E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

G. P. Agrawal, Nonlinear Fiber Optics, San Diego, CA, USA: Academic, 1989, ch. 2.

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Exp., vol. 17, no. 13, pp. 10814–10819, 2009.

E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightw. Technol., vol. 27, no. 22, pp. 5115–5126, 2009.

F. Pancaldi, G. M. Vitetta, R. Kalbasi, N. Al-Dhahir, M. Uysal, and H. Mheidat, “Single-carrier frequency domain equalization,” IEEE Signal Process. Mag., vol. 25, no. 5, pp. 37–56, 2008.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightw. Technol., vol. 10, no. 1, pp. 28–35, 1992.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Philipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmission,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2010, Paper OTuE1.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Philipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmission,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2010, Paper OTuE1.

R. Griffin and A. Carter, “Optical differential quadrature phase-shift key (oDQPSK) for high capacity optical transmission,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 17–22, 2002, Paper WX6.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon., vol. 7, no. 7, pp. 560–568, 2013.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon., vol. 7, no. 7, pp. 560–568, 2013.

K. Roberts, L. Chuandong, L. Strawczynski, M. O'Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett., vol. 18, no. 2, pp. 403–405, 2006.

L. Coelho and N. Hanik, “Global optimization of fiber-optic communication systems using four-dimensional modulation formats,” presented at the European Conf. Optical Communication, Geneva, Switzerland, , 2011, Paper Mo.2.B.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Philipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmission,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2010, Paper OTuE1.

A. W. Davis, M. J. Pettitt, P. J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightw. Technol., vol. 5, no. 4, pp. 561–572, 1987.

O. E. DeLange, “Wide-band optical communication systems—Part II: Frequency-division multiplexing,” Proc. IEEE, vol. 58, no. 10, pp. 1683–1690, 1970.

F. Derr, “Optical QPSK transmission system with novel digital receiver concept,” Electron Lett., vol. 27, no. 23, pp. 2177–2179, 1991.

L. Dou, Y. Zhao, Z. Tao, Y. Fan, T. Hoshida, and J. C. Rasmussen, “Advanced digital nonlinear distortion compensation,” presented at Optical Fiber Communication Conf., Los Angeles, CA, USA, , 2015, Paper Th3G.3.

T. Okoshi, K. Emura, K. Kikuchi, and R. Th. Kersten, “Computation of bit-error rate of various heterodyne and coherent-type optical communication schemes,” J. Opt. Commun., vol. 2, no. 4, pp. 134–141, 1981.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightw. Technol., vol. 10, no. 1, pp. 28–35, 1992.

L. Dou, Y. Zhao, Z. Tao, Y. Fan, T. Hoshida, and J. C. Rasmussen, “Advanced digital nonlinear distortion compensation,” presented at Optical Fiber Communication Conf., Los Angeles, CA, USA, , 2015, Paper Th3G.3.

Md. S. Faruk and K. Kikuchi, “Adaptive frequency-domain equalization in digital coherent receivers,” Opt. Exp., vol. 19, no. 13, pp. 12789–12798, 2011.

Md. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairment monitoring from adaptive finite-impulse-response filters in a digital coherent receiver,” Opt. Exp., vol. 18, no. 26, pp. 26929–26936. 2010.

F. Favre and D. LeGuen, “High frequency stability of laser diode for heterodyne communication systems,” Electron. Lett., vol. 16, no. 18, pp. 709–710, 1980.

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D. Hanson, D. McGhan, H. Sun, M. Moyer, and M. O'Sullivan, “Performance of a 46-Gb/s dual-polarization QPSK transceiver in a high-PMD fiber transmission experiment,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper PDP9.

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D. Hanson, D. McGhan, H. Sun, M. Moyer, and M. O'Sullivan, “Performance of a 46-Gb/s dual-polarization QPSK transceiver in a high-PMD fiber transmission experiment,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper PDP9.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Philipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmission,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2010, Paper OTuE1.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

B. Glance, “Polarization independent coherent optical receiver,” J. Lightw. Technol., vol. LT-5, no. 2, pp. 274–276, 1987.

D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun., vol. COM-28, no. 11, pp. 1867–1875, 1980.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightw. Technol., vol. 10, no. 1, pp. 28–35, 1992.

R. Griffin and A. Carter, “Optical differential quadrature phase-shift key (oDQPSK) for high capacity optical transmission,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 17–22, 2002, Paper WX6.

F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Exp., vol. 20, no. 2, pp. 1360–1368, 2012.

L. Coelho and N. Hanik, “Global optimization of fiber-optic communication systems using four-dimensional modulation formats,” presented at the European Conf. Optical Communication, Geneva, Switzerland, , 2011, Paper Mo.2.B.

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D. Hanson, D. McGhan, H. Sun, M. Moyer, and M. O'Sullivan, “Performance of a 46-Gb/s dual-polarization QPSK transceiver in a high-PMD fiber transmission experiment,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper PDP9.

K. Roberts, L. Chuandong, L. Strawczynski, M. O'Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett., vol. 18, no. 2, pp. 403–405, 2006.

H. Hodgikinson, R. A. Harmon, and D. W. Smith, Demodulation of optical DPSK using in-phase and quadrature detection,” Electron. Lett., vol. 21, no. 19, pp. 867–868, 1985.

Y. Yamamoto and H. Haus, “Preparation, measurement and information capacity of optical quantum states,” Rev. Mod. Phys., vol. 58, no. 4, pp. 1001–1020, 1986.

T. Imai, Y. Hayashi, N. Ohkawa, T. Sugie, Y. Ichihashi, and T. Ito, “Field demonstration of 2.5 Gbit/s coherent optical transmission through installed submarine fibre cables,” Electron. Lett., vol. 26, no. 17, pp. 1407–1409, 1990.

S. Haykin, Introduction to Adaptive Filters, New York, NY, USA: Macmillan, 2001, ch. 4.

K. Kikuchi, T. Okoshi, M. Nagamatsu, and N. Henmi, “Degradation of bit-error rate in coherent optical communications due to spectral spread of the transmitter and the local oscillator,” J. Lightw. Technol., vol. LT-2, no. 6, pp. 1024–1033, 1984.

