## Analysis and iterative equalization of transient and adiabatic chirp effects in DML-based OFDM transmission systems |

Optics Express, Vol. 20, Issue 23, pp. 25774-25789 (2012)

http://dx.doi.org/10.1364/OE.20.025774

Acrobat PDF (1164 KB)

### Abstract

This work theoretically studies the transmission performance of a DML-based OFDM system by small-signal approximation, and the model considers both the transient and adiabatic chirps. The dispersion-induced distortion is modeled as subcarrier-to-subcarrier intermixing interference (SSII), and the theoretical SSII agrees with the distortion obtained from large-signal simulation statistically and deterministically. The analysis shows that the presence of the adiabatic chirp will ease power fading or even provide gain, but will increase the SSII to deteriorate OFDM signals after dispersive transmission. Furthermore, this work also proposes a novel iterative equalization to eliminate the SSII. From the simulation, the distortion could be effectively mitigated by the proposed equalization such that the maximum transmission distance of the DML-based OFDM signal is significantly improved. For instance, the transmission distance of a 30-Gbps DML-based OFDM signal can be extended from 10 km to more than 100 km. Besides, since the dispersion-induced distortion could be effectively mitigated by the equalization, negative power penalties are observed at some distances due to chirp-induced power gain.

© 2012 OSA

## 1. Introduction

## 2. Analysis of the chirp effects

*N*(

*t*), the photon density in the laser cavity,

*S*(

*t*), and the phase of the optical field,

*φ*(

*t*) [13–15

15. K. Sato, S. Kuwahara, and Y. Miyamoto, “Chirp characteristics of 40-Gb/s directly modulated distributed- feedback laser diodes,” J. Lightwave Technol. **23**(11), 3790–3797 (2005). [CrossRef]

*I*is the injection current,

*V*is the active volume,

*q*is the electronic charge,

*g*is the optical gain,

*v*is the group velocity,

_{g}*AN*is the nonradiative recombination rate,

*BN*

^{2}is the radiative recombination rate,

*CN*

^{3}is the Auger recombination rate, Γ is the optical confinement factor,

*β*is the spontaneous emission factor,

_{sp}*τ*is the photon lifetime,

_{p}*α*is the linewidth enhancement factor,

*σ*is the differential gain, and

*N*is the carrier density at threshold. The output laser power is proportional to the photon density,

_{th}*η*is the total quantum efficiency including the coupling efficiency from laser to fiber, and

*hν*is the photon energy. In addition, the optical gain can be simplified as [13–15

15. K. Sato, S. Kuwahara, and Y. Miyamoto, “Chirp characteristics of 40-Gb/s directly modulated distributed- feedback laser diodes,” J. Lightwave Technol. **23**(11), 3790–3797 (2005). [CrossRef]

*N*is the transparent carrier density, and

_{tr}*ε*is the gain suppression coefficient, which characterizes the spectral hole burning (SHB). Because the SHB generates a small roughly symmetrical dip of the gain spectrum around the laser frequency, the Kramers-Kronig relation ensures that the symmetrical feature of the imaginary index alone will not produce any change of the real index at the laser frequency [16

16. T. L. Koch and R. A. Linke, “Effect of nonlinear gain reduction on semiconductor laser wavelength chirping,” Appl. Phys. Lett. **48**(10), 613–615 (1986). [CrossRef]

*ε*, and the frequency chirp above the laser threshold can be approximated as [16

16. T. L. Koch and R. A. Linke, “Effect of nonlinear gain reduction on semiconductor laser wavelength chirping,” Appl. Phys. Lett. **48**(10), 613–615 (1986). [CrossRef]

17. J. A. P. Morgado and A. V. T. Cartzxo, “Improved model to discriminate adiabatic and transient chirps in directly modulated semiconductor lasers,” J. Mod. Opt. **56**(21), 2309–2317 (2009). [CrossRef]

*I*is the bias current,

_{B}*M*is the subcarrier number,

*m*

^{th}subcarrier, and

*H*(

*m*), can be analytically derived such that the complex envelop of the output power,

*P*is the bias power,

_{B}*m*is the normalized power envelop,

*m*implies power is never complex, and

*m*indicates the signal is discrete-tone and DC-free. Besides, the optical phase is needed to determine the envelop of the optical field, i.e.

