Abstract

This paper presents a new channel estimation/equalization algorithm for coherent OFDM (CO-OFDM) digital receivers, which enables the elimination of the cyclic prefix (CP) for OFDM transmission. We term this new system as the zero-guard-interval (ZGI)-CO-OFDM. ZGI-CO-OFDM employs an overlapped frequency-domain equalizer (OFDE) to compensate both chromatic dispersion (CD) and polarization mode dispersion (PMD) before the OFDM demodulation. Despite the zero CP overhead, ZGI-CO-OFDM demonstrates a superior PMD tolerance than the previous reduced-GI (RGI)-CO-OFDM, which is verified under several different PMD conditions. Additionally, ZGI-CO-OFDM can improve the channel estimation accuracy under high PMD conditions by using a larger intra-symbol frequency-averaging (ISFA) length as compared to RGI-CO-OFDM. ZGI-CO-OFDM also enables the use of ever smaller fast Fourier transform (FFT) sizes (i.e. <128), while maintaining the zero CP overhead. Finally, we provide an analytical comparison of the computation complexity between the conventional, RGI- and ZGI- CO-OFDM. We show that ZGI-CO-OFDM requires reasonably small additional computation effort (~13.6%) compared to RGI-CO-OFDM for 112-Gb/s transmission over a 1600-km dispersion-uncompensated optical link.

© 2011 OSA

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References

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  1. Y. Qi, T. Yan, M. Yiran, and W. Shieh, “Experimental demonstration and numerical simulation of 107-Gb/s high spectral efficiency coherent optical OFDM,” J. Lightwave Technol. 27(3), 168–176 (2009).
    [CrossRef]
  2. S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1000 km of SSMF,” J. Lightwave Technol. 27(3), 177–188 (2009).
    [CrossRef]
  3. Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009).
    [CrossRef] [PubMed]
  4. X. Liu, S. Chandrasekhar, B. Zhu, 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 ROADMs,” J. Lightwave Technol. 29(4), 483–490 (2011).
    [CrossRef]
  5. H. Takahashi, K. Takeshima, I. Morita, and H. Tanaka, “400-Gbit/s optical OFDM transmission over 80 km in 50-GHz frequency grid,” in Proceedings of ECOC’10, Torino, Italy (2010), paper Tu.3.C.1.
  6. S. L. Jansen, B. Spinnler, I. Morita, S. Randel, and H. Tanaka, “100 GbE: QPSK versus OFDM,” Opt. Fiber Technol. 15(5-6), 407–413 (2009).
    [CrossRef]
  7. A. Barbieri, G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “OFDM versus single-carrier transmission for 100 Gbps optical communication,” J. Lightwave Technol. 28(17), 2537–2551 (2010).
    [CrossRef]
  8. B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE Sel. Top. J. Quantum Electron. 16(5), 1180–1192 (2010).
    [CrossRef]
  9. R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
    [CrossRef]
  10. L. B. Du, and A. J. Lowery, “Mitigation of dispersion penalty for short-cyclic prefix coherent optical OFDM systems,” in Proceedings of ECOC’10, Torino, Italy (2010), paper Tu.4.A.5.
  11. C. Chen, Q, Zhuge and D. V. Plant, “Reduced-guard-interval CO-OFDM with overlapped frequency-domain CD and PMD equalization,” in Proceedings of OFC’11, Los Angeles, CA (2011), paper OWE7.
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  13. S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” in Proceedings of ECOC’09, Vienna, Austria, PD2.6. (2009).
  14. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express 16(26), 21944–21957 (2008).
    [CrossRef] [PubMed]
  15. Y. Ma, W. Shieh, and X. Yi, “Characterization of nonlinearity performance for coherent optical OFDM signals under influence of PMD,” Electron. Lett. 43(17), 943–945 (2007).
    [CrossRef]
  16. Q. Yang, N. Kaneda, X. Liu, and W. Shieh, “Demonstration of frequency-domain averaging based channel estimation for 40-Gb/s CO-OFDM with high PMD,” IEEE Photon. Technol. Lett. 21(20), 1544–1546 (2009).
    [CrossRef]
  17. M. E. Mousa-Pasandi and D. V. Plant, “Zero-overhead phase noise compensation via decision-directed phase equalizer for coherent optical OFDM,” Opt. Express 18(20), 20651–20660 (2010).
    [CrossRef] [PubMed]
  18. Q. Zhuge, C. Chen, and D. V. Plant, “Impact of intra-channel fiber nonlinearity on reduced-guard-interval CO-OFDM transmission,” in Proceedings of OFC’11, Los Angeles, CA (2011), paper OWO3.
  19. S. Chen, Q. Yang, Y. Ma, and W. Shieh, “Real-time multi-gigabit receiver for coherent optical MIMO-OFDM signals,” J. Lightwave Technol. 27(16), 3699–3704 (2009).
    [CrossRef]
  20. N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y.-K. Chen, “Real-time 2.5 GS/s coherent optical receiver for 53.3-Gb/s sub-banded OFDM,” J. Lightwave Technol. 28(4), 494–501 (2010).
    [CrossRef]

