Abstract

We propose a simple, full-range carrier frequency offset (CFO) algorithm for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. By applying the Chinese remainder theorem (CRT) to training symbol of single frequency, the proposed CFO algorithm has wide range with shorter training symbol. We numerically and experimentally demonstrate the performance of CRT-based algorithms in a 16-ary quadrature amplitude modulation (QAM) CO-OFDM system. The results show that the estimation range of the CRT-based algorithm is full-range corresponding to the sampling frequency. Also, the bit error ratio (BER) degradation of the proposed algorithm with one training symbol is negligible. These results indicate that the proposed algorithm can be used as a wide range CFO estimator with an increased data rate in high speed CO-OFDM systems.

© 2013 Optical Society of America

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References

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  1. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett.42(10), 587–589 (2006).
    [CrossRef]
  2. Optical Internetworking Forum, “Integrable Tunable Transmitter Assembly Multi Source Agreement,” OIF-ITTA-MSA-01.0, Nov. (2008).
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    [CrossRef]
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    [CrossRef] [PubMed]
  5. Z. Wang, Y. Qiao, and Y. Ji, “A Novel Joint Frequency Offset and Channel Estimation Method for CO-OFDM System,” Communications and Photonics Conference and Exhibition (ACP) 607–608 (2010).
  6. S. Cao, S. Zhang, Y. Shaoliang, K. Changyuan, and P.-Y. Kam, “Full range pilot-assisted frequency offset estimation for OFDM systems,” in Proceedings of OFC’13, paper JW2A.53.
    [CrossRef]
  7. X.-H. Fan, J. Yu, D. Qian, and G.-K. Chang, “A Fast and Efficient Frequency Offset Correction Technique for Coherent Optical Orthogonal Frequency Division Multiplexing,” J. Lightwave Technol.29(13), 1997–2004 (2011).
    [CrossRef]
  8. X. Zhou, K. Long, R. Li, X. Yang, and Z. Zhang, “A simple and efficient frequency offset estimation algorithm for high-speed coherent optical OFDM systems,” Opt. Express20(7), 7350–7361 (2012).
    [CrossRef] [PubMed]
  9. H. Y. Rha, B. G. Jeon, and H. Choi, “Simple Wide Range Carrier Frequency Offset Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett.24(22), 2064–2066 (2012).
    [CrossRef]
  10. M. Lei, M. Zhao, J. Zhong, and Y. Cai, “ML-Based Estimation Algorithm of Frequency Offset for 2×2 STBC-OFDM Systems,” ETRI J.34(3), 458–461 (2012).
    [CrossRef]
  11. P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun.42(10), 2908–2914 (1994).
    [CrossRef]
  12. R. Bouziane, R. Koutsoyannis, P. Milder, Y. Benlachtar, J. C. Hoe, M. Glick, and R. I. Killey, “Optimizing FFT Precision in Optical OFDM Transceivers,” IEEE Photon. Technol. Lett.23(20), 1550–1552 (2011).
    [CrossRef]
  13. L. Xiang, S. Chandrasekhar, Z. Benyuan, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s Reduced-Guard-Interval CO-OFDM Transmission Over 2000 km of Ultra-Large-Area Fiber and Five 80-GHz-Grid ROADM,” J. Lightwave Technol.29(4), 483–490 (2011).
    [CrossRef]
  14. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express16(26), 21944–21957 (2008).
    [CrossRef] [PubMed]
  15. Z. Xian, Y. Xiaolong, L. Rui, and L. Keping, “Efficient Joint Carrier Frequency Offset and Phase Noise Compensation Scheme for High-Speed Coherent Optical OFDM Systems,” J. Lightwave Technol.31(11), 1755–1761 (2013).
    [CrossRef]
  16. W. Shieh, “Maximum-Likelihood Phase and Channel Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett.20(8), 605–607 (2008).
    [CrossRef]
  17. W. Shieh and I. Djordjevic, “Optical Communication Fundamentals,” in OFDM for Optical Communications, 1-st ed. (Academic Press, 2009).
  18. C.-H. Yih, “BER Analysis of OFDM Systems Impaired by DC Offset and Carrier Frequency Offset in Multipath Fading Channels,” IEEE Commun. Lett.11(11), 842–844 (2007).
    [CrossRef]

