Abstract

We propose and demonstrate a polarization-time coding (PTC) method which can effectively compensate both the CD and first order PMD in direct-detected OFDM transmission. Compared with the previous methods, the proposed PTC not only alleviates the need for the complex dynamic polarization controller but also exhibits superior transparencies to both the OFDM format and transmission data rate. For the proposed PTC method, we have analytically derived the transmission model with CD and first order PMD, and theoretically prove the PTC indeed can jointly compensate both CD and PMD. The numerical results show that, with the PTC method, both the previously proposed gapped and interleaved OFDM formats behave virtually immune to both CD and PMD with a price of 3-dB OSNR penalty in back-to-back (BtB). Aimed to mitigate this BtB 3-dB penalty, further partial PTC approach is proposed for trading the PMD tolerance with the BtB OSNR sensitivity. The interleaved OFDM system is found to gain profits in terms of lower sensitivity with the partial coding.

©2010 Optical Society of America

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References

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  1. Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, "1-Tb/s per Channel Coherent Optical OFDM Transmission with Subwavelength Bandwidth Access," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPC1.
  2. H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, and H. Tanaka, "DWDM Transmission with 7.0-bit/s/Hz Spectral Efficiency Using 8x65.1-Gbit/s Coherent PDM-OFDM Signals," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPB7.
  3. S. L. Jansen, A. Al Amin, H. Takahashi, I. Morita, and H. Tanaka, “132.2-Gb/s PDM-8QAM-OFDM Transmission at 4-b/s/Hz Spectral Efficiency,” IEEE Photon. Technol. Lett. 21(12), 802–804 (2009).
    [Crossref]
  4. B. J. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, "100 Gbit/s Transimssion Using Single-Band Direct-Detection Optical OFDM," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPC3.
  5. A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “Polarization multiplexed 100 Gbps direct detection OFDM transmission without MIMO processing,” ECOC’09, paper 1.3.1.
  6. W.-R. Peng, X. Wu, V. R. Arbab, K.-M. Feng, B. Shamee, L. C. Christen, J.-Y. Yang, A. E. Willner, and S. Chi, “Theoretical and experimental investigations of direct-detected RF-tone assisted optical OFDM systems,” J. Lightwave Technol. 27(10), 1332–1339 (2009).
    [Crossref]
  7. W.-R. Peng, X. Wu, K.-M. Feng, V. R. Arbab, B. Shamee, J.-Y. Yang, L. C. Christen, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission employing an iterative estimation and cancellation technique,” Opt. Express 17(11), 9099–9111 (2009).
    [Crossref] [PubMed]
  8. M. Mayrock and H. Haunstein, “PMD Tolerant Direct-Detection Optical OFDM System,” ECOC’07, paper 5.2.5.
  9. C. Xie, "PMD Insensitive Direct-Detection Optical OFDM Systems Using Self-Polarization Diversity," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OMM2.
  10. W.-R Peng, K.-M. Feng, and S. Chi, “Joint CD and PMD compensation for direct-detected optical OFDM using polarization-time coding approach,” ECOC’09, paper 2.3.2.
  11. C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, “Fading in lightwave systems due to polarization mode dispersion,” IEEE Photon. Technol. Lett. 3(1), 68–70 (1991).
    [Crossref]
  12. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Impact of PMD in Single-Receiver and Polarization-Diverse Direct-Detection Optical OFDM,” J. Lightwave Technol. 27(14), 2792–2799 (2009).
    [Crossref]
  13. S. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Comm. 16(8), 1451–1458 (1998).
    [Crossref]
  14. Y. Han, and G. Li, “Polarization diversity transmitter and optical nonlinearity mitigation using polarization time coding,” in Proc. COTA 2006, Paper no. CThC7, Whistler, Canada, 2006.
  15. I. B. Djordjevic, L. Xu, and T. Wang, “Alamouti-type polarization-time coding in coded-modulation schemes with coherent detection,” Opt. Express 16(18), 14163–14172 (2008).
    [Crossref] [PubMed]
  16. B. J. Schmidt, A. J. Lowery, and L. B. Du, "Low Sample Rate Transmitter for Direct-Detection Optical OFDM," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OWM4.
  17. W.-R. Peng, K.-M. Feng, A. E. Willner, and S. Chi, “Estimation of the bit error rate for direct-detected OFDM signals with optically pre-amplified receivers,” J. Lightwave Technol. 27(10), 1340–1346 (2009).
    [Crossref]
  18. N. Cvijetic, S. G. Wilson, and D. Qian, “System outage probability due to PMD in high-speed optical OFDM transmission,” J. Lightwave Technol. 26(14), 2118–2127 (2008).
    [Crossref]

