Carrier phase estimation for optically coherent QPSK based on Wiener-optimal and adaptive Multi-Symbol Delay Detection (MSDD) |
Optics Express, Vol. 20, Issue 3, pp. 1981-2003 (2012)
http://dx.doi.org/10.1364/OE.20.001981
Acrobat PDF (1520 KB)
Abstract
The MSDD carrier phase estimation technique is derived here for optically coherent QPSK transmission, introducing the principle of operation while providing intuitive insight in terms of a multi-symbol extension of naïve delay-detection. We derive here for the first time Wiener-optimized and LMS-adapted versions of MSDD, introduce simplified hardware realizations, and evaluate complexity and numerical performance tradeoffs of this highly robust and low-complexity carrier phase recovery method. A multiplier-free carrier phase recovery version of the MSDD provides nearly optimal performance for linewidths up to ~0.5 MHz, whereas for wider linewidths, the Wiener or LMS versions provide optimal performance at about 9 taps, using 1 or 2 complex multipliers per tap.
© 2012 OSA
1. Introduction
1. A. Viterbi and A. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983). [CrossRef]
1. A. Viterbi and A. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983). [CrossRef]
2. Carrier recovery (CR) concepts – naïve delay detector (DD)
2.1 Differential precoding
26. N. Kikuchi and S. Sasaki, “Highly sensitive optical multilevel transmission of arbitrary quadrature-amplitude modulation (QAM) signals with direct detection,” J. Lightwave Technol. 28(1), 123–130 (2010). [CrossRef]
2.2 Link model including the CR
2.3 Naïve delay detector
3. From the naïve DD to MSDD carrier recovery
3.1 MSDD principle: Generation of an improved reference from prior received samples
3.2 MSDD alternative formulation in terms of partial DD estimators
4. Optimal Wiener-filtering based Minimum Mean Square Error (MMSE) solution
5. LMS algorithm for the MSDD coefficients
6. Efficient hardware implementations
6.1 MSDD hardware realization complexity (excluding the adaptive coefficients control)
6.2 MSDD with adaptive coefficients control and its total complexity
7. Polyphase parallelization
9. M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol. 27(7), 901–914 (2009). [CrossRef]
7.1 The distant feedback (DF) problem in parallelized MSDD processing
8. Simulation results
34. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed]
9. Conclusions
1. A. Viterbi and A. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983). [CrossRef]
Appendix A: Uop and modulus preserving differential encoding math properties
Appendix B: Derivation of the Wiener-Hopf equations for the optimal coefficients
35. Y. Atzmon and M. Nazarathy, “A Gaussian polar model for error rates of differential phase detection impaired by linear, nonlinear, and laser phase noises,” J. Lightwave Technol. 27(21), 4650–4659 (2009). [CrossRef]
Appendix C: Abbreviations used in this paper
CFO = Carrier Frequency Offset | MMSE = Minimal Mean Square Error | ASE = Amplified Spontaneous Emission |
CM = Complex Multiplier | MP-DP = Modulus Preserving Diff. Precoder | FIR = Finite Impulse Response |
CPE = Carrier Phase Estimation | MSDD =
Multi-Symbol Delay/Differential Detection | QPSK = Quadrature Phase Shift Keying |
CR = Carrier Recovery | MSE = Mean Square Error | QAM = Quadrature Amplitude Modulation |
DD = Delay/Differential Detector/Demodulator | MSPE = Multi-Symbol Phase Estimation | OSNR – Optical Signal to Noise Ratio |
DP = Differential Precoder | PN = Phase Noise | SNR = Signal to Noise Ratio |
LMS = Least Mean Squares | SE = Squared Error | |
LPN = Laser Phase Noise | Uop = Unimodular Normalization (Eq. (2)) | |
LW = Linewidth | W-H = Wiener-Hopf (Equations) |
Acknowledgments
References and links
1. | A. Viterbi and A. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983). [CrossRef] |
2. | E. Ip and J. M. Kahn, “Carrier synchronization for 3- and 4-bit-per-symbol optical transmission,” J. Lightwave Technol. 23(12), 4110–4124 (2005). [CrossRef] |
