwave Technol. 25, 3008−3016 (2007).
    [CrossRef]
  77. A.G. Green, P.P. Mitra, L.G. L. Wegener, "Effect of chromatic dispersion on nonlinear phase noise," Opt. Lett. 28, 2455−2457 (2003).
    [CrossRef] [PubMed]
  78. S. Kumar, "Effect of dispersion on nonlinear phase noise in optical transmission systems," Opt. Lett. 30, 3278−3280 (2005).
    [CrossRef]
  79. K.-P. Ho and H.C. Wang, "On the effect of dispersion on nonlinear phase noise," Opt. Lett. 31, 2109−2111 (2006).
    [CrossRef] [PubMed]
  80. S. Kumar and L. Liu, "Reduction of nonlinear phase noise using optical phase conjugation in quasi-linear optical transmission systems," Opt. Express 15, 2166−2177 (2007).
    [CrossRef] [PubMed]
  81. D. Boivin, G.-K. Chang, J. R. Barry and M. Hanna, "Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion," J. Opt. Soc. Am. A. B 23, 2019−2023 (2006).
    [CrossRef]
  82. P. Serena, A. Orlandini and A. Bononi, "Parametric-Gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightwave Technol. 24, 2026−2037 (2006).
    [CrossRef]
  83. K.P. Ho and H.C. Wang, "Comparison of nonlinear phase noise and intrachannel four-wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426−1428 (2005).
    [CrossRef]
  84. F. Zhang, C. A. Bunge and K. Petermann, "Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems," Opt. Lett. 31, 1038−1040 (2006).
    [CrossRef] [PubMed]
  85. F. Zhang, C. A. Bunge, K. Petermann and A. Richter, "Optimum dispersion mapping of single-channel 40 Gbit/s return-to-zero differential phase-shift keying transmission systems," Optics Express 14, 6613−6618 (2006).
    [CrossRef] [PubMed]
  86. X. Zhu, S. Kumar and X. Li, "Analysis and comparison of impairments in differential phase-shift keying and on-off keying transmission systems based on the error probability," Appl. Opt. 45, 6812−6822 (2006).
    [CrossRef] [PubMed]
  87. C. Henry, "Theory of the phase noise and power spectrum of a single mode injection laser," J. Quantum Electron. 19, 1391-1397 (1983).
    [CrossRef]
  88. M. Tur, B. Moslehi and J. W. Goodman, "Theory of laser phase noise in recirculating fiber-optic delay lines," J. Lightwave Technol. 3, 20-31 (1985).
    [CrossRef]
  89. A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949, (1958).
    [CrossRef]
  90. F.M. Gardner, Phaselock Techniques, 3rd ed. (John Wiley, Hoboken, NJ, 2005).
    [CrossRef]
  91. M. A. Grant, W. C. Michie, M. J. Fletcher, "The performance of optical phase-locked loops in the presence of nonnegligible loop propagation delay," J. Lightwave Technol. 5, 592-597 (1987).
    [CrossRef]
  92. K. Kikuchi, "Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation," J. Sel. Top. Quantum Electron. 12, 563−570 (2006).
    [CrossRef]
  93. M. G. Taylor, "Accurate digital phase estimation process for coherent detection using a parallel digital processor," in Proceedings ECOC 2005, Glasgow, UK, 2005, Paper Tu4.2.6.
  94. D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with coherent phase estimation," J. Lightwave Technol. 24, 12-21, (2006).
    [CrossRef]
  95. F. J. Foschini, R. D. Gitlin and S. B. Weinstein, "On the selction of a two-dimensional signal constellation in the presence of phase jitter and Gaussian noise," Bell. Syst. Tech. J. 52, 927-965 (1973).
  96. A. Bahai, B. Saltzberg and M. Ergen, Multi-carrier Digital Communications: Theory and Applications of OFDM, 2nd Ed. (Springer, New York, 2004).
  97. R. Prasad, "OFDM for wireless communications systems," (Artech House Publishers, Boston, 2004).
  98. W. Shieh, X. Yi, and Y. Tang, "Experimental demonstration of transmission of coherent optical OFDM Systems," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2007), Paper OMP2.
  99. W. Shieh and C. Athaudage, "Coherent optical orthogonal frequency division multiplexing," Electron. Lett. 42, 587−589 (2006).
    [CrossRef]
  100. N. Cvijetic, L. Xu and T. Wang, "Adaptive PMD compensation using OFDM in long-haul 10 Gb/s DWDM systems," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2007), Paper OTuA5.
  101. A. Lowery and J. Armstrong, "Orthogonal-frequency-division multiplexing for optical dispersion compensation," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2007), Paper OTuA4.
  102. W. Henkel, G. Taubock, P. Odling, P. O. Borjesson and N. Petersson, "The cyclic prefix of OFDM/DMT - an analysis," IEEE International Seminar on Broadband Communications, (Institute of Electrical and Electronic Engineers, Zurich, 2002).
  103. D. J.F. Barros and J. M. Kahn are preparing a manuscript to be called "Optimized dispersion compensation using orthogonal frequency-division multiplexing."
  104. W. Shieh, X. Yi, Y. Ma and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Optics Express 15, 9936−9947 (2007).
    [CrossRef] [PubMed]
  105. C. Cover and J. Thomas, Elements of Information Theory. (John Wiley, New York, 1991).
    [CrossRef]
  106. C. Y. Wong, R. S. Cheng, K. B. Letaief and R. D. Murch, "Multiuser OFDM with adaptive subcarrier, bit, and power allocation," J. Sel. Top. Commun. 17, 1747−1758 (1999).
    [CrossRef]
  107. B. S. Krongold, K. Ramchandran and D. L. Jones, "Computationally efficient optimal power allocation algorithms for multicarrier communication systems," IEEE Trans. Commun. 48, 23−27 (2000).
    [CrossRef]
  108. J. Jang, K. B. Lee and Y.-H. Lee, "Transmit power and bit allocations for OFDM systems in a fading channel," in Proceedings of IEEE GLOBECOM, (Institute of Electrical and Electronics Engineers, San Francisco, 2003), pp. 858−862.
  109. S. Wu and Y. Bar-Ness, "OFDM systems in the presence of phase noise: consequences and solutions," IEEE Trans. Commun. 52, 1988−1996 (2004).
    [CrossRef]
  110. A. G. Armada and M. Calvo, "Phase noise and sub-carrier spacing effects on the performance of an OFDM communication system," IEEE Commun. Lett. 2, 11−13 (1998).
    [CrossRef]
  111. S. Wu and Y. Bar-Ness, "A phase noise suppression algorithm for OFDM based WLANs," IEEE Commun. Lett. 6, 535−537 (2002).
    [CrossRef]
  112. H. Ochiai and H. Imai, "On the distribution of the peak-to-average power ratio in OFDM signals," IEEE Trans. Commun. 49, 282−289 (2001).
    [CrossRef]
  113. A. J. Lowery, "Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation," IEEE Photon Technol. Lett. 19, 1556−1558 (2007).
    [CrossRef]
  114. A. J. Lowery, "Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM," Optics Express 15, 12965−12970 (2007).
    [CrossRef] [PubMed]
  115. A. J. Lowery, S. Wang and M. Premaratne, "Calculation of power limit due to fiber nonlinearity in optical OFDM systems," Optics Express 15, 13282−13287 (2007).
    [CrossRef] [PubMed]
  116. D.-S. Ly-Gagnon, "Information recovery using coherent detection and digital signal pocessing for phase-shift-keying modulation formats in optical communication systems," M.S. Thesis, University of Tokyo (2004).

2007 (10)

J. Hongo, K. Kasai, M. Yoshida and M. Nakazawa, "1-Gsymbol/s 64-QAM coherent optical transmission over 150 km," IEEE Photon. Technol. Lett. 19, 638-640 (2007).
[CrossRef]

G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19, 969−971 (2007).
[CrossRef]

W. Shieh, X. Yi, Y. Ma and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Optics Express 15, 9936−9947 (2007).
[CrossRef] [PubMed]

A. J. Lowery, "Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation," IEEE Photon Technol. Lett. 19, 1556−1558 (2007).
[CrossRef]

A. J. Lowery, "Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM," Optics Express 15, 12965−12970 (2007).
[CrossRef] [PubMed]

A. J. Lowery, S. Wang and M. Premaratne, "Calculation of power limit due to fiber nonlinearity in optical OFDM systems," Optics Express 15, 13282−13287 (2007).
[CrossRef] [PubMed]

S. Kumar and L. Liu, "Reduction of nonlinear phase noise using optical phase conjugation in quasi-linear optical transmission systems," Opt. Express 15, 2166−2177 (2007).
[CrossRef] [PubMed]

E. Ip and J.M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightwave Technol. 25, 2033-2043 (2007).
[CrossRef]

E. Ip and J. M. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightwave Technol.,  25, 2675-2692 (2007).
[CrossRef]

A. P. T. Lau and J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightwave Technol. 25, 3008−3016 (2007).
[CrossRef]

2006 (16)

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with coherent phase estimation," J. Lightwave Technol. 24, 12-21, (2006).
[CrossRef]

I.B. Djordjevic and B. Vasic, "Constrained coding techniques for suppression of intrachannel nonlinear effects in high-speed optical transmission," J. Lightwave Technol. 24, 411−419 (2006).
[CrossRef]

F. Zhang, C. A. Bunge and K. Petermann, "Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems," Opt. Lett. 31, 1038−1040 (2006).
[CrossRef] [PubMed]

A. P. T. Lau and J. M. Kahn, "Design of inline amplifiers gain and spacing to minimize phase noise in optical transmission systems," J. Lightwave Technol. 24, 1334−1341 (2006).
[CrossRef]

P. Serena, A. Orlandini and A. Bononi, "Parametric-Gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightwave Technol. 24, 2026−2037 (2006).
[CrossRef]

K.-P. Ho and H.C. Wang, "On the effect of dispersion on nonlinear phase noise," Opt. Lett. 31, 2109−2111 (2006).
[CrossRef] [PubMed]

X. Zhu, S. Kumar and X. Li, "Analysis and comparison of impairments in differential phase-shift keying and on-off keying transmission systems based on the error probability," Appl. Opt. 45, 6812−6822 (2006).
[CrossRef] [PubMed]

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]

W. Shieh and C. Athaudage, "Coherent optical orthogonal frequency division multiplexing," Electron. Lett. 42, 587−589 (2006).
[CrossRef]

A.P.T. Lau and J.M. Kahn, "Power profile optimization in phase-modulated systems in presence of nonlinear phase noise," IEEE Photon. Technol. Lett. 18, 2514−2516 (2006).
[CrossRef]

G. Zhu, L. Mollenauer and C. Xu, "Experimental demonstration of post-nonlinearity compensation in a multispan DPSK transmission," IEEE Photon. Technol. Lett. 18, 1007−1009 (2006).
[CrossRef]

D. Boivin, G.-K. Chang, J. R. Barry and M. Hanna, "Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion," J. Opt. Soc. Am. A. B 23, 2019−2023 (2006).
[CrossRef]

K. Kikuchi, "Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation," J. Sel. Top. Quantum Electron. 12, 563−570 (2006).
[CrossRef]

F. Zhang, C. A. Bunge, K. Petermann and A. Richter, "Optimum dispersion mapping of single-channel 40 Gbit/s return-to-zero differential phase-shift keying transmission systems," Optics Express 14, 6613−6618 (2006).
[CrossRef] [PubMed]

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandard, S. Ibrahim, O. Adamczyk, M. Porrmann, R. Noé and Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).
[CrossRef]

