## Orthogonal frequency division multiplexing for high-speed optical transmission

Optics Express, Vol. 14, Issue 9, pp. 3767-3775 (2006)

http://dx.doi.org/10.1364/OE.14.003767

Acrobat PDF (945 KB)

### Abstract

Optical Orthogonal frequency division multiplexing (OOFDM) is shown to outperform RZ-OOK transmission in high-speed optical communications systems in terms of transmission distance and spectral efficiency. The OOFDM in combination with the subcarrier multiplexing offers a significant improvement in spectral efficiency of at least 2.9 bits/s/Hz.

© 2006 Optical Society of America

## 1. Introduction

9. Q. Pan and R. J. Green, “Bit-error-rate performance of lightwave hybrid AM/OFDM systems with comparison with AM/QAM systems in the presence of clipping impulse noise,” IEEE Photon. Technol. Lett. **8**, 278–280 (1996). [CrossRef]

10. A. Kim, Y. Hun Joo, and Y. Kim, “60 GHz wireless communication systems with radio-over-fiber links for indoor wireless LANs,” IEEE Trans. Consum. Electron. **50**, 517–520 (2004). [CrossRef]

11. B. J. Dixon, R.D. Pollard, and S. Iezekiel, ”Orthogonal frequency-division multiplexing in wireless communication systems with multimode fiber feeds,” IEEE Trans. Microwave Theory and Techniques **49**, 1404 – 1409 (2001). [CrossRef]

## 2. Optical OFDM High-Speed Transmission

*B*bits. The

*B*bits in each block (frame) are subdivided into

*K*subgroups with the

*i*

^{th}subgroup containing

*b*bits,

_{i}*B*=Σ

*b*. The

_{i}*b*bits from the

_{i}*i*

^{th}subgroup are mapped into a complex-valued signal point from a 2

*bi*-point signal constellation such is, e.g., QAM, which is considered in this paper. The complex-valued signal points from all K subchannels are considered as the values of the discrete Fourier transform (DFT) of a multicarrier OFDM signal. Therefore, the symbol interval length in an OFDM system is

*T*=

*KT*, where

_{s}*T*is the symbol-interval length in a single-carrier system. By selecting

_{s}*K*, the number of subchannels, sufficiently large, the OFDM symbol interval can be made much larger than the dispersed pulse-width in a single-carrier system, resulting in an arbitrary small intersymbol interference.

*X*is the

_{i,k}*i*-th subcarrier of

*k*-th OFDM symbol,

*T*is the OFDM symbol duration,

*T*

_{FFT}is the OFDM symbol effective part,

*T*

_{guard}is the guard interval (the duration of cyclic extension),

*T*

_{win}is the length of the windowing interval, and

*w*(

*t*) is the window function. The OFDM symbol, shown in Figs. 1(c)–(d), is therefore generated as follows:

*N*

_{QAM}input QAM symbols are zero-padded to obtain

*N*

_{FFT}input samples for IFFT, the

*N*

_{gurad}samples are inserted to create the guard interval

*T*

_{guard}, and the OFDM symbol is multiplied by the window function (raised cosine function is used in [3]–[4], however the Kaiser, Blackman-Harris and other window functions are also applicable). After the appropriate sampling, the summation term in (1),

*N*). Therefore, the modulator and demodulator can be implemented by use of the FFT algorithm to calculate inverse and direct DFT. The purpose of cyclic extension is to preserve the orthogonality among subcarriers even when the neighboring OFDM symbols partially overlap due to dispersion, and the purpose of the windowing is to reduce the out-of band spectrum. The cyclic extension, illustrated in Fig. 1 (c), is done by repeating the last

*N*

_{guard}/2 samples of the effective OFDM symbol part (of duration

*T*

_{FFT}with

*N*

_{FFT}samples) as the prefix, and repeating the first

*N*

_{guard}/2 samples (out of

*N*

_{FFT}) as the suffix. (Notice that windowing is more effective for smaller numbers of subccarriers.) After a D/A conversion and RF up-coversion, the OFDM signal is driven to the MZM and then transmitted over the fiber. The DC component is inserted to be able to recover the QAM symbols incoherently. It is assumed that 50% is allocated for the transmission of carrier, for the reasons given in [14

14. R. Hui, B. Zhu, R. Huang, C. T. Allen, K. R. Demarest, and D. Richards, “Subcarrier multiplexing for highspeed optical transmission,” IEEE/OSA J. Lightwave Technology **20**, 417–427 (2002). [CrossRef]

*V*

_{π}voltages above 6 V. The OFDM signal bandwidth is set to 10 GHz, the number of subchannels is set to 256, FFT/IFFT is calculated in 8192 points, the bandwidth of optical filter is set to 60 GHz, the total averaged launched power is set to 0 dBm. No windowing or clipping is applied.

