## PMD tolerant direct-detection polarization division multiplexed OFDM systems with MIMO processing |

Optics Express, Vol. 20, Issue 7, pp. 7316-7322 (2012)

http://dx.doi.org/10.1364/OE.20.007316

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### Abstract

This work proposes a novel direct-detection polarization division multiplexed OFDM scheme without the need of dynamic polarization control at a polarization-diverse receiver, and the proposed scheme is robust against polarization mode dispersion. Setting the frequency difference between two polarization-orthogonal reference carriers as one subcarrier spacing, possible signal fading can be avoided, and the corresponding interference from adjacent subcarriers is eliminated by a novel MIMO algorithm. The penalty caused by high channel matrix condition number can be decreased by inserting empty tones among subcarriers, and the polarization-dependent OSNR penalty at the BER of 10^{−3} is <3.6 dB with an empty tone inserted every 8 subcarriers. Moreover, the numerical results demonstrate the 16 × 10^{3}-ps/nm chromatic dispersion and the 300-ps differential group delay will not induce additional penalty.

© 2012 OSA

## 1. Introduction

1. 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]

9. A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photon. Technol. Lett. **22**(7), 468–470 (2010). [CrossRef]

1. 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]

3. H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, and H. Tanaka, “Highly spectrally efficient DWDM transmission at 7.0 b/s/Hz using 8×65.1-Gb/s coherent PDM-OFDM,” J. Lightwave Technol. **28**(4), 406–414 (2010). [CrossRef]

4. D.-Z. Hsu, C.-C. Wei, H.-Y. Chen, W.-Y. Li, and J. Chen, “Cost-effective 33-Gbps intensity modulation direct detection multi-band OFDM LR-PON system employing a 10-GHz-based transceiver,” Opt. Express **19**(18), 17546–17556 (2011). [CrossRef] [PubMed]

9. A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photon. Technol. Lett. **22**(7), 468–470 (2010). [CrossRef]

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]

3. H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, and H. Tanaka, “Highly spectrally efficient DWDM transmission at 7.0 b/s/Hz using 8×65.1-Gb/s coherent PDM-OFDM,” J. Lightwave Technol. **28**(4), 406–414 (2010). [CrossRef]

5. B. J. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, “120 Gbit/s over 500-km using single-band polarization-multiplexed self-coherent optical OFDM,” J. Lightwave Technol. **28**(4), 328–335 (2010). [CrossRef]

8. D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightwave Technol. **28**(4), 484–493 (2010). [CrossRef]

9. A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photon. Technol. Lett. **22**(7), 468–470 (2010). [CrossRef]

8. D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightwave Technol. **28**(4), 484–493 (2010). [CrossRef]

**22**(7), 468–470 (2010). [CrossRef]

^{−3}to ~3.6 dB, and more empty tones would further decrease the penalty at the price of lower spectral efficiency. Furthermore, simulation is given to show the ability of the proposed scheme against CD and the first order PMD. With the CD of 16 × 10

^{3}ps/nm and the differential group delay (DGD) of 300 ps, 16-QAM 47-Gbps DD-PDM-OFDM signals suffer from negligible additional OSNR penalty.

## 2. Operation principle

*x*

_{1}and

*x*

_{2}, in the PDM scheme, their reference carriers turn out to be one completely polarized carrier shown in Fig. 1(a) . Hence, the reference carrier of the traditional DD-PDM-OFDM scheme could be generated directly in the form of single-polarization [5

5. B. J. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, “120 Gbit/s over 500-km using single-band polarization-multiplexed self-coherent optical OFDM,” J. Lightwave Technol. **28**(4), 328–335 (2010). [CrossRef]

5. B. J. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, “120 Gbit/s over 500-km using single-band polarization-multiplexed self-coherent optical OFDM,” J. Lightwave Technol. **28**(4), 328–335 (2010). [CrossRef]

*c*

_{2}, is shifted by one subcarrier spacing, Δ

*f*, shown in Fig. 1(b). As a result, the received total powers of the reference carriers after the PBS are independent of the received SOP. Although undesired signal fading is avoided in the proposed scheme, the received signals,

