Abstract

Transmitter in-phase/quadrature (IQ) mismatch in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems is difficult to mitigate at the receiver using conventional time domain methods such as the Gram-Schmidt orthogonalization procedure, particularly in the presence of channel distortion. In this paper, we present a scheme that mitigates both transmitter IQ mismatch and channel distortion. We propose a pilot structure to estimate both channel and IQ mismatch, and develop a minimum mean square error compensation method. Numerical results show that the proposed method is effective in reducing transmitter IQ mismatch for a CO-OFDM system.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14(9), 3767–3775 (2006).
    [CrossRef] [PubMed]
  2. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
    [CrossRef] [PubMed]
  3. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009).
    [CrossRef]
  4. H. S. Chung, S. H. Chung, and K. Kim, “Effect of IQ mismatch compensation in an optical coherent OFDM receiver,” IEEE Photon. Technol. Lett. 22(5), 308–310 (2010).
    [CrossRef]
  5. X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007).
    [CrossRef]
  6. I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK Coherent Receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
    [CrossRef]
  7. A. A. Amin, H. Takahashi, S. L. Jansen, I. Morita, and H. Tanaka, “Effect of hybrid IQ imbalance compensation in 27.3 Gbit/s direct-detection OFDM transmission,” in Proc. OFC2009, San Diego, CA, 2009, Paper OTuO2.
  8. W. R. Peng, B. Zhang, X. Wu, K. M. Feng, A. E. Willner, and S. Chi, “Compensation for I/Q imbalances and bias deviation of the Mach-Zehnder modulators in direct-detected optical OFDM systems,” IEEE Photon. Technol. Lett. 21(2), 103–105 (2009).
    [CrossRef]
  9. 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 1,000 km of SSMF,” J. Lightwave Technol. 27(3), 177–188 (2009).
    [CrossRef]
  10. S. G. Kang, Y. M. Ha, and E. K. Joo, “A Comparative Investigation on Channel Estimation Algorithms for OFDM in Mobile Communications,” IEEE Trans. Broadcast 49(2), 142–149 (2003).
    [CrossRef]
  11. M. K. Ozdemir and H. Arslan, “Channel Estimation for wireless OFDM systems,” IEEE Comm. Surveys & Tutorials 9(2), 18–48 (2007).
    [CrossRef]

2010 (1)

H. S. Chung, S. H. Chung, and K. Kim, “Effect of IQ mismatch compensation in an optical coherent OFDM receiver,” IEEE Photon. Technol. Lett. 22(5), 308–310 (2010).
[CrossRef]

2009 (3)

J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009).
[CrossRef]

W. R. Peng, B. Zhang, X. Wu, K. M. Feng, A. E. Willner, and S. Chi, “Compensation for I/Q imbalances and bias deviation of the Mach-Zehnder modulators in direct-detected optical OFDM systems,” IEEE Photon. Technol. Lett. 21(2), 103–105 (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 1,000 km of SSMF,” J. Lightwave Technol. 27(3), 177–188 (2009).
[CrossRef]

2008 (2)

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK Coherent Receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[CrossRef]

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
[CrossRef] [PubMed]

2007 (2)

X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007).
[CrossRef]

M. K. Ozdemir and H. Arslan, “Channel Estimation for wireless OFDM systems,” IEEE Comm. Surveys & Tutorials 9(2), 18–48 (2007).
[CrossRef]

2006 (1)

2003 (1)

S. G. Kang, Y. M. Ha, and E. K. Joo, “A Comparative Investigation on Channel Estimation Algorithms for OFDM in Mobile Communications,” IEEE Trans. Broadcast 49(2), 142–149 (2003).
[CrossRef]

Armstrong, J.

Arslan, H.

M. K. Ozdemir and H. Arslan, “Channel Estimation for wireless OFDM systems,” IEEE Comm. Surveys & Tutorials 9(2), 18–48 (2007).
[CrossRef]

Bao, H.

Chi, S.

W. R. Peng, B. Zhang, X. Wu, K. M. Feng, A. E. Willner, and S. Chi, “Compensation for I/Q imbalances and bias deviation of the Mach-Zehnder modulators in direct-detected optical OFDM systems,” IEEE Photon. Technol. Lett. 21(2), 103–105 (2009).
[CrossRef]

Chung, H. S.

H. S. Chung, S. H. Chung, and K. Kim, “Effect of IQ mismatch compensation in an optical coherent OFDM receiver,” IEEE Photon. Technol. Lett. 22(5), 308–310 (2010).
[CrossRef]

Chung, S. H.

H. S. Chung, S. H. Chung, and K. Kim, “Effect of IQ mismatch compensation in an optical coherent OFDM receiver,” IEEE Photon. Technol. Lett. 22(5), 308–310 (2010).
[CrossRef]

Djordjevic, I. B.

Fatadin, I.

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK Coherent Receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[CrossRef]

Feng, K. M.