S. Tsukamoto, K. Katoh and K. Kikuchi, "Coherent demodulation of optical multilevel phase-shift-keying signals using homodyne detection and digital signal processing," IEEE Photon. Technol. Lett. 18, 1131-1133 (2006).
[CrossRef]

2005 (9)

K. Sekine, N. Kikuchi, S. Sasaki, S. Hayase, C. Hasegawa and T. Sugawara, "40 Gbit/s, 16-ary (4 bit/symbol) optical modulation/demodulation scheme," Electron. Lett. 41, 430-432, (2005).
[CrossRef]

M. Nazarathy and E. Simony, "Multichip differential phase encoded optical transmission," IEEE Photon. Technol. Lett. 17, 1133-1135 (2005).
[CrossRef]

K.-P. Ho, "Exact evaluation of the capacity for intensity-modulated direct-detection channels with optical amplifier noises," IEEE Photon. Technol. Lett. 17, 858−860 (2005).
[CrossRef]

A. H. Gnauck, P. J. Winzer and S. Chandrasekhar, "Hybrid 10/40-G transmission on a 50-GHz Grid through 2800 km of SSMF and seven optical add-drops," IEEE Photon. Technol. Lett. 17, 2203−2205 (2005).
[CrossRef]

K.P. Ho and H.C. Wang, "Comparison of nonlinear phase noise and intrachannel four-wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426−1428 (2005).
[CrossRef]

K.P. Ho, "Mid-span compensation of nonlinear phase noise," Opt. Comm. 245, 391−398 (2005).
[CrossRef]

R. Noé, "Phase noise-tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedforward carrier recovery," J. Lightwave Technol. 23, 802−808 (2005).
[CrossRef]

S. Kumar, "Effect of dispersion on nonlinear phase noise in optical transmission systems," Opt. Lett. 30, 3278−3280 (2005).
[CrossRef]

E. Ip and J.M. Kahn, "Carrier synchronization for 3- and 4-bit-per-symbol optical transmission," J. Lightwave Technol. 23, 4110-4124 (2005).
[CrossRef]

2004 (9)

N. Alic and Y. Fainman, "Data-dependent phase coding for suppression of ghost pulses in optical fibers," IEEE Photon. Technol. Lett. 16, 1212−1214 (2004).
[CrossRef]

S. Wu and Y. Bar-Ness, "OFDM systems in the presence of phase noise: consequences and solutions," IEEE Trans. Commun. 52, 1988−1996 (2004).
[CrossRef]

K.-P. Ho and J. M. Kahn, "Detection technique to mitigate Kerr effect phase noise," J. Lightwave Technol. 22, 779−783 (2004).
[CrossRef]

F. Buchali and H. Bülow, "Adaptive PMD compensation by electrical and optical techniques," J. Lightwave Technol. 22, 1116-1126 (2004).
[CrossRef]

C. Vinegoni, M. Karlsson, M. Petersson and H. Sunnerud, "The statistics of polarization-dependent loss in a recirculating loop," J. Lightwave Technol. 22, 968−976 (2004).
[CrossRef]

E. Forestieri and G. Prati, "Exact analytical evaluation of second-order PMD impact on the outage probability for a compensated system," J. Lightwave Technol. 22, 988−996 (2004).
[CrossRef]

A. Striegler and B. Schmauss, "Compensation of intrachannel effects in symmetric dispersion-managed transmission systems," J. Lightwave Technol. 22, 1877−1882 (2004).
[CrossRef]

J. Wang and J. M. Kahn, "Performance of electrical equalizers in optical amplified OOK and DPSK systems," IEEE Photon. Technol. Lett. 16, 1397-1399 (2004).
[CrossRef]

J. M. Kahn and K.-P. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM Systems," J. Sel. Top. Quantum Electron. 10, 259-271 (2004).
[CrossRef]

2003 (3)

2002 (4)

H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson and P. Andrekson, "A comparison between different PMD compensation techniques," J. Lightwave Technol. 20, 368-378 (2002).
[CrossRef]

X. Liu, X. Wei, R. E. Slusher and C. J. McKinstrie, "Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27, 1616−1618 (2002).
[CrossRef]

S. Wu and Y. Bar-Ness, "A phase noise suppression algorithm for OFDM based WLANs," IEEE Commun. Lett. 6, 535−537 (2002).
[CrossRef]

T. Saida, K. Takiguchi, S. Kuwahara, Y. Kisaka, Y. Miyamoto, Y. Hashizume, T. Shibata and K. Okamoto, "Planar lightwave circuit polarization-mode dispersion compensator," IEEE Photon. Technol. Lett. 14, 507-509 (2002).
[CrossRef]

2001 (3)

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park and A. H. Gnauck, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445−447 (2001).
[CrossRef]

P.P. Mitra and J.B. Stark, "Nonlinear limits to the information capacity of optical fiber communications," Nature 411, 1027-1030 (2001).
[CrossRef] [PubMed]

H. Ochiai and H. Imai, "On the distribution of the peak-to-average power ratio in OFDM signals," IEEE Trans. Commun. 49, 282−289 (2001).
[CrossRef]

2000 (3)

B. S. Krongold, K. Ramchandran and D. L. Jones, "Computationally efficient optimal power allocation algorithms for multicarrier communication systems," IEEE Trans. Commun. 48, 23−27 (2000).
[CrossRef]

J. Rebola and A. Cartaxo, "Optimization of level spacing in quaternary optical communication systems," Proc. SPIE 4087, 49−59 (2000).
[CrossRef]

A. Mecozzi, C. B. Clausen and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392−394 (2000).
[CrossRef]

1999 (4)

S. Lee, R. Khosravani, J. Peng, V. Grubsky, D. S. Starodubov, A. E. Willner and J. Feinberg, "Adjustable compensation of polarization mode dispersion using a high-birefringence nonlinearly chirped fiber Bragg grating," IEEE Photon. Technol. Lett. 11, 1277-1279 (1999).
[CrossRef]

R.-J. Essiambre, B. Mikkelsen and G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576−1578 (1999).
[CrossRef]

R. Noé, D. Sandel, M. Yoshida-Dierolf, S. Hinz, V. Mirvoda, A. Schöpflin, C. Flingener, E. Gottwald, C. Scheerer, G. Fischer, T. Weyrauch and W. Haase, "Polarization mode dispersion compensation at 10, 20, and 40 Gb/s with various optical equalizer," J. Lightwave Technol. 17, 1602-1616 (1999).
[CrossRef]

C. Y. Wong, R. S. Cheng, K. B. Letaief and R. D. Murch, "Multiuser OFDM with adaptive subcarrier, bit, and power allocation," J. Sel. Top. Commun. 17, 1747−1758 (1999).
[CrossRef]

1998 (3)

A. G. Armada and M. Calvo, "Phase noise and sub-carrier spacing effects on the performance of an OFDM communication system," IEEE Commun. Lett. 2, 11−13 (1998).
[CrossRef]

I. Shake, H. Takara, K. Mori, S. Kawanishi and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600−1601 (1998).
[CrossRef]

H. Bülow, "System outage probability due to first- and second-order PMD," IEEE Photon. Technol. Lett. 10, 696-698 (1998).
[CrossRef]

1994 (1)

S. Benedetto and P. Poggiolini, "Multilevel polarization shift keying: optimum receiver structure and performance evaluation," IEEE Trans. Commun. 42, 1174-1186 (1994).
[CrossRef]

1992 (2)

J. R. Barry and J.M. Kahn, "Carrier synchronization for homodyne and heterodyne detection of optical quadriphase-shift keying," J. Lightwave Technol. 10, 1939-1951 (1992).
[CrossRef]

S. Benedetto and P. Poggiolini, "Theory of polarization shift keying modulation," IEEE Trans. Commun. 40, 708−721 (1992).
[CrossRef]

1991 (3)

N. Gisin, J.-P. Von der Weid and J.-P. Pellaux, "Polarization mode dispersion of short and long single-mode fibers," J. Lightwave Technol. 9, 821-827 (1991).
[CrossRef]

G. J. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single-mode fibers," J. Lightwave Technol. 9, 1439-1456 (1991).
[CrossRef]

C. D. Poole, R. W. Tkach, A. R. Chraplyvy and D. A. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).
[CrossRef]

1990 (3)

S. Betti, F. Curti, G. de Marchis and E. Iannone, "Multilevel coherent optical system based on Stokes parameters modulation," J. Lightwave Technol. 8, 1127−1136 (1990).
[CrossRef]

D. Divsalar and M. Simon, "Multiple-symbol differential detection of MPSK," IEEE Trans. Commun. 38, 300-308 (1990).
[CrossRef]

J. P. Gordon and L.F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. 15, 1351−1353 (1990).
[CrossRef] [PubMed]

1988 (1)

1987 (1)

M. A. Grant, W. C. Michie, M. J. Fletcher, "The performance of optical phase-locked loops in the presence of nonnegligible loop propagation delay," J. Lightwave Technol. 5, 592-597 (1987).
[CrossRef]

1985 (3)

M. Tur, B. Moslehi and J. W. Goodman, "Theory of laser phase noise in recirculating fiber-optic delay lines," J. Lightwave Technol. 3, 20-31 (1985).
[CrossRef]

S. Qureshi, "Adaptive equalization," Proceedings of the IEEE 73, 1349-1387 (1985).
[CrossRef]

J. Salz, "Digital transmission over cross-coupled linear channels," AT&T Tech. J. 64, 1147-1159 (1985).

1984 (1)

N. Amitay and J. Salz, "Linear Equalization Theory in Digital Data Transmission over Dually Polarized Fading Radio Channels," Bell. Syst. Tech. J. 63, 2215-2259 (1984).

1983 (1)

C. Henry, "Theory of the phase noise and power spectrum of a single mode injection laser," J. Quantum Electron. 19, 1391-1397 (1983).
[CrossRef]

1981 (1)

R.D. Gitlin and S. B. Weinstein, "Fractionally spaced equalization: an improved digital transversal equalizer," Bell. Syst. Tech. J. 60, 275-296 (1981).

1976 (1)

G. Ungerboeck, "Fractional tap-spacing equalizer and consequences for clock recovery in data modems," IEEE Trans. Commun. 24, 856-864 (1976).
[CrossRef]

1973 (1)

F. J. Foschini, R. D. Gitlin and S. B. Weinstein, "On the selction of a two-dimensional signal constellation in the presence of phase jitter and Gaussian noise," Bell. Syst. Tech. J. 52, 927-965 (1973).

1968 (1)

J. G. Proakis, "Probabilities of error for adaptive reception of M-phase signals," IEEE Trans. Commun. Tech. 16, 71-81 (1968).
[CrossRef]

1964 (1)

J. J. Bussgang and M. Leiter, "Error rate approximations for differential phase-shift keying." IEEE Trans. Commun. Systems 12, 18-27 (1964).
[CrossRef]

1958 (1)

A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949, (1958).
[CrossRef]

1948 (1)

C.E. Shannon, "A mathematical theory of communication," Bell. Syst. Tech. J. 27, 379−423 (1948).

Achiam, Y.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandard, S. Ibrahim, O. Adamczyk, M. Porrmann, R. Noé and Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).
[CrossRef]

Adamczyk, O.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandard, S. Ibrahim, O. Adamczyk, M. Porrmann, R. Noé and Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).
[CrossRef]

Alic, N.

N. Alic and Y. Fainman, "Data-dependent phase coding for suppression of ghost pulses in optical fibers," IEEE Photon. Technol. Lett. 16, 1212−1214 (2004).
[CrossRef]

Amitay, N.

N. Amitay and J. Salz, "Linear Equalization Theory in Digital Data Transmission over Dually Polarized Fading Radio Channels," Bell. Syst. Tech. J. 63, 2215-2259 (1984).

Andrekson, P.

Armada, A. G.

