Abstract

A low-complexity feed-forward carrier phase estimation (CPE) technique is presented for dual-polarization (DP)-16-QAM transmission systems. By combining QPSK partitioning, maximum likelihood (ML) detection and phase offset estimation between signals in different polarizations, simulation and experimental results for a 200Gb/s DP-16-QAM system demonstrate similar linewidth tolerance to the best feed-forward CPE reported to date while the computational complexity is at least three times lower compared with other simplified feed-forward CPE techniques.

© 2011 OSA

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References

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  1. E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol. 25(9), 2675–2692 (2007).
    [CrossRef]
  2. A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, and T. Li, “High-capacity optical transmission systems,” J. Lightwave Technol. 26(9), 1032–1045 (2008).
    [CrossRef]
  3. E. Ip, A. P. T. Lau, D. J. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16(2), 753–791 (2008).
    [CrossRef] [PubMed]
  4. G. Charlet, J. Renaudier, H. Mardoyan, P. Tran, O. Pardo, F. Verluise, M. Achouche, A. Boutin, F. Blache, J. Dupuy, and S. Bigo, “Transmission of 16.4 Tbit/s capacity over 2550 km using PDM QPSK modulation format and coherent receiver,” in Proceeding OFC/NFOEC, San Diego, CA, 2008, PDP3.
  5. P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010).
    [CrossRef]
  6. P. Andrekson, “Metrology of Complex Optical Modulation Formats,” in Proceeding OFC/NFOEC, Los Angeles, CA, 2011, OWN1.
  7. P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” J. Lightwave Technol. 28(4), 547–556 (2010).
    [CrossRef]
  8. C. Yu, S. Zhang, P. Y. Kam, and J. Chen, “Bit-error rate performance of coherent optical M-ary PSK/QAM using decision-aided maximum likelihood phase estimation,” Opt. Express 18(12), 12088–12103 (2010).
    [CrossRef] [PubMed]
  9. M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol. 27(7), 901–914 (2009).
    [CrossRef]
  10. M. Seimetz, Laser linewidth limitations for optical systems with high-order modulation employing feed forward digital carrier phase estimation,” in Proceedings OFC/NFOEC, San Diego, CA, 2008, OTuM2.
  11. 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]
  12. A. J. Viterbi and A. N. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
    [CrossRef]
  13. T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feed forward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009).
    [CrossRef]
  14. S. K. Oh and S. P. Stapleton, “Blind phase recovery using finite alphabet properties in digital communications,” Electron. Lett. 33(3), 175–176 (1997).
    [CrossRef]
  15. F. Rice, B. Cowley, B. Moran, and M. Rice, “Cramer-Rao lower bounds for QAM phase and frequency estimation,” IEEE Trans. Commun. 49(9), 1582–1591 (2001).
    [CrossRef]
  16. T. Pfau and R. Noe, “Phase-noise-tolerant two-stage carrier recovery concept for higher order QAM formats,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1210–1216 (2010).
    [CrossRef]
  17. X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photon. Technol. Lett. 22(14), 1051–1053 (2010).
    [CrossRef]
  18. X. Li, Y. Cao, S. Yu, W. Gu, and Y. Ji, “A simplified feed-forward carrier recovery algorithm for coherent optical QAM system,” J. Lightwave Technol. 29(5), 801–807 (2011).
    [CrossRef]
  19. Q. Zhuge, C. Chen, and D. V. Plant, “Low computation complexity two-stage feed forward carrier recovery algorithm for M-QAM,” in Proceedings OFC/NFOEC, Los Angeles, CA, 2011, Paper OMJ5.
  20. J. Li, L. Li, Z. Tao, T. Hoshida, and J. C. Rasmussen, “Laser-linewidth-tolerant feed-forward carrier phase estimator with reduced complexity for QAM,” J. Lightwave Technol. 29(16), 2358–2364 (2011).
  21. Y. Gao, A. P. T. Lau, C. Lu, Y. Li, J. Wu, K. Xu, W. Li, and J. Lin, “Low-complexity two-stage carrier phase estimation for 16-QAM systems using QPSK partitioning and maximum likelihood detection,” in Proceedings OFC/NFOEC, Los Angeles, CA, 2011, Paper OMJ6.
  22. A. H. Gnauck, G. Charlet, P. Tran, P. J. Winzer, C. R. Doerr, J. C. Centanni, E. C. Burrows, T. Kawanishi, T. Sakamoto, and K. Higuma, “25.6-Tb/s WDM transmission of polarization-multiplexed RZ-DQPSK signals,” J. Lightwave Technol. 26(1), 79–84 (2008).
    [CrossRef]
  23. R. R. Muller and D. A. D. A. Mello, “Phase-offset estimation for joint-polarization phase-recovery in DP-16-QAM systems,” IEEE Photon. Technol. Lett. 22(20), 1515–1517 (2010).
    [CrossRef]
  24. T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630 (1980).
    [CrossRef]
  25. I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
    [CrossRef]
  26. X. Zhou and Y. Sun, “Low-complexity, blind phase recovery for coherent receivers using QAM modulation,” in Proceedings OFC/NFOEC, Los Angeles, CA, 2011, Paper OMJ3.
  27. K. Piyawanno, M. Kuschnerov, B. Spinnler, and B. Lankl, “Low complexity carrier recovery for coherent QAM using superscalar parallelization,” in Proceeding ECOC 2010, Torino, Italy, Paper We.7.A.3.