2009 (5)

2008 (2)

1998 (1)

S. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Comm. 16(8), 1451–1458 (1998).
[Crossref]

1991 (1)

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, “Fading in lightwave systems due to polarization mode dispersion,” IEEE Photon. Technol. Lett. 3(1), 68–70 (1991).
[Crossref]

Al Amin, A.

S. L. Jansen, A. Al Amin, H. Takahashi, I. Morita, and H. Tanaka, “132.2-Gb/s PDM-8QAM-OFDM Transmission at 4-b/s/Hz Spectral Efficiency,” IEEE Photon. Technol. Lett. 21(12), 802–804 (2009).
[Crossref]

Alamouti, S.

S. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Comm. 16(8), 1451–1458 (1998).
[Crossref]

Arbab, V. R.

Armstrong, J.

Chi, S.

Chraplyvy, A. R.

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, “Fading in lightwave systems due to polarization mode dispersion,” IEEE Photon. Technol. Lett. 3(1), 68–70 (1991).
[Crossref]

Christen, L. C.

Cvijetic, N.

Djordjevic, I. B.

Feng, K.-M.

Fishman, D. A.

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, “Fading in lightwave systems due to polarization mode dispersion,” IEEE Photon. Technol. Lett. 3(1), 68–70 (1991).
[Crossref]

Jansen, S. L.

S. L. Jansen, A. Al Amin, H. Takahashi, I. Morita, and H. Tanaka, “132.2-Gb/s PDM-8QAM-OFDM Transmission at 4-b/s/Hz Spectral Efficiency,” IEEE Photon. Technol. Lett. 21(12), 802–804 (2009).
[Crossref]

Lowery, A. J.

Morita, I.

S. L. Jansen, A. Al Amin, H. Takahashi, I. Morita, and H. Tanaka, “132.2-Gb/s PDM-8QAM-OFDM Transmission at 4-b/s/Hz Spectral Efficiency,” IEEE Photon. Technol. Lett. 21(12), 802–804 (2009).
[Crossref]

Peng, W.-R.

Poole, C. D.

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, “Fading in lightwave systems due to polarization mode dispersion,” IEEE Photon. Technol. Lett. 3(1), 68–70 (1991).
[Crossref]

Qian, D.

Schmidt, B. J. C.

Shamee, B.

Takahashi, H.

S. L. Jansen, A. Al Amin, H. Takahashi, I. Morita, and H. Tanaka, “132.2-Gb/s PDM-8QAM-OFDM Transmission at 4-b/s/Hz Spectral Efficiency,” IEEE Photon. Technol. Lett. 21(12), 802–804 (2009).
[Crossref]

Tanaka, H.

S. L. Jansen, A. Al Amin, H. Takahashi, I. Morita, and H. Tanaka, “132.2-Gb/s PDM-8QAM-OFDM Transmission at 4-b/s/Hz Spectral Efficiency,” IEEE Photon. Technol. Lett. 21(12), 802–804 (2009).
[Crossref]

Tkach, R. W.

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, “Fading in lightwave systems due to polarization mode dispersion,” IEEE Photon. Technol. Lett. 3(1), 68–70 (1991).
[Crossref]

Wang, T.

Willner, A. E.

Wilson, S. G.

Wu, X.

Xu, L.

Yang, J.-Y.