2013

2012

X. Zhou, K. Long, R. Li, X. Yang, and Z. Zhang, “A simple and efficient frequency offset estimation algorithm for high-speed coherent optical OFDM systems,” Opt. Express20(7), 7350–7361 (2012).
[CrossRef] [PubMed]

H. Y. Rha, B. G. Jeon, and H. Choi, “Simple Wide Range Carrier Frequency Offset Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett.24(22), 2064–2066 (2012).
[CrossRef]

M. Lei, M. Zhao, J. Zhong, and Y. Cai, “ML-Based Estimation Algorithm of Frequency Offset for 2×2 STBC-OFDM Systems,” ETRI J.34(3), 458–461 (2012).
[CrossRef]

2011

2008

X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express16(26), 21944–21957 (2008).
[CrossRef] [PubMed]

W. Shieh, “Maximum-Likelihood Phase and Channel Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett.20(8), 605–607 (2008).
[CrossRef]

2007

C.-H. Yih, “BER Analysis of OFDM Systems Impaired by DC Offset and Carrier Frequency Offset in Multipath Fading Channels,” IEEE Commun. Lett.11(11), 842–844 (2007).
[CrossRef]

2006

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett.42(10), 587–589 (2006).
[CrossRef]

1997

T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun.45(12), 1613–1621 (1997).
[CrossRef]

1994

P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun.42(10), 2908–2914 (1994).
[CrossRef]

Athaudage, C.

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett.42(10), 587–589 (2006).
[CrossRef]

Benlachtar, Y.

R. Bouziane, R. Koutsoyannis, P. Milder, Y. Benlachtar, J. C. Hoe, M. Glick, and R. I. Killey, “Optimizing FFT Precision in Optical OFDM Transceivers,” IEEE Photon. Technol. Lett.23(20), 1550–1552 (2011).
[CrossRef]

Benyuan, Z.

Bouziane, R.

R. Bouziane, R. Koutsoyannis, P. Milder, Y. Benlachtar, J. C. Hoe, M. Glick, and R. I. Killey, “Optimizing FFT Precision in Optical OFDM Transceivers,” IEEE Photon. Technol. Lett.23(20), 1550–1552 (2011).
[CrossRef]

Buchali, F.

Cai, Y.

M. Lei, M. Zhao, J. Zhong, and Y. Cai, “ML-Based Estimation Algorithm of Frequency Offset for 2×2 STBC-OFDM Systems,” ETRI J.34(3), 458–461 (2012).
[CrossRef]

Chandrasekhar, S.

Chang, G.-K.

Choe, J. S.

Choi, H.

H. Y. Rha, B. G. Jeon, and H. Choi, “Simple Wide Range Carrier Frequency Offset Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett.24(22), 2064–2066 (2012).
[CrossRef]

Choi, K. S.

Cox, D. C.

T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun.45(12), 1613–1621 (1997).
[CrossRef]

Fan, X.-H.

Glick, M.

R. Bouziane, R. Koutsoyannis, P. Milder, Y. Benlachtar, J. C. Hoe, M. Glick, and R. I. Killey, “Optimizing FFT Precision in Optical OFDM Transceivers,” IEEE Photon. Technol. Lett.23(20), 1550–1552 (2011).
[CrossRef]

Gnauck, A. H.

Hoe, J. C.

R. Bouziane, R. Koutsoyannis, P. Milder, Y. Benlachtar, J. C. Hoe, M. Glick, and R. I. Killey, “Optimizing FFT Precision in Optical OFDM Transceivers,” IEEE Photon. Technol. Lett.23(20), 1550–1552 (2011).
[CrossRef]

Jeon, B. G.

H. Y. Rha, B. G. Jeon, and H. Choi, “Simple Wide Range Carrier Frequency Offset Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett.24(22), 2064–2066 (2012).
[CrossRef]

Ji, Y.

Z. Wang, Y. Qiao, and Y. Ji, “A Novel Joint Frequency Offset and Channel Estimation Method for CO-OFDM System,” Communications and Photonics Conference and Exhibition (ACP) 607–608 (2010).

Keping, L.

Killey, R. I.