2011

2010

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]

T. Pfau and R. Noe, “Phase-noise-tolerant two-stage carrier recovery concept for higher order QAM formats,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1210–1216 (2010).
[CrossRef]

X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photon. Technol. Lett. 22(14), 1051–1053 (2010).
[CrossRef]

R. R. Muller and D. A. D. A. Mello, “Phase-offset estimation for joint-polarization phase-recovery in DP-16-QAM systems,” IEEE Photon. Technol. Lett. 22(20), 1515–1517 (2010).
[CrossRef]

P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” J. Lightwave Technol. 28(4), 547–556 (2010).
[CrossRef]

C. Yu, S. Zhang, P. Y. Kam, and J. Chen, “Bit-error rate performance of coherent optical M-ary PSK/QAM using decision-aided maximum likelihood phase estimation,” Opt. Express 18(12), 12088–12103 (2010).
[CrossRef] [PubMed]

2009

2008

2007

2001

F. Rice, B. Cowley, B. Moran, and M. Rice, “Cramer-Rao lower bounds for QAM phase and frequency estimation,” IEEE Trans. Commun. 49(9), 1582–1591 (2001).
[CrossRef]

1997

S. K. Oh and S. P. Stapleton, “Blind phase recovery using finite alphabet properties in digital communications,” Electron. Lett. 33(3), 175–176 (1997).
[CrossRef]

1983

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

1980

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630 (1980).
[CrossRef]

Barros, D. J.

Buhl, L. L.

Burrows, E. C.

Cao, Y.

Centanni, J. C.

Charlet, G.

Chen, J.

Chraplyvy, A. R.

Cowley, B.

F. Rice, B. Cowley, B. Moran, and M. Rice, “Cramer-Rao lower bounds for QAM phase and frequency estimation,” IEEE Trans. Commun. 49(9), 1582–1591 (2001).
[CrossRef]

Doerr, C. R.

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]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[CrossRef]

Gnauck, A. H.

Gu, W.

Higuma, K.

Hoffmann, S.

Hoshida, T.

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]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[CrossRef]

Ji, Y.

Kahn, J. M.

Kam, P. Y.

Kawanishi, T.

Kikuchi, K.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630 (1980).
[CrossRef]

Lau, A. P. T.

Li, J.

Li, L.

Li, T.

Li, X.

Magarini, M.

Mello, D. A. D. A.

R. R. Muller and D. A. D. A. Mello, “Phase-offset estimation for joint-polarization phase-recovery in DP-16-QAM systems,” IEEE Photon. Technol. Lett. 22(20), 1515–1517 (2010).
[CrossRef]

Moran, B.

F. Rice, B. Cowley, B. Moran, and M. Rice, “Cramer-Rao lower bounds for QAM phase and frequency estimation,” IEEE Trans. Commun. 49(9), 1582–1591 (2001).
[CrossRef]

Muller, R. R.

R. R. Muller and D. A. D. A. Mello, “Phase-offset estimation for joint-polarization phase-recovery in DP-16-QAM systems,” IEEE Photon. Technol. Lett. 22(20), 1515–1517 (2010).
[CrossRef]

Nakayama, A.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630 (1980).
[CrossRef]

Noe, R.

T. Pfau and R. Noe, “Phase-noise-tolerant two-stage carrier recovery concept for higher order QAM formats,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1210–1216 (2010).
[CrossRef]

T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feed forward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009).
[CrossRef]

Oh, S. K.

S. K. Oh and S. P. Stapleton, “Blind phase recovery using finite alphabet properties in digital communications,” Electron. Lett. 33(3), 175–176 (1997).
[CrossRef]

Okoshi, T.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630 (1980).
[CrossRef]

Pfau, T.

T. Pfau and R. Noe, “Phase-noise-tolerant two-stage carrier recovery concept for higher order QAM formats,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1210–1216 (2010).
[CrossRef]

T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feed forward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009).
[CrossRef]

Rasmussen, J. C.

Rice, F.

F. Rice, B. Cowley, B. Moran, and M. Rice, “Cramer-Rao lower bounds for QAM phase and frequency estimation,” IEEE Trans. Commun. 49(9), 1582–1591 (2001).
[CrossRef]

Rice, M.