A. G. Armada and M. Calvo, "Phase noise and sub-carrier spacing effects on the performance of an OFDM communication system," IEEE Commun. Lett. 2, 11−13 (1998).
[CrossRef]

Athaudage, C.

W. Shieh and C. Athaudage, "Coherent optical orthogonal frequency division multiplexing," Electron. Lett. 42, 587−589 (2006).
[CrossRef]

Bar-Ness, Y.

S. Wu and Y. Bar-Ness, "OFDM systems in the presence of phase noise: consequences and solutions," IEEE Trans. Commun. 52, 1988−1996 (2004).
[CrossRef]

S. Wu and Y. Bar-Ness, "A phase noise suppression algorithm for OFDM based WLANs," IEEE Commun. Lett. 6, 535−537 (2002).
[CrossRef]

Barry, J. R.

D. Boivin, G.-K. Chang, J. R. Barry and M. Hanna, "Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion," J. Opt. Soc. Am. A. B 23, 2019−2023 (2006).
[CrossRef]

J. R. Barry and J.M. Kahn, "Carrier synchronization for homodyne and heterodyne detection of optical quadriphase-shift keying," J. Lightwave Technol. 10, 1939-1951 (1992).
[CrossRef]

Benedetto, S.

S. Benedetto and P. Poggiolini, "Multilevel polarization shift keying: optimum receiver structure and performance evaluation," IEEE Trans. Commun. 42, 1174-1186 (1994).
[CrossRef]

S. Benedetto and P. Poggiolini, "Theory of polarization shift keying modulation," IEEE Trans. Commun. 40, 708−721 (1992).
[CrossRef]

Betti, S.

S. Betti, F. Curti, G. de Marchis and E. Iannone, "Multilevel coherent optical system based on Stokes parameters modulation," J. Lightwave Technol. 8, 1127−1136 (1990).
[CrossRef]

Bhandard, S.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandard, S. Ibrahim, O. Adamczyk, M. Porrmann, R. Noé and Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).
[CrossRef]

Boivin, D.

D. Boivin, G.-K. Chang, J. R. Barry and M. Hanna, "Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion," J. Opt. Soc. Am. A. B 23, 2019−2023 (2006).
[CrossRef]

Bononi, A.

Buchali, F.

Bülow, H.

F. Buchali and H. Bülow, "Adaptive PMD compensation by electrical and optical techniques," J. Lightwave Technol. 22, 1116-1126 (2004).
[CrossRef]

H. Bülow, "System outage probability due to first- and second-order PMD," IEEE Photon. Technol. Lett. 10, 696-698 (1998).
[CrossRef]

Bunge, C. A.

F. Zhang, C. A. Bunge, K. Petermann and A. Richter, "Optimum dispersion mapping of single-channel 40 Gbit/s return-to-zero differential phase-shift keying transmission systems," Optics Express 14, 6613−6618 (2006).
[CrossRef] [PubMed]

F. Zhang, C. A. Bunge and K. Petermann, "Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems," Opt. Lett. 31, 1038−1040 (2006).
[CrossRef] [PubMed]

Bussgang, J. J.

J. J. Bussgang and M. Leiter, "Error rate approximations for differential phase-shift keying." IEEE Trans. Commun. Systems 12, 18-27 (1964).
[CrossRef]

Calvo, M.

A. G. Armada and M. Calvo, "Phase noise and sub-carrier spacing effects on the performance of an OFDM communication system," IEEE Commun. Lett. 2, 11−13 (1998).
[CrossRef]

Cartaxo, A.

J. Rebola and A. Cartaxo, "Optimization of level spacing in quaternary optical communication systems," Proc. SPIE 4087, 49−59 (2000).
[CrossRef]

Chandrasekhar, S.

A. H. Gnauck, P. J. Winzer and S. Chandrasekhar, "Hybrid 10/40-G transmission on a 50-GHz Grid through 2800 km of SSMF and seven optical add-drops," IEEE Photon. Technol. Lett. 17, 2203−2205 (2005).
[CrossRef]

Chang, G.-K.

D. Boivin, G.-K. Chang, J. R. Barry and M. Hanna, "Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion," J. Opt. Soc. Am. A. B 23, 2019−2023 (2006).
[CrossRef]

Cheng, R. S.

C. Y. Wong, R. S. Cheng, K. B. Letaief and R. D. Murch, "Multiuser OFDM with adaptive subcarrier, bit, and power allocation," J. Sel. Top. Commun. 17, 1747−1758 (1999).
[CrossRef]

Chraplyvy, A. R.

C. D. Poole, R. W. Tkach, A. R. Chraplyvy and D. A. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).
[CrossRef]

Clausen, C. B.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park and A. H. Gnauck, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445−447 (2001).
[CrossRef]

A. Mecozzi, C. B. Clausen and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392−394 (2000).
[CrossRef]

Colavolpe, G.

Curti, F.

S. Betti, F. Curti, G. de Marchis and E. Iannone, "Multilevel coherent optical system based on Stokes parameters modulation," J. Lightwave Technol. 8, 1127−1136 (1990).
[CrossRef]

de Marchis, G.

S. Betti, F. Curti, G. de Marchis and E. Iannone, "Multilevel coherent optical system based on Stokes parameters modulation," J. Lightwave Technol. 8, 1127−1136 (1990).
[CrossRef]

Divsalar, D.

D. Divsalar and M. Simon, "Multiple-symbol differential detection of MPSK," IEEE Trans. Commun. 38, 300-308 (1990).
[CrossRef]

Djordjevic, I.B.

Edagawa, N.

Essiambre, R.-J.

R.-J. Essiambre, B. Mikkelsen and G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576−1578 (1999).
[CrossRef]

Fainman, Y.

N. Alic and Y. Fainman, "Data-dependent phase coding for suppression of ghost pulses in optical fibers," IEEE Photon. Technol. Lett. 16, 1212−1214 (2004).
[CrossRef]

Feinberg, J.

S. Lee, R. Khosravani, J. Peng, V. Grubsky, D. S. Starodubov, A. E. Willner and J. Feinberg, "Adjustable compensation of polarization mode dispersion using a high-birefringence nonlinearly chirped fiber Bragg grating," IEEE Photon. Technol. Lett. 11, 1277-1279 (1999).
[CrossRef]

Fischer, G.

Fishman, D. A.

C. D. Poole, R. W. Tkach, A. R. Chraplyvy and D. A. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).
[CrossRef]

Fletcher, M. J.

M. A. Grant, W. C. Michie, M. J. Fletcher, "The performance of optical phase-locked loops in the presence of nonnegligible loop propagation delay," J. Lightwave Technol. 5, 592-597 (1987).
[CrossRef]

Flingener, C.

Foggi, T.

Forestieri, E.

Foschini, F. J.

F. J. Foschini, R. D. Gitlin and S. B. Weinstein, "On the selction of a two-dimensional signal constellation in the presence of phase jitter and Gaussian noise," Bell. Syst. Tech. J. 52, 927-965 (1973).

Foschini, G. J.

G. J. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single-mode fibers," J. Lightwave Technol. 9, 1439-1456 (1991).
[CrossRef]

Gisin, N.

N. Gisin, J.-P. Von der Weid and J.-P. Pellaux, "Polarization mode dispersion of short and long single-mode fibers," J. Lightwave Technol. 9, 821-827 (1991).
[CrossRef]

Gitlin, R. D.

F. J. Foschini, R. D. Gitlin and S. B. Weinstein, "On the selction of a two-dimensional signal constellation in the presence of phase jitter and Gaussian noise," Bell. Syst. Tech. J. 52, 927-965 (1973).

Gitlin, R.D.

R.D. Gitlin and S. B. Weinstein, "Fractionally spaced equalization: an improved digital transversal equalizer," Bell. Syst. Tech. J. 60, 275-296 (1981).

Gnauck, A. H.

A. H. Gnauck, P. J. Winzer and S. Chandrasekhar, "Hybrid 10/40-G transmission on a 50-GHz Grid through 2800 km of SSMF and seven optical add-drops," IEEE Photon. Technol. Lett. 17, 2203−2205 (2005).
[CrossRef]

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park and A. H. Gnauck, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445−447 (2001).
[CrossRef]

Goldfarb, G.

G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19, 969−971 (2007).
[CrossRef]

Goodman, J. W.

M. Tur, B. Moslehi and J. W. Goodman, "Theory of laser phase noise in recirculating fiber-optic delay lines," J. Lightwave Technol. 3, 20-31 (1985).
[CrossRef]

Gordon, J. P.

Gottwald, E.

Grant, M. A.

M. A. Grant, W. C. Michie, M. J. Fletcher, "The performance of optical phase-locked loops in the presence of nonnegligible loop propagation delay," J. Lightwave Technol. 5, 592-597 (1987).
[CrossRef]

Green, A.G.

Grubsky, V.

S. Lee, R. Khosravani, J. Peng, V. Grubsky, D. S. Starodubov, A. E. Willner and J. Feinberg, "Adjustable compensation of polarization mode dispersion using a high-birefringence nonlinearly chirped fiber Bragg grating," IEEE Photon. Technol. Lett. 11, 1277-1279 (1999).
[CrossRef]

Haase, W.

Hanna, M.

D. Boivin, G.-K. Chang, J. R. Barry and M. Hanna, "Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion," J. Opt. Soc. Am. A. B 23, 2019−2023 (2006).
[CrossRef]

Hasegawa, C.

K. Sekine, N. Kikuchi, S. Sasaki, S. Hayase, C. Hasegawa and T. Sugawara, "40 Gbit/s, 16-ary (4 bit/symbol) optical modulation/demodulation scheme," Electron. Lett. 41, 430-432, (2005).
[CrossRef]

Hashizume, Y.

T. Saida, K. Takiguchi, S. Kuwahara, Y. Kisaka, Y. Miyamoto, Y. Hashizume, T. Shibata and K. Okamoto, "Planar lightwave circuit polarization-mode dispersion compensator," IEEE Photon. Technol. Lett. 14, 507-509 (2002).
[CrossRef]

Hayase, S.

K. Sekine, N. Kikuchi, S. Sasaki, S. Hayase, C. Hasegawa and T. Sugawara, "40 Gbit/s, 16-ary (4 bit/symbol) optical modulation/demodulation scheme," Electron. Lett. 41, 430-432, (2005).
[CrossRef]

Henry, C.

C. Henry, "Theory of the phase noise and power spectrum of a single mode injection laser," J. Quantum Electron. 19, 1391-1397 (1983).
[CrossRef]

Hinz, S.

Ho, K.P.

K.P. Ho, "Mid-span compensation of nonlinear phase noise," Opt. Comm. 245, 391−398 (2005).
[CrossRef]

K.P. Ho and H.C. Wang, "Comparison of nonlinear phase noise and intrachannel four-wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426−1428 (2005).
[CrossRef]

Ho, K.-P.

K.-P. Ho and H.C. Wang, "On the effect of dispersion on nonlinear phase noise," Opt. Lett. 31, 2109−2111 (2006).
[CrossRef] [PubMed]

K.-P. Ho, "Exact evaluation of the capacity for intensity-modulated direct-detection channels with optical amplifier noises," IEEE Photon. Technol. Lett. 17, 858−860 (2005).
[CrossRef]

K.-P. Ho and J. M. Kahn, "Detection technique to mitigate Kerr effect phase noise," J. Lightwave Technol. 22, 779−783 (2004).
[CrossRef]

J. M. Kahn and K.-P. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM Systems," J. Sel. Top. Quantum Electron. 10, 259-271 (2004).
[CrossRef]

Hoffmann, S.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandard, S. Ibrahim, O. Adamczyk, M. Porrmann, R. Noé and Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).
[CrossRef]

Hongo, J.

