Abstract

We exploit pilot-aided (PA) transmission enabled by single-sideband (SSB) subcarrier modulation of both quadrature signals in the DSP domain to achieve fully feedforward carrier recovery (FFCR) in single-carrier (SC) coherent systems with arbitrary M-QAM constellations. A thorough mathematical description of the proposed PA-FFCR is presented, its linewidth tolerance is assessed by simulations and compared to other FFCR schemes in literature. Also, implementation and complexity issues of PA-FFCR are presented and briefly compared with other CR schemes. Simulation results show that PA-FFCR performs close to the best known CR technique in the literature with less computation complexity. Quantitatively, for 1 dB optical-signal-to-noise-ratio (OSNR) penalty at BER = 3.8 × 10−3, PA-FFCR tolerates linewidth-symbol-duration products (Δf.Ts) of 1.5 × 10−4 (4-QAM), 4 × 10−5 (16-QAM) and 1 × 10−5 (64-QAM). Finally, we propose the use of maximum likelihood (ML) phase estimation next to pilot phase compensation. This significantly improves tolerable Δf.Ts values to 7.5 × 10−4 (4-QAM), 1.8 × 10−4 (16-QAM) and 3.5 × 10−5 (64-QAM). It turns out that PA-FFCR with ML always performs better or at least the same compared to other CR techniques known in literature with lower complexity in addition to the fact that pilot information can be as well exploited for tasks other than CR e.g., fiber nonlinearity compensation, with no extra complexity.

© 2011 OSA

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References

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  1. E. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Lightwave Technol. 28(4), 502–519 (2010).
    [CrossRef]
  2. S. J. Savory, “Coherent detection—why is it back?” in The 20th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2007. LEOS 2007(IEEE/LEOS, 2007), pp. 212–213.
  3. E. Ip, A. P. Lau, D. J. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16(2), 753–791 (2008).
    [CrossRef] [PubMed]
  4. S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
    [CrossRef]
  5. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004).
    [CrossRef]
  6. E. Ip and J. M. Kahn, “Digital equalization of chromatic dispersion and polarization mode dispersion,” J. Lightwave Technol. 25(8), 2033–2043 (2007).
    [CrossRef]
  7. E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008).
    [CrossRef]
  8. G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photonics 1(2), 279–307 (2009).
    [CrossRef]
  9. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008).
    [CrossRef] [PubMed]
  10. M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol. 27(7), 901–914 (2009).
    [CrossRef]
  11. P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010).
    [CrossRef]
  12. K. Roberts, M. O'Sullivan, K.-T. Wu, H. Sun, A. Awadalla, D. Krause, and C. Laperle, “Performance of dual-polarization QPSK for optical transport systems,” J. Lightwave Technol. 27(16), 3546–3559 (2009).
    [CrossRef]
  13. IEEE Std 802.3baTM-2010, Amendment 4: Media Access Control Parameters, Physical Layers, and Management Parameters for 40 Gb/s and 100 Gb/s Operation.
  14. P. J. Winzer, A. Gnauck, S. Chandrasekhar, S. Draving, J. Evangelista, and B. Zhu, “Generation and 1200-km transmission of 448-Gb/s ETDM 56-Gbaud PDM 16-QAM using a single I/Q modulator,” in 2010 36th European Conference and Exhibition on Optical Communication (ECOC) (2010), paper PD2.2.
  15. X. Zhou, L. E. Nelson, P. Magill, B. Zhu, and D. W. Peckham, “8x450-Gb/s,50-GHz-spaced, PDM-32QAM transmission over 400km and one 50GHz-grid ROADM,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB3.
  16. A. H. Gnauck, P. Winzer, A. Konczykowska, F. Jorge, J. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a high-power DAC driving a single I/Q modulator,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB2.
  17. T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009).
    [CrossRef]
  18. A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
    [CrossRef]
  19. I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photon. Technol. Lett. 22(9), 631–633 (2010).
    [CrossRef]
  20. M. H. Morsy-Osman, L. R. Chen, and D. V. Plant, “Joint mitigation of laser phase noise and fiber nonlinearity using pilot-aided transmission for single-carrier systems,” in in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Tu.3.A.3.
  21. J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, New York, 2001).
  22. B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).
  23. Y. Benlachtar, S. J. Savory, B. C. Thomsen, G. Gavioli, P. Bayvel, and R. I. Killey, “Robust long-haul transmission utilizing electronic precompensation and MLSE equalization,” in National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JWA52.
  24. A. Oppenheim and R. Shafer, Discrete-Time Signal Processing, 2nd ed. (Prentice-Hall, New Jersey, 1999).
  25. H. Sorensen, D. Jones, M. Heideman, and C. Burrus, “Real-valued fast Fourier transform algorithms,” IEEE Trans. Acoust. Speech Signal Process. 35(6), 849–863 (1987).
    [CrossRef]
  26. S. L. Marple., “Computing the discrete-time `analytic' signal via FFT,” IEEE Trans. Signal Process. 47(9), 2600–2603 (1999).
    [CrossRef]
  27. H. Sorensen and C. Burrus, “Efficient computation of the DFT with only a subset of input or output points,” IEEE Trans. Signal Process. 41(3), 1184–1200 (1993).
    [CrossRef]