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron., vol. QE-18, no. 2, pp. 259–264, 1982.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

J. M. Kahn and K.-P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Topics Quantum Electron., vol. 10, no. 2, pp. 259–272, 2004.

H. Hodgikinson, R. A. Harmon, and D. W. Smith, Demodulation of optical DPSK using in-phase and quadrature detection,” Electron. Lett., vol. 21, no. 19, pp. 867–868, 1985.

N. Shibata, Y. Sasaki, K. Okamoto, and T. Hosaka, “Fabrication of polarization-maintaining and absorption-reducing fibers,” J. Lightw. Technol., vol. LT-1, no. 1, pp. 38–43, 1983.

L. Dou, Y. Zhao, Z. Tao, Y. Fan, T. Hoshida, and J. C. Rasmussen, “Advanced digital nonlinear distortion compensation,” presented at Optical Fiber Communication Conf., Los Angeles, CA, USA, , 2015, Paper Th3G.3.

T. Imai, Y. Hayashi, N. Ohkawa, T. Sugie, Y. Ichihashi, and T. Ito, “Field demonstration of 2.5 Gbit/s coherent optical transmission through installed submarine fibre cables,” Electron. Lett., vol. 26, no. 17, pp. 1407–1409, 1990.

F. Koyama and K. Iga, “Frequency chirping in external modulators,” J. Lightw. Technol., vol. LT-6, no. 1, pp. 87–93, 1988.

Md. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairment monitoring from adaptive finite-impulse-response filters in a digital coherent receiver,” Opt. Exp., vol. 18, no. 26, pp. 26929–26936. 2010.

Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Exp., vol. 17, no. 32, pp. 1435–1441, 2009.

T. Imai, Y. Hayashi, N. Ohkawa, T. Sugie, Y. Ichihashi, and T. Ito, “Field demonstration of 2.5 Gbit/s coherent optical transmission through installed submarine fibre cables,” Electron. Lett., vol. 26, no. 17, pp. 1407–1409, 1990.

E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightw. Technol., vol. 26, no. 20, pp. 3416–3425, 2008.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightw. Technol., vol. 27, no. 16, pp. 3721–3718, 2009.

S. Tsukamoto, Y. Ishikawa, and K. Kikuchi, “Optical homodyne receiver comprising phase and polarization diversities with digital signal processing,” presented at the European Conf. on Optical Communication, Cannes, France, , 2006, Paper Mo4.2.1.

S. Ishimura and K. Kikuchi, “Multi-dimensional permutation-modulation format for coherent optical communications,” Opt. Exp., vol. 23, no. 12, pp. 15587–15597, 2015.

T. Imai, Y. Hayashi, N. Ohkawa, T. Sugie, Y. Ichihashi, and T. Ito, “Field demonstration of 2.5 Gbit/s coherent optical transmission through installed submarine fibre cables,” Electron. Lett., vol. 26, no. 17, pp. 1407–1409, 1990.

S. Norimatsu, K. Iwashita, and K. Sato, “PSK optical homodyne detection using external cavity laser diodes in Costas loop,” IEEE Photon. Technol. Lett., vol. 2, no. 5, pp. 374–376, 1990.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO$_3$ integrated modulator consisting of four-phase modulator waveguides,” IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 364–366, 2001.

R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, “Low-noise Erbium-doped fibre amplifier at 1.54 $\mu$m,” Electron. Lett., vol. 23, no. 19, pp. 1026–1028, 1987.

L. Jeunhomme and N. Monerie, “Polarization-maintaining single-mode fiber cable design,” Electron. Lett., vol. 16, no. 24, pp. 921–922, 1980.

E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightw. Technol., vol. 26, no. 20, pp. 3416–3425, 2008.

J. M. Kahn and K.-P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Topics Quantum Electron., vol. 10, no. 2, pp. 259–272, 2004.

F. Pancaldi, G. M. Vitetta, R. Kalbasi, N. Al-Dhahir, M. Uysal, and H. Mheidat, “Single-carrier frequency domain equalization,” IEEE Signal Process. Mag., vol. 25, no. 5, pp. 37–56, 2008.

E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightw. Technol., vol. 27, no. 22, pp. 5115–5126, 2009.

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Exp., vol. 17, no. 13, pp. 10814–10819, 2009.

Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Exp., vol. 17, no. 32, pp. 1435–1441, 2009.

S. Tsukamoto, K. Katoh, and K. Kikuchi, “Unrepeated transmission of 20-Gbit/s optical quadrature phase-shift keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation,” IEEE Photon. Technol. Lett., vol. 18, no. 9, pp. 1016–1018, 2006.

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightw. Technol., vol. 24, no. 1, pp. 12–21, 2006.

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., vol. 18, no. 10, pp. 1131–1133, 2006.

S. Tsukamoto, D.-S. Ly-Gagnon, K. Katoh, and K. Kikuchi, “Coherent demodulation of 40-Gbit/s polarization-multiplexed QPSK signals with 16-GHz spacing after 200-km transmission,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 6–11, 2005, Paper PDP29.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO$_3$ integrated modulator consisting of four-phase modulator waveguides,” IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 364–366, 2001.

T. Okoshi, K. Emura, K. Kikuchi, and R. Th. Kersten, “Computation of bit-error rate of various heterodyne and coherent-type optical communication schemes,” J. Opt. Commun., vol. 2, no. 4, pp. 134–141, 1981.

S. Ishimura and K. Kikuchi, “Multi-dimensional permutation-modulation format for coherent optical communications,” Opt. Exp., vol. 23, no. 12, pp. 15587–15597, 2015.

Y. Mori, C. Zhang, and K. Kikuchi, “Novel configuration of finite-impulse-response filters tolerant to carrier-phase fluctuations in digital coherent optical receivers for higher-order quadrature amplitude modulation signals,” Opt. Exp., vol. 20, no. 24, pp. 26236–26251, 2012.

K. Kikuchi, “Clock recovering characteristics of adaptive finite-impulse-response filters in digital coherent optical receivers,” Opt. Exp., vol. 19, no. 6, pp. 5611–5619, 2011.

