OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 12 — Jun. 7, 2010
  • pp: 12088–12103

Bit-error rate performance of coherent optical M-ary PSK/QAM using decision-aided maximum likelihood phase estimation

S. Zhang, P. Y. Kam, J. Chen, and C. Yu  »View Author Affiliations

Optics Express, Vol. 18, Issue 12, pp. 12088-12103 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (1003 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The bit-error rate (BER) expressions of 16- phase-shift keying (PSK) and 16- quadrature amplitude modulation (QAM) are analytically obtained in the presence of a phase error. By averaging over the statistics of the phase error, the performance penalty can be analytically examined as a function of the phase error variance. The phase error variances leading to a 1-dB signal-to-noise ratio per bit penalty at BER=10−4 have been found to be 8.7×10−2 rad2, 1.2×10−2 rad2, 2.4×10−3 rad2, 6.0×10−4 rad2 and 2.3×10−3 rad2 for binary, quadrature, 8-, and 16-PSK and 16QAM, respectively. With the knowledge of the allowable phase error variance, the corresponding laser linewidth tolerance can be predicted. We extend the phase error variance analysis of decision-aided maximum likelihood carrier phase estimation in M-ary PSK to 16QAM, and successfully predict the laser linewidth tolerance in different modulation formats, which agrees well with the Monte Carlo simulations. Finally, approximate BER expressions for different modulation formats are introduced to allow a quick estimation of the BER performance as a function of the phase error variance. Further, the BER approximations give a lower bound on the laser linewidth requirements in M-ary PSK and 16QAM. It is shown that as far as laser linewidth tolerance is concerned, 16QAM outperforms 16PSK which has the same spectral efficiency (SE), and has nearly the same performance as 8PSK which has lower SE. Thus, 16-QAM is a promising modulation format for high SE coherent optical communications.

© 2010 Optical Society of America

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.1660) Fiber optics and optical communications : Coherent communications
(060.5060) Fiber optics and optical communications : Phase modulation

ToC Category:
Fiber Optics and Optical Communications

Original Manuscript: March 9, 2010
Revised Manuscript: May 7, 2010
Manuscript Accepted: May 15, 2010
Published: May 24, 2010