F. Rice, B. Cowley, B. Moran, and M. Rice, “Cramer-Rao lower bounds for QAM phase and frequency estimation,” IEEE Trans. Commun. 49(9), 1582–1591 (2001).
[CrossRef]

Sakamoto, T.

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]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[CrossRef]

Stapleton, S. P.

S. K. Oh and S. P. Stapleton, “Blind phase recovery using finite alphabet properties in digital communications,” Electron. Lett. 33(3), 175–176 (1997).
[CrossRef]

Tao, Z.

Taylor, M. G.

Tkach, R. W.

Tran, P.

Viterbi, A. J.

A. J. Viterbi and A. N. 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. N.

A. J. Viterbi and A. N. 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.

Yu, C.

Yu, S.

Zhang, S.

Zhou, X.

X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photon. Technol. Lett. 22(14), 1051–1053 (2010).
[CrossRef]

Electron. Lett.

S. K. Oh and S. P. Stapleton, “Blind phase recovery using finite alphabet properties in digital communications,” Electron. Lett. 33(3), 175–176 (1997).
[CrossRef]

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630 (1980).
[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.

T. Pfau and R. Noe, “Phase-noise-tolerant two-stage carrier recovery concept for higher order QAM formats,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1210–1216 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photon. Technol. Lett. 22(14), 1051–1053 (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]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[CrossRef]

R. R. Muller and D. A. D. A. Mello, “Phase-offset estimation for joint-polarization phase-recovery in DP-16-QAM systems,” IEEE Photon. Technol. Lett. 22(20), 1515–1517 (2010).
[CrossRef]

IEEE Trans. Commun.

F. Rice, B. Cowley, B. Moran, and M. Rice, “Cramer-Rao lower bounds for QAM phase and frequency estimation,” IEEE Trans. Commun. 49(9), 1582–1591 (2001).
[CrossRef]

IEEE Trans. Inf. Theory

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

J. Lightwave Technol.

A. H. Gnauck, G. Charlet, P. Tran, P. J. Winzer, C. R. Doerr, J. C. Centanni, E. C. Burrows, T. Kawanishi, T. Sakamoto, and K. Higuma, “25.6-Tb/s WDM transmission of polarization-multiplexed RZ-DQPSK signals,” J. Lightwave Technol. 26(1), 79–84 (2008).
[CrossRef]

A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, and T. Li, “High-capacity optical transmission systems,” J. Lightwave Technol. 26(9), 1032–1045 (2008).
[CrossRef]

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

T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feed forward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009).
[CrossRef]

P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” J. Lightwave Technol. 28(4), 547–556 (2010).
[CrossRef]

E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol. 25(9), 2675–2692 (2007).
[CrossRef]

X. Li, Y. Cao, S. Yu, W. Gu, and Y. Ji, “A simplified feed-forward carrier recovery algorithm for coherent optical QAM system,” J. Lightwave Technol. 29(5), 801–807 (2011).
[CrossRef]

J. Li, L. Li, Z. Tao, T. Hoshida, and J. C. Rasmussen, “Laser-linewidth-tolerant feed-forward carrier phase estimator with reduced complexity for QAM,” J. Lightwave Technol. 29(16), 2358–2364 (2011).

Opt. Express

Other

P. Andrekson, “Metrology of Complex Optical Modulation Formats,” in Proceeding OFC/NFOEC, Los Angeles, CA, 2011, OWN1.

M. Seimetz, Laser linewidth limitations for optical systems with high-order modulation employing feed forward digital carrier phase estimation,” in Proceedings OFC/NFOEC, San Diego, CA, 2008, OTuM2.

Q. Zhuge, C. Chen, and D. V. Plant, “Low computation complexity two-stage feed forward carrier recovery algorithm for M-QAM,” in Proceedings OFC/NFOEC, Los Angeles, CA, 2011, Paper OMJ5.

Y. Gao, A. P. T. Lau, C. Lu, Y. Li, J. Wu, K. Xu, W. Li, and J. Lin, “Low-complexity two-stage carrier phase estimation for 16-QAM systems using QPSK partitioning and maximum likelihood detection,” in Proceedings OFC/NFOEC, Los Angeles, CA, 2011, Paper OMJ6.

G. Charlet, J. Renaudier, H. Mardoyan, P. Tran, O. Pardo, F. Verluise, M. Achouche, A. Boutin, F. Blache, J. Dupuy, and S. Bigo, “Transmission of 16.4 Tbit/s capacity over 2550 km using PDM QPSK modulation format and coherent receiver,” in Proceeding OFC/NFOEC, San Diego, CA, 2008, PDP3.