3. | R. Noé, “PLL-free synchronous QPSK polarization multiplex / diversity receiver concept with digital I & Q baseband processing,” IEEE Photon. Technol. Lett. 17(4), 887–889 (2005). [CrossRef] |
4. | M. G. Taylor, “Accurate digital phase estimation process for coherent detection using a parallel digital processor,” in ECOC’05 European Conf. of Optical Communication, Tu 4.2.6 (2005). |
5. | E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol. 25(9), 2675–2692 (2007). [CrossRef] |
6. | S. Hoffmann, S. Bhandare, T. Pfau, O. Adamczyk, C. Wordehoff, R. Peveling, M. Porrmann, and R. Noe, “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” IEEE Photon. Technol. Lett. 20(18), 1569–1571 (2008). [CrossRef] |
7. | M. G. Taylor, “Detection using digital signal processing,” J. Lightwave Technol. 27(7), 901–914 (2009). [CrossRef] |
8. | M. G. Taylor, “Algorithms for coherent detection what can we learn from other fields?” in OFC/NFOEC’10, Conf. on Optical Fiber Communication, OThL4 (2010). |
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. | K. Piyawanno, M. Kuschnerov, B. Spinnler, and B. Lankl, “Low complexity carrier recovery for coherent QAM using superscalar parallelization,” in ECOC’10 European Conf. of Optical Communication, We.7.A.3 (2010). |
11. | D. Divsalar and M. K. Simon, “Multiple-symbol differential detection of MPSK,” IEEE Trans. Commun. 38(3), 300–308 (1990). [CrossRef] |
12. | F. Edbauer, “Bit error rate of binary and quaternary DPSK signals with multiple differential feedback detection,” IEEE Trans. Commun. 40(3), 457–460 (1992). [CrossRef] |
13. | M. Adachi and F. Sawahashi, “Decision feedback multiple-symbol differential detection for M-ary DPSK,” Electron. Lett. 29(15), 1385–1387 (1993). [CrossRef] |
14. | F. Adachi and M. Sawahashi, “Decision feedback differential phase detection of M-ary DPSK signals,” IEEE Trans. Vehicular Technol. 44(2), 203–210 (1995). [CrossRef] |
15. | S. Zhang, P. Y. Kam, J. Chen, and C. Yu, “Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system,” Opt. Express 17(2), 703–715 (2009). [CrossRef] [PubMed] |
16. | 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] |
17. | S. Zhang, P. -yuen Kam, C. Yu, and J. Chen, “Decision-aided carrier phase estimation for coherent optical communications,” J. Lightwave Technol. 28(11), 1597–1607 (2010). [CrossRef] |
18. | D. van den Borne, S. Calabro, S. L. Jansen, E. Gottwald, G. D. Khoe, and H. de Waardt, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” in OFC’05 Conference on Optical Fiber Communication (2005). |
19. | M. Nazarathy and Y. Yadin, “Approaching coherent homodyne performance with direct detection low-complexity advanced modulation formats,” in COTA’06 Coherent Optical Technologies and Applications (2006). |
20. | X. Liu, “Data-aided multi-symbol phase estimation for receiver sensitivity enhancement in optical DQPSK, CThB4,” in COTA’06 Coherent Optical Techniques and Applications (2006). |
21. | M. Nazarathy and Y. Atzmon, “Approaching coherent homodyne performance with direct detection low-complexity advanced modulation formats,” in COTA’08 Coherent Optical Techniques and Applications (2008). |
22. | X. Liu, S. Chandrasekhar, and A. Leven, “Digital self-coherent detection,” Opt. Express 16(2), 792–803 (2008). [CrossRef] [PubMed] |
23. | M. Nazarathy, X. Liu, L. Christen, Y. K. Lize, and A. E. Willner, “Self-coherent multisymbol detection of optical differential phase-shift keying,” J. Lightwave Technol. 26(13), 1921–1934 (2008). [CrossRef] |
24. | Y. Takushima, H. Y. Choi, and Y. C. Chung, “Transmission of 108-Gb/s PDM 16ADPSK signal on 25-GHz grid using non-coherent receivers,” Opt. Express 17(16), 13458–13466 (2009). [CrossRef] [PubMed] |
25. | J. Li, R. Schmogrow, D. Hillerkuss, M. Lauermann, M. Winter, K. Worms, C. Schubert, C. Koos, W. Freude, and W. J. Leuthold, “Self-coherent receiver for PolMUX coherent signals,” in OFC’11 Conference on Optical Fiber Communication, OWV5 (2011). |
26. | N. Kikuchi and S. Sasaki, “Highly sensitive optical multilevel transmission of arbitrary quadrature-amplitude modulation (QAM) signals with direct detection,” J. Lightwave Technol. 28(1), 123–130 (2010). [CrossRef] |