K. Kikuchi, “Performance analyses of polarization demultiplexing based on constant-modulus algorithm in digital coherent optical receivers,” Opt. Exp., vol. 19, no. 10, pp. 9868–9880, 2011.

K. Kikuchi, “Analyses of wavelength- and polarization-division multiplexed transmission characteristics of optical quadrature-amplitude-modulation signals,” Opt. Exp., vol. 19, no. 19, pp. 17985–17995, 2011.

Md. S. Faruk and K. Kikuchi, “Adaptive frequency-domain equalization in digital coherent receivers,” Opt. Exp., vol. 19, no. 13, pp. 12789–12798, 2011.

K. Kikuchi, “Digital coherent optical communication systems: Fundamentals and future prospects,” IEICE Electron. Exp., vol. 8, no. 20, pp. 1642–1662, 2011.

Md. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairment monitoring from adaptive finite-impulse-response filters in a digital coherent receiver,” Opt. Exp., vol. 18, no. 26, pp. 26929–26936. 2010.

Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Exp., vol. 17, no. 32, pp. 1435–1441, 2009.

K. Kikuchi and S. Tsukamoto, “Evaluation of sensitivity of the digital coherent receiver,” J. Lightw. Technol., vol. 20, no. 13, pp. 1817–1822, 2008.

K. Kikuchi, “Electronic post-compensation for nonlinear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver,” Opt. Exp., vol. 16, no. 2, pp. 889–896, 2008.

S. Tsukamoto, K. Katoh, and K. Kikuchi, “Unrepeated transmission of 20-Gbit/s optical quadrature phase-shift keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation,” IEEE Photon. Technol. Lett., vol. 18, no. 9, pp. 1016–1018, 2006.

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., vol. 18, no. 10, pp. 1131–1133, 2006.

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightw. Technol., vol. 24, no. 1, pp. 12–21, 2006.

K. Kikuchi, “Phase-diversity homodyne detection of multi-level optical modulation with digital carrier phase estimation,” IEEE J. Sel. TopicQuantum Electron., vol. 12, no. 4, pp. 563–570, 2006.

T. Tanemura and K. Kikuchi, “Circular-birefringence fiber for nonlinear optical signal processing,” J. Lightw. Technol., vol. 24, no. 11, pp. 4108–4119, 2006.

K. Kikuchi and T. Okoshi, “Measurement of FM noise, AM noise, and field spectra of 1.3 $\mu$m InGaAsP DFB lasers and determination of the linewidth enhancement factor,” IEEE J. Quantum Electron., vol. QE-21, no. 11, pp. 1814–1818, 1985.

K. Kikuchi, T. Okoshi, M. Nagamatsu, and N. Henmi, “Degradation of bit-error rate in coherent optical communications due to spectral spread of the transmitter and the local oscillator,” J. Lightw. Technol., vol. LT-2, no. 6, pp. 1024–1033, 1984.

T. Okoshi, K. Emura, K. Kikuchi, and R. Th. Kersten, “Computation of bit-error rate of various heterodyne and coherent-type optical communication schemes,” J. Opt. Commun., vol. 2, no. 4, pp. 134–141, 1981.

T. Okoshi and K. Kikuchi, “Frequency stabilization of semiconductor lasers for heterodyne-type optical communication systems,” Electron. Lett., vol. 16, no. 5, pp. 179–181, 1980.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett., vol. 16, no. 16, pp. 630–631, 1980.

K. Kikuchi, “Coherent optical communication technology,” presented at the Optical Fiber Communications Conf., Los Angeles, CA, USA, , 2015, Paper Th4F.4.

S. Tsukamoto, D.-S. Ly-Gagnon, K. Katoh, and K. Kikuchi, “Coherent demodulation of 40-Gbit/s polarization-multiplexed QPSK signals with 16-GHz spacing after 200-km transmission,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 6–11, 2005, Paper PDP29.

T. Okoshi and K. Kikuchi, Coherent Optical Communication Systems. Tokyo, Japan: KTK Scientific Publisher, 1988, ch. 1.

T. Okoshi, S. Ryu, and K. Kikuchi, “Polarization-diversity receiver for heterodyne/coherent optical fiber communications,” presented at the International Conf. on Integrated Optics and Optical Fiber Communication, Tokyo, Japan, , 1983, Paper 30C3-2.

S. Tsukamoto, Y. Ishikawa, and K. Kikuchi, “Optical homodyne receiver comprising phase and polarization diversities with digital signal processing,” presented at the European Conf. on Optical Communication, Cannes, France, , 2006, Paper Mo4.2.1.

K. Kikuchi, “Coherent optical communications: Historical perspectives and future directions,” in High Spectral Density Optical Communication Technology, M. Nakazawa, K. Kikuchi, and T. Miyazaki, Eds., Heidelberg, Germany: Springer-Verlag, 2010, ch. 2.

K. Kikuchi, “Performance analyses of digital coherent receivers with symbol-rate analog-to-digital conversion,” presented at the Signal Processing in Photonics Communications, Boston MA, USA, , 2015, Paper SpT3D.4.

A. W. Davis, M. J. Pettitt, P. J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightw. Technol., vol. 5, no. 4, pp. 561–572, 1987.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightw. Technol., vol. 27, no. 16, pp. 3721–3718, 2009.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

F. Koyama and K. Iga, “Frequency chirping in external modulators,” J. Lightw. Technol., vol. LT-6, no. 1, pp. 87–93, 1988.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO$_3$ integrated modulator consisting of four-phase modulator waveguides,” IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 364–366, 2001.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightw. Technol., vol. 27, no. 16, pp. 3721–3718, 2009.

D. MacGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, “5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 6–11, 2005, Paper PDP27.

F. Favre and D. LeGuen, “High frequency stability of laser diode for heterodyne communication systems,” Electron. Lett., vol. 16, no. 18, pp. 709–710, 1980.

D. MacGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, “5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 6–11, 2005, Paper PDP27.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon., vol. 7, no. 7, pp. 560–568, 2013.

