Abstract

Blind phase search (BPS) algorithm for M-QAM has excellent tolerance to laser linewidth at the expense of rather high computation complexity (CC). Here, we first theoretically obtain the quadratic relationship between the test angle and corresponding distance matric during the BPS implementation. Afterwards, we propose a carrier phase estimation (CPE) based on a two-stage BPS with quadratic approximation (QA). Instead of searching the phase blindly with fixed step-size for the BPS algorithm, QA can significantly accelerate the speed of phase searching. As a result, a group factor of 2.96/3.05, 4.55/4.67 and 2.27/2.3 (in the form of multipliers/adders) reduction of CC is achieved for 16QAM, 64QAM and 256QAM, respectively, in comparison with the traditional BPS scheme. Meanwhile, a guideline for determining the summing filter block length is put forward during performance optimization. Under the condition of optimum filter block length, our proposed scheme shows similar performance as traditional BPS scheme. At 1 dB required ES/N0 penalty @ BER = 10−2, our proposed CPE scheme can tolerate a times symbol duration productΔfTS of 1.7 × 10−4, 6 × 10−5 and 1.5 × 10−5 for 16/64/256-QAM, respectively.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Linewidth-tolerant and multi-format carrier phase estimation schemes for coherent optical m-QAM flexible transmission systems

Tao Yang, Chen Shi, Xue Chen, Min Zhang, Yuefeng Ji, Feng Hua, and Yufei Chen
Opt. Express 26(8) 10599-10615 (2018)

Modulation-format-independent blind phase search algorithm for coherent optical square M-QAM systems

Xian Zhou, Kangping Zhong, Yuliang Gao, Chao Lu, Alan Pak Tao Lau, and Keping Long
Opt. Express 22(20) 24044-24054 (2014)

Pilot-aided carrier phase recovery for M-QAM using superscalar parallelization based PLL

Qunbi Zhuge, Mohamed Morsy-Osman, Xian Xu, Mohammad E. Mousa-Pasandi, Mathieu Chagnon, Ziad A. El-Sahn, and David V. Plant
Opt. Express 20(17) 19599-19609 (2012)