R. Bouziane, R. Koutsoyannis, P. Milder, Y. Benlachtar, J. C. Hoe, M. Glick, and R. I. Killey, “Optimizing FFT Precision in Optical OFDM Transceivers,” IEEE Photon. Technol. Lett.23(20), 1550–1552 (2011).
[CrossRef]

Kim, D. J.

Kim, J.-H.

Koutsoyannis, R.

R. Bouziane, R. Koutsoyannis, P. Milder, Y. Benlachtar, J. C. Hoe, M. Glick, and R. I. Killey, “Optimizing FFT Precision in Optical OFDM Transceivers,” IEEE Photon. Technol. Lett.23(20), 1550–1552 (2011).
[CrossRef]

Kwon, Y.-H.

Lei, M.

M. Lei, M. Zhao, J. Zhong, and Y. Cai, “ML-Based Estimation Algorithm of Frequency Offset for 2×2 STBC-OFDM Systems,” ETRI J.34(3), 458–461 (2012).
[CrossRef]

Li, R.

Liu, X.

Long, K.

Milder, P.

R. Bouziane, R. Koutsoyannis, P. Milder, Y. Benlachtar, J. C. Hoe, M. Glick, and R. I. Killey, “Optimizing FFT Precision in Optical OFDM Transceivers,” IEEE Photon. Technol. Lett.23(20), 1550–1552 (2011).
[CrossRef]

Moose, P. H.

P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun.42(10), 2908–2914 (1994).
[CrossRef]

Nam, E. S.

Peckham, D. W.

Qian, D.

Qiao, Y.

Z. Wang, Y. Qiao, and Y. Ji, “A Novel Joint Frequency Offset and Channel Estimation Method for CO-OFDM System,” Communications and Photonics Conference and Exhibition (ACP) 607–608 (2010).

Rha, H. Y.

H. Y. Rha, B. G. Jeon, and H. Choi, “Simple Wide Range Carrier Frequency Offset Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett.24(22), 2064–2066 (2012).
[CrossRef]

Rui, L.

Schmidl, T. M.

T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun.45(12), 1613–1621 (1997).
[CrossRef]

Shieh, W.

W. Shieh, “Maximum-Likelihood Phase and Channel Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett.20(8), 605–607 (2008).
[CrossRef]

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett.42(10), 587–589 (2006).
[CrossRef]

Wang, Z.

Z. Wang, Y. Qiao, and Y. Ji, “A Novel Joint Frequency Offset and Channel Estimation Method for CO-OFDM System,” Communications and Photonics Conference and Exhibition (ACP) 607–608 (2010).

Winzer, P. J.

Xian, Z.

Xiang, L.

Xiaolong, Y.

Yang, X.

Yih, C.-H.

C.-H. Yih, “BER Analysis of OFDM Systems Impaired by DC Offset and Carrier Frequency Offset in Multipath Fading Channels,” IEEE Commun. Lett.11(11), 842–844 (2007).
[CrossRef]

Youn, C. J.

Yu, J.

Zhang, Z.

Zhao, M.

M. Lei, M. Zhao, J. Zhong, and Y. Cai, “ML-Based Estimation Algorithm of Frequency Offset for 2×2 STBC-OFDM Systems,” ETRI J.34(3), 458–461 (2012).
[CrossRef]

Zhong, J.

M. Lei, M. Zhao, J. Zhong, and Y. Cai, “ML-Based Estimation Algorithm of Frequency Offset for 2×2 STBC-OFDM Systems,” ETRI J.34(3), 458–461 (2012).
[CrossRef]

Zhou, X.

Electron. Lett.

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett.42(10), 587–589 (2006).
[CrossRef]

ETRI J.

M. Lei, M. Zhao, J. Zhong, and Y. Cai, “ML-Based Estimation Algorithm of Frequency Offset for 2×2 STBC-OFDM Systems,” ETRI J.34(3), 458–461 (2012).
[CrossRef]

IEEE Commun. Lett.

C.-H. Yih, “BER Analysis of OFDM Systems Impaired by DC Offset and Carrier Frequency Offset in Multipath Fading Channels,” IEEE Commun. Lett.11(11), 842–844 (2007).
[CrossRef]

IEEE Photon. Technol. Lett.