2010

E. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Lightwave Technol. 28(4), 502–519 (2010).
[CrossRef]

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[CrossRef]

P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010).
[CrossRef]

I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photon. Technol. Lett. 22(9), 631–633 (2010).
[CrossRef]

B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

2009

2008

2007

2004

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004).
[CrossRef]

1999

S. L. Marple., “Computing the discrete-time `analytic' signal via FFT,” IEEE Trans. Signal Process. 47(9), 2600–2603 (1999).
[CrossRef]

1993

H. Sorensen and C. Burrus, “Efficient computation of the DFT with only a subset of input or output points,” IEEE Trans. Signal Process. 41(3), 1184–1200 (1993).
[CrossRef]

1987

H. Sorensen, D. Jones, M. Heideman, and C. Burrus, “Real-valued fast Fourier transform algorithms,” IEEE Trans. Acoust. Speech Signal Process. 35(6), 849–863 (1987).
[CrossRef]

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 29(4), 543–551 (1983).
[CrossRef]

Awadalla, A.

Barros, D. J.

Borowiec, A.

B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Burrus, C.

H. Sorensen and C. Burrus, “Efficient computation of the DFT with only a subset of input or output points,” IEEE Trans. Signal Process. 41(3), 1184–1200 (1993).
[CrossRef]

H. Sorensen, D. Jones, M. Heideman, and C. Burrus, “Real-valued fast Fourier transform algorithms,” IEEE Trans. Acoust. Speech Signal Process. 35(6), 849–863 (1987).
[CrossRef]

Cartledge, J. C.

B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Chagnon, M.

B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Chatelain, B.

B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Fatadin, I.

I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photon. Technol. Lett. 22(9), 631–633 (2010).
[CrossRef]

Gagnon, F.

B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Heideman, M.

H. Sorensen, D. Jones, M. Heideman, and C. Burrus, “Real-valued fast Fourier transform algorithms,” IEEE Trans. Acoust. Speech Signal Process. 35(6), 849–863 (1987).
[CrossRef]

Hoffmann, S.

Ip, E.

Ives, D.

I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photon. Technol. Lett. 22(9), 631–633 (2010).
[CrossRef]

Jones, D.

H. Sorensen, D. Jones, M. Heideman, and C. Burrus, “Real-valued fast Fourier transform algorithms,” IEEE Trans. Acoust. Speech Signal Process. 35(6), 849–863 (1987).
[CrossRef]

Kahn, J. M.

Krause, D.

B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

K. Roberts, M. O'Sullivan, K.-T. Wu, H. Sun, A. Awadalla, D. Krause, and C. Laperle, “Performance of dual-polarization QPSK for optical transport systems,” J. Lightwave Technol. 27(16), 3546–3559 (2009).
[CrossRef]

Laperle, C.

B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

K. Roberts, M. O'Sullivan, K.-T. Wu, H. Sun, A. Awadalla, D. Krause, and C. Laperle, “Performance of dual-polarization QPSK for optical transport systems,” J. Lightwave Technol. 27(16), 3546–3559 (2009).
[CrossRef]

Lau, A. P.