References

  • View by:
  • |
  • |
  • |

  1. R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (2010).
    [Crossref]
  2. S. K. Korotky, “Traffic trends: Drivers and measures of cost-effective and energy-efficient technologies and architectures for backbone optical networks,” in Proceedings of OFC (Los Angeles, California, 2012), paper OM2G.1.
    [Crossref]
  3. E. Lach and W. Idler, “Modulation formats for 100 G and beyond,” Opt. Fiber Technol. 17(5), 377–386 (2011).
    [Crossref]
  4. X. Zhou, L. Nelson, and K. Carlson, “4000 km transmission of 50 GHz spaced, 10 × 494.85-Gb/s Hybrid 32–64 QAM using cascaded equalization and training-assisted phase recovery,” in Proceedings of OFC (Los Angeles, California, 2012), paper PDP5C.
  5. P. Winzer, “High-spectral-efficiency optical modulation formats,” J. Lightwave Technol. 30(8), 3824–3835 (2012).
    [Crossref]
  6. E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol. 25(9), 2675–2692 (2007).
    [Crossref]
  7. T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent dig-ital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(24), 989–999 (2009).
    [Crossref]
  8. M. Seimetz, “Laser linewidth limitations for optical systems with high-order modulation employing feedforward digital carrier phase estimation,” in Proceedings of OFC (San Diego, California, 2008), paper OTuM2.
  9. Y. Gao, A. P. T. Lau, S. Yan, and C. Lu, “Low-complexity and phase noise tolerant carrier phase estimation for dual-polarization 16-QAM systems,” Opt. Express 19(22), 21717–21729 (2011).
    [Crossref] [PubMed]
  10. I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16QAM coherent optical systems using QPSK partitioning,” IEEE Photonics Technol. Lett. 22(9), 631–633 (2010).
    [Crossref]
  11. S. M. Bilal, G. Bosco, J. Chen, and C. Lu, “Carrier phase estimation through the rotation algorithm for 64-QAM optical systems,” J. Lightwave Technol. 33(9), 1766–1773 (2015).
    [Crossref]
  12. 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 Photonics Technol. Lett. 21(15), 1075–1077 (2009).
    [Crossref]
  13. K. Zhong, J. H. Ke, Y. Gao, and J. C. Cartledge, “Linewidth-tolerant and low-complexity two-stage carrier phase estimation based on modified QPSK partitioning for dual-polarization 16-QAM systems,” J. Lightwave Technol. 31(1), 50–57 (2013).
    [Crossref]
  14. I. Fatadin, D. Ives, and S. J. Savory, “Carrier-phase estimation for 16-QAM optical coherent systems using QPSK partitioning with barycenter approximation,” J. Lightwave Technol. 32(13), 2420–2427 (2014).
    [Crossref]
  15. S. M. Bilal, C. Fludger, and G. Bosco, “Multi-stage CPE algorithms for 64-QAM constellations,” in Proceedings of OFC (San Francisco, California, 2014), paper. M2A.8.
  16. Y. Gao, A. P. T. Lau, C. Lu, J. Wu, Y. Li, K. Xu, W. Li, and J. Lin, “Multi-stage CPE algorithms for 64-QAM constellations,” in Proceedings of OFC (Los Angeles, California, 2011), paper. OMJ6.
  17. F. Rice, B. Cowley, B. Moran, and M. Rice, “Cramér-Rao lower bounds for QAM phase and frequency estimation,” IEEE Trans. Commun. 49(9), 1582–1591 (2001).
    [Crossref]
  18. S. K. Oh and S. Stapleton, “Blind phase recovery using finite alpha-bet properties in digital communications,” Electron. Lett. 33(3), 175–176 (1997).
    [Crossref]
  19. T. Pfau and R. Noé, “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]
  20. X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photonics Technol. Lett. 22(14), 1051–1053 (2010).
    [Crossref]
  21. 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]
  22. Q. Zhuge, C. Chen, and D. V. Plant, “Low computation complexity two-stage feedforward carrier recovery algorithm for M-QAM,” in Proceedings of OFC (Los Angeles, California, 2011), paper OMJ5.
    [Crossref]
  23. 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).
    [Crossref]
  24. J. K. Hwang, Y. L. Chiu, and C. S. Liao, “Angle differential-QAM scheme for resolving phase ambiguity in continuous transmission system,” Int. J. Commun. Syst. 21(6), 631–641 (2008).
    [Crossref]
  25. A. Bisplinghoff, C. Vogel, and B. Schmauss, “Slip-reduced carrier phase estimation for coherent transmission in the presence of non-linear phase noise,” in Proceedings of OFC (Anaheim, California, 2013), paper OTu3I.1.
    [Crossref]
  26. Y. Miyata, K. Sugihara, W. Matsumoto, K. Onohara, T. Sugihara, K. Kubo, H. Yoshida, and T. Mizuochi, “A triple-concatenated FEC using soft-decision decoding for 100 Gb/s optical transmission,” in Proceedings of OFC (San Diego, California, 2010), paper OThL3.
    [Crossref]
  27. K. Zhong, J. H. Ke, and Y. Gao, “Linewidth-tolerant and low-complexity two-stage carrier phase estimation for dual-polarization16-QAM coherent optical fiber communications,” J. Lightwave Technol. 30(24), 3987–3992 (2012).
    [Crossref]

2015 (1)

2014 (1)

2013 (1)

2012 (2)

2011 (4)

2010 (4)

T. Pfau and R. Noé, “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 Photonics Technol. Lett. 22(14), 1051–1053 (2010).
[Crossref]

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

R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (2010).
[Crossref]

2009 (2)

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 Photonics Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent dig-ital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(24), 989–999 (2009).
[Crossref]

2008 (1)

J. K. Hwang, Y. L. Chiu, and C. S. Liao, “Angle differential-QAM scheme for resolving phase ambiguity in continuous transmission system,” Int. J. Commun. Syst. 21(6), 631–641 (2008).
[Crossref]

2007 (1)

2001 (1)

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

1997 (1)

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

Bilal, S. M.

Bosco, G.

Cao, Y.

Cartledge, J. C.

Chen, J.