27. | N. Kikuchi, “Chromatic dispersion-tolerant higher-order multilevel transmission with optical delay detection,” in SPPCom’11 Signal Processing in Photonic Communications - OSA Technical Digest (2011). |
28. | S. Adhikari, S. L. Jansen, M. Alfiad, B. Inan, V. A. J. M. Sleiffer, A. Lobato, P. Leoni, and W. Rosenkranz, “Self-coherent optical OFDM : an interesting alternative to direct or coherent detection” in ICTON’11 13th International Conference on Transparent Optical Networks (2011). |
29. | S. Kumar, Impact of Nonlinearities on Fiber Optic Communications, (Springer, 2011). |
30. | N. Sigron, I. Tselniker, M. Nazarathy, A. Gorshtein, D. Sadot, and I. Zelniker, “Ultimate single-carrier recovery for coherent detection,” in OFC’11 Conference on Optical Fiber Communication, OMJ2 (2011). |
31. | M. Nazarathy, N. Sigron, and I. Tselniker, “Integrated carrier phase and frequency estimation for coherent detection based on multi-symbol differential detection (MSDD),” in SPPCom’11 Signal Processing in Photonic Communications - OSA Technical Digest, Invited paper SPMC1 (2011). |
32. | N. Kikuchi, S. Sasaki, and T. Uda, “Phase-noise tolerant coherent polarization-multiplexed 16QAM Transmission with digital delay-detection, in ECOC’11 European Conference of Optical Communication (ECOC), Tu.3.A (2011). |
33. | T. Adali and S. Haykin, Adaptive Signal Processing—Next Generation Solutions (John Wiley, 2010). |
34. | W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed] |
35. | Y. Atzmon and M. Nazarathy, “A Gaussian polar model for error rates of differential phase detection impaired by linear, nonlinear, and laser phase noises,” J. Lightwave Technol. 27(21), 4650–4659 (2009). [CrossRef] |
OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(060.2920) Fiber optics and optical communications : Homodyning
ToC Category:
Fiber Optics and Optical Communications
History
Original Manuscript: November 14, 2011
Revised Manuscript: December 14, 2011
Manuscript Accepted: December 14, 2011
Published: January 13, 2012
Citation
Netta Sigron, Igor Tselniker, and Moshe Nazarathy, "Carrier phase estimation for optically coherent QPSK based on Wiener-optimal and adaptive Multi-Symbol Delay Detection (MSDD)," Opt. Express 20, 1981-2003 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-1981
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References
- A. Viterbi and A. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory29(4), 543–551 (1983). [CrossRef]
- E. Ip and J. M. Kahn, “Carrier synchronization for 3- and 4-bit-per-symbol optical transmission,” J. Lightwave Technol.23(12), 4110–4124 (2005). [CrossRef]
- R. Noé, “PLL-free synchronous QPSK polarization multiplex / diversity receiver concept with digital I & Q baseband processing,” IEEE Photon. Technol. Lett.17(4), 887–889 (2005). [CrossRef]
- M. G. Taylor, “Accurate digital phase estimation process for coherent detection using a parallel digital processor,” in ECOC’05 European Conf. of Optical Communication, Tu 4.2.6 (2005).
- E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol.25(9), 2675–2692 (2007). [CrossRef]
- S. Hoffmann, S. Bhandare, T. Pfau, O. Adamczyk, C. Wordehoff, R. Peveling, M. Porrmann, and R. Noe, “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” IEEE Photon. Technol. Lett.20(18), 1569–1571 (2008). [CrossRef]
- M. G. Taylor, “Detection using digital signal processing,” J. Lightwave Technol.27(7), 901–914 (2009). [CrossRef]
- M. G. Taylor, “Algorithms for coherent detection what can we learn from other fields?” in OFC/NFOEC’10, Conf. on Optical Fiber Communication, OThL4 (2010).
- M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Lightwave Technol.27(7), 901–914 (2009). [CrossRef]
- K. Piyawanno, M. Kuschnerov, B. Spinnler, and B. Lankl, “Low complexity carrier recovery for coherent QAM using superscalar parallelization,” in ECOC’10 European Conf. of Optical Communication, We.7.A.3 (2010).