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightw. Technol., vol. 24, no. 1, pp. 12–21, 2006.

S. Tsukamoto, D.-S. Ly-Gagnon, K. Katoh, and K. Kikuchi, “Coherent demodulation of 40-Gbit/s polarization-multiplexed QPSK signals with 16-GHz spacing after 200-km transmission,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 6–11, 2005, Paper PDP29.

D. MacGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, “5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 6–11, 2005, Paper PDP27.

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D. Hanson, D. McGhan, H. Sun, M. Moyer, and M. O'Sullivan, “Performance of a 46-Gb/s dual-polarization QPSK transceiver in a high-PMD fiber transmission experiment,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper PDP9.

D. MacGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, “5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 6–11, 2005, Paper PDP27.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D. Hanson, D. McGhan, H. Sun, M. Moyer, and M. O'Sullivan, “Performance of a 46-Gb/s dual-polarization QPSK transceiver in a high-PMD fiber transmission experiment,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper PDP9.

R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, “Low-noise Erbium-doped fibre amplifier at 1.54 $\mu$m,” Electron. Lett., vol. 23, no. 19, pp. 1026–1028, 1987.

F. Pancaldi, G. M. Vitetta, R. Kalbasi, N. Al-Dhahir, M. Uysal, and H. Mheidat, “Single-carrier frequency domain equalization,” IEEE Signal Process. Mag., vol. 25, no. 5, pp. 37–56, 2008.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO$_3$ integrated modulator consisting of four-phase modulator waveguides,” IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 364–366, 2001.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightw. Technol., vol. 27, no. 16, pp. 3721–3718, 2009.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

T. Mizuochi, “Next generation FEC for optical communication,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper OTuE5.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightw. Technol., vol. 10, no. 1, pp. 28–35, 1992.

L. Jeunhomme and N. Monerie, “Polarization-maintaining single-mode fiber cable design,” Electron. Lett., vol. 16, no. 24, pp. 921–922, 1980.

Y. Mori, C. Zhang, and K. Kikuchi, “Novel configuration of finite-impulse-response filters tolerant to carrier-phase fluctuations in digital coherent optical receivers for higher-order quadrature amplitude modulation signals,” Opt. Exp., vol. 20, no. 24, pp. 26236–26251, 2012.

Md. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairment monitoring from adaptive finite-impulse-response filters in a digital coherent receiver,” Opt. Exp., vol. 18, no. 26, pp. 26929–26936. 2010.

Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Exp., vol. 17, no. 32, pp. 1435–1441, 2009.

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D. Hanson, D. McGhan, H. Sun, M. Moyer, and M. O'Sullivan, “Performance of a 46-Gb/s dual-polarization QPSK transceiver in a high-PMD fiber transmission experiment,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper PDP9.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

K. Kikuchi, T. Okoshi, M. Nagamatsu, and N. Henmi, “Degradation of bit-error rate in coherent optical communications due to spectral spread of the transmitter and the local oscillator,” J. Lightw. Technol., vol. LT-2, no. 6, pp. 1024–1033, 1984.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett., vol. 16, no. 16, pp. 630–631, 1980.

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D. Hanson, D. McGhan, H. Sun, M. Moyer, and M. O'Sullivan, “Performance of a 46-Gb/s dual-polarization QPSK transceiver in a high-PMD fiber transmission experiment,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper PDP9.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Philipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmission,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2010, Paper OTuE1.

R. Noé, “Phase noise tolerant synchronous QPSK receiver concept with digital I&Q baseband processing,” presented at the Opto-Electronics and Communications Conf., Yokohama, Japan, Jul. 12–16, 2004, Paper 16C2-5.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

S. Norimatsu, K. Iwashita, and K. Sato, “PSK optical homodyne detection using external cavity laser diodes in Costas loop,” IEEE Photon. Technol. Lett., vol. 2, no. 5, pp. 374–376, 1990.

T. Imai, Y. Hayashi, N. Ohkawa, T. Sugie, Y. Ichihashi, and T. Ito, “Field demonstration of 2.5 Gbit/s coherent optical transmission through installed submarine fibre cables,” Electron. Lett., vol. 26, no. 17, pp. 1407–1409, 1990.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO$_3$ integrated modulator consisting of four-phase modulator waveguides,” IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 364–366, 2001.

N. Shibata, Y. Sasaki, K. Okamoto, and T. Hosaka, “Fabrication of polarization-maintaining and absorption-reducing fibers,” J. Lightw. Technol., vol. LT-1, no. 1, pp. 38–43, 1983.

K. Kikuchi and T. Okoshi, “Measurement of FM noise, AM noise, and field spectra of 1.3 $\mu$m InGaAsP DFB lasers and determination of the linewidth enhancement factor,” IEEE J. Quantum Electron., vol. QE-21, no. 11, pp. 1814–1818, 1985.

K. Kikuchi, T. Okoshi, M. Nagamatsu, and N. Henmi, “Degradation of bit-error rate in coherent optical communications due to spectral spread of the transmitter and the local oscillator,” J. Lightw. Technol., vol. LT-2, no. 6, pp. 1024–1033, 1984.

T. Okoshi, K. Emura, K. Kikuchi, and R. Th. Kersten, “Computation of bit-error rate of various heterodyne and coherent-type optical communication schemes,” J. Opt. Commun., vol. 2, no. 4, pp. 134–141, 1981.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett., vol. 16, no. 16, pp. 630–631, 1980.

T. Okoshi and K. Kikuchi, “Frequency stabilization of semiconductor lasers for heterodyne-type optical communication systems,” Electron. Lett., vol. 16, no. 5, pp. 179–181, 1980.

T. Okoshi and K. Kikuchi, Coherent Optical Communication Systems. Tokyo, Japan: KTK Scientific Publisher, 1988, ch. 1.

T. Okoshi, S. Ryu, and K. Kikuchi, “Polarization-diversity receiver for heterodyne/coherent optical fiber communications,” presented at the International Conf. on Integrated Optics and Optical Fiber Communication, Tokyo, Japan, , 1983, Paper 30C3-2.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

K. Roberts, L. Chuandong, L. Strawczynski, M. O'Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett., vol. 18, no. 2, pp. 403–405, 2006.