S. M. Bilal, G. Bosco, J. Chen, and C. Lu, “Carrier phase estimation through the rotation algorithm for 64-QAM optical systems,” J. Lightwave Technol. 33(9), 1766–1773 (2015).
[Crossref]

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 Photonics Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

Chiu, Y. L.

J. K. Hwang, Y. L. Chiu, and C. S. Liao, “Angle differential-QAM scheme for resolving phase ambiguity in continuous transmission system,” Int. J. Commun. Syst. 21(6), 631–641 (2008).
[Crossref]

Cowley, B.

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

Fatadin, I.

I. Fatadin, D. Ives, and S. J. Savory, “Carrier-phase estimation for 16-QAM optical coherent systems using QPSK partitioning with barycenter approximation,” J. Lightwave Technol. 32(13), 2420–2427 (2014).
[Crossref]

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

Gao, Y.

Gu, W.

Hoffmann, S.

Hoshida, T.

Hwang, J. K.

J. K. Hwang, Y. L. Chiu, and C. S. Liao, “Angle differential-QAM scheme for resolving phase ambiguity in continuous transmission system,” Int. J. Commun. Syst. 21(6), 631–641 (2008).
[Crossref]

Idler, W.

E. Lach and W. Idler, “Modulation formats for 100 G and beyond,” Opt. Fiber Technol. 17(5), 377–386 (2011).
[Crossref]

Ip, E.

Ives, D.

I. Fatadin, D. Ives, and S. J. Savory, “Carrier-phase estimation for 16-QAM optical coherent systems using QPSK partitioning with barycenter approximation,” J. Lightwave Technol. 32(13), 2420–2427 (2014).
[Crossref]

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

Ji, Y.

Kahn, J. M.

Kam, P. Y.

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 Photonics Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

Ke, J. H.

Lach, E.

E. Lach and W. Idler, “Modulation formats for 100 G and beyond,” Opt. Fiber Technol. 17(5), 377–386 (2011).
[Crossref]

Lau, A. P. T.

Li, J.

Li, L.

Li, X.

Liao, C. S.

J. K. Hwang, Y. L. Chiu, and C. S. Liao, “Angle differential-QAM scheme for resolving phase ambiguity in continuous transmission system,” Int. J. Commun. Syst. 21(6), 631–641 (2008).
[Crossref]

Lu, C.

Moran, B.

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

Noé, R.

T. Pfau and R. Noé, “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. Noé, “Hardware-efficient coherent dig-ital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(24), 989–999 (2009).
[Crossref]

Oh, S. K.

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

Pfau, T.

T. Pfau and R. Noé, “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. Noé, “Hardware-efficient coherent dig-ital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(24), 989–999 (2009).
[Crossref]

Rasmussen, J. C.

Rice, F.

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

Savory, S. J.

I. Fatadin, D. Ives, and S. J. Savory, “Carrier-phase estimation for 16-QAM optical coherent systems using QPSK partitioning with barycenter approximation,” J. Lightwave Technol. 32(13), 2420–2427 (2014).
[Crossref]

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

Stapleton, S.

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

Tao, Z.

Tkach, R. W.

R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (2010).
[Crossref]

Winzer, P.

Yan, S.

Yu, C.

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 Photonics Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

Yu, S.

Zhang, S.

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 Photonics Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

Zhong, K.

Zhou, X.

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

Bell Labs Tech. J. (1)

R. W. Tkach, “Scaling optical communications for the next decade and beyond,” Bell Labs Tech. J. 14(4), 3–9 (2010).
[Crossref]

Electron. Lett. (1)

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

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

T. Pfau and R. Noé, “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 Photonics Technol. Lett. (3)

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

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

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 Photonics Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

IEEE Trans. Commun. (1)

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

Int. J. Commun. Syst. (1)

J. K. Hwang, Y. L. Chiu, and C. S. Liao, “Angle differential-QAM scheme for resolving phase ambiguity in continuous transmission system,” Int. J. Commun. Syst. 21(6), 631–641 (2008).
[Crossref]

J. Lightwave Technol. (9)

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

T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent dig-ital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(24), 989–999 (2009).
[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).
[Crossref]

P. Winzer, “High-spectral-efficiency optical modulation formats,” J. Lightwave Technol. 30(8), 3824–3835 (2012).
[Crossref]