*T*), suggesting that OFDM is an efficient way for increasing the spectral efficiency, because the partial overlapping between neighboring sub-carriers is allowed. The spectral efficiency of a WDM system can be also improved by combining the OFDM channels using the subcarrier multiplexing [14

14. R. Hui, B. Zhu, R. Huang, C. T. Allen, K. R. Demarest, and D. Richards, “Subcarrier multiplexing for highspeed optical transmission,” IEEE/OSA J. Lightwave Technology **20**, 417–427 (2002). [CrossRef]

21. B. Vasic, I. B. Djordjevic, and R. Kostuk, “Low-density parity check codes and iterative decoding for long haul optical communication systems,” IEEE/OSA J. Lightwave Technol. **21**, 438–446 (2003). [CrossRef]

^{-8}, and at the same time allows transmitting a 40 Gb/s signal over a 10 GHz bandwidth.

## 3. Simulation Results

*N*spans of length

*L*=120 km, consisting of 2

*L*/3 km of D

_{+}fiber followed by

*L*/3 km of D- fiber, with pre-compensation of -320 ps/nm and corresponding post-compensation. The dispersion map II (Fig. 4(b)) is similar to dispersion map I, in which the sections of D

_{+}and D

_{-}fibers are replaced with conventional SMF and DCF, respectively. The SMF and DCF lengths in a span (of the dispersion map II) are 101.9 km and 18.1 km, respectively, and the pre- and post-compensation sections lengths are set to 3.34 and 18.75 km respectively. In simulations, two different OFDM schemes are considered. In both schemes the signal bandwidth is set to 10 GHz, while the number of subchannels is set to either 256 or 64, and FFT/IFFT is calculated in either 8192 or 1024 points. In the first scheme (with 256 subchannels) no windowing or clipping is applied, while the second scheme (with 64 subchannels) uses the windowing based on Blackman-Harris windowing function. To reduce the peak-to-average ratio, the peak windowing [3] based on Hann windowing function is applied. In both schemes the bandwidth of optical filter is set to 60 GHz, the total averaged launched power is set to 0 dBm, and the RF carrier frequency is set to 25 GHz. 16-QAM, 4-QAM (QPSK) and 2-QAM (BPSK) are observed. The de-mapper is based on a Euclidean distance receiver. For regular dispersion maps (map I and map II), Fig. 6, only the

*M*=2 case is able to outperform RZ-OOK (of duty cycle 33%) operating at 40 Gb/s. The OOFDM system and RZ-OOK are compared with respect to the BER rather than Q-factor, because the Q-factor is not a good figure of merit when the fiber nonlinearities are important.

*M*=4. The phase noise introduced by the self-phase modulation (SPM) causes the rotation of the constellation diagram, and this effect is known as the

*common phase error*[19

19. A. G. Armada, “Understanding the effects of phase noise in orthogonal frequency division multiplexing (OFDM),” IEEE Trans. Broadcasting **47**, 153–159 (2001). [CrossRef]

19. A. G. Armada, “Understanding the effects of phase noise in orthogonal frequency division multiplexing (OFDM),” IEEE Trans. Broadcasting **47**, 153–159 (2001). [CrossRef]

20. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communication systems using linear amplifiers,” Opt. Lett. **15**, 1351–1353 (1990). [CrossRef] [PubMed]

17. T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Comm. **45**, 1613–1621 (1997). [CrossRef]

18. M. Morelli and U. Mengali, “A comparison of pilot-aided channel estimation methods for OFDM systems,” IEEE Trans. Signal Process. **49**, 3065–3073 (2001). [CrossRef]

18. M. Morelli and U. Mengali, “A comparison of pilot-aided channel estimation methods for OFDM systems,” IEEE Trans. Signal Process. **49**, 3065–3073 (2001). [CrossRef]

*N*

_{guard}/2 samples of the effective OFDM symbol part are identical to the last

*N*

_{guard}/2 samples of the effective OFDM symbol part and the suffix, spaced

*T*

_{FFT}seconds apart. By calculating the autocorrelation of these two parts we are able to estimate the frequency offset and remove it (see Fig. 7). At the same time correlation peaks obtained after every OFDM symbol can be used for timing as explained in [15].

