## Performance evaluation of intensity modulated optical OFDM system with digital baseband distortion |

Optics Express, Vol. 19, Issue 5, pp. 4280-4293 (2011)

http://dx.doi.org/10.1364/OE.19.004280

Acrobat PDF (1095 KB)

### Abstract

Bit-Error-Ratio (BER) of intensity modulated optical orthogonal frequency division multiplexing (OFDM) system is analytically evaluated accounting for nonlinear digital baseband distortion in the transmitter and additive noise in the photo receiver. The nonlinear distortion that is caused by signal clipping and quantization is taken into consideration. The signal clipping helps to overcome the system performance limitation related to high peak-to-average power ratio (PAPR) of the OFDM signal and to minimize the value of optical power that is required for achieving specified BER. The signal quantization due to a limited bit resolution of the digital to analog converter (DAC) causes an optical power penalty in the case when the bit resolution is too low. By introducing an effective signal to noise ratio (SNR) the optimum signal clipping ratio, system BER and required optical power at the input to the receiver is evaluated for the OFDM system with multi-level quadrature amplitude modulation (QAM) applied to the optical signal subcarriers. Minimum required DAC bit resolution versus the size of QAM constellation is identified. It is demonstrated that the bit resolution of 7 and higher causes negligibly small optical power penalty at the system BER = 10^{−3} when 256-QAM and a constellation of lower size is applied. The performance of the optical OFDM system is compared to the performance of the multi-level amplitude-shift keying (M-ASK) system for the same number of information bits transmitted per signal sample. It is demonstrated that in the case of the matched receiver the M-ASK system outperforms OFDM and requires 3 – 3.5 dB less of optical power at BER = 10^{−3} when 1 – 4 data bits are transmitted per signal sample.

© 2011 OSA

## 1. Introduction

5. J. M. Tang and K. A. Shore, “30-Gb/s signal transmission over 40-km directly modulated DFB-laser-based single-mode-fiber links without optical amplification and dispersion compensation,” J. Lightwave Technol. **24**(6), 2318–2327 (2006). [CrossRef]

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

9. S. C. Jeffrey Lee, F. Breyer, S. Randel, H. P. A. van den Boom, and A. M. J. Koonen, “High-speed transmission over multimode fiber using discrete multitone modulation,” J. Opt. Netw. **7**(2), 183–196 (2008). [CrossRef]

## 2. Theoretical outline

*N*is the size of FFT. The OFDM symbol is the superposition of Fourier harmonics (subcarriers) with complex amplitudes

*M*is used at all non-zero subcarriers. The digital OFDM symbol given by Eq. (1) is distorted and converted into analog waveform in the DAC. The time duration of the OFDM symbol at the output of DAC is equal to

15. S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun. Mag. **12**(2), 56–65 (2005). [CrossRef]

16. H. Ochiai and H. Imai, “Performance analysis of deliberately clipped OFDM signals,” IEEE Trans. Commun. **50**(1), 89–101 (2002). [CrossRef]

*ρ*- optical receiver responsivity,

*s*-th signal level,

## 3. Nonlinear distortion noise and effective signal to noise ratio

*x*reduced in amplitude by a factor of

*α*, and distortion noise

*d*:

*d*in Eq. (5) leads to uncertainty in the data recovery and is equivalent to a noise contribution with the mean square current:where

*q*- electron charge. The system performance can now be easily evaluated by using well know results for the system BER evaluation. For instance, in the case of rectangular QAM the system BER is evaluated by using the following expression (see for instance [19] or [20]):

21. P. K. Vitthaladevuni, M.-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wirel. Comm. **4**(6), 3039–3050 (2005). [CrossRef]

## 4. Optimum clipping ratio

*α*and mean square of clipped signal amplitude: where

^{−3}. From Eq. (11) we find that such BER is achieved when

## 5. Signal quantization due to finite bit resolution of DAC

## 6. Analytical model verification

^{5}bits has been used in the numerical simulations in order to model the signal pattern. At the receiver site the detected signal pattern has been loaded with additive receiver noise. In each simulation run a new random binary sequence has been generated using CPU clock as the seed in order to test the BER convergence in terms of data pattern length. If simulations are performed in such a way, observing large “oscillations” of BER versus clipping ratio instead of a smooth curve would indicate that the data pattern length is too short. Small irregular oscillations in the simulation results, shown in Fig. 4 by symbols, indicate that the data pattern length of a few of 10

^{5}bits is long enough in order to achieve a nearly converged BER.

## 7. Evaluation of IM optical OFDM system performance

- • Minimum required bit resolution of DAC,
- • Optimum clipping ratio,
- • Required optical power at the input to the receiver,
- • Power penalty due to signal quantization in DAC versus bit resolution,
- • All at any specified level of BER and size of QAM constellation.

^{−2}and substantially exceeds the limit for the forward error correction (FEC). The minimum required bit resolution for 64-QAM is 5. At this value of the bit resolution the optimum clipping ratio is 8.8 dB at BER = 10

^{−3}and the parameter

^{−3}the minimum required bit resolution is 3 for QPSK, 4 for 16-QAM, 5 for 32-QAM and 64-QAM, and 6 for 128-QAM and 256-QAM. When the bit resolution is equal to 7 the optical power penalty due to signal quantization is very small for all considered QAM constellations. These estimates provide a simple and practical tool for selection of DAC bit resolution when designing the IM optical OFDM system.