*y*

_{1}and

*y*

_{2}, would contain the interference from not only the mixed polarization subcarriers but also adjacent subcarriers due to the different frequencies of the reference carriers. Hence, to remove the interference and recover the mixed signals, the channel model is needed to apply MIMO processing. While the beating term between a subcarrier and the carrier of

*c*

_{2}will up-convert the frequency of the subcarrier by Δ

*f*compared with the traditional DD-OFDM in Fig. 1(a), the received

*i*

^{th}subcarriers would be composed of the transmitted

*i*

^{th}and (

*i*

**-**1)

^{th}subcarriers:

**h**

*and*

_{i}**w**

*represent the channel response and noise, respectively. Notably, the contribution of*

_{i}*x*

_{1,}

_{i-}_{1}and

*x*

_{2,}

*in Eq. (1) comes from polarization mixing. Without polarization mixing, all the entries of*

_{i}**h**

*, except*

_{i}*h*

_{i}_{,12}and

*h*

_{i}_{,23}or

*h*

_{i}_{,22}and

*h*

_{i}_{,13}, will be zero. Assuming

*N*subcarriers for each polarization, the whole MIMO relation is

**Y**=

**HX**+

**W**, or

*N*

^{th}subcarrier and the carrier of

*c*

_{2}will become the (

*N*+ 1)

^{th}subcarriers,

**Y**and

**W**are (2

*N*+ 2) × 1 vectors, and

**H**is a (2

*N*+ 2) × (2

*N*) matrix. Moreover, the transmitted OFDM signals are assigned from the 1

^{st}to the

*N*

^{th}subcarriers, and therefore,

**h**

_{1}and

**h**

_{N}_{+1}in Eq. (2) are

**h**

*is estimated by proper training symbols, the MIMO demodulation can be realized by the zero-forcing algorithm of*

_{i}**H**

^{−1}

**Y**, where

**H**

^{−1}indicates the pseudo inverse of

**H**.

**X**and the noise term of

**H**

^{−1}

**W**. Accordingly, the noise would be intensified, if the condition number of

**H**is high. Unfortunately, since

*N*of an OFDM signal is generally large, the condition number of

**H**might be high. Without considering CD and PMD for simplicity, the optical channel could be treated as a frequency- irrelevant random orientated Jones matrix,

**R**, with the entries of

*r*

_{11},

*r*

_{12},

*r*

_{21}, and

*r*

_{22}. Figure 2(a) shows the corresponding relations among the transmitted and received optical signals. For example,

*y*

_{1,}

*will include*

_{i}*r*

_{11}

*x*

_{1,}

_{i}_{-1}and

*r*

_{12}

*c*

_{2}. Hence, let the powers of both carriers be unity, the channel response,

**h**

*, can be represent as*

_{i}**R**is diagonal or anti-diagonal indicating no polarization mixing, the condition number of

**H**is unit and irrelevant to

*N*, and the powers of

**W**and

**H**

^{−1}

**W**will be identical. Nevertheless, if two orthogonal signals are equally separated into two receivers and |

*r*

_{11}| = |

*r*

_{12}| = |

*r*

_{21}| = |

*r*

_{22}|, the condition number and the power of

**H**

^{−1}

**W**will become the highest and increase with

*N*. Because the condition number is independent of the relative phase among the entries of

**R**,

**R**can be assumed real and

*r*

_{11}=

*r*

_{22}= cos

*θ*and

*r*

_{12}=

**-**

*r*

_{21}= sin

*θ*, where

*θ*can be understood as the relative angle between the PBC at the transmitter and the PBS at the receiver. Consequently, the best and the worst cases can be denoted by

*θ*of 0 and 45°, respectively. Moreover, with a large

*N*, the computational complexity of

**H**

^{−1}would also be high for hardware implementation. Hence, to lower both the condition number of

**H**and the computational complexity of

**H**

^{−1}, empty tones are required to separate subcarriers into groups shown in Fig. 2(b). When each group is composed of

*N*subcarriers, the numbers of groups and empty tones are both

_{g}*N*/

*N*, and therefore, the spectral efficiency of the proposed scheme becomes ~2 ×

_{g}*N*/(1 +

_{g}*N*) times, compared with a single-polarization DD-OFDM system.

