Abstract

The interest for short-reach links of the kind needed for inter-data-center communications has fueled in recent years the search for transmission schemes that are simultaneously highly performing and cost effective. In this work we propose a direct-detection coherent receiver that combines the advantages of coherent transmission and the cost-effectiveness of direct detection. The working principle of the proposed receiver is based on the famous Kramers–Kronig (KK) relations, and its implementation requires transmitting a continuous-wave signal at one edge of the information-carrying signal spectrum. The KK receiver scheme allows digital postcompensation of linear propagation impairments and, as compared to other existing solutions, is more efficient in terms of spectral occupancy and energy consumption.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Coherent detection in optical fiber systems

Ezra Ip, Alan Pak Tao Lau, Daniel J. F. Barros, and Joseph M. Kahn
Opt. Express 16(2) 753-791 (2008)

Digital self-coherent detection

Xiang Liu, S. Chandrasekhar, and Andreas Leven
Opt. Express 16(2) 792-803 (2008)

A dual-polarization coherent communication system with simplified optical receiver for UDWDM-PON architecture

Jianyu Zheng, Feng Lu, Mu Xu, Ming Zhu, Md Ibrahim Khalil, Xu Bao, Daniel Guidotti, Jianguo Liu, Ninghua Zhu, and Gee-Kung Chang
Opt. Express 22(26) 31735-31745 (2014)

References

  • View by:
  • |
  • |
  • |

  1. S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16, 1280–1289 (2010).
    [Crossref]
  2. T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. Rasmussen, “Discrete multi-tone for 100  Gb/s optical access networks,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2I.1.
  3. A. Weiss, A. Yeredor, and M. Shtaif, “Iterative symbol recovery for power efficient DC biased optical OFDM systems,” J. Lightwave Technol. 34, 2331–2338 (2016).
    [Crossref]
  4. A. J. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14, 2079–2084 (2006).
    [Crossref]
  5. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. 26, 196–203 (2008).
    [Crossref]
  6. M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
    [Crossref]
  7. S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. J. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in Proceedings of European Conference of Optical Communications 2015 (ECOC), Valencia, Spain (2015), paper 0697.
  8. Toward the completion of this paper, we discovered that a similar scheme was proposed in Ref. [9]. That scheme was presented in the context of analog radio systems and it contained none of the features that characterize fiber-optic transmission, which are discussed in this paper.
  9. H. Voelcker, “Demodulation of single-sideband signals via envelope detection,” IEEE Trans. Commun. Technol. 14, 22–30 (1966).
    [Crossref]
  10. R. L. Kronig, “On the theory of the dispersion of x-rays,” J. Opt. Soc. Am. 12, 547–557 (1926).
    [Crossref]
  11. H. A. Kramers, “La diffusion de la lumiere par les atomes,” Atti Cong. Intern. Fis. 2, 545–557 (1927).
  12. M. Cini, “The response characteristics of linear systems,” J. Appl. Phys. 21, 8–10 (1950).
    [Crossref]
  13. M. Gell-Mann and M. L. Goldberger, “The formal theory of scattering,” Phys. Rev. 91, 398–408 (1953).
    [Crossref]
  14. W. Heisenberg, “Quantum theory of fields and elementary particles,” Rev. Mod. Phys. 29, 269–278 (1957).
    [Crossref]
  15. A. Mecozzi, “Retrieving the full optical response from amplitude data by Hilbert transform,” Opt. Commun. 282, 4183–4187 (2009).
    [Crossref]
  16. A. Mecozzi, “A necessary and sufficient condition for minimum phase and implications for phase retrieval,” arXiv:1606.04861 (2016).
  17. Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
    [Crossref]
  18. H. W. Bode, Network Analysis and Feedback Amplifier Design (Van Nostrand, 1945), Chap. 8.
  19. Polarization multiplexing can also be accommodated by the scheme of Fig. 2(a), but envisageable extensions of the KK scheme would imply a considerable increase of the receiver cost and complexity.
  20. We note that B represents the bandwidth of the optical signal impinging upon the receiver, which is meant to be reconstructed. The information-carrying bandwidth may be smaller than B, depending on the tightness of the optical filter that is used.
  21. A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing (Prentice Hall, 1999).
  22. Recall that, contrary to [21] and to most of the existing literature, we are considering signals that are “causal” in the frequency domain, i.e., such that they vanish for ω<0.
  23. To see why the minimum energy-delay property implies that of all signals with the same intensity profile, the minimum phase signal is contained within the smallest bandwidth, consider the following situation. Assume that E(t) is a minimum phase signal, whose spectrum |E˜(ω)|2 is contained in the bandwidth B, but exceeds any bandwidth B′<B. If there were a signal E′(t) such that |E′(t)|2=|E(t)|2, with a spectrum |E˜(ω)|2 that is contained in B′<B, then we would have ∫ω0∞|E˜(ω)|2dω>∫ω0∞|E˜′(ω)|2dω=0 for every ω0∈(B′,B), contrary to the minimum energy-delay property.
  24. J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, 2001), Chap. 5.
  25. The lower spectral efficiency of IMDD follows from the fact that, with intensity modulation, no information is encoded into the optical phase. This makes IMDD inferior even to single-quadrature modulation, where positive and negative amplitude values can be used.
  26. The rate R is in general different from the actual sampling rate. For instance, in the experimental implementation of the scheme of [4] presented in [5], the sampled photocurrent includes the contribution of the spurious signal–signal beat, which is filtered out in the digital domain, so that the minimum sampling rate is 2R. In addition, in most practical implementations, the sampling rate is equal to twice the symbol rate, and hence it is higher than R.