2011

2010

2009

2008

2007

Y. Ma, W. Shieh, and X. Yi, “Characterization of nonlinearity performance for coherent optical OFDM signals under influence of PMD,” Electron. Lett. 43(17), 943–945 (2007).
[CrossRef]

Barbieri, A.

Buchali, F.

Chandrasekhar, S.

Chen, S.

Chen, Y.-K.

Colavolpe, G.

Foggi, T.

Forestieri, E.

Gnauck, A. H.

Ishihara, K.

Jansen, S. L.

Kaneda, N.

N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y.-K. Chen, “Real-time 2.5 GS/s coherent optical receiver for 53.3-Gb/s sub-banded OFDM,” J. Lightwave Technol. 28(4), 494–501 (2010).
[CrossRef]

Q. Yang, N. Kaneda, X. Liu, and W. Shieh, “Demonstration of frequency-domain averaging based channel estimation for 40-Gb/s CO-OFDM with high PMD,” IEEE Photon. Technol. Lett. 21(20), 1544–1546 (2009).
[CrossRef]

Kobayashi, T.

Kudo, R.

Liu, X.

Ma, Y.

Miyamoto, Y.

Morita, I.

Mousa-Pasandi, M. E.

Peckham, D. W.

Plant, D. V.

Prati, G.

Qi, Y.

Randel, S.

S. L. Jansen, B. Spinnler, I. Morita, S. Randel, and H. Tanaka, “100 GbE: QPSK versus OFDM,” Opt. Fiber Technol. 15(5-6), 407–413 (2009).
[CrossRef]

Sano, A.

Schenk, T. C. W.

Shieh, W.

Spinnler, B.

B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE Sel. Top. J. Quantum Electron. 16(5), 1180–1192 (2010).
[CrossRef]

S. L. Jansen, B. Spinnler, I. Morita, S. Randel, and H. Tanaka, “100 GbE: QPSK versus OFDM,” Opt. Fiber Technol. 15(5-6), 407–413 (2009).
[CrossRef]

Takatori, Y.

Tanaka, H.

Tang, Y.

Winzer, P. J.

Yan, T.

Yang, Q.

Yi, X.

Y. Ma, W. Shieh, and X. Yi, “Characterization of nonlinearity performance for coherent optical OFDM signals under influence of PMD,” Electron. Lett. 43(17), 943–945 (2007).
[CrossRef]

Yiran, M.

Zhu, B.

Electron. Lett.

Y. Ma, W. Shieh, and X. Yi, “Characterization of nonlinearity performance for coherent optical OFDM signals under influence of PMD,” Electron. Lett. 43(17), 943–945 (2007).
[CrossRef]

IEEE Photon. Technol. Lett.

Q. Yang, N. Kaneda, X. Liu, and W. Shieh, “Demonstration of frequency-domain averaging based channel estimation for 40-Gb/s CO-OFDM with high PMD,” IEEE Photon. Technol. Lett. 21(20), 1544–1546 (2009).
[CrossRef]

IEEE Sel. Top. J. Quantum Electron.