X. Zhou and Y. Sun, “Low-complexity, blind phase recovery for coherent receivers using QAM modulation,” in Proceedings OFC/NFOEC, Los Angeles, CA, 2011, Paper OMJ3.

K. Piyawanno, M. Kuschnerov, B. Spinnler, and B. Lankl, “Low complexity carrier recovery for coherent QAM using superscalar parallelization,” in Proceeding ECOC 2010, Torino, Italy, Paper We.7.A.3.

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Figures (10)

Fig. 1
Fig. 1

QPSK partitioning for 16-QAM signals based on the received signal amplitude. The initial estimate of the laser phase can be obtained by VVPE for Class I and Class III symbols.

Fig. 3
Fig. 3

(a) Residue phase-offset and (b) BER versus convergence length for an OSNR penalty of 1dB and a line-width symbol duration product of 2E-4. The data points are obtained from the average of 50 independent trials.

Fig. 4
Fig. 4

Estimated phase offset using various methods (1. Continuous, 2. Periodic, 3. One-time)

Fig. 2
Fig. 2

Block diagram of the proposed two-stage CPE: (a) first stage estimator using QPSK partitioning, VVPE and phase-offset cancellation; (b) second stage ML estimator to improve estimation accuracy. Note that the filter half widths of filters used in first and second stage (N and M) are different in general.

Fig. 5
Fig. 5

Optimal filter half width N for the first stage estimator vs. OSNR for different linewidth times symbol duration products ( Δv T s ). The symbol rate is 25 GBaud and each data point is obtained by averaging the result of 10 independent trials.

Fig. 6
Fig. 6

OSNR penalties versus linewidth times symbol duration product ( Δv T s ) for various feed-forward CPE techniques for 16-QAM systems.

Fig. 7
Fig. 7

Experimental setup for CPE performance investigation for a 200Gb/s DP-16-QAM system. The 16-QAM signal is generated by applying two four-level electrical signals to IQ modulator, which are generated by combining two 25G/s two-level signals with different amplitudes. PC: polarization controller; EDFA: Erbium-doped optical fiber amplifier; OSA: optical spectrum analyzer; OBPF: optical band-pass filter; SMF: single mode fiber; Pol. Mux: polarization multiplexer; PBS: polarization beam splitter; PBC: polarization beam combiner.

Fig. 8
Fig. 8

Receiver DSP block diagram for a 200 Gb/s DP-16-QAM system using self-homodyne detection. Two samples per symbol sequences from both polarizations (Ix, Qx, Iy, Qy) are first fed into orthogonalization algorithms to equalize quadrature imbalance in modulator and detector imperfections, followed by a 13 taps Ts/2-spaced FIR filters for timing phase recovery and polarization de-multiplexing. The output is then down-sampled to one sample per symbol and passes into five different carrier phase estimation techniques: BPS, BPS + ML, QPSK partitioning, single and dual polarization QPSK partitioning + ML. The CPE outputs are then detected and BER is calculated.

Fig. 9
Fig. 9

OSNR vs. laser linewidth times symbol duration product ( Δv T s ) for a 200Gb/s DP-16-QAM system obtained from experiments. The combined linewidth of the transmitter laser and local oscillator are 0.3 MHz, 0.9 MHz, 2 MHz, 3 MHz, 4 MHz, and 5.63 MHz. At large laser linewidth, a BER of 1E-3 can only be achieved by dual pol. QPSK paritioning + ML.

Fig. 10
Fig. 10

Received signal distributions for Δv T s of 2.25E-4 and OSNR of 37.2 dB using (a) QPSK partitioning (BER = 2.8E-3), (b) BPS (BER = 1.2E-3), (c) BPS + ML (BER = 1.7E-3), (d) single pol. QPSK partitioning + ML (BER = 1.4E-3), (e) dual pol. QPSK partitioning + ML (BER = 9.8E-4), (f) dual pol. BPS (BER = 8.8E-4).

Tables (1)

Tables Icon

Table 1 Number of operations required for Various Feed-forward CPE Techniques

Equations (7)

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

s n,x(y) = b n,x(y) exp(j θ n,x(y) )+ z n,x(y)
θ n est1 = 1 4 arg( i: s i,x C 1 C 3 s i,x 4 | s i,x 4 | + e j θ offset i: s i,y C 1 C 3 s i,y 4 | s i,y 4 | ),i{ nN,...,n+N }
q k =α[ ( s k,x 4 ) / | s k,x 4 | ] [ ( s k,y 4 ) / | s k,y 4 | ] * + q k1 ( 1α ),k:( s k,x C 1 C 3 )( s k,y C 1 C 3 ),
θ offset =arg( q k )
h n = p=x,y i=nM n+M u i,p v ^ i,p *
θ n est2 = tan 1 [ Im( h n ) / Re( h n ) ]
θ n est = θ n est1 + θ n est2 .

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