J. Hongo, K. Kasai, M. Yoshida and M. Nakazawa, "1-Gsymbol/s 64-QAM coherent optical transmission over 150 km," IEEE Photon. Technol. Lett. 19, 638-640 (2007).
[CrossRef]

Iannone, E.

S. Betti, F. Curti, G. de Marchis and E. Iannone, "Multilevel coherent optical system based on Stokes parameters modulation," J. Lightwave Technol. 8, 1127−1136 (1990).
[CrossRef]

Ibrahim, S.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandard, S. Ibrahim, O. Adamczyk, M. Porrmann, R. Noé and Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).
[CrossRef]

Imai, H.

H. Ochiai and H. Imai, "On the distribution of the peak-to-average power ratio in OFDM signals," IEEE Trans. Commun. 49, 282−289 (2001).
[CrossRef]

Ip, E.

Jones, D. L.

B. S. Krongold, K. Ramchandran and D. L. Jones, "Computationally efficient optimal power allocation algorithms for multicarrier communication systems," IEEE Trans. Commun. 48, 23−27 (2000).
[CrossRef]

Kahn, J. M.

Kahn, J.M.

E. Ip and J.M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightwave Technol. 25, 2033-2043 (2007).
[CrossRef]

A.P.T. Lau and J.M. Kahn, "Power profile optimization in phase-modulated systems in presence of nonlinear phase noise," IEEE Photon. Technol. Lett. 18, 2514−2516 (2006).
[CrossRef]

E. Ip and J.M. Kahn, "Carrier synchronization for 3- and 4-bit-per-symbol optical transmission," J. Lightwave Technol. 23, 4110-4124 (2005).
[CrossRef]

J. R. Barry and J.M. Kahn, "Carrier synchronization for homodyne and heterodyne detection of optical quadriphase-shift keying," J. Lightwave Technol. 10, 1939-1951 (1992).
[CrossRef]

Karlsson, M.

Kasai, K.

J. Hongo, K. Kasai, M. Yoshida and M. Nakazawa, "1-Gsymbol/s 64-QAM coherent optical transmission over 150 km," IEEE Photon. Technol. Lett. 19, 638-640 (2007).
[CrossRef]

Katoh, K.

S. Tsukamoto, K. Katoh and K. Kikuchi, "Coherent demodulation of optical multilevel phase-shift-keying signals using homodyne detection and digital signal processing," IEEE Photon. Technol. Lett. 18, 1131-1133 (2006).
[CrossRef]

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with coherent phase estimation," J. Lightwave Technol. 24, 12-21, (2006).
[CrossRef]

Kawanishi, S.

I. Shake, H. Takara, K. Mori, S. Kawanishi and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600−1601 (1998).
[CrossRef]

Khosravani, R.

S. Lee, R. Khosravani, J. Peng, V. Grubsky, D. S. Starodubov, A. E. Willner and J. Feinberg, "Adjustable compensation of polarization mode dispersion using a high-birefringence nonlinearly chirped fiber Bragg grating," IEEE Photon. Technol. Lett. 11, 1277-1279 (1999).
[CrossRef]

Kikuchi, K.

K. Kikuchi, "Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation," J. Sel. Top. Quantum Electron. 12, 563−570 (2006).
[CrossRef]

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with coherent phase estimation," J. Lightwave Technol. 24, 12-21, (2006).
[CrossRef]

S. Tsukamoto, K. Katoh and K. Kikuchi, "Coherent demodulation of optical multilevel phase-shift-keying signals using homodyne detection and digital signal processing," IEEE Photon. Technol. Lett. 18, 1131-1133 (2006).
[CrossRef]

Kikuchi, N.

K. Sekine, N. Kikuchi, S. Sasaki, S. Hayase, C. Hasegawa and T. Sugawara, "40 Gbit/s, 16-ary (4 bit/symbol) optical modulation/demodulation scheme," Electron. Lett. 41, 430-432, (2005).
[CrossRef]

Kisaka, Y.

T. Saida, K. Takiguchi, S. Kuwahara, Y. Kisaka, Y. Miyamoto, Y. Hashizume, T. Shibata and K. Okamoto, "Planar lightwave circuit polarization-mode dispersion compensator," IEEE Photon. Technol. Lett. 14, 507-509 (2002).
[CrossRef]

Krongold, B. S.

B. S. Krongold, K. Ramchandran and D. L. Jones, "Computationally efficient optimal power allocation algorithms for multicarrier communication systems," IEEE Trans. Commun. 48, 23−27 (2000).
[CrossRef]

Kumar, S.

Kuwahara, S.

T. Saida, K. Takiguchi, S. Kuwahara, Y. Kisaka, Y. Miyamoto, Y. Hashizume, T. Shibata and K. Okamoto, "Planar lightwave circuit polarization-mode dispersion compensator," IEEE Photon. Technol. Lett. 14, 507-509 (2002).
[CrossRef]

Lau, A. P. T.

Lau, A.P.T.

A.P.T. Lau and J.M. Kahn, "Power profile optimization in phase-modulated systems in presence of nonlinear phase noise," IEEE Photon. Technol. Lett. 18, 2514−2516 (2006).
[CrossRef]

Lee, S.

S. Lee, R. Khosravani, J. Peng, V. Grubsky, D. S. Starodubov, A. E. Willner and J. Feinberg, "Adjustable compensation of polarization mode dispersion using a high-birefringence nonlinearly chirped fiber Bragg grating," IEEE Photon. Technol. Lett. 11, 1277-1279 (1999).
[CrossRef]

Leiter, M.

J. J. Bussgang and M. Leiter, "Error rate approximations for differential phase-shift keying." IEEE Trans. Commun. Systems 12, 18-27 (1964).
[CrossRef]

Letaief, K. B.

C. Y. Wong, R. S. Cheng, K. B. Letaief and R. D. Murch, "Multiuser OFDM with adaptive subcarrier, bit, and power allocation," J. Sel. Top. Commun. 17, 1747−1758 (1999).
[CrossRef]

Li, G.

G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19, 969−971 (2007).
[CrossRef]

Li, X.

Liu, L.

Liu, X.

Lowery, A. J.

A. J. Lowery, "Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM," Optics Express 15, 12965−12970 (2007).
[CrossRef] [PubMed]

A. J. Lowery, "Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation," IEEE Photon Technol. Lett. 19, 1556−1558 (2007).
[CrossRef]

A. J. Lowery, S. Wang and M. Premaratne, "Calculation of power limit due to fiber nonlinearity in optical OFDM systems," Optics Express 15, 13282−13287 (2007).
[CrossRef] [PubMed]

Ly-Gagnon, D.-S.

Ma, Y.

W. Shieh, X. Yi, Y. Ma and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Optics Express 15, 9936−9947 (2007).
[CrossRef] [PubMed]

McKinstrie, C. J.

Mecozzi, A.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park and A. H. Gnauck, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445−447 (2001).
[CrossRef]

A. Mecozzi, C. B. Clausen and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392−394 (2000).
[CrossRef]

Michie, W. C.

M. A. Grant, W. C. Michie, M. J. Fletcher, "The performance of optical phase-locked loops in the presence of nonnegligible loop propagation delay," J. Lightwave Technol. 5, 592-597 (1987).
[CrossRef]

Mikkelsen, B.

R.-J. Essiambre, B. Mikkelsen and G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576−1578 (1999).
[CrossRef]

Mirvoda, V.

Mitra, P.P.

A.G. Green, P.P. Mitra, L.G. L. Wegener, "Effect of chromatic dispersion on nonlinear phase noise," Opt. Lett. 28, 2455−2457 (2003).
[CrossRef] [PubMed]

P.P. Mitra and J.B. Stark, "Nonlinear limits to the information capacity of optical fiber communications," Nature 411, 1027-1030 (2001).
[CrossRef] [PubMed]

Miyamoto, Y.

T. Saida, K. Takiguchi, S. Kuwahara, Y. Kisaka, Y. Miyamoto, Y. Hashizume, T. Shibata and K. Okamoto, "Planar lightwave circuit polarization-mode dispersion compensator," IEEE Photon. Technol. Lett. 14, 507-509 (2002).
[CrossRef]

Mollenauer, L.

G. Zhu, L. Mollenauer and C. Xu, "Experimental demonstration of post-nonlinearity compensation in a multispan DPSK transmission," IEEE Photon. Technol. Lett. 18, 1007−1009 (2006).
[CrossRef]

Mollenauer, L.F.

Mori, K.

I. Shake, H. Takara, K. Mori, S. Kawanishi and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600−1601 (1998).
[CrossRef]

Moslehi, B.

M. Tur, B. Moslehi and J. W. Goodman, "Theory of laser phase noise in recirculating fiber-optic delay lines," J. Lightwave Technol. 3, 20-31 (1985).
[CrossRef]

Murch, R. D.

C. Y. Wong, R. S. Cheng, K. B. Letaief and R. D. Murch, "Multiuser OFDM with adaptive subcarrier, bit, and power allocation," J. Sel. Top. Commun. 17, 1747−1758 (1999).
[CrossRef]

Nakazawa, M.

J. Hongo, K. Kasai, M. Yoshida and M. Nakazawa, "1-Gsymbol/s 64-QAM coherent optical transmission over 150 km," IEEE Photon. Technol. Lett. 19, 638-640 (2007).
[CrossRef]

Nazarathy, M.

M. Nazarathy and E. Simony, "Multichip differential phase encoded optical transmission," IEEE Photon. Technol. Lett. 17, 1133-1135 (2005).
[CrossRef]

Noé, R.

Ochiai, H.

H. Ochiai and H. Imai, "On the distribution of the peak-to-average power ratio in OFDM signals," IEEE Trans. Commun. 49, 282−289 (2001).
[CrossRef]

Okamoto, K.

T. Saida, K. Takiguchi, S. Kuwahara, Y. Kisaka, Y. Miyamoto, Y. Hashizume, T. Shibata and K. Okamoto, "Planar lightwave circuit polarization-mode dispersion compensator," IEEE Photon. Technol. Lett. 14, 507-509 (2002).
[CrossRef]

Orlandini, A.

Park, S.-G.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park and A. H. Gnauck, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445−447 (2001).
[CrossRef]

Pellaux, J.-P.

N. Gisin, J.-P. Von der Weid and J.-P. Pellaux, "Polarization mode dispersion of short and long single-mode fibers," J. Lightwave Technol. 9, 821-827 (1991).
[CrossRef]

Peng, J.

S. Lee, R. Khosravani, J. Peng, V. Grubsky, D. S. Starodubov, A. E. Willner and J. Feinberg, "Adjustable compensation of polarization mode dispersion using a high-birefringence nonlinearly chirped fiber Bragg grating," IEEE Photon. Technol. Lett. 11, 1277-1279 (1999).
[CrossRef]

Petermann, K.

F. Zhang, C. A. Bunge and K. Petermann, "Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems," Opt. Lett. 31, 1038−1040 (2006).
[CrossRef] [PubMed]

F. Zhang, C. A. Bunge, K. Petermann and A. Richter, "Optimum dispersion mapping of single-channel 40 Gbit/s return-to-zero differential phase-shift keying transmission systems," Optics Express 14, 6613−6618 (2006).
[CrossRef] [PubMed]

Petersson, M.

Peveling, R.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandard, S. Ibrahim, O. Adamczyk, M. Porrmann, R. Noé and Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).
[CrossRef]

Pfau, T.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandard, S. Ibrahim, O. Adamczyk, M. Porrmann, R. Noé and Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).
[CrossRef]

Poggiolini, P.