2016 (1)

2015 (1)

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

2010 (1)

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16, 1280–1289 (2010).
[Crossref]

2009 (1)

A. Mecozzi, “Retrieving the full optical response from amplitude data by Hilbert transform,” Opt. Commun. 282, 4183–4187 (2009).
[Crossref]

2008 (2)

B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. 26, 196–203 (2008).
[Crossref]

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

2006 (1)

1966 (1)

H. Voelcker, “Demodulation of single-sideband signals via envelope detection,” IEEE Trans. Commun. Technol. 14, 22–30 (1966).
[Crossref]

1957 (1)

W. Heisenberg, “Quantum theory of fields and elementary particles,” Rev. Mod. Phys. 29, 269–278 (1957).
[Crossref]

1953 (1)

M. Gell-Mann and M. L. Goldberger, “The formal theory of scattering,” Phys. Rev. 91, 398–408 (1953).
[Crossref]

1950 (1)

M. Cini, “The response characteristics of linear systems,” J. Appl. Phys. 21, 8–10 (1950).
[Crossref]

1927 (1)

H. A. Kramers, “La diffusion de la lumiere par les atomes,” Atti Cong. Intern. Fis. 2, 545–557 (1927).

1926 (1)

Armstrong, J.

Bode, H. W.

H. W. Bode, Network Analysis and Feedback Amplifier Design (Van Nostrand, 1945), Chap. 8.

Breyer, F.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16, 1280–1289 (2010).
[Crossref]

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

Buck, J. R.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing (Prentice Hall, 1999).

Bunge, C. A.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

Chandrasekhar, S.

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. J. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in Proceedings of European Conference of Optical Communications 2015 (ECOC), Valencia, Spain (2015), paper 0697.

Chapman, H. N.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

Cini, M.

M. Cini, “The response characteristics of linear systems,” J. Appl. Phys. 21, 8–10 (1950).
[Crossref]

Cohen, O.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

Eldar, Y. C.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

Gell-Mann, M.

M. Gell-Mann and M. L. Goldberger, “The formal theory of scattering,” Phys. Rev. 91, 398–408 (1953).
[Crossref]

Goldberger, M. L.

M. Gell-Mann and M. L. Goldberger, “The formal theory of scattering,” Phys. Rev. 91, 398–408 (1953).
[Crossref]

Heisenberg, W.

W. Heisenberg, “Quantum theory of fields and elementary particles,” Rev. Mod. Phys. 29, 269–278 (1957).
[Crossref]

Kai, Y.

T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. Rasmussen, “Discrete multi-tone for 100  Gb/s optical access networks,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2I.1.

Kramers, H. A.

H. A. Kramers, “La diffusion de la lumiere par les atomes,” Atti Cong. Intern. Fis. 2, 545–557 (1927).

Kronig, R. L.

Lee, S. C. J.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16, 1280–1289 (2010).
[Crossref]

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

Li, L.

T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. Rasmussen, “Discrete multi-tone for 100  Gb/s optical access networks,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2I.1.

Lowery, A. J.

Mecozzi, A.

A. Mecozzi, “Retrieving the full optical response from amplitude data by Hilbert transform,” Opt. Commun. 282, 4183–4187 (2009).
[Crossref]

A. Mecozzi, “A necessary and sufficient condition for minimum phase and implications for phase retrieval,” arXiv:1606.04861 (2016).

Miao, J.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

Nishihara, M.

T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. Rasmussen, “Discrete multi-tone for 100  Gb/s optical access networks,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2I.1.

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing (Prentice Hall, 1999).

Petermann, K.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

Pilori, D.