_{g}## 3. Numerical results and discussion

10. C.-T. Lin, C.-C. Wei, and M.-I. Chao, “Phase noise suppression of optical OFDM signals in 60-GHz RoF transmission system,” Opt. Express **19**(11), 10423–10428 (2011). [CrossRef] [PubMed]

^{nd}order Gaussian filter with the 3-dB bandwidth of 30 GHz. Furthermore, the laser linewidth is set as 100 kHz to decrease the dispersion-induced phase noise [11

11. W.-R. Peng, “Analysis of laser phase noise effect in direct-detection optical OFDM transmission,” J. Lightwave Technol. **28**(17), 2526–2536 (2010). [CrossRef]

*N*of 8 at back-to-back (BtB). In addition to the average SNR penalty of ~3.5 dB caused by polarization mixing, the subcarriers at the middle of each group show worse SNRs, compared with the subcarriers at the edge of each group which suffer the least interference from adjacent subcarriers. With

_{g}*N*of 8, Fig. 3(b) plots the required OSNR to reach the BER of 10

_{g}^{−3}as a function of

*θ*at BtB, and the OSNR penalty caused by polarization mixing is smaller than 3.6 dB. Furthermore, Fig. 4(a) depicts the demodulated SNRs for the worst case with the same OSNR of 24 dB but different

*N*of 8 and 40 at BtB. The subcarriers at the edges show similar SNRs for both cases, but for

_{g}*N*of 40, those at the middle of each group suffer from the additional penalty of ~6 dB due to the higher condition number. Besides, the required OSNR for the BER of 10

_{g}^{−3}is plotted in Fig. 4(b) with different

*N*. While the required OSNRs for the case without polarization mixing are irrelevant to

_{g}*N*, the required OSNRs of the worst cases will increase with

_{g}*N*. In addition, the power of the beating noise between the subcarriers and ASE noise is frequency-dependent [12], and this result in tilt SNR in Figs. 3(a) and 4(a).

_{g}^{3}ps/nm equivalent to 1000-km single-mode fiber transmission. Compared with the cases at BtB, the BER curves show negligible OSNR penalties after transmission for both

*θ*of 0 and 45°. Furthermore, the effect of DGD on the required OSNR is illustrated in Fig. 5(b), where the dashed curves are the cases with only 16 × 10

^{3}-ps/nm CD and the solid curves represents the cases with 16 × 10

^{3}-ps/nm CD and 300-ps DGD. While

*θ*is fixed at 0 or 45°, the required OSNRs are evaluated over different relative angles,

*ϕ*, between the PBC and the fiber fast axis. Because DGD would induce frequency-dependent polarization rotation, the performance with

*θ*of 0 might be worse than that with

*θ*of 45°. In fact, the signal performance depends on how the PBS splits the reference carriers, and coexistence of both carriers after the PBS will result in higher condition number. Thus, the results of Fig. 5(b) rely on how the DGD rotates the SOP of the reference carriers. When

*ø*is ~22.5°, for instance, the best case with

*θ*of 0 turns into the worst case. Nonetheless, from Fig. 5(b), the DGD does not contribute additional penalty except polarization mixing, since all the required OSNR are between those in the DGD-free cases with

*θ*of 0 and 45°.

## 4. Conclusions

*N*of 8, and it is possible to further decrease this penalty by more empty tones. With the CD of 16 × 10

_{g}^{3}ps/nm, the proposed 16-QAM 47-Gbps DD-PDM-OFDM signals demonstrate negligible OSNR penalty. Moreover, although PMD would change the received SOP, the simulation results show that the DGD of 300 ps does not induce additional OSNR penalty except polarization rotation. Hence, the proposed scheme is also robust to PMD. In short, compared with a single-polarization DD-OFDM system which suffers from PMD, our PMD tolerant system can increase the spectral efficiency by ~2 ×

*N*/(1 +

_{g}*N*), but careful optimization of

_{g}*N*is needed to maximize capacity owing to the trade-off between the spectral efficiency and the OSNR penalty from polarization mixing.