Li, G.

G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photonics 1(2), 279–307 (2009).
[CrossRef]

Marple, S. L.

S. L. Marple., “Computing the discrete-time `analytic' signal via FFT,” IEEE Trans. Signal Process. 47(9), 2600–2603 (1999).
[CrossRef]

Noe, R.

O'Sullivan, M.

Pfau, T.

Plant, D. V.

B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Roberts, K.

B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

K. Roberts, M. O'Sullivan, K.-T. Wu, H. Sun, A. Awadalla, D. Krause, and C. Laperle, “Performance of dual-polarization QPSK for optical transport systems,” J. Lightwave Technol. 27(16), 3546–3559 (2009).
[CrossRef]

Savory, S. J.

I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photon. Technol. Lett. 22(9), 631–633 (2010).
[CrossRef]

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[CrossRef]

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

Sorensen, H.

H. Sorensen and C. Burrus, “Efficient computation of the DFT with only a subset of input or output points,” IEEE Trans. Signal Process. 41(3), 1184–1200 (1993).
[CrossRef]

H. Sorensen, D. Jones, M. Heideman, and C. Burrus, “Real-valued fast Fourier transform algorithms,” IEEE Trans. Acoust. Speech Signal Process. 35(6), 849–863 (1987).
[CrossRef]

Sun, H.

Taylor, M. G.

M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol. 27(7), 901–914 (2009).
[CrossRef]

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004).
[CrossRef]

Viterbi, A. J.

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[CrossRef]

Viterbi, A. M.

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[CrossRef]

Winzer, P. J.

P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010).
[CrossRef]

Wu, K.-T.

Xu, X.

B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Adv. Opt. Photonics

G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photonics 1(2), 279–307 (2009).
[CrossRef]

IEEE Commun. Mag.

P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004).
[CrossRef]

I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photon. Technol. Lett. 22(9), 631–633 (2010).
[CrossRef]

B. Chatelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

IEEE Trans. Acoust. Speech Signal Process.

H. Sorensen, D. Jones, M. Heideman, and C. Burrus, “Real-valued fast Fourier transform algorithms,” IEEE Trans. Acoust. Speech Signal Process. 35(6), 849–863 (1987).
[CrossRef]

IEEE Trans. Inf. Theory

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[CrossRef]

IEEE Trans. Signal Process.

S. L. Marple., “Computing the discrete-time `analytic' signal via FFT,” IEEE Trans. Signal Process. 47(9), 2600–2603 (1999).
[CrossRef]

H. Sorensen and C. Burrus, “Efficient computation of the DFT with only a subset of input or output points,” IEEE Trans. Signal Process. 41(3), 1184–1200 (1993).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Other

IEEE Std 802.3baTM-2010, Amendment 4: Media Access Control Parameters, Physical Layers, and Management Parameters for 40 Gb/s and 100 Gb/s Operation.

P. J. Winzer, A. Gnauck, S. Chandrasekhar, S. Draving, J. Evangelista, and B. Zhu, “Generation and 1200-km transmission of 448-Gb/s ETDM 56-Gbaud PDM 16-QAM using a single I/Q modulator,” in 2010 36th European Conference and Exhibition on Optical Communication (ECOC) (2010), paper PD2.2.

X. Zhou, L. E. Nelson, P. Magill, B. Zhu, and D. W. Peckham, “8x450-Gb/s,50-GHz-spaced, PDM-32QAM transmission over 400km and one 50GHz-grid ROADM,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB3.

A. H. Gnauck, P. Winzer, A. Konczykowska, F. Jorge, J. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a high-power DAC driving a single I/Q modulator,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB2.

S. J. Savory, “Coherent detection—why is it back?” in The 20th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2007. LEOS 2007(IEEE/LEOS, 2007), pp. 212–213.

Y. Benlachtar, S. J. Savory, B. C. Thomsen, G. Gavioli, P. Bayvel, and R. I. Killey, “Robust long-haul transmission utilizing electronic precompensation and MLSE equalization,” in National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JWA52.