K. Zhong, J. H. Ke, and Y. Gao, “Linewidth-tolerant and low-complexity two-stage carrier phase estimation for dual-polarization16-QAM coherent optical fiber communications,” J. Lightwave Technol. 30(24), 3987–3992 (2012).
[Crossref]

K. Zhong, J. H. Ke, Y. Gao, and J. C. Cartledge, “Linewidth-tolerant and low-complexity two-stage carrier phase estimation based on modified QPSK partitioning for dual-polarization 16-QAM systems,” J. Lightwave Technol. 31(1), 50–57 (2013).
[Crossref]

I. Fatadin, D. Ives, and S. J. Savory, “Carrier-phase estimation for 16-QAM optical coherent systems using QPSK partitioning with barycenter approximation,” J. Lightwave Technol. 32(13), 2420–2427 (2014).
[Crossref]

S. M. Bilal, G. Bosco, J. Chen, and C. Lu, “Carrier phase estimation through the rotation algorithm for 64-QAM optical systems,” J. Lightwave Technol. 33(9), 1766–1773 (2015).
[Crossref]

Opt. Express (1)

Opt. Fiber Technol. (1)

E. Lach and W. Idler, “Modulation formats for 100 G and beyond,” Opt. Fiber Technol. 17(5), 377–386 (2011).
[Crossref]

Other (8)

X. Zhou, L. Nelson, and K. Carlson, “4000 km transmission of 50 GHz spaced, 10 × 494.85-Gb/s Hybrid 32–64 QAM using cascaded equalization and training-assisted phase recovery,” in Proceedings of OFC (Los Angeles, California, 2012), paper PDP5C.

M. Seimetz, “Laser linewidth limitations for optical systems with high-order modulation employing feedforward digital carrier phase estimation,” in Proceedings of OFC (San Diego, California, 2008), paper OTuM2.

S. K. Korotky, “Traffic trends: Drivers and measures of cost-effective and energy-efficient technologies and architectures for backbone optical networks,” in Proceedings of OFC (Los Angeles, California, 2012), paper OM2G.1.
[Crossref]

S. M. Bilal, C. Fludger, and G. Bosco, “Multi-stage CPE algorithms for 64-QAM constellations,” in Proceedings of OFC (San Francisco, California, 2014), paper. M2A.8.

Y. Gao, A. P. T. Lau, C. Lu, J. Wu, Y. Li, K. Xu, W. Li, and J. Lin, “Multi-stage CPE algorithms for 64-QAM constellations,” in Proceedings of OFC (Los Angeles, California, 2011), paper. OMJ6.

A. Bisplinghoff, C. Vogel, and B. Schmauss, “Slip-reduced carrier phase estimation for coherent transmission in the presence of non-linear phase noise,” in Proceedings of OFC (Anaheim, California, 2013), paper OTu3I.1.
[Crossref]

Y. Miyata, K. Sugihara, W. Matsumoto, K. Onohara, T. Sugihara, K. Kubo, H. Yoshida, and T. Mizuochi, “A triple-concatenated FEC using soft-decision decoding for 100 Gb/s optical transmission,” in Proceedings of OFC (San Diego, California, 2010), paper OThL3.
[Crossref]

Q. Zhuge, C. Chen, and D. V. Plant, “Low computation complexity two-stage feedforward carrier recovery algorithm for M-QAM,” in Proceedings of OFC (Los Angeles, California, 2011), paper OMJ5.
[Crossref]

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 Normalized distance matric versus test phase angle without phase noise loading.
Fig. 2
Fig. 2 Flowchart of proposed CPE scheme based on BPS with QA.
Fig. 3
Fig. 3 Optimization of the number of test angles B1.
Fig. 4
Fig. 4 (a) Contour diagram of the summing filter block length on the condition of Δ f T S = 5 × 10 5 . (b) Achieved Q-Factor under different summing filter block length N 2 for our proposed CPE scheme and N for traditional BPS(64) scheme.
Fig. 5
Fig. 5 Performance of phase noise tolerance for (a) 16-QAM, (b) 64-QAM, (c) 256-QAM.
Fig. 6
Fig. 6 , Relationship between BER and ES /N0 for 16QAM ( Δ f T S = 5 × 10 5 ), 64QAM ( Δ f T S = 1 × 10 5 ), and 256QAM ( Δ f T S = 8 × 10 6 ), respectively.
Fig. 7
Fig. 7 Probability distribution of iterations K .