S. Benedetto and P. Poggiolini, "Multilevel polarization shift keying: optimum receiver structure and performance evaluation," IEEE Trans. Commun. 42, 1174-1186 (1994).
[CrossRef]

S. Benedetto and P. Poggiolini, "Theory of polarization shift keying modulation," IEEE Trans. Commun. 40, 708−721 (1992).
[CrossRef]

Poole, C. D.

G. J. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single-mode fibers," J. Lightwave Technol. 9, 1439-1456 (1991).
[CrossRef]

C. D. Poole, R. W. Tkach, A. R. Chraplyvy and D. A. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).
[CrossRef]

C. D. Poole, "Statistical treatment of polarization dispersion in single-mode fiber," Opt. Lett. 13, 687-689 (1988).
[CrossRef] [PubMed]

Porrmann, M.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandard, S. Ibrahim, O. Adamczyk, M. Porrmann, R. Noé and Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).
[CrossRef]

Prati, G.

Premaratne, M.

A. J. Lowery, S. Wang and M. Premaratne, "Calculation of power limit due to fiber nonlinearity in optical OFDM systems," Optics Express 15, 13282−13287 (2007).
[CrossRef] [PubMed]

Proakis, J. G.

J. G. Proakis, "Probabilities of error for adaptive reception of M-phase signals," IEEE Trans. Commun. Tech. 16, 71-81 (1968).
[CrossRef]

Qureshi, S.

S. Qureshi, "Adaptive equalization," Proceedings of the IEEE 73, 1349-1387 (1985).
[CrossRef]

Ramchandran, K.

B. S. Krongold, K. Ramchandran and D. L. Jones, "Computationally efficient optimal power allocation algorithms for multicarrier communication systems," IEEE Trans. Commun. 48, 23−27 (2000).
[CrossRef]

Raybon, G.

R.-J. Essiambre, B. Mikkelsen and G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576−1578 (1999).
[CrossRef]

Rebola, J.

J. Rebola and A. Cartaxo, "Optimization of level spacing in quaternary optical communication systems," Proc. SPIE 4087, 49−59 (2000).
[CrossRef]

Richter, A.

F. Zhang, C. A. Bunge, K. Petermann and A. Richter, "Optimum dispersion mapping of single-channel 40 Gbit/s return-to-zero differential phase-shift keying transmission systems," Optics Express 14, 6613−6618 (2006).
[CrossRef] [PubMed]

Saida, T.

T. Saida, K. Takiguchi, S. Kuwahara, Y. Kisaka, Y. Miyamoto, Y. Hashizume, T. Shibata and K. Okamoto, "Planar lightwave circuit polarization-mode dispersion compensator," IEEE Photon. Technol. Lett. 14, 507-509 (2002).
[CrossRef]

Salz, J.

J. Salz, "Digital transmission over cross-coupled linear channels," AT&T Tech. J. 64, 1147-1159 (1985).

N. Amitay and J. Salz, "Linear Equalization Theory in Digital Data Transmission over Dually Polarized Fading Radio Channels," Bell. Syst. Tech. J. 63, 2215-2259 (1984).

Samuelsson, R.

Sandel, D.

Sasaki, S.

K. Sekine, N. Kikuchi, S. Sasaki, S. Hayase, C. Hasegawa and T. Sugawara, "40 Gbit/s, 16-ary (4 bit/symbol) optical modulation/demodulation scheme," Electron. Lett. 41, 430-432, (2005).
[CrossRef]

Schawlow, A. L.

A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949, (1958).
[CrossRef]

Scheerer, C.

Schmauss, B.

Schöpflin, A.

Sekine, K.

K. Sekine, N. Kikuchi, S. Sasaki, S. Hayase, C. Hasegawa and T. Sugawara, "40 Gbit/s, 16-ary (4 bit/symbol) optical modulation/demodulation scheme," Electron. Lett. 41, 430-432, (2005).
[CrossRef]

Serena, P.

Shake, I.

I. Shake, H. Takara, K. Mori, S. Kawanishi and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600−1601 (1998).
[CrossRef]

Shannon, C.E.

C.E. Shannon, "A mathematical theory of communication," Bell. Syst. Tech. J. 27, 379−423 (1948).

Shibata, T.

T. Saida, K. Takiguchi, S. Kuwahara, Y. Kisaka, Y. Miyamoto, Y. Hashizume, T. Shibata and K. Okamoto, "Planar lightwave circuit polarization-mode dispersion compensator," IEEE Photon. Technol. Lett. 14, 507-509 (2002).
[CrossRef]

Shieh, W.

W. Shieh, X. Yi, Y. Ma and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Optics Express 15, 9936−9947 (2007).
[CrossRef] [PubMed]

W. Shieh and C. Athaudage, "Coherent optical orthogonal frequency division multiplexing," Electron. Lett. 42, 587−589 (2006).
[CrossRef]

Shtaif, M.

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park and A. H. Gnauck, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445−447 (2001).
[CrossRef]

A. Mecozzi, C. B. Clausen and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392−394 (2000).
[CrossRef]

Simon, M.

D. Divsalar and M. Simon, "Multiple-symbol differential detection of MPSK," IEEE Trans. Commun. 38, 300-308 (1990).
[CrossRef]

Simony, E.

M. Nazarathy and E. Simony, "Multichip differential phase encoded optical transmission," IEEE Photon. Technol. Lett. 17, 1133-1135 (2005).
[CrossRef]

Slusher, R. E.

Stark, J.B.

P.P. Mitra and J.B. Stark, "Nonlinear limits to the information capacity of optical fiber communications," Nature 411, 1027-1030 (2001).
[CrossRef] [PubMed]

Starodubov, D. S.

S. Lee, R. Khosravani, J. Peng, V. Grubsky, D. S. Starodubov, A. E. Willner and J. Feinberg, "Adjustable compensation of polarization mode dispersion using a high-birefringence nonlinearly chirped fiber Bragg grating," IEEE Photon. Technol. Lett. 11, 1277-1279 (1999).
[CrossRef]

Striegler, A.

Sugawara, T.

K. Sekine, N. Kikuchi, S. Sasaki, S. Hayase, C. Hasegawa and T. Sugawara, "40 Gbit/s, 16-ary (4 bit/symbol) optical modulation/demodulation scheme," Electron. Lett. 41, 430-432, (2005).
[CrossRef]

Sunnerud, H.

Suzuki, M.

Takara, H.

I. Shake, H. Takara, K. Mori, S. Kawanishi and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600−1601 (1998).
[CrossRef]

Takiguchi, K.

T. Saida, K. Takiguchi, S. Kuwahara, Y. Kisaka, Y. Miyamoto, Y. Hashizume, T. Shibata and K. Okamoto, "Planar lightwave circuit polarization-mode dispersion compensator," IEEE Photon. Technol. Lett. 14, 507-509 (2002).
[CrossRef]

Tang, Y.

W. Shieh, X. Yi, Y. Ma and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Optics Express 15, 9936−9947 (2007).
[CrossRef] [PubMed]

Tkach, R. W.

C. D. Poole, R. W. Tkach, A. R. Chraplyvy and D. A. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).
[CrossRef]

Townes, C. H.

A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949, (1958).
[CrossRef]

Tsukamoto, S.

S. Tsukamoto, K. Katoh and K. Kikuchi, "Coherent demodulation of optical multilevel phase-shift-keying signals using homodyne detection and digital signal processing," IEEE Photon. Technol. Lett. 18, 1131-1133 (2006).
[CrossRef]

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with coherent phase estimation," J. Lightwave Technol. 24, 12-21, (2006).
[CrossRef]

Tur, M.

M. Tur, B. Moslehi and J. W. Goodman, "Theory of laser phase noise in recirculating fiber-optic delay lines," J. Lightwave Technol. 3, 20-31 (1985).
[CrossRef]

Ungerboeck, G.

G. Ungerboeck, "Fractional tap-spacing equalizer and consequences for clock recovery in data modems," IEEE Trans. Commun. 24, 856-864 (1976).
[CrossRef]

Vasic, B.

Vinegoni, C.

Von der Weid, J.-P.

N. Gisin, J.-P. Von der Weid and J.-P. Pellaux, "Polarization mode dispersion of short and long single-mode fibers," J. Lightwave Technol. 9, 821-827 (1991).
[CrossRef]

Wang, H.C.

K.-P. Ho and H.C. Wang, "On the effect of dispersion on nonlinear phase noise," Opt. Lett. 31, 2109−2111 (2006).
[CrossRef] [PubMed]

K.P. Ho and H.C. Wang, "Comparison of nonlinear phase noise and intrachannel four-wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426−1428 (2005).
[CrossRef]

Wang, J.

J. Wang and J. M. Kahn, "Performance of electrical equalizers in optical amplified OOK and DPSK systems," IEEE Photon. Technol. Lett. 16, 1397-1399 (2004).
[CrossRef]

Wang, S.

A. J. Lowery, S. Wang and M. Premaratne, "Calculation of power limit due to fiber nonlinearity in optical OFDM systems," Optics Express 15, 13282−13287 (2007).
[CrossRef] [PubMed]

Wegener, L.G. L.

Wei, X.

Weinstein, S. B.

R.D. Gitlin and S. B. Weinstein, "Fractionally spaced equalization: an improved digital transversal equalizer," Bell. Syst. Tech. J. 60, 275-296 (1981).

F. J. Foschini, R. D. Gitlin and S. B. Weinstein, "On the selction of a two-dimensional signal constellation in the presence of phase jitter and Gaussian noise," Bell. Syst. Tech. J. 52, 927-965 (1973).

Weyrauch, T.

Willner, A. E.

S. Lee, R. Khosravani, J. Peng, V. Grubsky, D. S. Starodubov, A. E. Willner and J. Feinberg, "Adjustable compensation of polarization mode dispersion using a high-birefringence nonlinearly chirped fiber Bragg grating," IEEE Photon. Technol. Lett. 11, 1277-1279 (1999).
[CrossRef]

Winzer, P. J.

A. H. Gnauck, P. J. Winzer and S. Chandrasekhar, "Hybrid 10/40-G transmission on a 50-GHz Grid through 2800 km of SSMF and seven optical add-drops," IEEE Photon. Technol. Lett. 17, 2203−2205 (2005).
[CrossRef]

Wong, C. Y.

C. Y. Wong, R. S. Cheng, K. B. Letaief and R. D. Murch, "Multiuser OFDM with adaptive subcarrier, bit, and power allocation," J. Sel. Top. Commun. 17, 1747−1758 (1999).
[CrossRef]

Wu, S.

S. Wu and Y. Bar-Ness, "OFDM systems in the presence of phase noise: consequences and solutions," IEEE Trans. Commun. 52, 1988−1996 (2004).
[CrossRef]

S. Wu and Y. Bar-Ness, "A phase noise suppression algorithm for OFDM based WLANs," IEEE Commun. Lett. 6, 535−537 (2002).
[CrossRef]

Xie, C.

Xu, C.

G. Zhu, L. Mollenauer and C. Xu, "Experimental demonstration of post-nonlinearity compensation in a multispan DPSK transmission," IEEE Photon. Technol. Lett. 18, 1007−1009 (2006).
[CrossRef]

Yamabayashi, Y.

I. Shake, H. Takara, K. Mori, S. Kawanishi and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600−1601 (1998).
[CrossRef]

Yi, X.

W. Shieh, X. Yi, Y. Ma and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Optics Express 15, 9936−9947 (2007).
[CrossRef] [PubMed]

Yoshida, M.

J. Hongo, K. Kasai, M. Yoshida and M. Nakazawa, "1-Gsymbol/s 64-QAM coherent optical transmission over 150 km," IEEE Photon. Technol. Lett. 19, 638-640 (2007).
[CrossRef]

Yoshida-Dierolf, M.

Zhang, F.

F. Zhang, C. A. Bunge and K. Petermann, "Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems," Opt. Lett. 31, 1038−1040 (2006).
[CrossRef] [PubMed]

F. Zhang, C. A. Bunge, K. Petermann and A. Richter, "Optimum dispersion mapping of single-channel 40 Gbit/s return-to-zero differential phase-shift keying transmission systems," Optics Express 14, 6613−6618 (2006).
[CrossRef] [PubMed]

Zhu, G.

G. Zhu, L. Mollenauer and C. Xu, "Experimental demonstration of post-nonlinearity compensation in a multispan DPSK transmission," IEEE Photon. Technol. Lett. 18, 1007−1009 (2006).
[CrossRef]

Zhu, X.

Appl. Opt. (1)

AT&T Tech. J. (1)

J. Salz, "Digital transmission over cross-coupled linear channels," AT&T Tech. J. 64, 1147-1159 (1985).

Bell. Syst. Tech. J. (4)

N. Amitay and J. Salz, "Linear Equalization Theory in Digital Data Transmission over Dually Polarized Fading Radio Channels," Bell. Syst. Tech. J. 63, 2215-2259 (1984).

R.D. Gitlin and S. B. Weinstein, "Fractionally spaced equalization: an improved digital transversal equalizer," Bell. Syst. Tech. J. 60, 275-296 (1981).

C.E. Shannon, "A mathematical theory of communication," Bell. Syst. Tech. J. 27, 379−423 (1948).

F. J. Foschini, R. D. Gitlin and S. B. Weinstein, "On the selction of a two-dimensional signal constellation in the presence of phase jitter and Gaussian noise," Bell. Syst. Tech. J. 52, 927-965 (1973).

Electron. Lett. (4)

W. Shieh and C. Athaudage, "Coherent optical orthogonal frequency division multiplexing," Electron. Lett. 42, 587−589 (2006).
[CrossRef]

K. Sekine, N. Kikuchi, S. Sasaki, S. Hayase, C. Hasegawa and T. Sugawara, "40 Gbit/s, 16-ary (4 bit/symbol) optical modulation/demodulation scheme," Electron. Lett. 41, 430-432, (2005).
[CrossRef]

I. Shake, H. Takara, K. Mori, S. Kawanishi and Y. Yamabayashi, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600−1601 (1998).
[CrossRef]

R.-J. Essiambre, B. Mikkelsen and G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576−1578 (1999).
[CrossRef]

IEEE Commun. Lett. (2)

A. G. Armada and M. Calvo, "Phase noise and sub-carrier spacing effects on the performance of an OFDM communication system," IEEE Commun. Lett. 2, 11−13 (1998).
[CrossRef]

S. Wu and Y. Bar-Ness, "A phase noise suppression algorithm for OFDM based WLANs," IEEE Commun. Lett. 6, 535−537 (2002).
[CrossRef]

IEEE Photon Technol. Lett. (1)

A. J. Lowery, "Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation," IEEE Photon Technol. Lett. 19, 1556−1558 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (18)

K.P. Ho and H.C. Wang, "Comparison of nonlinear phase noise and intrachannel four-wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426−1428 (2005).
[CrossRef]

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park and A. H. Gnauck, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445−447 (2001).
[CrossRef]

A. H. Gnauck, P. J. Winzer and S. Chandrasekhar, "Hybrid 10/40-G transmission on a 50-GHz Grid through 2800 km of SSMF and seven optical add-drops," IEEE Photon. Technol. Lett. 17, 2203−2205 (2005).
[CrossRef]

G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19, 969−971 (2007).
[CrossRef]

S. Lee, R. Khosravani, J. Peng, V. Grubsky, D. S. Starodubov, A. E. Willner and J. Feinberg, "Adjustable compensation of polarization mode dispersion using a high-birefringence nonlinearly chirped fiber Bragg grating," IEEE Photon. Technol. Lett. 11, 1277-1279 (1999).
[CrossRef]

T. Saida, K. Takiguchi, S. Kuwahara, Y. Kisaka, Y. Miyamoto, Y. Hashizume, T. Shibata and K. Okamoto, "Planar lightwave circuit polarization-mode dispersion compensator," IEEE Photon. Technol. Lett. 14, 507-509 (2002).
[CrossRef]

J. Wang and J. M. Kahn, "Performance of electrical equalizers in optical amplified OOK and DPSK systems," IEEE Photon. Technol. Lett. 16, 1397-1399 (2004).
[CrossRef]

N. Alic and Y. Fainman, "Data-dependent phase coding for suppression of ghost pulses in optical fibers," IEEE Photon. Technol. Lett. 16, 1212−1214 (2004).
[CrossRef]

A. Mecozzi, C. B. Clausen and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392−394 (2000).
[CrossRef]

A.P.T. Lau and J.M. Kahn, "Power profile optimization in phase-modulated systems in presence of nonlinear phase noise," IEEE Photon. Technol. Lett. 18, 2514−2516 (2006).
[CrossRef]

G. Zhu, L. Mollenauer and C. Xu, "Experimental demonstration of post-nonlinearity compensation in a multispan DPSK transmission," IEEE Photon. Technol. Lett. 18, 1007−1009 (2006).
[CrossRef]

J. Hongo, K. Kasai, M. Yoshida and M. Nakazawa, "1-Gsymbol/s 64-QAM coherent optical transmission over 150 km," IEEE Photon. Technol. Lett. 19, 638-640 (2007).
[CrossRef]

S. Tsukamoto, K. Katoh and K. Kikuchi, "Coherent demodulation of optical multilevel phase-shift-keying signals using homodyne detection and digital signal processing," IEEE Photon. Technol. Lett. 18, 1131-1133 (2006).
[CrossRef]

M. Nazarathy and E. Simony, "Multichip differential phase encoded optical transmission," IEEE Photon. Technol. Lett. 17, 1133-1135 (2005).
[CrossRef]

K.-P. Ho, "Exact evaluation of the capacity for intensity-modulated direct-detection channels with optical amplifier noises," IEEE Photon. Technol. Lett. 17, 858−860 (2005).
[CrossRef]

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandard, S. Ibrahim, O. Adamczyk, M. Porrmann, R. Noé and Y. Achiam, "First real-time data recovery for synchronous QPSK transmission with standard DFB lasers," IEEE Photon. Technol. Lett. 18, 1907-1909 (2006).
[CrossRef]

C. D. Poole, R. W. Tkach, A. R. Chraplyvy and D. A. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).
[CrossRef]

H. Bülow, "System outage probability due to first- and second-order PMD," IEEE Photon. Technol. Lett. 10, 696-698 (1998).
[CrossRef]

IEEE Trans. Commun. (7)

S. Benedetto and P. Poggiolini, "Multilevel polarization shift keying: optimum receiver structure and performance evaluation," IEEE Trans. Commun. 42, 1174-1186 (1994).
[CrossRef]

D. Divsalar and M. Simon, "Multiple-symbol differential detection of MPSK," IEEE Trans. Commun. 38, 300-308 (1990).
[CrossRef]

S. Benedetto and P. Poggiolini, "Theory of polarization shift keying modulation," IEEE Trans. Commun. 40, 708−721 (1992).
[CrossRef]

G. Ungerboeck, "Fractional tap-spacing equalizer and consequences for clock recovery in data modems," IEEE Trans. Commun. 24, 856-864 (1976).
[CrossRef]

H. Ochiai and H. Imai, "On the distribution of the peak-to-average power ratio in OFDM signals," IEEE Trans. Commun. 49, 282−289 (2001).
[CrossRef]

S. Wu and Y. Bar-Ness, "OFDM systems in the presence of phase noise: consequences and solutions," IEEE Trans. Commun. 52, 1988−1996 (2004).
[CrossRef]

B. S. Krongold, K. Ramchandran and D. L. Jones, "Computationally efficient optimal power allocation algorithms for multicarrier communication systems," IEEE Trans. Commun. 48, 23−27 (2000).
[CrossRef]

IEEE Trans. Commun. Systems (1)

J. J. Bussgang and M. Leiter, "Error rate approximations for differential phase-shift keying." IEEE Trans. Commun. Systems 12, 18-27 (1964).
[CrossRef]

IEEE Trans. Commun. Tech. (1)

J. G. Proakis, "Probabilities of error for adaptive reception of M-phase signals," IEEE Trans. Commun. Tech. 16, 71-81 (1968).
[CrossRef]

J. Lightwave Technol. (24)

J. R. Barry and J.M. Kahn, "Carrier synchronization for homodyne and heterodyne detection of optical quadriphase-shift keying," J. Lightwave Technol. 10, 1939-1951 (1992).
[CrossRef]

R. Noé, "Phase noise-tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedforward carrier recovery," J. Lightwave Technol. 23, 802−808 (2005).
[CrossRef]

M. Suzuki and N. Edagawa, "Dispersion-managed high-capacity ultra-long-haul transmission," J. Lightwave Technol. 21, 916−929 (2003).
[CrossRef]

E. Forestieri and G. Prati, "Exact analytical evaluation of second-order PMD impact on the outage probability for a compensated system," J. Lightwave Technol. 22, 988−996 (2004).
[CrossRef]

H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson and P. Andrekson, "A comparison between different PMD compensation techniques," J. Lightwave Technol. 20, 368-378 (2002).
[CrossRef]

F. Buchali and H. Bülow, "Adaptive PMD compensation by electrical and optical techniques," J. Lightwave Technol. 22, 1116-1126 (2004).
[CrossRef]

R. Noé, D. Sandel, M. Yoshida-Dierolf, S. Hinz, V. Mirvoda, A. Schöpflin, C. Flingener, E. Gottwald, C. Scheerer, G. Fischer, T. Weyrauch and W. Haase, "Polarization mode dispersion compensation at 10, 20, and 40 Gb/s with various optical equalizer," J. Lightwave Technol. 17, 1602-1616 (1999).
[CrossRef]

N. Gisin, J.-P. Von der Weid and J.-P. Pellaux, "Polarization mode dispersion of short and long single-mode fibers," J. Lightwave Technol. 9, 821-827 (1991).
[CrossRef]

G. J. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single-mode fibers," J. Lightwave Technol. 9, 1439-1456 (1991).
[CrossRef]

S. Betti, F. Curti, G. de Marchis and E. Iannone, "Multilevel coherent optical system based on Stokes parameters modulation," J. Lightwave Technol. 8, 1127−1136 (1990).
[CrossRef]

E. Ip and J. M. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightwave Technol.,  25, 2675-2692 (2007).
[CrossRef]

E. Ip and J.M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightwave Technol. 25, 2033-2043 (2007).
[CrossRef]

E. Ip and J.M. Kahn, "Carrier synchronization for 3- and 4-bit-per-symbol optical transmission," J. Lightwave Technol. 23, 4110-4124 (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]

A. Striegler and B. Schmauss, "Compensation of intrachannel effects in symmetric dispersion-managed transmission systems," J. Lightwave Technol. 22, 1877−1882 (2004).
[CrossRef]

C. Vinegoni, M. Karlsson, M. Petersson and H. Sunnerud, "The statistics of polarization-dependent loss in a recirculating loop," J. Lightwave Technol. 22, 968−976 (2004).
[CrossRef]

K.-P. Ho and J. M. Kahn, "Detection technique to mitigate Kerr effect phase noise," J. Lightwave Technol. 22, 779−783 (2004).
[CrossRef]

A. P. T. Lau and J. M. Kahn, "Design of inline amplifiers gain and spacing to minimize phase noise in optical transmission systems," J. Lightwave Technol. 24, 1334−1341 (2006).
[CrossRef]

I.B. Djordjevic and B. Vasic, "Constrained coding techniques for suppression of intrachannel nonlinear effects in high-speed optical transmission," J. Lightwave Technol. 24, 411−419 (2006).
[CrossRef]