W. R. Peng, B. Zhang, X. Wu, K. M. Feng, A. E. Willner, and S. Chi, “Compensation for I/Q imbalances and bias deviation of the Mach-Zehnder modulators in direct-detected optical OFDM systems,” IEEE Photon. Technol. Lett. 21(2), 103–105 (2009).
[CrossRef]

Ha, Y. M.

S. G. Kang, Y. M. Ha, and E. K. Joo, “A Comparative Investigation on Channel Estimation Algorithms for OFDM in Mobile Communications,” IEEE Trans. Broadcast 49(2), 142–149 (2003).
[CrossRef]

Ives, D.

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK Coherent Receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[CrossRef]

Jansen, S. L.

Joo, E. K.

S. G. Kang, Y. M. Ha, and E. K. Joo, “A Comparative Investigation on Channel Estimation Algorithms for OFDM in Mobile Communications,” IEEE Trans. Broadcast 49(2), 142–149 (2003).
[CrossRef]

Kang, S. G.

S. G. Kang, Y. M. Ha, and E. K. Joo, “A Comparative Investigation on Channel Estimation Algorithms for OFDM in Mobile Communications,” IEEE Trans. Broadcast 49(2), 142–149 (2003).
[CrossRef]

Kim, K.

H. S. Chung, S. H. Chung, and K. Kim, “Effect of IQ mismatch compensation in an optical coherent OFDM receiver,” IEEE Photon. Technol. Lett. 22(5), 308–310 (2010).
[CrossRef]

Morita, I.

Ozdemir, M. K.

M. K. Ozdemir and H. Arslan, “Channel Estimation for wireless OFDM systems,” IEEE Comm. Surveys & Tutorials 9(2), 18–48 (2007).
[CrossRef]

Peng, W. R.

W. R. Peng, B. Zhang, X. Wu, K. M. Feng, A. E. Willner, and S. Chi, “Compensation for I/Q imbalances and bias deviation of the Mach-Zehnder modulators in direct-detected optical OFDM systems,” IEEE Photon. Technol. Lett. 21(2), 103–105 (2009).
[CrossRef]

Savory, S. J.

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK Coherent Receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[CrossRef]

Schenk, T. C. W.

Shieh, W.

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
[CrossRef] [PubMed]

X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007).
[CrossRef]

Tanaka, H.

Tang, Y.

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
[CrossRef] [PubMed]

X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007).
[CrossRef]

Vasic, B.

Willner, A. E.

W. R. Peng, B. Zhang, X. Wu, K. M. Feng, A. E. Willner, and S. Chi, “Compensation for I/Q imbalances and bias deviation of the Mach-Zehnder modulators in direct-detected optical OFDM systems,” IEEE Photon. Technol. Lett. 21(2), 103–105 (2009).
[CrossRef]

Wu, X.

W. R. Peng, B. Zhang, X. Wu, K. M. Feng, A. E. Willner, and S. Chi, “Compensation for I/Q imbalances and bias deviation of the Mach-Zehnder modulators in direct-detected optical OFDM systems,” IEEE Photon. Technol. Lett. 21(2), 103–105 (2009).
[CrossRef]

Yi, X.

X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007).
[CrossRef]

Zhang, B.

W. R. Peng, B. Zhang, X. Wu, K. M. Feng, A. E. Willner, and S. Chi, “Compensation for I/Q imbalances and bias deviation of the Mach-Zehnder modulators in direct-detected optical OFDM systems,” IEEE Photon. Technol. Lett. 21(2), 103–105 (2009).
[CrossRef]

IEEE Comm. Surveys & Tutorials (1)

M. K. Ozdemir and H. Arslan, “Channel Estimation for wireless OFDM systems,” IEEE Comm. Surveys & Tutorials 9(2), 18–48 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

H. S. Chung, S. H. Chung, and K. Kim, “Effect of IQ mismatch compensation in an optical coherent OFDM receiver,” IEEE Photon. Technol. Lett. 22(5), 308–310 (2010).
[CrossRef]

X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007).
[CrossRef]

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK Coherent Receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008).
[CrossRef]

W. R. Peng, B. Zhang, X. Wu, K. M. Feng, A. E. Willner, and S. Chi, “Compensation for I/Q imbalances and bias deviation of the Mach-Zehnder modulators in direct-detected optical OFDM systems,” IEEE Photon. Technol. Lett. 21(2), 103–105 (2009).
[CrossRef]

IEEE Trans. Broadcast (1)

S. G. Kang, Y. M. Ha, and E. K. Joo, “A Comparative Investigation on Channel Estimation Algorithms for OFDM in Mobile Communications,” IEEE Trans. Broadcast 49(2), 142–149 (2003).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Express (2)

Other (1)

A. A. Amin, H. Takahashi, S. L. Jansen, I. Morita, and H. Tanaka, “Effect of hybrid IQ imbalance compensation in 27.3 Gbit/s direct-detection OFDM transmission,” in Proc. OFC2009, San Diego, CA, 2009, Paper OTuO2.