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. J. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in Proceedings of European Conference of Optical Communications 2015 (ECOC), Valencia, Spain (2015), paper 0697.

Proakis, J. G.

J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, 2001), Chap. 5.

Randel, S.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16, 1280–1289 (2010).
[Crossref]

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. J. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in Proceedings of European Conference of Optical Communications 2015 (ECOC), Valencia, Spain (2015), paper 0697.

Rasmussen, J.

T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. Rasmussen, “Discrete multi-tone for 100  Gb/s optical access networks,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2I.1.

Raybon, G.

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. J. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in Proceedings of European Conference of Optical Communications 2015 (ECOC), Valencia, Spain (2015), paper 0697.

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing (Prentice Hall, 1999).

Schmidt, B. J. C.

Schuster, M.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

Segev, M.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

Shechtman, Y.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

Shtaif, M.

Spinnler, B.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

Takahara, T.

T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. Rasmussen, “Discrete multi-tone for 100  Gb/s optical access networks,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2I.1.

Tanaka, T.

T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. Rasmussen, “Discrete multi-tone for 100  Gb/s optical access networks,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2I.1.

Tao, Z.

T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. Rasmussen, “Discrete multi-tone for 100  Gb/s optical access networks,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2I.1.

Voelcker, H.

H. Voelcker, “Demodulation of single-sideband signals via envelope detection,” IEEE Trans. Commun. Technol. 14, 22–30 (1966).
[Crossref]

Walewski, J. W.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16, 1280–1289 (2010).
[Crossref]

Weiss, A.

Winzer, P. J.

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. J. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in Proceedings of European Conference of Optical Communications 2015 (ECOC), Valencia, Spain (2015), paper 0697.

Yeredor, A.

Atti Cong. Intern. Fis. (1)

H. A. Kramers, “La diffusion de la lumiere par les atomes,” Atti Cong. Intern. Fis. 2, 545–557 (1927).

IEEE J. Sel. Top. Quantum Electron. (1)

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16, 1280–1289 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (1)

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

IEEE Signal Process. Mag. (1)

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

IEEE Trans. Commun. Technol. (1)

H. Voelcker, “Demodulation of single-sideband signals via envelope detection,” IEEE Trans. Commun. Technol. 14, 22–30 (1966).
[Crossref]

J. Appl. Phys. (1)

M. Cini, “The response characteristics of linear systems,” J. Appl. Phys. 21, 8–10 (1950).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

A. Mecozzi, “Retrieving the full optical response from amplitude data by Hilbert transform,” Opt. Commun. 282, 4183–4187 (2009).
[Crossref]

Opt. Express (1)

Phys. Rev. (1)

M. Gell-Mann and M. L. Goldberger, “The formal theory of scattering,” Phys. Rev. 91, 398–408 (1953).
[Crossref]

Rev. Mod. Phys. (1)

W. Heisenberg, “Quantum theory of fields and elementary particles,” Rev. Mod. Phys. 29, 269–278 (1957).
[Crossref]

Other (13)

A. Mecozzi, “A necessary and sufficient condition for minimum phase and implications for phase retrieval,” arXiv:1606.04861 (2016).

T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. Rasmussen, “Discrete multi-tone for 100  Gb/s optical access networks,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper M2I.1.

H. W. Bode, Network Analysis and Feedback Amplifier Design (Van Nostrand, 1945), Chap. 8.

Polarization multiplexing can also be accommodated by the scheme of Fig. 2(a), but envisageable extensions of the KK scheme would imply a considerable increase of the receiver cost and complexity.

We note that B represents the bandwidth of the optical signal impinging upon the receiver, which is meant to be reconstructed. The information-carrying bandwidth may be smaller than B, depending on the tightness of the optical filter that is used.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing (Prentice Hall, 1999).

Recall that, contrary to [21] and to most of the existing literature, we are considering signals that are “causal” in the frequency domain, i.e., such that they vanish for ω<0.

To see why the minimum energy-delay property implies that of all signals with the same intensity profile, the minimum phase signal is contained within the smallest bandwidth, consider the following situation. Assume that E(t) is a minimum phase signal, whose spectrum |E˜(ω)|2 is contained in the bandwidth B, but exceeds any bandwidth B′<B. If there were a signal E′(t) such that |E′(t)|2=|E(t)|2, with a spectrum |E˜(ω)|2 that is contained in B′<B, then we would have ∫ω0∞|E˜(ω)|2dω>∫ω0∞|E˜′(ω)|2dω=0 for every ω0∈(B′,B), contrary to the minimum energy-delay property.

J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, 2001), Chap. 5.

The lower spectral efficiency of IMDD follows from the fact that, with intensity modulation, no information is encoded into the optical phase. This makes IMDD inferior even to single-quadrature modulation, where positive and negative amplitude values can be used.

The rate R is in general different from the actual sampling rate. For instance, in the experimental implementation of the scheme of [4] presented in [5], the sampled photocurrent includes the contribution of the spurious signal–signal beat, which is filtered out in the digital domain, so that the minimum sampling rate is 2R. In addition, in most practical implementations, the sampling rate is equal to twice the symbol rate, and hence it is higher than R.

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. J. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in Proceedings of European Conference of Optical Communications 2015 (ECOC), Valencia, Spain (2015), paper 0697.

Toward the completion of this paper, we discovered that a similar scheme was proposed in Ref. [9]. That scheme was presented in the context of analog radio systems and it contained none of the features that characterize fiber-optic transmission, which are discussed in this paper.

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 (7)

Fig. 1.
Fig. 1.

(a) Time trajectory of a 16 QAM modulated signal s(t) of bandwidth B in the complex plane. (b) The time trajectory of the single-sideband signal A+s(t)exp(iπBt) (blue dashed) and of the signal reconstructed from its intensity (red solid). We set the phase of A to 45° for the convenience of illustration. The blue and red dots are the original and reconstructed symbols, respectively. The quality of the reconstruction is poor because the original signal encircles the origin multiple times. (c) Same as (b), but with a larger value of |A|. Here the trajectory of the original signal does not encircle the origin, and the reconstruction is perfect.

Fig. 2.
Fig. 2.

(a) KK receiver scheme: the transmitted waveform, which consists of a modulated signal of bandwidth B and a CW field at the left edge of the signal spectrum, is directly detected, then sampled at the sampling rate of 2B. The digital samples are finally processed for chromatic dispersion compensation and extraction of the transmitted symbols. (b) An alternative version of the KK scheme. In this case, the CW field at the left edge of the modulated signal spectrum is added at the receiver using a frequency selective coupler.

Fig. 3.
Fig. 3.

Top panel shows the absolute values of the original (solid blue) and reconstructed (dashed red) waveforms. The bottom left and right panels zoom in to the beginning and the center of the frame, respectively.

Fig. 4.
Fig. 4.

Received constellations in the back-to-back configuration. In the leftmost panel, the LO power was set to 1.1 times the maximum value of the information carrying signal power—corresponding to about 11 dB above the average signal power. In this case, the minimum-phase condition [15,16] is rigorously fulfilled. In the second, third, and fourth panels, the LO power level was reduced by 3, 5, and 8 dB, respectively, while not modifying the signal.

Fig. 5.
Fig. 5.

BER versus OSNR for a 24 Gbaud 16 QAM modulated signal. Each curve was obtained by setting the power of the LO to the value shown in the legend. Open symbols refer to the back-to-back configuration, while the solid symbols were obtained for a 100 km single-span link, where CD was compensated electronically at the receiver after signal reconstruction.

Fig. 6.
Fig. 6.

BER versus total transmit power for the channel of interest of a DWDM system with five transmitted channels. The solid symbols were obtained for 16 QAM modulation based on the use of the KK scheme with various levels of the LO power; the open circles show the results obtained for 8 PAM modulation. In the KK scheme CD was compensated digitally after signal reconstruction, whereas in the case of 8 PAM, CD was compensated optically. Top and bottom panels differ by the number of spans.

Fig. 7.
Fig. 7.

Same as Fig. 6, except that the BER is plotted versus the OSNR. At low OSNR values, increasing the LO power yields a reduction in BER.

Tables (1)

Tables Icon

Table 1. Comparison among Various Schemes in Terms of Optical Bandwidth, Suitability for Digital Compensation of Linear Impairments, and Power Efficiencya

Equations (12)

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

h(t)=A+s(t)exp(iπBt),
φ(t)=1πp.v.dtlog[|h(t)|]tt,
φ˜(ω)=isign(ω)F{log[|h(t)|]},
Es(t)={I(t)exp[iφE(t)]E0}exp(iπBt),
φE(t)=12πp.v.dtlog[I(t)]tt.
BERAWGN=4log2(M)(11M)Q(6ρM1OSNR),
ur(t)=p.v.ui(t)dtπ(tt),ui(t)=p.v.ur(t)dtπ(tt).
ϕ(t)=p.v.dtlog|1+u(t)|22π(tt).
φE(t)=p.v.dtlog|E0+Es(t)|22π(tt),
Es,i(t)=1πp.v.dtEs,r(t)tt.
I(t)=E02+Es,r2(t)+Es,i2(t)+2E0Es,r(t).
Es,r(t)=|I(t)Es,i2(t)|E0,

Metrics