A. P. T. Lau and J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightwave Technol. 25, 3008−3016 (2007).
[CrossRef]

M. Tur, B. Moslehi and J. W. Goodman, "Theory of laser phase noise in recirculating fiber-optic delay lines," J. Lightwave Technol. 3, 20-31 (1985).
[CrossRef]

M. A. Grant, W. C. Michie, M. J. Fletcher, "The performance of optical phase-locked loops in the presence of nonnegligible loop propagation delay," J. Lightwave Technol. 5, 592-597 (1987).
[CrossRef]

P. Serena, A. Orlandini and A. Bononi, "Parametric-Gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightwave Technol. 24, 2026−2037 (2006).
[CrossRef]

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with coherent phase estimation," J. Lightwave Technol. 24, 12-21, (2006).
[CrossRef]

J. Opt. Soc. Am. A. B (1)

D. Boivin, G.-K. Chang, J. R. Barry and M. Hanna, "Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion," J. Opt. Soc. Am. A. B 23, 2019−2023 (2006).
[CrossRef]

J. Quantum Electron. (1)

C. Henry, "Theory of the phase noise and power spectrum of a single mode injection laser," J. Quantum Electron. 19, 1391-1397 (1983).
[CrossRef]

J. Sel. Top. Commun. (1)

C. Y. Wong, R. S. Cheng, K. B. Letaief and R. D. Murch, "Multiuser OFDM with adaptive subcarrier, bit, and power allocation," J. Sel. Top. Commun. 17, 1747−1758 (1999).
[CrossRef]

J. Sel. Top. Quantum Electron. (2)

K. Kikuchi, "Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation," J. Sel. Top. Quantum Electron. 12, 563−570 (2006).
[CrossRef]

J. M. Kahn and K.-P. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM Systems," J. Sel. Top. Quantum Electron. 10, 259-271 (2004).
[CrossRef]

Nature (1)

P.P. Mitra and J.B. Stark, "Nonlinear limits to the information capacity of optical fiber communications," Nature 411, 1027-1030 (2001).
[CrossRef] [PubMed]

Opt. Comm. (1)

K.P. Ho, "Mid-span compensation of nonlinear phase noise," Opt. Comm. 245, 391−398 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (8)

Optics Express (4)

F. Zhang, C. A. Bunge, K. Petermann and A. Richter, "Optimum dispersion mapping of single-channel 40 Gbit/s return-to-zero differential phase-shift keying transmission systems," Optics Express 14, 6613−6618 (2006).
[CrossRef] [PubMed]

W. Shieh, X. Yi, Y. Ma and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Optics Express 15, 9936−9947 (2007).
[CrossRef] [PubMed]

A. J. Lowery, "Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM," Optics Express 15, 12965−12970 (2007).
[CrossRef] [PubMed]

A. J. Lowery, S. Wang and M. Premaratne, "Calculation of power limit due to fiber nonlinearity in optical OFDM systems," Optics Express 15, 13282−13287 (2007).
[CrossRef] [PubMed]

Phys. Rev. (1)

A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949, (1958).
[CrossRef]

Proc. SPIE (1)

J. Rebola and A. Cartaxo, "Optimization of level spacing in quaternary optical communication systems," Proc. SPIE 4087, 49−59 (2000).
[CrossRef]

Proceedings of the IEEE (1)

S. Qureshi, "Adaptive equalization," Proceedings of the IEEE 73, 1349-1387 (1985).
[CrossRef]

Other (29)

B. Widrow and S. D. Stearns, Adaptive Signal Processing, (Prentice Hall, Englewood Cliffs, NJ, 1985).

A. Oppenheim and R. Schafer, Discrete-Time Signal Processing, (Prentice Hall, Englewood Cliffs, NJ, 1989).

K.-P. Ho, Phase-Modulated Optical Communication Systems, (Springer, New York, 2005).

K.-P. Ho, "Statistical properties of nonlinear phase noise," in Advances in Optics and Laser Research3, (Nova Science Publishers, New York, 2003).

H. Meyr, M. Moeneclaey and S. Fechtel, Digital Communication Receivers. (John Wiley, New York, 1997).

A. P. T. Lau, S. Rabbani and J. M. Kahn are preparing a manuscript to be called "On the statistics of intra-channel four-wave-mixing induced phase noise in phase modulated systems."

K. Kikuchi, M. Fukase and S.-Y. Kim, "Electronic post-compensation for nonlinear phase noise in a 1000-km 20-Gbit/s optical QPSK transmission system using the homodyne receiver with digital signal processing," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2007), Paper OTuA2.

G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran and S. Bigo, "Transmission of 40 Gb/s QPSK with coherent detection over ultra-long distance improved by nonlinearity mitigation," in Proceedings ECOC 2006, Cannes, France, 2006, Postdeadline paper Th4.3.4.

D.-S. Ly-Gagnon and K. Kikuchi, "Cancellation of nonlinear phase noise in DPSK transmission," 2004 Optoelectronics and Communications Conference and International Conference on Optical Internet (OECC/COIN2004), paper 14C3-3 (2004).

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

H. Bülow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Küppers and W. Weiershausen, "Measurement of the maximum speed of PMD fluctuation in installed field fiber," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, San Diego, 1999), Paper OWE4.

J. M. Geist, "Capacity and cutoff rate for dense M-ary PSK constellations," in MILCOM 1990, (Monterey, CA, USA, 1990), pp. 768−770.

V. Jungnickel, A. Forck, T. Haustein, S. Schiffermuller, C. Helmolt, F. Luhn, M. Pollock, C. Juchems, M. Lampe, S. Eichnger, W. Zirwas, E. Schulz, "1 Gbit/s MIMO-OFDM transmission experiments," in Proceedings of IEEE Conference on Vehicular Technol. (Institute of Electrical and Electronics Engineers, Dallas, 2005), pp. 861-866.

K. Kikuchi, "Coherent detection of phase-shift keying signals using digital carrier-phase estimation," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2006), Paper OTuI4.

A. Leven, N. Kaneda, U.-V. Koc and Y.-K. Chen, "Coherent receivers for practical optical communication systems," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2007), Paper OThK4.

S. J. Savory, G. Gavioli, R. I. Killey, P. Bayvel, "Transmission of 42.8 Gbit/s polarization multiplexed NRZ-QPSK over 6400 km of standard fiber with no optical dispersion compensation," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2007), Paper OTuA1.

G. P. Agrawal, Fiber-Optic Communiation Systems, 3rd ed. (Wiley, New York, 2002).
[CrossRef]

F.M. Gardner, Phaselock Techniques, 3rd ed. (John Wiley, Hoboken, NJ, 2005).
[CrossRef]

M. G. Taylor, "Accurate digital phase estimation process for coherent detection using a parallel digital processor," in Proceedings ECOC 2005, Glasgow, UK, 2005, Paper Tu4.2.6.

C. Cover and J. Thomas, Elements of Information Theory. (John Wiley, New York, 1991).
[CrossRef]

J. Jang, K. B. Lee and Y.-H. Lee, "Transmit power and bit allocations for OFDM systems in a fading channel," in Proceedings of IEEE GLOBECOM, (Institute of Electrical and Electronics Engineers, San Francisco, 2003), pp. 858−862.

N. Cvijetic, L. Xu and T. Wang, "Adaptive PMD compensation using OFDM in long-haul 10 Gb/s DWDM systems," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2007), Paper OTuA5.

A. Lowery and J. Armstrong, "Orthogonal-frequency-division multiplexing for optical dispersion compensation," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2007), Paper OTuA4.

W. Henkel, G. Taubock, P. Odling, P. O. Borjesson and N. Petersson, "The cyclic prefix of OFDM/DMT - an analysis," IEEE International Seminar on Broadband Communications, (Institute of Electrical and Electronic Engineers, Zurich, 2002).

D. J.F. Barros and J. M. Kahn are preparing a manuscript to be called "Optimized dispersion compensation using orthogonal frequency-division multiplexing."

A. Bahai, B. Saltzberg and M. Ergen, Multi-carrier Digital Communications: Theory and Applications of OFDM, 2nd Ed. (Springer, New York, 2004).

R. Prasad, "OFDM for wireless communications systems," (Artech House Publishers, Boston, 2004).

W. Shieh, X. Yi, and Y. Tang, "Experimental demonstration of transmission of coherent optical OFDM Systems," in Proceedings of IEEE Conference on Optical Fiber Communications, (Institute of Electrical and Electronics Engineers, Anaheim, 2007), Paper OMP2.

D.-S. Ly-Gagnon, "Information recovery using coherent detection and digital signal pocessing for phase-shift-keying modulation formats in optical communication systems," M.S. Thesis, University of Tokyo (2004).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (23)

Fig. 1.
Fig. 1.

Noncoherent receivers for (a) amplitude-shift modulation (ASK) and (b) binary frequency-shift keying (FSK).

Fig. 2.
Fig. 2.

Differentially coherent phase detection of (a) 2-DPSK (b) M-DPSK, M>2.

Fig. 3.
Fig. 3.

Polarization-shift keying (PolSK) receiver.

Fig. 4.
Fig. 4.

Coherent transmission system (a) implementation, (b) system model.

Fig. 5.
Fig. 5.

Single-polarization downconverter employing a (a) heterodyne and (b) homodyne design.

Fig. 6.
Fig. 6.

Spectrum of a (a) heterodyne and (b) homodyne downconverter measured at the output of the balanced photodetector.

Fig. 7.
Fig. 7.

Emulating (a) direct detection, (b) 4-DPSK detection and (c) PolSK detection with optoelectronic downconversion followed by non-linear signal processing in the electronic domain. The signals Ex (t) and Ey (t) are the complex-valued analog outputs described by Eq. (12) for each polarization. We note that in the case of the heterodyne downconverter, the non-linear operations shown can be performed at the IF output(s) of the balanced photoreceiver.

Fig. 8.
Fig. 8.

8-QAM constellation.

Fig. 9.
Fig. 9.

Spectral efficiency vs. SNR per bit required for different modulation formats at a target BER of 10-3. We assume polarization multiplexing for all schemes except PolSK. Also shown is the Shannon limit (15), which corresponds to zero BER.

Fig. 10.
Fig. 10.

First-order polarization-mode dispersion.

Fig. 11.
Fig. 11.

Digital equalization for a dually polarized linear channel.

Fig. 12.
Fig. 12.

Adaptive equalizer for polarization-multiplexed coherent detection.

Fig. 13.
Fig. 13.

Autocorrelation function for IFWM phase noise in 80 Gbit/s QPSK transmission with 33% Gaussian pulses. Each span consists of 80 km of SMF with α=0.25 dB/km, D=17 ps/nm-km, γ=1.2 W-1km-1, followed by DCF with α=0.6 dB/km, D=-85 ps/nm-km, γ=5.3 W-1km-1. The mean nonlinear phase shift is Φ NL =0.0215 rad/span.

Fig. 14.
Fig. 14.

Constellation diagrams of the received signal showing ML decision boundaries for (a) no NLPN, (b) with NLPN before compensation by θopt , and (c) with NLPN after compensation by θopt .

Fig. 15.
Fig. 15.

Phase-locked loop: (a) System model, (b) analytical model, (c) phase estimation.

Fig. 16.
Fig. 16.

σϕ versus ωn for 16-QAM at 100 Gbit/s in a single polarization employing a second-order PLL, withΔν=100 kHz and an OSNR of 11.5 dB.

Fig. 17.
Fig. 17.

Feedforward carrier phase estimation. (a) System model, (b) soft phase estimation, (c) analytical model.

Fig. 18.
Fig. 18.