IEEE J. Sel. Areas Comm. (1)

S. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Comm. 16(8), 1451–1458 (1998).
[Crossref]

IEEE Photon. Technol. Lett. (2)

S. L. Jansen, A. Al Amin, H. Takahashi, I. Morita, and H. Tanaka, “132.2-Gb/s PDM-8QAM-OFDM Transmission at 4-b/s/Hz Spectral Efficiency,” IEEE Photon. Technol. Lett. 21(12), 802–804 (2009).
[Crossref]

C. D. Poole, R. W. Tkach, A. R. Chraplyvy, and D. A. Fishman, “Fading in lightwave systems due to polarization mode dispersion,” IEEE Photon. Technol. Lett. 3(1), 68–70 (1991).
[Crossref]

J. Lightwave Technol. (4)

Opt. Express (2)

Other (9)

B. J. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, "100 Gbit/s Transimssion Using Single-Band Direct-Detection Optical OFDM," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPC3.

A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “Polarization multiplexed 100 Gbps direct detection OFDM transmission without MIMO processing,” ECOC’09, paper 1.3.1.

M. Mayrock and H. Haunstein, “PMD Tolerant Direct-Detection Optical OFDM System,” ECOC’07, paper 5.2.5.

C. Xie, "PMD Insensitive Direct-Detection Optical OFDM Systems Using Self-Polarization Diversity," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OMM2.

W.-R Peng, K.-M. Feng, and S. Chi, “Joint CD and PMD compensation for direct-detected optical OFDM using polarization-time coding approach,” ECOC’09, paper 2.3.2.

Y. Han, and G. Li, “Polarization diversity transmitter and optical nonlinearity mitigation using polarization time coding,” in Proc. COTA 2006, Paper no. CThC7, Whistler, Canada, 2006.

B. J. Schmidt, A. J. Lowery, and L. B. Du, "Low Sample Rate Transmitter for Direct-Detection Optical OFDM," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OWM4.

Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, "1-Tb/s per Channel Coherent Optical OFDM Transmission with Subwavelength Bandwidth Access," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPC1.

H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, and H. Tanaka, "DWDM Transmission with 7.0-bit/s/Hz Spectral Efficiency Using 8x65.1-Gbit/s Coherent PDM-OFDM Signals," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPB7.

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Figures (6)

Fig. 1
Fig. 1 Transmitter and receiver methods with the proposed Alamouti-type polarization-time coding (PTC) approach. CW: continuous wave, I/Q: inphase/quadradure, PBC: polarization beam combiner, EDFA: Erbium-doped fiber amplifier, PD: photodiode. RF: radio frequency.
Fig. 2
Fig. 2 (a) Without PTC approach the outer subcarriers, far from the optical carrier, will suffer severely the PMD fading. (b) The proposed partial PTC approach encodes only the outer subcarriers for protecting them from PMD. Nx : number of data subcarriers, Ny : number of protected (encoded) subcarriers.
Fig. 3
Fig. 3 OSNR vs. CSPR with and without PTC for the gapped- (typical) and interleaved-OFDM systems.
Fig. 4
Fig. 4 BER vs. OSNR with and without PTC approach for the (a) gapped OFDM systems and the (b) interleaved OFDM systems. Note that the DGD shown here is the instantaneous value and it can be related to its mean value of <DGD> via DGD ≈3.18<DGD> at an outage probability = 10−5 ;
Fig. 5
Fig. 5 Optimum CSPR and OSNR vs. the coding ratio for (a) gapped OFDM systems and (b) interleave OFDM systems.
Fig. 6
Fig. 6 OSNR sensitivities vs. differential group delay (DGD) for (a) gapped OFDM systems and (b) interleaved OFDM systems. Note that the DGD shown here is the instantaneous value and it can be related to its mean value of <DGD> via DGD ≈3.18<DGD> at an outage probability = 10−5;

Equations (17)