## 4. Conclusion

^{-2}, which is a sufficient level for advanced FEC (see [12–13

12. I. B. Djordjevic, O. Milenkovic, and B. Vasic, “Generalized Low-Density Parity-Check Codes for Optical Communication Systems,” IEEE/OSA J. Lightwave Technol. **23**, 1939– 1946 (2005). [CrossRef]

## Acknowledgments

## References and Links

1. | R. R. Mosier and R. G. Clabaugh, “Kineplex, a bandwidth efficient binary transmission system,” AIEE Trans. |

2. | R. W. Chang, “Orthogonal frequency division multiplexing,” U.S. Patent |

3. | R. Van Nee and R. Prasad, |

4. | R. Prasad, |

5. | L. M. Cimini Jr., “Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing,” IEEE Trans. Comm. |

6. | Y. Sun, “Bandwidth-efficient wireless OFDM,” IEEE Selected Areas Comm. |

7. | T. Wang, J. G. Proakis, and J. R. Zeidler, “Techniques for suppression of intercarrier interference in OFDM systems,” in Proc. |

8. | Y. Wu and B. Caron, “Digital television terrestrial broadcasting,” |

9. | Q. Pan and R. J. Green, “Bit-error-rate performance of lightwave hybrid AM/OFDM systems with comparison with AM/QAM systems in the presence of clipping impulse noise,” IEEE Photon. Technol. Lett. |

10. | A. Kim, Y. Hun Joo, and Y. Kim, “60 GHz wireless communication systems with radio-over-fiber links for indoor wireless LANs,” IEEE Trans. Consum. Electron. |

11. | B. J. Dixon, R.D. Pollard, and S. Iezekiel, ”Orthogonal frequency-division multiplexing in wireless communication systems with multimode fiber feeds,” IEEE Trans. Microwave Theory and Techniques |

12. | I. B. Djordjevic, O. Milenkovic, and B. Vasic, “Generalized Low-Density Parity-Check Codes for Optical Communication Systems,” IEEE/OSA J. Lightwave Technol. |

13. | T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Selected Topics Quant. Electron. |

14. | R. Hui, B. Zhu, R. Huang, C. T. Allen, K. R. Demarest, and D. Richards, “Subcarrier multiplexing for highspeed optical transmission,” IEEE/OSA J. Lightwave Technology |

15. | M. Sandell, J. J. van de Beek, and P. O. Börjesson, “Timing and frequency synchronization in OFDM systems using cyclic prefix,” in Proc. |

16. | R. Böhnke and T. Dölle, “Preamble structures for HiperLAN type 2 system,” ETSI BRAN Doc. No. HL13SON1A, Apr. 7, 1999. |

17. | T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Comm. |

18. | M. Morelli and U. Mengali, “A comparison of pilot-aided channel estimation methods for OFDM systems,” IEEE Trans. Signal Process. |

19. | A. G. Armada, “Understanding the effects of phase noise in orthogonal frequency division multiplexing (OFDM),” IEEE Trans. Broadcasting |

20. | J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communication systems using linear amplifiers,” Opt. Lett. |

21. | B. Vasic, I. B. Djordjevic, and R. Kostuk, “Low-density parity check codes and iterative decoding for long haul optical communication systems,” IEEE/OSA J. Lightwave Technol. |

22. | A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems” in Proc. OFC Postdeadline Papers, Paper no. PDP39, 2006. |

**OCIS Codes**

(060.2310) Fiber optics and optical communications : Fiber optics

(060.4080) Fiber optics and optical communications : Modulation

(060.4230) Fiber optics and optical communications : Multiplexing

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: January 3, 2006

Revised Manuscript: April 11, 2006

Manuscript Accepted: April 15, 2006

Published: May 1, 2006

**Citation**

Ivan B. Djordjevic and Bane Vasic, "Orthogonal frequency division multiplexing for high-speed optical transmission," Opt. Express **14**, 3767-3775 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-3767

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### References

- R. R. Mosier, and R. G. Clabaugh, "Kineplex, a bandwidth efficient binary transmission system," AIEE Trans. 76, 723-728 (1958).
- R. W. Chang, "Orthogonal frequency division multiplexing," U.S. Patent 3 488 445, 1970.
- R. Van Nee, and R. Prasad, OFDM Wireless Multimedia Communications (Artech House, Boston, 2000).
- R. Prasad, OFDM for Wireless Communications Systems (Artech House, Boston, 2004).
- L. M. Cimini, Jr., "Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing," IEEE Trans. Comm. COM-33, 665-675(1985). [CrossRef]
- Y. Sun, "Bandwidth-efficient wireless OFDM," IEEE Selected Areas Comm. 19, 2267 - 2278 (2001). [CrossRef]
- T. Wang, J. G. Proakis, and J. R. Zeidler, "Techniques for suppression of intercarrier interference in OFDM systems," in Proc. 2005 IEEE Wireless Communications and Networking Conference, pp. 39-44 (2005).
- Y. Wu and B. Caron, "Digital television terrestrial broadcasting," IEEE Commun. Mag., 46-52 (1994).
- Q. Pan, and R. J. Green, "Bit-error-rate performance of lightwave hybrid AM/OFDM systems with comparison with AM/QAM systems in the presence of clipping impulse noise," IEEE Photon. Technol. Lett. 8, 278-280 (1996). [CrossRef]
- A. Kim, Y. Hun Joo, and Y. Kim, "60 GHz wireless communication systems with radio-over-fiber links for indoor wireless LANs," IEEE Trans. Consum. Electron. 50, 517-520 (2004). [CrossRef]
- B. J. Dixon, R.D. Pollard, and S. Iezekiel, "Orthogonal frequency-division multiplexing in wireless communication systems with multimode fiber feeds," IEEE Trans. Microwave Theory and Techniques 49, 1404 - 1409 (2001). [CrossRef]
- I. B. Djordjevic, O. Milenkovic, and B. Vasic, "Generalized Low-Density Parity-Check Codes for Optical Communication Systems," IEEE/OSA J.Lightwave Technol. 23, 1939- 1946 (2005). [CrossRef]
- T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, "Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems," IEEE J. Selected Topics Quant. Electron. 10, 376-386 (2004). [CrossRef]
- R. Hui, B. Zhu, R. Huang, C. T. Allen, K. R. Demarest, and D. Richards, "Subcarrier multiplexing for high-speed optical transmission," IEEE/OSA J.Lightwave Technology 20, 417-427 (2002). [CrossRef]
- M. SandellJ. J. van de Beek, and P. O. Börjesson, "Timing and frequency synchronization in OFDM systems using cyclic prefix," in Proc. Int. Symp. Synchron., Saalbau, Essen, Germany, pp. 16-19, 1995.
- <other>. R. Böhnke, and T. Dölle, "Preamble structures for HiperLAN type 2 system," ETSI BRAN Doc. No. HL13SON1A, Apr. 7, 1999.</other>
- T. M. Schmidl, and D. C. Cox, "Robust frequency and timing synchronization for OFDM," IEEE Trans. Comm. 45, 1613-1621 (1997). [CrossRef]
- M. Morelli, and U. Mengali, "A comparison of pilot-aided channel estimation methods for OFDM systems," IEEE Trans. Signal Process. 49, 3065-3073 (2001). [CrossRef]
- A. G. Armada, "Understanding the effects of phase noise in orthogonal frequency division multiplexing (OFDM)," IEEE Trans. Broadcasting 47, 153-159 (2001). [CrossRef]
- J. P. Gordon, and L. F. Mollenauer, "Phase noise in photonic communication systems using linear amplifiers," Opt. Lett. 15, 1351-1353 (1990). [CrossRef] [PubMed]
- B. Vasic, I. B. Djordjevic, and R. Kostuk, "Low-density parity check codes and iterative decoding for long haul optical communication systems," IEEE/OSA J.Lightwave Technol. 21, 438-446 (2003). [CrossRef]
- <other>. A. J. Lowery, L. Du, and J. Armstrong, "Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems" in Proc. OFC Postdeadline Papers, Paper no. PDP39, 2006. </other>

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