^{−3}. This level of power is rather high and substantially limits the available power budget of the system.

*M*is the number of optical power levels. The BER in this case is straightforward to derive (see for instance Section 4.2.7 in [20])

## 8. Discussions

## 9. Conclusions

## Acknowledgments

## References and links

1. | R. W. Chang, “Synthesis of band-limited orthogonal signals for multichannel data transmission,” Bell Syst. Tech. J. |

2. | R. W. Chang, “Orthogonal frequency division multiplexing,” U.S. Patent 3 488 445, 1970. |

3. | A. R. Bahai, and B. R. Saltzberg, |

4. | R. van Nee, and R. Prasad, |

5. | J. M. Tang and K. A. Shore, “30-Gb/s signal transmission over 40-km directly modulated DFB-laser-based single-mode-fiber links without optical amplification and dispersion compensation,” J. Lightwave Technol. |

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

7. | A. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express |

8. | B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. |

9. | S. C. Jeffrey Lee, F. Breyer, S. Randel, H. P. A. van den Boom, and A. M. J. Koonen, “High-speed transmission over multimode fiber using discrete multitone modulation,” J. Opt. Netw. |

10. | S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. |

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

12. | W. Shieh, and I. Djordjevic, |

13. | D. Dardari, “Joint clip and quantization effects characterization in OFDM receivers,” IEEE Trans. Circuits Syst. I Regul. Pap. |

14. | S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. |

15. | S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun. Mag. |

16. | H. Ochiai and H. Imai, “Performance analysis of deliberately clipped OFDM signals,” IEEE Trans. Commun. |

17. | J. J. Bussgang, “Crosscorrelation functions of amplitude-distorted Gaussian signals,” Research Lab. Electron, M.I.T., Cambridge, MA, USA, Tech. Rep. 216 (March 1952). |

18. | A. Papoulis, and S. U. Pillai, |

19. | S. Benedetto, E. Biglieri, and V. Castellani, |

20. | J. G. Proakis, |

21. | P. K. Vitthaladevuni, M.-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wirel. Comm. |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(060.4080) Fiber optics and optical communications : Modulation

(060.4230) Fiber optics and optical communications : Multiplexing

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: January 19, 2011

Manuscript Accepted: February 6, 2011

Published: February 17, 2011

**Citation**

Evgeny Vanin, "Performance evaluation of intensity modulated optical OFDM system with digital baseband distortion," Opt. Express **19**, 4280-4293 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-5-4280

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### References

- R. W. Chang, “Synthesis of band-limited orthogonal signals for multichannel data transmission,” Bell Syst. Tech. J. 45, 1775–1796 (1970).
- R. W. Chang, “Orthogonal frequency division multiplexing,” U.S. Patent 3 488 445, 1970.
- A. R. Bahai, and B. R. Saltzberg, Multi-Carrier Digital Communications: Theory and Applications of OFDM (Plenum Publishing Corp., 1999).
- R. van Nee, and R. Prasad, OFDM for Wireless Multimedia Communications (Artech House, 2000).
- J. M. Tang and K. A. Shore, “30-Gb/s signal transmission over 40-km directly modulated DFB-laser-based single-mode-fiber links without optical amplification and dispersion compensation,” J. Lightwave Technol. 24(6), 2318–2327 (2006). [CrossRef]
- I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14(9), 3767–3775 (2006). [CrossRef] [PubMed]
- A. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14(6), 2079–2084 (2006). [CrossRef] [PubMed]
- B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. 26(1), 196–203 (2008). [CrossRef]
- S. C. Jeffrey Lee, F. Breyer, S. Randel, H. P. A. van den Boom, and A. M. J. Koonen, “High-speed transmission over multimode fiber using discrete multitone modulation,” J. Opt. Netw. 7(2), 183–196 (2008). [CrossRef]
- S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]
- J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009). [CrossRef]
- W. Shieh, and I. Djordjevic, OFDM for Optical Communications (Academic Press, 2010).
- D. Dardari, “Joint clip and quantization effects characterization in OFDM receivers,” IEEE Trans. Circuits Syst. I Regul. Pap. 53(8), 1741–1748 (2006). [CrossRef]
- S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1280–1289 (2010). [CrossRef]
- S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun. Mag. 12(2), 56–65 (2005). [CrossRef]
- H. Ochiai and H. Imai, “Performance analysis of deliberately clipped OFDM signals,” IEEE Trans. Commun. 50(1), 89–101 (2002). [CrossRef]
- J. J. Bussgang, “Crosscorrelation functions of amplitude-distorted Gaussian signals,” Research Lab. Electron, M.I.T., Cambridge, MA, USA, Tech. Rep. 216 (March 1952).
- A. Papoulis, and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw Hill, 2002).
- S. Benedetto, E. Biglieri, and V. Castellani, Digital Transmission Theory (Prentice-Hall, Inc., 1987).
- J. G. Proakis, Digital Communications (McGraw-Hill, 1989).
- P. K. Vitthaladevuni, M.-S. Alouini, and J. C. Kieffer, “Exact BER computation for cross QAM constellations,” IEEE Trans. Wirel. Comm. 4(6), 3039–3050 (2005). [CrossRef]

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