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D. Hanson, D. McGhan, H. Sun, M. Moyer, and M. O'Sullivan, “Performance of a 46-Gb/s dual-polarization QPSK transceiver in a high-PMD fiber transmission experiment,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper PDP9.

D. MacGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, “5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 6–11, 2005, Paper PDP27.

F. Pancaldi, G. M. Vitetta, R. Kalbasi, N. Al-Dhahir, M. Uysal, and H. Mheidat, “Single-carrier frequency domain equalization,” IEEE Signal Process. Mag., vol. 25, no. 5, pp. 37–56, 2008.

R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, “Low-noise Erbium-doped fibre amplifier at 1.54 $\mu$m,” Electron. Lett., vol. 23, no. 19, pp. 1026–1028, 1987.

A. W. Davis, M. J. Pettitt, P. J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightw. Technol., vol. 5, no. 4, pp. 561–572, 1987.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Philipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmission,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2010, Paper OTuE1.

F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Exp., vol. 20, no. 2, pp. 1360–1368, 2012.

J. Proakis, Digital Communications, 4th ed. New York, USA: McGraw Hill, 2007, ch. 7.

S. U. H. Qureshi, “Adaptive equalization,” Proc. IEEE, vol. 73, no. 9, pp. 1349–1387, 1985.

L. Dou, Y. Zhao, Z. Tao, Y. Fan, T. Hoshida, and J. C. Rasmussen, “Advanced digital nonlinear distortion compensation,” presented at Optical Fiber Communication Conf., Los Angeles, CA, USA, , 2015, Paper Th3G.3.

R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, “Low-noise Erbium-doped fibre amplifier at 1.54 $\mu$m,” Electron. Lett., vol. 23, no. 19, pp. 1026–1028, 1987.

F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Exp., vol. 20, no. 2, pp. 1360–1368, 2012.

H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40-Gb/s coherent system,” Opt. Exp., vol. 16, no. 2, pp. 873–879, 2008.

K. Roberts, L. Chuandong, L. Strawczynski, M. O'Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett., vol. 18, no. 2, pp. 403–405, 2006.

H. P. Robertson, “The uncertainty principle,” Phys. Rev., vol. 34, no. 1, pp. 163–164, 1929.

T. Okoshi, S. Ryu, and K. Kikuchi, “Polarization-diversity receiver for heterodyne/coherent optical fiber communications,” presented at the International Conf. on Integrated Optics and Optical Fiber Communication, Tokyo, Japan, , 1983, Paper 30C3-2.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO$_3$ integrated modulator consisting of four-phase modulator waveguides,” IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 364–366, 2001.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightw. Technol., vol. 27, no. 16, pp. 3721–3718, 2009.

N. Shibata, Y. Sasaki, K. Okamoto, and T. Hosaka, “Fabrication of polarization-maintaining and absorption-reducing fibers,” J. Lightw. Technol., vol. LT-1, no. 1, pp. 38–43, 1983.

S. Norimatsu, K. Iwashita, and K. Sato, “PSK optical homodyne detection using external cavity laser diodes in Costas loop,” IEEE Photon. Technol. Lett., vol. 2, no. 5, pp. 374–376, 1990.

D. MacGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, “5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 6–11, 2005, Paper PDP27.

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Exp., vol. 16, no. 2, pp. 804–817, 2008.

M. Seimetz, “Performance of coherent optical square-16-QAM-systems based on IQ-transmitters and homodyne receivers with digital phase estimation,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, , 2006, Paper NWA4.

C. E. Shannon, “A mathematical theory of communication,” Bell Sys. Tech. J., vol. 27, no. 3, pp. 379–423, 1948 and vol. 27, no. 4, pp. 623–656, 1948.

N. Shibata, Y. Sasaki, K. Okamoto, and T. Hosaka, “Fabrication of polarization-maintaining and absorption-reducing fibers,” J. Lightw. Technol., vol. LT-1, no. 1, pp. 38–43, 1983.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO$_3$ integrated modulator consisting of four-phase modulator waveguides,” IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 364–366, 2001.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Philipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmission,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2010, Paper OTuE1.

H. Hodgikinson, R. A. Harmon, and D. W. Smith, Demodulation of optical DPSK using in-phase and quadrature detection,” Electron. Lett., vol. 21, no. 19, pp. 867–868, 1985.

K. Roberts, L. Chuandong, L. Strawczynski, M. O'Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett., vol. 18, no. 2, pp. 403–405, 2006.

T. Imai, Y. Hayashi, N. Ohkawa, T. Sugie, Y. Ichihashi, and T. Ito, “Field demonstration of 2.5 Gbit/s coherent optical transmission through installed submarine fibre cables,” Electron. Lett., vol. 26, no. 17, pp. 1407–1409, 1990.

H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40-Gb/s coherent system,” Opt. Exp., vol. 16, no. 2, pp. 873–879, 2008.

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D. Hanson, D. McGhan, H. Sun, M. Moyer, and M. O'Sullivan, “Performance of a 46-Gb/s dual-polarization QPSK transceiver in a high-PMD fiber transmission experiment,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper PDP9.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightw. Technol., vol. 27, no. 16, pp. 3721–3718, 2009.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

T. Tanemura and K. Kikuchi, “Circular-birefringence fiber for nonlinear optical signal processing,” J. Lightw. Technol., vol. 24, no. 11, pp. 4108–4119, 2006.

L. Dou, Y. Zhao, Z. Tao, Y. Fan, T. Hoshida, and J. C. Rasmussen, “Advanced digital nonlinear distortion compensation,” presented at Optical Fiber Communication Conf., Los Angeles, CA, USA, , 2015, Paper Th3G.3.

M. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett., vol. 16, no. 2, pp. 674–676, 2004.

F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Exp., vol. 20, no. 2, pp. 1360–1368, 2012.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon., vol. 7, no. 7, pp. 560–568, 2013.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

K. Kikuchi and S. Tsukamoto, “Evaluation of sensitivity of the digital coherent receiver,” J. Lightw. Technol., vol. 20, no. 13, pp. 1817–1822, 2008.