Changyuan Yu, Shaoliang Zhang, Pooi Yuen Kam, and Jian Chen, "Bit-Error Rate Performance of Coherent Optical M-ary PSK/QAM using Decision-Aided Maximum Likelihood Phase Estimation," Opt. Express 18, 12088-12103 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. P. Agrawal, Fiber-Optic Communication Systems (New York: Wiley-Interscience, 2002). [CrossRef]
  2. L. G. Kazovsky, G. Kalogerakis, and W.-T. Shaw, “Homodyne phase-shift-keying systems: Past challenges and future opportunities,” J. Lightwave Technol. 24,4876–4884 (2006). [CrossRef]
  3. E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol. 25,2675–2692 (2007). [CrossRef]
  4. R. Noé, “Phase noise-tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedfoward carrier recovery,” J. Lightwave Technol. 23,802–808 (2005). [CrossRef]
  5. K. Kikuchi, T. Okoshi, M. Nagamatsu, and N. Henmi, “Degradation of bit-error rate in coherent optical communications due to spectrum spread of the transmitter and the local oscillator,” J. Lightwave Technol. LT-2,1024–1033 (1984). [CrossRef]
  6. L. G. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communications systems,” J. Lightwave Technol. LT-4, 415–425 (1986). [CrossRef]
  7. S. Norimatsu and K. Iwashita, “Damping factor influence on linewidth requirements for optical PSK coherent detection systems,” J. Lightwave Technol. 11,1226–1233 (1993). [CrossRef]
  8. C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Sel. Top. Quantum Electron. 10,281–293 (2004). [CrossRef]
  9. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23,115–130 (2005). [CrossRef]
  10. Y. Cai, “Coherent detection in long-haul transmission systems,” in Proceedings of Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2008), paper OTuM1.
  11. A. Leven, N. Kaneda, and Y.-K. Chen, “A real-time CMA-based 10Gb/s polarization demultiplexing coherent receiver implmented in an FPGA,” in Proceedings of Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2008), paper OTuO2.
  12. 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. Lightwave Technol. 24,12–21 (2006). [CrossRef]
  13. X. Zhou, J. Yu, D. Qian, T. Wang, G. Zhang, and P. D. Magill, “ High-spectral-efficiency 114-Gb/s transmission using PolMux-RZ-8PSK modulation format and single-ended digital coherent detection technique,” J. Lightwave Technol. 27,146–152 (2009). [CrossRef]
  14. N. Xie, T. Zhang, and E. F. Haratsch, “Improving burst error tolerance of LDPC-centric coding systems in read channel, ” IEEE Trans. Magnetics 46,933–941 (2010). [CrossRef]
  15. A. J. Viterbi and A. N. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory IT-29,543–551 (1983). [CrossRef]
  16. 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. Express 17,1435–1441 (2009), http://www. opticsinfobase.org/abstract.cfm?uri=oe-17-3-1435. [CrossRef] [PubMed]
  17. M. G. Taylor, “Accurate digital phase estimation for coherent detection using a parallel digital processor,” in Proceedings of European Conference on Optical Communication2005, paper Tu 4.2.6.
  18. L. M. Pessoa, H. M. Salgado, and I. Darwazeh, “Joint mitigation of optical impairments and phase estimation in coherent optical systems,” in Proceedings of IEEE LEOS Summer Topical Meetings (Mexico, 2008), pp.169–170.
  19. 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, 703–715 (2009), http://www.opticsinfobase.org/oe/ abstract.cfm?uri=oe-17-2-703. [CrossRef] [PubMed]
  20. H. Ghafouri-Shiraz, Y. H. Heng, and T. Aruga, “Effect of phase noise on the performance of 10-Gbits/s coherent optical synchronous receivers,” Microwave Opt. Technol. Lett. 11,14–17 (1996). [CrossRef]
  21. G. Goldfarb and G. Li, “BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing,” Opt. Express 14, 8043–8053 (2006), http://www.opticsinfobase.org/ abstract.cfm?uri=oe-14-18-8043. [CrossRef] [PubMed]
  22. P. Y. Kam, S. K. Teo, Y. K. Some, and T. T. Tjhung, “Approximate results for the bit error probability of binary PSK with noisy phase reference,” IEEE Trans. Commun. 41,1020–1022 (1993). [CrossRef]
  23. Y. K. Some and P. Y. Kam, “Bit-error probability of QPSK with noisy phase reference,” IEE Proc. Commun. 142,292–296 (1995). [CrossRef]
  24. M. P. Fitz and R. J. M. Cramer, “A performance analysis of a digital PLL-based MPSK demodulator,” IEEE Trans. Commun. 43,1192–1201 (1995). [CrossRef]
  25. M. Seimetz, M. Noelle, and E. Patzak, “ Optical systems with high-order DPSK and star QAM modulation based on interferometric direct detection,” J. Lightwave Technol. 25,1515–1530 (2007). [CrossRef]
  26. J. Lassing, E. Str¨om, E. Agrell, and T. Ottosson, “Computation of the exact bit-error rate of coherent M-ary PSK with gray code bit mapping,” IEEE Trans. Commun. 51,1758–1760 (2003). [CrossRef]
  27. H. Fu and P. Y. Kam, “A simple bit error probability analysis for square QAM in Rayleigh fading with channel estimation,” IEEE Trans. Commun. 57,2200–2206 (2009). [CrossRef]
  28. S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Laser linewidth tolerance of decision-aided maximum likelihood phase estimation in coherent optical M-ary PSK and QAM systems,” IEEE Photon. Technol. Lett. 21,1075–1077 (2009). [CrossRef]
  29. J. G. Proakis, Digital Communications 4th ed. (New York: McGraw-Hill, 2000).
  30. T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27,989–999 (2009). [CrossRef]
  31. P. Y. Kam, “Maximum-likelihood carrier phase recovery for linear suppressed-carrier digital data modulations,” IEEE Trans. Commun. COM-34,522-527 (1986).
  32. S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Decision-aided carrier phase estimation for coherent optical communications,” to appear in J. Lightwave Technol.
  33. S. Zhang, C. Yu, P. Y. Kam, and J. Chen, “Parallel implementation of decision-aided maximum likelihood phase estimation in coherent M-ary phase-shifted keying systems,” IEEE Photon. Technol. Lett. 21,1471–1473 (2009). [CrossRef]
  34. X. Zhou et al., “64-Tb/s (640107-Gb/s) PDM-36QAM transmission over 320km using both pre- and posttransmission digital equalization,” in Proceedings of Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2010), paper PDPB9.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited