## Transmitter IQ mismatch compensation in coherent optical OFDM systems using pilot signals |

Optics Express, Vol. 18, Issue 20, pp. 21308-21314 (2010)

http://dx.doi.org/10.1364/OE.18.021308

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### 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

## 1. Introduction

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]

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]

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]

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]

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]

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]

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

## 2. Tx IQ mismatch in CO-OFDM systems

*W*denote the discrete Fourier matrix (DFT) and

*k*

^{th}OFDM symbol vector. The discrete time domain signal is obtained by inverse DFT (IDFT),

*ϕ*and the amplitude imbalance

*ϵ*, and

*C*is the channel effect and

**w**

_{k}is an additive white Gaussian noise vector:

*N*-point DFT of the channel. We defineNote that

*Λ*is a diagonal matrix of dimension

*N*, and

*G*is a constant.

*G*and distortion from the scalar channel

## 3. Proposed IQ mismatch compensation method

### 3.1 Pilot symbol design for estimating channel and Tx IQ mismatch

*Λ*and G, which include

*N*+ 1 unknown variables. Because the channel

*N*, we may theoretically estimate

_{p}*Λ*and G when the number of pilot tones is greater than

*N*+ 1 [10

_{p}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]

*Λ*and G using pilots with the following structure.

*N*, a subset of subcarriers indexed by

*N*is not divisible by

*M*. We can build the desired pilot symbol by selecting

*A*to be a sequence of pseudorandom signals. Using this rule, an OFDM symbol containing

*M*decreases the number of pilot tones increases and the channel estimation performance is enhanced, but data throughput is decreased.

*A*does not experience IQ mismatch distortion because the mirror imaged signals are zero. Furthermore, the received group of pilot signals

*n*:

*A*, we can extend the channel estimation to all subfrequencies using standard interpolation methods, such as low-pass interpolation [10

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]

*Λ*is known,

*G*can be estimated using the pilots in

### 3.2 MMSE compensation

*f*and

*g*that minimize the following MSE): where we assume that each subcarrier has the same signal power and noise power, denoted by

## 4. Numerical Results

*M*= 3 in Eq. (10) was inserted every 10 OFDM symbols to estimate the channel and IQ mismatch. The Tx laser and LO laser line width were set to 10 kHz to exclude the effect of phase noise. CD was considered as the cause of ISI in the optical fiber channel, a standard single-mode fiber (SSMF).

^{−3}versus Tx IQ phase imbalance for 200 km of SSMF in the case of conventional equalization only, equalization with pre-GSOP, and the proposed combined IQ compensation and equalization scheme. The performance of the proposed algorithm was superior to that of the other methods. Figure 5 compares MMSE equalizers and ZF equalizers in terms of OSNR penalty for 300km SMMF. MMSE equalizers perform better than ZF equalizers, but the difference is marginal. Considering the complexity of MMSE equalizers, ZF equalizers can be used as a good approximation of the optimal MMSE equalizers. Figure 6 illustrates the performance of the above three methods for CD distortion in up to 1000 km of SSMF as a function of the OSNR penalty (target BER of 10

^{−3}). The result indicates that the GSOP does not perform better than the equalization-only scheme for more than 200 km of SSMF.

## 7. Conclusions

## Acknowledgement

## References and links

1. | I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express |

2. | W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express |

3. | J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. |

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. |

5. | X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. |

6. | I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK Coherent Receiver,” IEEE Photon. Technol. Lett. |

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. |

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. |

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 |

11. | M. K. Ozdemir and H. Arslan, “Channel Estimation for wireless OFDM systems,” IEEE Comm. Surveys & Tutorials |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: August 12, 2010

Revised Manuscript: September 14, 2010

Manuscript Accepted: September 17, 2010

Published: September 22, 2010

**Citation**

Wonzoo Chung, "Transmitter IQ mismatch compensation in coherent optical OFDM systems using pilot signals," Opt. Express **18**, 21308-21314 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-21308

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### References

- I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14(9), 3767–3775 (2006). [CrossRef] [PubMed]
- W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008). [CrossRef] [PubMed]
- J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009). [CrossRef]
- 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]
- 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.
- 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]
- 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]
- M. K. Ozdemir and H. Arslan, “Channel Estimation for wireless OFDM systems,” IEEE Comm. Surveys & Tutorials 9(2), 18–48 (2007). [CrossRef]

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