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 (6)

Fig. 1
Fig. 1

Baseband equivalent of the CO-OFDM system.

Fig. 2
Fig. 2

Back-to-back CO-OFDM with ϵ = 0.7 and ϕ = 25 ° IQ mismatch: (a) received signal, (b) equalization only, (c) GSOP compensation and equalization, and (d) proposed IQ compensation and equalization.

Fig. 3
Fig. 3

200-km SSMF CO-OFDM with ϵ = 0.7 and ϕ = 25 ° IQ mismatch: (a) received signal, (b) equalization only, (c) GSOP compensation and equalization, and (d) proposed IQ compensation and equalization.

Fig. 4
Fig. 4

OSNR penalty versus IQ mismatch (200-km SSMF, target BER = 10−3).

Fig. 5
Fig. 5

Performance compassion: MMSE and ZF equalizers (300-km SSMF, target BER = 10−3).

Fig. 6
Fig. 6

OSNR penalty versus CD (SSMF length) for 25° IQ imbalance (target BER = 10−3).

Equations (22)

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

x k = W H s k .
x i q ( t ) = G 1 x ( t ) + G 2 x * ( t ) ,
x k = G 1 W H s k + G 2 W s k * .
m = 0 N 1 s k * ( m ) e j 2 π n m N = m = 0 N 1 s k * ( mod ( N m , N ) ) e j 2 π n m N ,
x k = G 1 W H s k + G 2 W H s ¯ k * ,
s ¯ k * ( n ) = s k * ( m o d ( N n ) , N ) ) .
r k = W C x k + w k .
r k = G 1 W C W H s k + G 2 W C W H s ¯ k * + w k = G 1 Λ c s k + G 2 Λ c s ¯ k * + w k = G 1 Λ c ( s k + G 2 G 1 s ¯ k * ) + w k = Λ ( s k + G s ¯ k * ) + w k ,
Λ : = G 1 Λ c   and   G : = G 2 G 1 = 1 ϵ e j ϕ 1 + ϵ e j ϕ .
p k ( n ) = { 0 i f n = M i + N N / M M p ( i ) i f n = M i               s ( m ) e l s e                    
r k ( n ) = { Λ ( n ) s k ( n ) + w k ( n ) n A Λ ( n ) G s k * ( n ¯ ) + w k ( n ) n A ¯ Λ ( n ) ( s k ( n ) + G s k * ( n ¯ ) ) + w k ( n ) e l s e
n ¯ : = m o d ( N n , N ) .
G ^ = 1 | A ¯ | n A ¯ r ( n ) Λ ( n ) s * ( n ) .
f Z F ( n ) r ( n ) + g Z F ( n ) r * ( n ¯ ) = f Λ ( n ) ( s k ( n ) + G s k * ( n ¯ ) ) + g Λ * ( n ¯ ) ( s k * ( n ¯ ) + G s k ( n ) ) = s ( n )
( f ( n ) , g ( n ) ) M M S E = arg min f , g E | f r ( n ) + g r * ( n ¯ ) s ( n ) | 2
= arg min f , g | f Λ ( n ) + g Λ * ( n ¯ ) G * 1 | 2 σ s 2 + | f Λ ( n ) G + g Λ * ( n ¯ ) | 2 σ s 2 + σ w 2 ( | f | 2 + | g | 2 )
λ : = σ w 2 σ s 2
[ | Λ ( n ) | 2 ( 1 + | G | 2 ) + λ 2 Λ * ( n ) Λ * ( n ¯ ) G * 2 Λ ( n ) Λ ( n ¯ ) G | Λ ( n ¯ ) | 2 ( 1 + | G | 2 ) + λ ] [ f M M S E ( n ) g M M S E ( n ) ] = [ Λ * ( n ) Λ ( n ¯ ) G ]
f M M S E ( n ) = Λ * ( n ) ( | Λ ( n ¯ ) | 2 ( 1 | G | 2 ) + λ ) | Λ ( n ) | 2 | Λ ( n ¯ ) | 2 ( 1 | G | 2 ) 2 + λ ( 1 + | G | 2 ) ( | Λ ( n ) | 2 + | Λ ( n ¯ ) | 2 ) + λ 2
g M M S E ( n ) = Λ ( n ¯ ) G ( | Λ ( n ) | 2 ( 1 | G | 2 ) + λ ) | Λ ( n ) | 2 | Λ ( n ¯ ) | 2 ( 1 | G | 2 ) 2 + λ ( 1 + | G | 2 ) ( | Λ ( n ) | 2 + | Λ ( n ¯ ) | 2 ) + λ 2
f Z F ( n ) = 1 Λ ( n ) ( 1 | G | 2 )
g Z F ( n ) = G Λ * ( n ¯ ) ( 1 | G | 2 )

Metrics