Tables (5)

Tables Icon

Table 1 Optimum summing filter block length under various Δ f T S for 64QAM.

Tables Icon

Table 2 Optimum summing filter block length under various Δ f T S for 16QAM.

Tables Icon

Table 3 Optimum summing filter block length under various Δ f T S for 256QAM.

Tables Icon

Table 4 Comparison of optimum summing filter block length under various Δ f T S for 64 QAM.

Tables Icon

Table 5 CC comparison. LUT: look-up table.

Equations (12)

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

R k = s k e ( j θ k + j ϕ ) + p k e j φ k
ϕ b = b B π 2 π 4 , b = 0 , 1 , , B 1
d k , b 2 = | R k e - j ϕ b [ R k e - j ϕ b ] D | 2
e k , b = n = k c e i l ( N / 2 ) + 1 k + f l o o r ( N / 2 ) d n , b 2
e k , b = n = k c e i l ( N / 2 ) + 1 k + f l o o r ( N / 2 ) | s n e ( j θ n + j ϕ j ϕ b ) + p n e ( j φ n j ϕ b ) s n e ( j θ n ) | 2 = n = k c e i l ( N / 2 ) + 1 k + f l o o r ( N / 2 ) | [ s n cos ( θ n + ϕ ϕ b ) + p n cos ( φ n ϕ b ) s n cos ( θ n ) ] + j [ s n sin ( θ n + ϕ ϕ b ) + p n sin ( φ n ϕ b ) s n sin ( θ n ) ] | 2 = n = k c e i l ( N / 2 ) + 1 k + f l o o r ( N / 2 ) [ 2 s n 2 [ 1 cos ( ϕ ϕ b ) ] + p n s n [ cos ( ϕ φ n + θ n ) cos ( ϕ b φ n + θ n ) ] + p n 2 ] = n = k c e i l ( N / 2 ) + 1 k + f l o o r ( N / 2 ) [ 4 s n 2 sin 2 ( ϕ ϕ b 2 ) + p n 2 4 s n p n sin ( ϕ ϕ b 2 ) sin ( θ n φ n + ϕ + ϕ b 2 ) ]
{ a + b ϕ b 1 + c ϕ b 1 2 = e b 1 = f ( ϕ b 1 ) a + b ϕ b 2 + c ϕ b 2 2 = e b 2 = f ( ϕ b 2 ) a + b ϕ b 3 + c ϕ b 3 2 = e b 3 = f ( ϕ b 3 )
{ B 1 = ( ϕ b 2 2 ϕ b 3 2 ) f ( ϕ b 1 ) , B 2 = ( ϕ b 3 2 ϕ b 1 2 ) f ( ϕ b 2 ) B 3 = ( ϕ b 1 2 ϕ b 2 2 ) f ( ϕ b 3 ) , C 1 = ( ϕ b 2 ϕ b 3 ) f ( ϕ b 1 ) C 2 = ( ϕ b 3 ϕ b 1 ) f ( ϕ b 2 ) , C 3 = ( ϕ b 1 ϕ b 2 ) f ( ϕ b 3 ) D = ( ϕ b 1 ϕ b 2 ) ( ϕ b 2 ϕ b 3 ) ( ϕ b 3 ϕ b 1 )
b = B 1 + B 2 + B 3 D , c = C 1 + C 2 + C 3 D , a = f ( ϕ b 1 ) c ϕ b 1 2 b ϕ b 1
ϕ ¯ 1 = b 2 c , e ¯ 1 = f ( ϕ ¯ 1 ) = a + b ϕ ¯ 1 + c ϕ ¯ 1 2
| ϕ ¯ K ϕ ¯ K 1 | < ε
e b 2 < m i n ( e b 1 , e b 3 )
{ B E R = { 1 ( 1 2 l o g 2 M ( 1 1 M ) Q [ 3 M 1 E S N 0 ] ) } F F = 1 + l o g 2 M 2 ( M 1 )

Metrics