B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE Sel. Top. J. Quantum Electron. 16(5), 1180–1192 (2010).
[CrossRef]

J. Lightwave Technol.

S. Chen, Q. Yang, Y. Ma, and W. Shieh, “Real-time multi-gigabit receiver for coherent optical MIMO-OFDM signals,” J. Lightwave Technol. 27(16), 3699–3704 (2009).
[CrossRef]

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
[CrossRef]

N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y.-K. Chen, “Real-time 2.5 GS/s coherent optical receiver for 53.3-Gb/s sub-banded OFDM,” J. Lightwave Technol. 28(4), 494–501 (2010).
[CrossRef]

Y. Qi, T. Yan, M. Yiran, and W. Shieh, “Experimental demonstration and numerical simulation of 107-Gb/s high spectral efficiency coherent optical OFDM,” J. Lightwave Technol. 27(3), 168–176 (2009).
[CrossRef]

S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1000 km of SSMF,” J. Lightwave Technol. 27(3), 177–188 (2009).
[CrossRef]

A. Barbieri, G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “OFDM versus single-carrier transmission for 100 Gbps optical communication,” J. Lightwave Technol. 28(17), 2537–2551 (2010).
[CrossRef]

X. Liu, S. Chandrasekhar, B. Zhu, 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 ROADMs,” J. Lightwave Technol. 29(4), 483–490 (2011).
[CrossRef]

Opt. Express

Opt. Fiber Technol.

S. L. Jansen, B. Spinnler, I. Morita, S. Randel, and H. Tanaka, “100 GbE: QPSK versus OFDM,” Opt. Fiber Technol. 15(5-6), 407–413 (2009).
[CrossRef]

Other

H. Takahashi, K. Takeshima, I. Morita, and H. Tanaka, “400-Gbit/s optical OFDM transmission over 80 km in 50-GHz frequency grid,” in Proceedings of ECOC’10, Torino, Italy (2010), paper Tu.3.C.1.

Q. Zhuge, C. Chen, and D. V. Plant, “Impact of intra-channel fiber nonlinearity on reduced-guard-interval CO-OFDM transmission,” in Proceedings of OFC’11, Los Angeles, CA (2011), paper OWO3.

L. B. Du, and A. J. Lowery, “Mitigation of dispersion penalty for short-cyclic prefix coherent optical OFDM systems,” in Proceedings of ECOC’10, Torino, Italy (2010), paper Tu.4.A.5.

C. Chen, Q, Zhuge and D. V. Plant, “Reduced-guard-interval CO-OFDM with overlapped frequency-domain CD and PMD equalization,” in Proceedings of OFC’11, Los Angeles, CA (2011), paper OWE7.

A. Sano, Y. Takatori, and Y. Miyamoto, “No-guard-interval coherent optical OFDM for 100-Gb/s/ch long-haul transmission systems,” in Proceedings of OFC’09, San Diego, USA (2009), paper OTuO3.

S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” in Proceedings of ECOC’09, Vienna, Austria, PD2.6. (2009).

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Figures (12)

Fig. 1
Fig. 1

(a) CO-OFDM receiver structure and (b) OFDM frame. ADC: analog-digital converter, S/P: serial to parallel.

Fig. 2
Fig. 2

(a) Schematic of FDI. (b) OFDM spectrum before and after applying HFDI - 1 . The top curve shows the real part of a in the channel matrix H (open dot) and the interpolated channel matrix HFDI (thin line). Phase variations across modulated subcarriers before and after PMD compensation in Step (4) for a (c) deterministic DGD = 320ps and (d) stochastic PMD with <DGD> = 100ps.

Fig. 3
Fig. 3

Q vs. deterministic DGD for three different CO-OFDM systems.

Fig. 4
Fig. 4

Contour plot of the estimated phase variations across modulated subcarriers on x-polarization before (a) and after (b) Step 4. <DGD> = 5 ps is assumed.

Fig. 5
Fig. 5

Contour plot of the estimated phase variations across modulated subcarriers on x-polarization before (a) and after (b) Step 4. <DGD> = 10 ps is assumed.

Fig. 6
Fig. 6

Contour plot of the estimated phase variations across modulated subcarriers on x-polarization before (a) and after (b) Step 4. <DGD> = 25 ps is assumed.