_{g}## Acknowledgment

## References and links

1. | 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 |

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. |

3. | H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, and H. Tanaka, “Highly spectrally efficient DWDM transmission at 7.0 b/s/Hz using 8×65.1-Gb/s coherent PDM-OFDM,” J. Lightwave Technol. |

4. | D.-Z. Hsu, C.-C. Wei, H.-Y. Chen, W.-Y. Li, and J. Chen, “Cost-effective 33-Gbps intensity modulation direct detection multi-band OFDM LR-PON system employing a 10-GHz-based transceiver,” Opt. Express |

5. | B. J. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, “120 Gbit/s over 500-km using single-band polarization-multiplexed self-coherent optical OFDM,” J. Lightwave Technol. |

6. | M. Mayrock and H. Haunstein, “PMD tolerant direct-detection optical OFDM system,” in |

7. | W.-R. Peng, K.-M. Feng, and A. E. Willner, “Direct-detected polarization division multiplexed OFDM systems with self-polarization diversity,” in |

8. | D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightwave Technol. |

9. | A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photon. Technol. Lett. |

10. | C.-T. Lin, C.-C. Wei, and M.-I. Chao, “Phase noise suppression of optical OFDM signals in 60-GHz RoF transmission system,” Opt. Express |

11. | W.-R. Peng, “Analysis of laser phase noise effect in direct-detection optical OFDM transmission,” J. Lightwave Technol. |

12. | A. J. Lowery, “Improving sensitivity and spectra efficiency in direct-detection optical OFDM systems,” in |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.4080) Fiber optics and optical communications : Modulation

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: December 5, 2011

Revised Manuscript: February 3, 2012

Manuscript Accepted: March 3, 2012

Published: March 15, 2012

**Citation**

Chia-Chien Wei, Chun-Ting Lin, and Chih-Yun Wang, "PMD tolerant direct-detection polarization division multiplexed OFDM systems with MIMO processing," Opt. Express **20**, 7316-7322 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-7316

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### References

- Y. Ma, Q. Yang, Y. Tang, S. Chen, 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]
- S. L. Jansen, A. Al Amin, H. Takahashi, I. Morita, 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]
- H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, H. Tanaka, “Highly spectrally efficient DWDM transmission at 7.0 b/s/Hz using 8×65.1-Gb/s coherent PDM-OFDM,” J. Lightwave Technol. 28(4), 406–414 (2010). [CrossRef]
- D.-Z. Hsu, C.-C. Wei, H.-Y. Chen, W.-Y. Li, J. Chen, “Cost-effective 33-Gbps intensity modulation direct detection multi-band OFDM LR-PON system employing a 10-GHz-based transceiver,” Opt. Express 19(18), 17546–17556 (2011). [CrossRef] [PubMed]
- B. J. Schmidt, Z. Zan, L. B. Du, A. J. Lowery, “120 Gbit/s over 500-km using single-band polarization-multiplexed self-coherent optical OFDM,” J. Lightwave Technol. 28(4), 328–335 (2010). [CrossRef]
- M. Mayrock and H. Haunstein, “PMD tolerant direct-detection optical OFDM system,” in Proc. ECOC’07 (2007), paper 5.2.5.
- W.-R. Peng, K.-M. Feng, and A. E. Willner, “Direct-detected polarization division multiplexed OFDM systems with self-polarization diversity,” in Proc. CLEOS’08 (2008), paper MH3.
- D. Qian, N. Cvijetic, J. Hu, T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightwave Technol. 28(4), 484–493 (2010). [CrossRef]
- A. Amin, H. Takahashi, I. Morita, H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photon. Technol. Lett. 22(7), 468–470 (2010). [CrossRef]
- C.-T. Lin, C.-C. Wei, M.-I. Chao, “Phase noise suppression of optical OFDM signals in 60-GHz RoF transmission system,” Opt. Express 19(11), 10423–10428 (2011). [CrossRef] [PubMed]
- W.-R. Peng, “Analysis of laser phase noise effect in direct-detection optical OFDM transmission,” J. Lightwave Technol. 28(17), 2526–2536 (2010). [CrossRef]
- A. J. Lowery, “Improving sensitivity and spectra efficiency in direct-detection optical OFDM systems,” in Proc. OFC’08. (2008), paper OMM4.

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