A. Oppenheim and R. Shafer, Discrete-Time Signal Processing, 2nd ed. (Prentice-Hall, New Jersey, 1999).

M. H. Morsy-Osman, L. R. Chen, and D. V. Plant, “Joint mitigation of laser phase noise and fiber nonlinearity using pilot-aided transmission for single-carrier systems,” in in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Tu.3.A.3.

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

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Figures (6)

Fig. 1
Fig. 1

Architecture of a DSP-based coherent transmission system (DAC: Digital-to-Analog Converter, PBS: Polarization Beam Splitter, PBC: Polarization Beam Combiner, ADC: Analog-to-Digital Converter).

Fig. 2
Fig. 2

Spectrum of I-component on X-Pol. of a 28 Gbaud PDM 16-QAM signala) At Tx before SSB, b) At Tx after SSB and pilot insertion with fsc = 500 MHz and PSR = −14 dB, c) Zoomed version of pilot spectral gap at Tx, d) At Rx with laser PN (Δf = 2MHz) and noise loaded (OSNR = 16.7 dB),e) Zoomed version of pilot spectral gap at Rx together with a Gaussian LPF with BLPF = 80 MHz.

Fig. 3
Fig. 3

Canonical system model in presence of LTI impairments and laser phase noise.

Fig. 4
Fig. 4

DSP tasks for PA-FFCR and PA-FFCR with ML in: a) Tx side aided with illustrative constellations for data and pilot symbols, and b) Rx side aided and the measured constellation of the filtered pilot.

Fig. 5
Fig. 5

a) BER surface versus the pilot-to-signal power ratio and the bandwidth of the pilot LPF at two different laser linewidths for 16-QAM at OSNR = 16.7 dB, and linewidth tolerance of various CR schemes against laser phase noise for b) QPSK, c) 16-QAM, and d) 64-QAM constellations.

Fig. 6
Fig. 6

Performance of PA-FFCR with ML for different M-QAM formats with finite bit resolution of(a) DACs, and (b) ADCs.

Tables (1)

Tables Icon

Table 1 Linewidth tolerance of various CR schemes for different M-QAM formats

Equations (16)

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

r(t)=( s tr (t) e j ϕ Tx (t) +N(t) )× e j ϕ Rx (t) =( k= ( s k e j ϕ Tx (t) h ps (tk T s ) ) +N(t) )× e j ϕ Rx (t)
s o (t)= k= ( s k e j[ ϕ Tx (t)+ ϕ Rx (t) ] h ps (tk T s ) ) + N (t)
s k '= s k e j[ ϕ Tx (k T s )+ ϕ Rx (k T s ) ] + N (k T s )
ϕ(k T s ) ϕ k = i= k f i
σ f 2 =2π(Δf T s )
x SSB (t)=Re{ x + (t) e j2π f sc t }, y SSB (t)=Re{ y + (t) e j2π f sc t }
x + (t)=x(t)+j x ^ (t), y + (t)=y(t)+j y ^ (t)
H Hilbert (f)={ j, f>0 0, f=0 j, f<0
X SSB (f)=X(f f sc )u(f f sc )+X(f+ f sc )u(f f sc )
Y SSB (f)=Y(f f sc )u(f f sc )+Y(f+ f sc )u(f f sc )
x SSB,PA (t)= x SSB (t)+ P pilot /2 , y SSB,PA (t)= y SSB (t)+ P pilot /2
s tr (t)=[ x SSB (t)+j y SSB (t) ]+ P pilot /2 ×( 1+j )
r(t)=( s tr (t) e j φ Tx (t) +N(t) )× e j φ Rx (t) =[ x SSB (t)+j y SSB (t) ]× e j[ φ Tx (t)+ φ Rx (t) ] + P pilot /2 ×( 1+j1 )× e j[ φ Tx (t)+ φ Rx (t) ] + N ' (t)
ϕ pilot (t)= ϕ Tx (t)+ ϕ Rx (t)+π/4+ ϕ n (t)
H k = n=k N ML +1 k+ N ML s n PA [ s ^ n PA ] *
ϕ k ML = tan 1 { Im{ H k } Re{ H k } }

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