S. Tsukamoto, K. Katoh, and K. Kikuchi, “Unrepeated transmission of 20-Gbit/s optical quadrature phase-shift keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation,” IEEE Photon. Technol. Lett., vol. 18, no. 9, pp. 1016–1018, 2006.

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., vol. 18, no. 10, pp. 1131–1133, 2006.

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightw. Technol., vol. 24, no. 1, pp. 12–21, 2006.

S. Tsukamoto, Y. Ishikawa, and K. Kikuchi, “Optical homodyne receiver comprising phase and polarization diversities with digital signal processing,” presented at the European Conf. on Optical Communication, Cannes, France, , 2006, Paper Mo4.2.1.

S. Tsukamoto, D.-S. Ly-Gagnon, K. Katoh, and K. Kikuchi, “Coherent demodulation of 40-Gbit/s polarization-multiplexed QPSK signals with 16-GHz spacing after 200-km transmission,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 6–11, 2005, Paper PDP29.

F. Pancaldi, G. M. Vitetta, R. Kalbasi, N. Al-Dhahir, M. Uysal, and H. Mheidat, “Single-carrier frequency domain equalization,” IEEE Signal Process. Mag., vol. 25, no. 5, pp. 37–56, 2008.

K. Vahala and A. Yariv, “Semiclassical theory of noise in semiconductor lasers—Part I,” IEEE J. Quantum Electron., vol. QE-19, no. 6, pp. 1096–1101, 1983.

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory, vol. IT-29, no. 4, pp. 543–551, 1983.

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory, vol. IT-29, no. 4, pp. 543–551, 1983.

F. Pancaldi, G. M. Vitetta, R. Kalbasi, N. Al-Dhahir, M. Uysal, and H. Mheidat, “Single-carrier frequency domain equalization,” IEEE Signal Process. Mag., vol. 25, no. 5, pp. 37–56, 2008.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon., vol. 7, no. 7, pp. 560–568, 2013.

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D. Hanson, D. McGhan, H. Sun, M. Moyer, and M. O'Sullivan, “Performance of a 46-Gb/s dual-polarization QPSK transceiver in a high-PMD fiber transmission experiment,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper PDP9.

A. W. Davis, M. J. Pettitt, P. J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightw. Technol., vol. 5, no. 4, pp. 561–572, 1987.

H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40-Gb/s coherent system,” Opt. Exp., vol. 16, no. 2, pp. 873–879, 2008.

Y. Yamamoto and H. Haus, “Preparation, measurement and information capacity of optical quantum states,” Rev. Mod. Phys., vol. 58, no. 4, pp. 1001–1020, 1986.

Y. Yamamoto, “AM and FM quantum noise in semiconductor lasers—Part I: Theoretical analysis,” IEEE J. Quantum Electron., vol. QE-19, no. 1, pp. 34–461983.

Y. Yamamoto, “Receiver performance evaluation of various digital optical modulation–demodulation systems in the 0.5–10 $\mu$m wavelength region,” IEEE J. Quantum Electron., vol. QE-16, no. 11, pp. 1251–1259, 1980.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

K. Vahala and A. Yariv, “Semiclassical theory of noise in semiconductor lasers—Part I,” IEEE J. Quantum Electron., vol. QE-19, no. 6, pp. 1096–1101, 1983.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

Y. Mori, C. Zhang, and K. Kikuchi, “Novel configuration of finite-impulse-response filters tolerant to carrier-phase fluctuations in digital coherent optical receivers for higher-order quadrature amplitude modulation signals,” Opt. Exp., vol. 20, no. 24, pp. 26236–26251, 2012.

Md. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairment monitoring from adaptive finite-impulse-response filters in a digital coherent receiver,” Opt. Exp., vol. 18, no. 26, pp. 26929–26936. 2010.

Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Exp., vol. 17, no. 32, pp. 1435–1441, 2009.

L. Dou, Y. Zhao, Z. Tao, Y. Fan, T. Hoshida, and J. C. Rasmussen, “Advanced digital nonlinear distortion compensation,” presented at Optical Fiber Communication Conf., Los Angeles, CA, USA, , 2015, Paper Th3G.3.

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D. Hanson, D. McGhan, H. Sun, M. Moyer, and M. O'Sullivan, “Performance of a 46-Gb/s dual-polarization QPSK transceiver in a high-PMD fiber transmission experiment,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper PDP9.

C. E. Shannon, “A mathematical theory of communication,” Bell Sys. Tech. J., vol. 27, no. 3, pp. 379–423, 1948 and vol. 27, no. 4, pp. 623–656, 1948.

F. Derr, “Optical QPSK transmission system with novel digital receiver concept,” Electron Lett., vol. 27, no. 23, pp. 2177–2179, 1991.

T. Imai, Y. Hayashi, N. Ohkawa, T. Sugie, Y. Ichihashi, and T. Ito, “Field demonstration of 2.5 Gbit/s coherent optical transmission through installed submarine fibre cables,” Electron. Lett., vol. 26, no. 17, pp. 1407–1409, 1990.

R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, “Low-noise Erbium-doped fibre amplifier at 1.54 $\mu$m,” Electron. Lett., vol. 23, no. 19, pp. 1026–1028, 1987.

T. Okoshi and K. Kikuchi, “Frequency stabilization of semiconductor lasers for heterodyne-type optical communication systems,” Electron. Lett., vol. 16, no. 5, pp. 179–181, 1980.

F. Favre and D. LeGuen, “High frequency stability of laser diode for heterodyne communication systems,” Electron. Lett., vol. 16, no. 18, pp. 709–710, 1980.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett., vol. 16, no. 16, pp. 630–631, 1980.

L. Jeunhomme and N. Monerie, “Polarization-maintaining single-mode fiber cable design,” Electron. Lett., vol. 16, no. 24, pp. 921–922, 1980.

H. Hodgikinson, R. A. Harmon, and D. W. Smith, Demodulation of optical DPSK using in-phase and quadrature detection,” Electron. Lett., vol. 21, no. 19, pp. 867–868, 1985.