Fig. 7
Fig. 7

Q factor distribution after transmission over a fiber link with 500 different PMD for (a) ZGI-CO-OFDM (0% CP) (b) ZGI-CO-OFDM (0.8% CP) and (c) RGI-CO-OFDM (3.13% CP). We assume <DGD> = 10 ps.

Fig. 9
Fig. 9

Q factor distribution after transmission over a fiber link with 500 different PMD for (a) ZGI-CO-OFDM (0% CP) (b) ZGI-CO-OFDM (0.8% CP) and (c) RGI-CO-OFDM (3.13% CP). We assume <DGD> = 50 ps.

Fig. 8
Fig. 8

Q factor distribution after transmission over a fiber link with 500 different PMD for (a) ZGI-CO-OFDM (0% CP) (b) ZGI-CO-OFDM (0.8% CP) and (c) RGI-CO-OFDM (3.13% CP). We assume <DGD> = 25 ps.

Fig. 10
Fig. 10

Q vs. ISFA length m for 3 different deterministic DGD values for (a) RGI and (c) ZGI CO-OFDM.

Fig. 11
Fig. 11

Q vs. NFFT with different deterministic DGD values. The launch power of −2 dBm and the laser linewidth of 100 kHz are assumed.

Fig. 12
Fig. 12

(a) Number of complex multiplications per useful bit as a function of NFFT for the conventional, RGI- and ZGI-CO-OFDM. (b) Percentage of extra computation complexity of ZGI- over RGI- CO-OFDM, as a function of NOFDE and oversampling factor.

Tables (3)

Tables Icon

Table 1 Comparison of the Conventional, RGI-, and ZGI-CO-OFDM

Tables Icon

Table 2 Number of Complex Multiplications for Conventional, RGI-, and ZGI-CO-OFDM for Each Polarization

Tables Icon

Table 3 Total Number of Complex Multiplications for Each Useful Bit for Each Polarization

Equations (10)

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

H c d [ k O F D E ] = e j D L λ 2 ( k O F D E N O F D E / 2 ) Δ f n / c , k O F D E = 1 , , N O F D E ,
H [ k ] = ( a [ k ] b [ k ] c [ k ] c [ k ] ) , k = 1 , , N s c .
H F D I [ k ' ] = ( a F D I [ k ' ] b F D I [ k ' ] c F D I [ k ' ] c F D I [ k ' ] ) , k ' = 1 , , N S C ( N O F D E / N F F T ) .
r o u t [ k ] = H c d 1 H F D I 1 H ' [ k ] 1 r i n [ k ] .
r o u t [ k ] = H c d 1 H R G I [ k ] 1 r i n [ k ] .
r o u t [ k ] = H C O N V [ k ] 1 r i n [ k ] .
m < 10 6 N S C 8 π Δ f O F D M 2 | C D I S F A | ,
m < 10 2 N S C Δ f O F D M | P M D I S F A | ,
N F F T 2 log 2 N F F T + 4 N s c T S % + 2 N s c ( 1 T S % ) + 2 ( N O F D E log 2 N O F D E + 2 N O F D E ) + 2 N O F D E + N s c P S % ( 1 T S % ) + N s c ( 1 P S % ) ( 1 T S % ) = N F F T 2 log 2 N F F T + 3 N s c + N s c T S % + 2 ( N O F D E log 2 N O F D E + 2 N O F D E ) + 2 N O F D E .
N F F T log 2 N F F T / 2 + 3 N s c + N s c T S % N s c log 2 M ( 1 P S % ) + 2 ( N O F D E log 2 N O F D E + 2 N O F D E ) + 2 N O F D E N s c log 2 M ( N O F D E / N F F T ) ( 1 P S % ) = γ log 2 N F F T / 2 + 3 + T S % log 2 M ( 1 P S % ) + 2 γ ( log 2 N O F D E + 2 ) + 2 γ log 2 M ( 1 P S % ) = γ log 2 N F F T / 2 + 3 + T S % + γ ( 2 log 2 N O F D E + 6 ) log 2 M ( 1 P S % ) .

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