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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  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.
  12. 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.
  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 (1)

2010 (4)

2009 (7)

2008 (1)

2007 (1)

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. (1)

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. (1)

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. (1)

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. (7)

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]

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]

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]

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]

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]

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]

Opt. Express (3)

Opt. Fiber Technol. (1)

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 (6)

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.

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.

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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