Carrier synchronization for polarization-multiplexed systems, (a) PLL approach, (b) feedforward carrier synchronization approach.

Fig. 19.
Fig. 19.

Possible integration of nonlinear phase noise compensation, adaptive digital equalization and carrier synchronization.

Fig. 20.
Fig. 20.

Multi-carrier transmitter and receiver (a) analog implementation, (b) OFDM implementation.

Fig. 21.
Fig. 21.

OFDM symbol with cyclic prefix.

Fig. 22.
Fig. 22.

Fourier transform of OFDM signal.

Fig. 23.
Fig. 23.

Polarization-multiplexed OFDM transmitter and receiver with PMD compensation.

Tables (11)

Tables Icon

Table 1. SNR per symbol for various receiver configurations. For the ASE-limited cases, s is the average number of photons received per symbol, NA is the number of fiber spans, and nsp is the spontaneous emission noise factor of the inline amplifiers. For the LO shot-noise-limited cases, r =ηn̄s is the number of detected photons per symbol, where η is the quantum efficiency of the photodiodes.

Tables Icon

Table 2. Comparison between homodyne and heterodyne downconverters.

Tables Icon

Table 3. Comparison of carrier synchronization options. All three can be used with either homodyne or heterodyne downconversion.

Tables Icon

Table 4. Comparison between noncoherent, differentially coherent and coherent detection. For the first two detection methods, direct detection refers to the receiver implementations shown in Figs. 1–3, while homodyne/heterodyne refers to the equivalent implementations shown in Fig. 7.

Tables Icon

Table 5. Parameters for computing the BER in polarization-shift keying (PolSK).

Tables Icon

Table 6. SNR per bit (in dB) required to achieve BER=10-3.

Tables Icon

Table 7. Equalizer length required (N) to compensate CD in a system using polarization-multiplexed 4-QAM at 100 Gbit/s. SMF (D=17 ps/nm-km) with 2% under-compensation of CD is assumed. The oversampling ratio is 3/2.

Tables Icon

Table 8. Linewidth requirements for various single-polarization modulation formats using a PLL and a FF carrier synchronizer at a target BER of 10-3.

Tables Icon

Table 9. OFDM parameters for 100 Gbit/s transmission using polarization-multiplexed 4-QAM. SMF (D=17ps/nm-km) with 2% under-compensation of CD is assumed. Target excess bandwidth factor of κ 1≤0.25, oversampling ratio of κ 2≤1.25, and impulse energy containment factor of κ 3≥0.98 are assumed.

Tables Icon

Table 10. No. of ADC bits required for different modulation formats at a target BER of10-3.

Tables Icon

Table 11. Comparison of the computational complexity of single-carrier transmission versus OFDM for polarization-multiplexed 4-QAM at 100 Gbit/s (Rs =25 GHz). Listed are the number of complex multiplications required per symbol period Ts =1/Rs .

Equations (63)

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

I D P S K ( t ) = R Re { E s ( t ) E s * ( t T s ) } ,
I D P S K , i ( t ) = 1 2 R Re { E s ( t ) E s * ( t T s ) } , and
I D P S K , q ( t ) = 1 2 R Im { E s ( t ) E s * ( t T s ) } .
E t x ( t ) = [ E t x , 1 ( t ) E t x , 2 ( t ) ] = P t k x k b ( t k T s ) e j ( ω s t + ϕ s ( t ) ) ,
h ( t ) = [ h 11 ( t )       h 12 ( t ) h 21 ( t ) h 22 ( t ) ] F [ H 11 ( ω ) H 12 ( ω ) H 21 ( ω ) H 22 ( ω ) ] = H ( ω ) ,
E s , l ( t ) = P r K m = 1 2 x m , k c l m ( t k T s ) e j ( ω s t + ϕ s ( t ) ) + E s p , l ( t ) .
I h e t , l ( t ) = R ( E 1 ( t ) 2 E 2 ( t ) 2 ) = 2 R Im { E s , l ( t ) E L O , l * ( t ) } + I s h , l ( t ) ,
I h e t , l ( t ) = 2 R P L O , l ( P r ( y l i ( t ) sin ( ω I F t ) + y l q ( t ) cos ( ω I F t ) ) + E s p , l ( t ) ) + I s h , l ( t ) ,
y l 0 ( t ) = k m = 1 2 x m , k c l m ( t k T s ) e j ϕ ( t ) .
I h o m , l , i ( t ) = R ( E 1 ( t ) 2 E 2 ( t ) 2 ) = R P L O , l ( P r y l i ( t ) + E s p , l i ( t ) ) + I s h , l i ( t ) , and
I h o m , l , q ( t ) = R ( E 3 ( t ) 2 E 4 ( t ) 2 ) = R P L O , l ( P r y l q ( t ) + E s p , l q ( t ) ) + I s h , l q ( t ) ,
y l ( t ) = k m = 1 2 x m , k c lm ( t kT s ) e j ϕ ( t ) + n l ( t ) ,
S nn ( f ) = N 0 = T s γ s .
y k = x k + n k ,
b max = log 2 ( 1 + γ s ) .
P b ASK ( M ) 1 b ( M 1 M ) erfc ( 3 b γ b 2 ( M 1 ) ( 2 M 1 ) ) .
P b D P S K ( M ) 1 b π M π 1 π 0 π 2 sin χ [ 1 + b γ b ( 1 + cos η sin χ ) ] exp ( b γ b ( 1 cos η sin χ ) ) d χ d η .
P b DPSK ( 2 ) = 1 2 exp ( γ b ) .
P b DPSK ( 4 ) = Q 1 ( α , β ) 1 2 I 0 ( α β ) exp [ 1 2 ( α 2 + β 2 ) ] ,
P b P o l S K ( 2 ) = 1 2 exp ( γ b ) .
P b P o l S K ( M ) 1 b [ 1 F θ ( θ 1 ) + n π θ 0 θ 1 cos 1 ( tan θ 0 tan t ) f θ ( t ) d t ] ,
F θ ( t ) = 1 1 2 exp ( b γ b ( 1 cos t ) ) ( 1 + cos t ) , and
f θ ( t ) = sin t 2 exp ( b γ b ( 1 cos t ) ) ( 1 + b γ b ( 1 + cos t ) ) .
P b P S K ( M ) 1 b e r f c ( b γ b sin ( π M ) ) .
P b P S K ( 2 ) = P b P S K ( 4 ) = 1 2 e r f c ( γ b ) .
P b Q A M ( M ) 2 b ( M 1 M ) e r f c ( 3 b γ b 2 ( M 1 ) ) .
P b Q A M ( 8 ) 11 16 e r f c ( 3 γ b 3 + 3 ) .
H C D ( ω ) = e j ( 1 2 β 2 L f i b e r ( ω ω s ) 2 + 1 6 β 3 L f i b e r ( ω ω s ) 3 ) I ,
H P M D ( ω ) = R 1 1 D R 2 ,
y i ( k T ) y i , k = n j = i 2 x j , n q i j ( k T n T s ) + n i ( k T ) .
x k ˜ = [ x ˜ 1 , k x ˜ 2 , k ] = [ W 11 T W 21 T W 12 T W 22 T ] [ y 1 , k y 2 , k ] = W T y k ,
W o p t = A 1 α ,
= E ε k * ε k T = ( W W o p t ) H A ( W W o p t ) + ( P x I α H A 1 α ) ,
W ( m + 1 ) = W ( m ) + 2 μ y k * ε k T ,
N = 2 π β 2 L R s 2 ( M K ) , and
N = τ D G D M K T s ,
E z + j β 2 2 2 E t 2 + α 2 E = j γ E 2 E ,
Δ E z + j β 2 2 Δ E t 2 + α 2 Δ E = j γ E ( lin ) 2 E ( lin ) = j γ l , m , p x l x m x p * b l ( lin ) b m ( lin ) b p ( lin ) * .
Δ b 0 z + j β 2 2 Δ b 0 t 2 + α 2 Δ b 0 = j γ l , m x l x m x l + m * b l ( lin ) b m ( lin ) b l + m ( lin ) * .
C l , m z + j β 2 2 C l , m t 2 + α 2 C l , m = j γ b l ( lin ) b m ( lin ) b l + m ( lin ) * ,
ϕ IFWM ( t ) = Im { l , m 0 x l x m x l + m * C l , m ( t ) x 0 ( b 0 ( lin ) + Δ b ( S + X ) ) } = Im { l , m 0 x l x m x l + m * x 0 * C l , m ( t ) } ,
R ( 0 ) = 1 2 l , m Im { C l , m } 2 ,
R ( k ) = 1 2 m Re { C m , k m C m , m k * } 1 2 m Re { C m , k C m , k }
+ 1 2 m Re { C m , k C m , k * } 1 2 m Re { C m , k m C m , m k } , k > 0
R ( 0 ) = 1 2 l , m C l , m 2 , R ( k ) = 1 2 m Re { C m , k m C m , m k * } 1 2 m Re { C m , k C m , k } , k > 0
ϕ NL = γ L eff i = 1 N E + k = 1 i n k 2 .
σ N L 2 = 2 3 N ( N + 1 ) ( γ L e f f σ ) 2 [ ( 2 N + 1 ) E 2 + ( N 2 + N + 1 ) σ 2 ] ,
θ opt = γ L eff N + 1 2 P rec .
ϕ NL ( t ) = Im [ 2 0 L k b k ( lin ) ( z , t ) 2 n ( z , t ) h z ( t ) e αz dz E ( lin ) ( L , t ) ] ,
ϕ ( t ) = t δ ω ( τ ) d τ ,
ϕ ( s ) = s s + F ( s ) e s τ d ϕ s ( s ) F ( s ) e S τ d s + F ( s ) e S τ d n ( s ) ,
σ ϕ 2 = σ p 2 2 ζω n T s Γ PN ( ω n τ d ) + ( 1 + 4 ζ 2 ) ω n T s 4 ζ η c 2 γ s Γ AWGN ( ω n τ d ) ,
Γ PN ( ω n τ d ) = 2 ζ ω n π + e j ω τ d F ( ω ) 2 , and
Γ AWGN ( ω n τ d ) = 2 ζ π ( 1 + 4 ζ 2 ) ω n F ( ω ) j ω + e j ω τ d F ( ω ) 2 d ω .
w n = { αr 1 α 2 α n n 0 αr 1 α 2 α n n < 0 ,
σ ϕ 2 ( W , Δ ) = σ p 2 · [ m = 0 Δ 1 ( l = 0 m w l ) 2 + m = Δ + 1 L p 1 ( l = m L p 1 w l ) 2 ] + η c 2 γ s · [ l = 0 L p 1 w l 2 ] .
x ofdm ( t ) = m n = N c 2 N c 2 1 x n , m b ( t m T ofdm ) e j 2 πn f d t ,
x ofdm ( k T c ) = m n = N c 2 N c 2 1 x n , m b ( ( k m ( N c + N pre ) ) T c ) e j 2 πn k N c .
S xx ( ω ) = T ofdm n = N c 2 N c 2 P n sin c 2 ( T ofdm 2 π ( ω 2 πn f d ) ) ,
σ ISI + ICI 2 [ k ] 2 σ x 2 ( m = 0 H + [ N pre 2 + m + 1 ; N ; k ] 2 + m = 0 H [ N pre 2 + m + 1 ; N ; k ] 2 ) ,
n = N pre ( i ) 2 N pre ( i ) 2 1 h ( i ) [ n ] 2 κ 3 n = h ( i ) [ n ] 2 .
N c ( i ) = 2 log 2 N pre ( i ) κ 1 ( 0 ) , N u ( i ) = N c ( i ) κ 2 ( 0 ) ,
N Δ = 2 k 2 P d Δ = k 2 3 k 1 γ s .

Metrics