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron., vol. QE-18, no. 2, pp. 259–264, 1982.

Y. Yamamoto, “AM and FM quantum noise in semiconductor lasers—Part I: Theoretical analysis,” IEEE J. Quantum Electron., vol. QE-19, no. 1, pp. 34–461983.

K. Vahala and A. Yariv, “Semiclassical theory of noise in semiconductor lasers—Part I,” IEEE J. Quantum Electron., vol. QE-19, no. 6, pp. 1096–1101, 1983.

K. Kikuchi and T. Okoshi, “Measurement of FM noise, AM noise, and field spectra of 1.3 $\mu$m InGaAsP DFB lasers and determination of the linewidth enhancement factor,” IEEE J. Quantum Electron., vol. QE-21, no. 11, pp. 1814–1818, 1985.

Y. Yamamoto, “Receiver performance evaluation of various digital optical modulation–demodulation systems in the 0.5–10 $\mu$m wavelength region,” IEEE J. Quantum Electron., vol. QE-16, no. 11, pp. 1251–1259, 1980.

K. Kikuchi, “Phase-diversity homodyne detection of multi-level optical modulation with digital carrier phase estimation,” IEEE J. Sel. TopicQuantum Electron., vol. 12, no. 4, pp. 563–570, 2006.

J. M. Kahn and K.-P. Ho, “Spectral efficiency limits and modulation/detection techniques for DWDM systems,” IEEE J. Sel. Topics Quantum Electron., vol. 10, no. 2, pp. 259–272, 2004.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO$_3$ integrated modulator consisting of four-phase modulator waveguides,” IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 364–366, 2001.

S. Norimatsu, K. Iwashita, and K. Sato, “PSK optical homodyne detection using external cavity laser diodes in Costas loop,” IEEE Photon. Technol. Lett., vol. 2, no. 5, pp. 374–376, 1990.

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., vol. 18, no. 10, pp. 1131–1133, 2006.

M. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett., vol. 16, no. 2, pp. 674–676, 2004.

S. Tsukamoto, K. Katoh, and K. Kikuchi, “Unrepeated transmission of 20-Gbit/s optical quadrature phase-shift keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation,” IEEE Photon. Technol. Lett., vol. 18, no. 9, pp. 1016–1018, 2006.

K. Roberts, L. Chuandong, L. Strawczynski, M. O'Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett., vol. 18, no. 2, pp. 403–405, 2006.

F. Pancaldi, G. M. Vitetta, R. Kalbasi, N. Al-Dhahir, M. Uysal, and H. Mheidat, “Single-carrier frequency domain equalization,” IEEE Signal Process. Mag., vol. 25, no. 5, pp. 37–56, 2008.

D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun., vol. COM-28, no. 11, pp. 1867–1875, 1980.

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory, vol. IT-29, no. 4, pp. 543–551, 1983.

K. Kikuchi, “Digital coherent optical communication systems: Fundamentals and future prospects,” IEICE Electron. Exp., vol. 8, no. 20, pp. 1642–1662, 2011.

T. Tanemura and K. Kikuchi, “Circular-birefringence fiber for nonlinear optical signal processing,” J. Lightw. Technol., vol. 24, no. 11, pp. 4108–4119, 2006.

B. Glance, “Polarization independent coherent optical receiver,” J. Lightw. Technol., vol. LT-5, no. 2, pp. 274–276, 1987.

N. Shibata, Y. Sasaki, K. Okamoto, and T. Hosaka, “Fabrication of polarization-maintaining and absorption-reducing fibers,” J. Lightw. Technol., vol. LT-1, no. 1, pp. 38–43, 1983.

D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightw. Technol., vol. 24, no. 1, pp. 12–21, 2006.

K. Kikuchi, T. Okoshi, M. Nagamatsu, and N. Henmi, “Degradation of bit-error rate in coherent optical communications due to spectral spread of the transmitter and the local oscillator,” J. Lightw. Technol., vol. LT-2, no. 6, pp. 1024–1033, 1984.

E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightw. Technol., vol. 26, no. 20, pp. 3416–3425, 2008.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightw. Technol., vol. 10, no. 1, pp. 28–35, 1992.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightw. Technol., vol. 27, no. 16, pp. 3721–3718, 2009.

A. W. Davis, M. J. Pettitt, P. J. King, and S. Wright, “Phase diversity techniques for coherent optical receivers,” J. Lightw. Technol., vol. 5, no. 4, pp. 561–572, 1987.

K. Kikuchi and S. Tsukamoto, “Evaluation of sensitivity of the digital coherent receiver,” J. Lightw. Technol., vol. 20, no. 13, pp. 1817–1822, 2008.

F. Koyama and K. Iga, “Frequency chirping in external modulators,” J. Lightw. Technol., vol. LT-6, no. 1, pp. 87–93, 1988.

E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightw. Technol., vol. 27, no. 22, pp. 5115–5126, 2009.

T. Okoshi, K. Emura, K. Kikuchi, and R. Th. Kersten, “Computation of bit-error rate of various heterodyne and coherent-type optical communication schemes,” J. Opt. Commun., vol. 2, no. 4, pp. 134–141, 1981.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photon., vol. 7, no. 7, pp. 560–568, 2013.

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Exp., vol. 17, no. 13, pp. 10814–10819, 2009.

F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Exp., vol. 20, no. 2, pp. 1360–1368, 2012.

Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Exp., vol. 17, no. 32, pp. 1435–1441, 2009.

S. Ishimura and K. Kikuchi, “Multi-dimensional permutation-modulation format for coherent optical communications,” Opt. Exp., vol. 23, no. 12, pp. 15587–15597, 2015.

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Exp., vol. 16, no. 2, pp. 804–817, 2008.

H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40-Gb/s coherent system,” Opt. Exp., vol. 16, no. 2, pp. 873–879, 2008.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Exp., vol. 19, no. 14, pp. 13139–13184, 2011.