- D. Divsalar and M. K. Simon, “Multiple-symbol differential detection of MPSK,” IEEE Trans. Commun.38(3), 300–308 (1990). [CrossRef]
- F. Edbauer, “Bit error rate of binary and quaternary DPSK signals with multiple differential feedback detection,” IEEE Trans. Commun.40(3), 457–460 (1992). [CrossRef]
- M. Adachi and F. Sawahashi, “Decision feedback multiple-symbol differential detection for M-ary DPSK,” Electron. Lett.29(15), 1385–1387 (1993). [CrossRef]
- F. Adachi and M. Sawahashi, “Decision feedback differential phase detection of M-ary DPSK signals,” IEEE Trans. Vehicular Technol.44(2), 203–210 (1995). [CrossRef]
- S. Zhang, P. Y. Kam, J. Chen, and C. Yu, “Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system,” Opt. Express17(2), 703–715 (2009). [CrossRef] [PubMed]
- 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. Express18(12), 12088–12103 (2010). [CrossRef] [PubMed]
- S. Zhang, P. -yuen Kam, C. Yu, and J. Chen, “Decision-aided carrier phase estimation for coherent optical communications,” J. Lightwave Technol.28(11), 1597–1607 (2010). [CrossRef]
- D. van den Borne, S. Calabro, S. L. Jansen, E. Gottwald, G. D. Khoe, and H. de Waardt, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” in OFC’05 Conference on Optical Fiber Communication (2005).
- M. Nazarathy and Y. Yadin, “Approaching coherent homodyne performance with direct detection low-complexity advanced modulation formats,” in COTA’06 Coherent Optical Technologies and Applications (2006).
- X. Liu, “Data-aided multi-symbol phase estimation for receiver sensitivity enhancement in optical DQPSK, CThB4,” in COTA’06 Coherent Optical Techniques and Applications (2006).
- M. Nazarathy and Y. Atzmon, “Approaching coherent homodyne performance with direct detection low-complexity advanced modulation formats,” in COTA’08 Coherent Optical Techniques and Applications (2008).
- X. Liu, S. Chandrasekhar, and A. Leven, “Digital self-coherent detection,” Opt. Express16(2), 792–803 (2008). [CrossRef] [PubMed]
- M. Nazarathy, X. Liu, L. Christen, Y. K. Lize, and A. E. Willner, “Self-coherent multisymbol detection of optical differential phase-shift keying,” J. Lightwave Technol.26(13), 1921–1934 (2008). [CrossRef]
- Y. Takushima, H. Y. Choi, and Y. C. Chung, “Transmission of 108-Gb/s PDM 16ADPSK signal on 25-GHz grid using non-coherent receivers,” Opt. Express17(16), 13458–13466 (2009). [CrossRef] [PubMed]
- J. Li, R. Schmogrow, D. Hillerkuss, M. Lauermann, M. Winter, K. Worms, C. Schubert, C. Koos, W. Freude, and W. J. Leuthold, “Self-coherent receiver for PolMUX coherent signals,” in OFC’11 Conference on Optical Fiber Communication, OWV5 (2011).
- N. Kikuchi and S. Sasaki, “Highly sensitive optical multilevel transmission of arbitrary quadrature-amplitude modulation (QAM) signals with direct detection,” J. Lightwave Technol.28(1), 123–130 (2010). [CrossRef]
- N. Kikuchi, “Chromatic dispersion-tolerant higher-order multilevel transmission with optical delay detection,” in SPPCom’11 Signal Processing in Photonic Communications - OSA Technical Digest (2011).
- S. Adhikari, S. L. Jansen, M. Alfiad, B. Inan, V. A. J. M. Sleiffer, A. Lobato, P. Leoni, and W. Rosenkranz, “Self-coherent optical OFDM : an interesting alternative to direct or coherent detection” in ICTON’11 13th International Conference on Transparent Optical Networks (2011).
- S. Kumar, Impact of Nonlinearities on Fiber Optic Communications, (Springer, 2011).
- N. Sigron, I. Tselniker, M. Nazarathy, A. Gorshtein, D. Sadot, and I. Zelniker, “Ultimate single-carrier recovery for coherent detection,” in OFC’11 Conference on Optical Fiber Communication, OMJ2 (2011).
- M. Nazarathy, N. Sigron, and I. Tselniker, “Integrated carrier phase and frequency estimation for coherent detection based on multi-symbol differential detection (MSDD),” in SPPCom’11 Signal Processing in Photonic Communications - OSA Technical Digest, Invited paper SPMC1 (2011).
- N. Kikuchi, S. Sasaki, and T. Uda, “Phase-noise tolerant coherent polarization-multiplexed 16QAM Transmission with digital delay-detection, in ECOC’11 European Conference of Optical Communication (ECOC), Tu.3.A (2011).
- T. Adali and S. Haykin, Adaptive Signal Processing—Next Generation Solutions (John Wiley, 2010).
- W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express16(20), 15718–15727 (2008). [CrossRef] [PubMed]
- Y. Atzmon and M. Nazarathy, “A Gaussian polar model for error rates of differential phase detection impaired by linear, nonlinear, and laser phase noises,” J. Lightwave Technol.27(21), 4650–4659 (2009). [CrossRef]
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