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T 1 ( t ) = [ A + d 1 ( k ) e j 2 π f k t d 2 * ( k ) e j 2 π f k t ]
T 2 ( t ) = [ A + d 2 ( k ) e j 2 π f k t d 1 * ( k ) e j 2 π f k t ]
C 1 ( t ) = [ ( A + d 1 ( k ) e j 2 π f k t ) cos ( φ ) + ( d 2 * ( k ) e j 2 π f k t ) sin ( φ ) ( A + d 1 ( k ) e j 2 π f k t ) sin ( φ ) ( d 2 * ( k ) e j 2 π f k t ) cos ( φ ) ]
C 2 ( t ) = [ ( A + d 2 ( k ) e j 2 π f k t ) cos ( φ ) ( d 1 * ( k ) e j 2 π f k t ) sin ( φ ) ( A + d 2 ( k ) e j 2 π f k t ) sin ( φ ) + ( d 1 * ( k ) e j 2 π f k t ) cos ( φ ) ]
S 1 ( t ) = [ ( A + d 1 ( k ) e j 2 π f k ( t + T d / 2 ) + j θ C D ( k ) ) cos ( φ ) + ( d 2 * ( k ) e j 2 π f k ( t + T d / 2 ) + j θ C D ( k ) ) sin ( φ ) ( A + d 1 ( k ) e j 2 π f k ( t T d / 2 ) + j θ C D ( k ) ) sin ( φ ) ( d 2 * ( k ) e j 2 π f k ( t T d / 2 ) + j θ C D ( k ) ) cos ( φ ) ]
S 2 ( t ) = [ ( A + d 2 ( k ) e j 2 π f k ( t + T d / 2 ) + j θ C D ( k ) ) cos ( φ ) ( d 1 * ( k ) e j 2 π f k ( t + T d / 2 ) + j θ C D ( k ) ) sin ( φ ) ( A + d 2 ( k ) e j 2 π f k ( t T d / 2 ) + j θ C D ( k ) ) sin ( φ ) + ( d 1 * ( k ) e j 2 π f k ( t T d / 2 ) + j θ C D ( k ) ) cos ( φ ) ]
R 1 ( t ) = ( A * d 1 ( k ) [ e j 2 π f k ( t + T d / 2 ) + j θ C D ( k ) cos 2 ( φ ) + e j 2 π f k ( t T d / 2 ) + j θ C D ( k ) sin 2 ( φ ) ] ) + ( A * d 2 * ( k ) [ e j 2 π f k ( t + T d / 2 ) + j θ C D ( k ) e j 2 π f k ( t T d / 2 ) + j θ C D ( k ) ] sin ( φ ) cos ( φ ) )
R 2 ( t ) = ( A * d 2 ( k ) [ e j 2 π f k ( t + T d / 2 ) + j θ C D ( k ) cos 2 ( φ ) + e j 2 π f k ( t T d / 2 ) + j θ C D ( k ) sin 2 ( φ ) ] ) + ( A * d 1 * ( k ) [ e j 2 π f k ( t + T d / 2 ) + j θ C D ( k ) + e j 2 π f k ( t T d / 2 ) + j θ C D ( k ) ] sin ( φ ) cos ( φ ) )
R 1 ( k ) = A * { d 1 ( k ) [ e j π f k T d cos 2 ( φ ) + e j π f k T d sin 2 ( φ ) ] + d 2 * ( k ) [ e j π f k T d e j 2 π f k T d ] sin ( φ ) cos ( φ ) } e j θ C D ( k )
R 2 * ( k ) = A { d 2 * ( k ) [ e j π f k T d cos 2 ( φ ) + e j π f k T d sin 2 ( φ ) ] + d 1 ( k ) [ e j π f k T d + e j π f k T d ] sin ( φ ) cos ( φ ) } e j θ C D ( k )
[ R 1 ( k ) R 2 * ( k ) ] = H ¯ [ d 1 ( k ) d 2 * ( k ) ]
H ¯ = [ A * [ e j π f k T d cos 2 ( φ ) + e j π f k T d sin 2 ( φ ) ] e j θ C D ( k ) A * [ e j π f k T d e j π f k T d ] sin ( φ ) cos ( φ ) e j θ C D ( k ) A [ e j π f k T d + e j π f k T d ] sin ( φ ) cos ( φ ) e j θ C D ( k ) A [ e j π f k T d cos 2 ( φ ) + e j π f k T d sin 2 ( φ ) ] e j θ C D ( k ) ]
[ d 1 ( k ) d 2 * ( k ) ] = H ¯ 1 [ R 1 ( k ) R 2 * ( k ) ]
D e t ( H ¯ ) = | A | 2 [ cos 4 ( θ ) + sin 4 ( θ ) + 2 sin 2 ( θ ) cos 2 ( θ ) ] = | A | 2
α = N y N x
CSPR = | A | 2 ( 1 + α ) N x | d i | 2
OSNR = ( 1 + CSPR ) CSPR  | A | 2 ( 2 N o × B W o )

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