Md. S. Faruk and K. Kikuchi, “Adaptive frequency-domain equalization in digital coherent receivers,” Opt. Exp., vol. 19, no. 13, pp. 12789–12798, 2011.

Md. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairment monitoring from adaptive finite-impulse-response filters in a digital coherent receiver,” Opt. Exp., vol. 18, no. 26, pp. 26929–26936. 2010.

K. Kikuchi, “Performance analyses of polarization demultiplexing based on constant-modulus algorithm in digital coherent optical receivers,” Opt. Exp., vol. 19, no. 10, pp. 9868–9880, 2011.

Y. Mori, C. Zhang, and K. Kikuchi, “Novel configuration of finite-impulse-response filters tolerant to carrier-phase fluctuations in digital coherent optical receivers for higher-order quadrature amplitude modulation signals,” Opt. Exp., vol. 20, no. 24, pp. 26236–26251, 2012.

K. Kikuchi, “Clock recovering characteristics of adaptive finite-impulse-response filters in digital coherent optical receivers,” Opt. Exp., vol. 19, no. 6, pp. 5611–5619, 2011.

K. Kikuchi, “Analyses of wavelength- and polarization-division multiplexed transmission characteristics of optical quadrature-amplitude-modulation signals,” Opt. Exp., vol. 19, no. 19, pp. 17985–17995, 2011.

K. Kikuchi, “Electronic post-compensation for nonlinear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver,” Opt. Exp., vol. 16, no. 2, pp. 889–896, 2008.

H. P. Robertson, “The uncertainty principle,” Phys. Rev., vol. 34, no. 1, pp. 163–164, 1929.

Y. Yamamoto and H. Haus, “Preparation, measurement and information capacity of optical quantum states,” Rev. Mod. Phys., vol. 58, no. 4, pp. 1001–1020, 1986.

K. Kikuchi, “Coherent optical communications: Historical perspectives and future directions,” in High Spectral Density Optical Communication Technology, M. Nakazawa, K. Kikuchi, and T. Miyazaki, Eds., Heidelberg, Germany: Springer-Verlag, 2010, ch. 2.

L. E. Nelson, S. L. Woodward, M. D. Feuer, X. Zhou, P. D. Magill, S. Foo, D. Hanson, D. McGhan, H. Sun, M. Moyer, and M. O'Sullivan, “Performance of a 46-Gb/s dual-polarization QPSK transceiver in a high-PMD fiber transmission experiment,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper PDP9.

J. Proakis, Digital Communications, 4th ed. New York, USA: McGraw Hill, 2007, ch. 7.

L. Coelho and N. Hanik, “Global optimization of fiber-optic communication systems using four-dimensional modulation formats,” presented at the European Conf. Optical Communication, Geneva, Switzerland, , 2011, Paper Mo.2.B.

T. Mizuochi, “Next generation FEC for optical communication,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2008, Paper OTuE5.

K. Kikuchi, “Performance analyses of digital coherent receivers with symbol-rate analog-to-digital conversion,” presented at the Signal Processing in Photonics Communications, Boston MA, USA, , 2015, Paper SpT3D.4.

S. Haykin, Introduction to Adaptive Filters, New York, NY, USA: Macmillan, 2001, ch. 4.

L. Dou, Y. Zhao, Z. Tao, Y. Fan, T. Hoshida, and J. C. Rasmussen, “Advanced digital nonlinear distortion compensation,” presented at Optical Fiber Communication Conf., Los Angeles, CA, USA, , 2015, Paper Th3G.3.

G. P. Agrawal, Nonlinear Fiber Optics, San Diego, CA, USA: Academic, 1989, ch. 2.

M. Seimetz, “Performance of coherent optical square-16-QAM-systems based on IQ-transmitters and homodyne receivers with digital phase estimation,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, , 2006, Paper NWA4.

S. U. H. Qureshi, “Adaptive equalization,” Proc. IEEE, vol. 73, no. 9, pp. 1349–1387, 1985.

S. Tsukamoto, Y. Ishikawa, and K. Kikuchi, “Optical homodyne receiver comprising phase and polarization diversities with digital signal processing,” presented at the European Conf. on Optical Communication, Cannes, France, , 2006, Paper Mo4.2.1.

R. Noé, “Phase noise tolerant synchronous QPSK receiver concept with digital I&Q baseband processing,” presented at the Opto-Electronics and Communications Conf., Yokohama, Japan, Jul. 12–16, 2004, Paper 16C2-5.

D. MacGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, “5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 6–11, 2005, Paper PDP27.

R. Griffin and A. Carter, “Optical differential quadrature phase-shift key (oDQPSK) for high capacity optical transmission,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 17–22, 2002, Paper WX6.

K. Kikuchi, “Coherent optical communication technology,” presented at the Optical Fiber Communications Conf., Los Angeles, CA, USA, , 2015, Paper Th4F.4.

O. E. DeLange, “Wide-band optical communication systems—Part II: Frequency-division multiplexing,” Proc. IEEE, vol. 58, no. 10, pp. 1683–1690, 1970.

T. Okoshi and K. Kikuchi, Coherent Optical Communication Systems. Tokyo, Japan: KTK Scientific Publisher, 1988, ch. 1.

S. Tsukamoto, D.-S. Ly-Gagnon, K. Katoh, and K. Kikuchi, “Coherent demodulation of 40-Gbit/s polarization-multiplexed QPSK signals with 16-GHz spacing after 200-km transmission,” presented at the Optical Fiber Communication Conf., Anaheim, CA, USA, Mar. 6–11, 2005, Paper PDP29.

T. Okoshi, S. Ryu, and K. Kikuchi, “Polarization-diversity receiver for heterodyne/coherent optical fiber communications,” presented at the International Conf. on Integrated Optics and Optical Fiber Communication, Tokyo, Japan, , 1983, Paper 30C3-2.

Y. Cai, D. G. Foursa, C. R. Davidson, J. X. Cai, O. Sinkin, M. Nissov, and A. Philipetskii, “Experimental demonstration of coherent MAP detection for nonlinearity mitigation in long-haul transmission,” presented at the Optical Fiber Communication Conf., San Diego, CA, USA, , 2010, Paper OTuE1.