R. Bouziane, R. Koutsoyannis, P. Milder, Y. Benlachtar, J. C. Hoe, M. Glick, and R. I. Killey, “Optimizing FFT Precision in Optical OFDM Transceivers,” IEEE Photon. Technol. Lett.23(20), 1550–1552 (2011).
[CrossRef]

H. Y. Rha, B. G. Jeon, and H. Choi, “Simple Wide Range Carrier Frequency Offset Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett.24(22), 2064–2066 (2012).
[CrossRef]

W. Shieh, “Maximum-Likelihood Phase and Channel Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett.20(8), 605–607 (2008).
[CrossRef]

IEEE Trans. Commun.

P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun.42(10), 2908–2914 (1994).
[CrossRef]

T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun.45(12), 1613–1621 (1997).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Other

Z. Wang, Y. Qiao, and Y. Ji, “A Novel Joint Frequency Offset and Channel Estimation Method for CO-OFDM System,” Communications and Photonics Conference and Exhibition (ACP) 607–608 (2010).

S. Cao, S. Zhang, Y. Shaoliang, K. Changyuan, and P.-Y. Kam, “Full range pilot-assisted frequency offset estimation for OFDM systems,” in Proceedings of OFC’13, paper JW2A.53.
[CrossRef]

Optical Internetworking Forum, “Integrable Tunable Transmitter Assembly Multi Source Agreement,” OIF-ITTA-MSA-01.0, Nov. (2008).

W. Shieh and I. Djordjevic, “Optical Communication Fundamentals,” in OFDM for Optical Communications, 1-st ed. (Academic Press, 2009).

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Figures (9)

Fig. 1
Fig. 1

(a) The training symbol structure for the previous CRT-based CFO algorithm; S1, and S2 are subsymbols and CP is cyclic prefix. The proposed training symbol structure with (b) one, or (c) two training symbols.

Fig. 2
Fig. 2

The schematic of the DSP structures of (a) transmitter, and (b) receiver, (c) frame format for dual polarization and (d) experimental setup; LD: laser diode; EDFA: Erbium-doped fiber amplifier; ASE: Amplified spontaneous emission source; PC: polarization controller; OSA: optical spectrum analyzer; ECL: external cavity laser, OFDE: overlapped frequency domain equalizer, TS: Training symbol for CFO estimation, GI: Guard interval; OFDE was applied only in simulation.

Fig. 3
Fig. 3

CFO monitoring in frequency domain.

Fig. 4
Fig. 4

BER as a function of CFO.

Fig. 5
Fig. 5

MSEE as a function of OSNR in the absence of CFO.

Fig. 6
Fig. 6

BER as a function of OSNR in the absence of CFO.

Fig. 7
Fig. 7

Estimated CFO and estimation error as a function of monitored CFO; (a) Zhou’s algorithm [8] with the sample interval of four; (b) previous CRT-based algorithm; (c) proposed algorithm with two training symbols; (d) proposed algorithm with one training symbol. The real lines are the expected CFO values.

Fig. 8
Fig. 8

MSEE as a function of monitored CFO.

Fig. 9
Fig. 9

BER as a function of monitored CFO.

Equations (9)

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

r(n)= e j2πnΔf T s s(n)+η(n)
ε ^ =Δ f ^ N T s = N 2πL angle( P L ), P L = m=0 L1 (r (m) * r(m+L))
CRB( ε ^ )=CRB(Δ f ^ N T s )= 1 π 2 1 LSNR .
ε ^ L i = L 2π L i angle( P L i ) for i=1 and 2, ε ^ L = 1 2π angle( P L )
ε ^ I = ε ^ L 1 L 1 ( L 1 1 mod L 2 )+ ε ^ L 2 L 2 ( L 2 1 mod L 1 ).
t(n)= t 0 e jn φ S , for n=0, 1,, N TS 1
r(n)= t 0 e jn( φ S +2πΔf T S ) +η(n).
ε ^ L i = L 2π L i (angle( P L i ) φ S L i ) for i=1 and 2, ε ^ L = 1 2π (angle( P L ) - φ S L).
Δ φ sample 2 = 2πΔν T S L .

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