*α*and

*κ*of commercial DMLs are about 2-5 and 10-15 GHz/mW, respectively, and therefore, Ω is about 20-75 GHz assuming

*P*is 0 dBm [14

_{B}14. L. Bjerkan, A. Røyset, L. Hafskjær, and D. Myhre, “Measurement of laser parameters for simulation of high-speed fiberoptic systems,” J. Lightwave Technol. **14**(5), 839–850 (1996). [CrossRef]

*S*

_{1}, indicates the desired OFDM signal, but the second bracket,

*S*

_{2}, is the 2nd-order distortion in the optical field domain composed of the intermixing terms among subcarriers. After fiber transmission with the distance of

*L*, the group-velocity dispersion parameter of

*β*

_{2}and no fiber loss, the

*m*

^{th}frequency component of

*m*

^{th}subcarrier of the detected signal,

11. B. Wedding, “Analysis of fibre transfer function and determination of receiver frequency response for dispersion supported transmission,” Electron. Lett. **30**(1), 58–59 (1994). [CrossRef]

7. 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]

18. U. Gliese, S. Nørskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimieter-wave links,” IEEE Trans. Microw. Theory Tech. **44**(10), 1716–1724 (1996). [CrossRef]

*α*is fixed to 3 in the following content, since the effect of the transient chirp has been studied in [8

8. C.-C. Wei, “Small-signal analysis of OOFDM signal transmission with directly modulated laser and direct detection,” Opt. Lett. **36**(2), 151–153 (2011). [CrossRef] [PubMed]

6. A. Gharba, P. Chanclou, M. Ouzzif, J. L. Masson, L. A. Neto, R. Xia, N. Genay, B. Charbonnier, M. Hélard, E. Grard, and V. Rodrigues, “Optical transmission performance for DML considering laser chirp and fiber dispersion using AMOOFDM,” in *2010 International Congress on Ultra Modern Telecommunications and Control Systems and Workshops* (2010), pp. 1022–1026.

8. C.-C. Wei, “Small-signal analysis of OOFDM signal transmission with directly modulated laser and direct detection,” Opt. Lett. **36**(2), 151–153 (2011). [CrossRef] [PubMed]

*m*

^{th}frequency component of the total SSII,

*ξ*and

_{R}*ξ*is zero, and the detected OFDM signal is SSII-free. Moreover, the subcarriers are assumed to have equal power of

_{T}*M*, and the expectation values of the cross terms are zero. If the adiabatic chirp is zero, Eq. (13) could be further simplified as an analytical form [8

8. C.-C. Wei, “Small-signal analysis of OOFDM signal transmission with directly modulated laser and direct detection,” Opt. Lett. **36**(2), 151–153 (2011). [CrossRef] [PubMed]

*w*

^{2}in Eq. (13) can be replaced by

*M*and

*w*are set as 400 and 2.5 × 10

^{−5}, respectively. Comparing Figs. 2(a) and 2(b), more dispersion roughly induces higher SSII power. Besides, although increasing the adiabatic chirp may not enlarge the SSII power at all the frequencies as shown in Fig. 2(a), the in-band (≤ 8 GHz) SSII power roughly increases with larger adiabatic chirp. To further investigate the effects of power fading and the SSII on the transmission performance, the signal-to-interference ratios (SIR) with different dispersion and adiabatic chirp are plotted in Fig. 3 , where the SIR is calculated by

## 3. Numerical simulation

## 4. Iterative equalization

4. W.-R. Peng, B. Zhang, K.-M. Feng, X. Wu, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission incorporating a tunable frequency gap and an iterative detection techniques,” J. Lightwave Technol. **27**(24), 5723–5735 (2009). [CrossRef]

*x*in Eq. (4), the most challenge part of the proposed iterative equalization is the necessary knowledge of the transfer function from the drive current to the power envelop, i.e.

_{m}*H*(

*m*). This transfer function must be measured at BtB and sent to the receiver. Once the transfer function is known, the other important parameters including

*α*and Ω can be estimated by fitting the relative power of each subcarrier according to Eq. (9). As to

*L*, it can be measured in advance, for instance, by the optical time-domain reflectometer (OTDR) [20]. As a consequence, the demodulated data could be obtained as

*l*indicates the result of the

*l*

^{th}iterative process. Combined with the known transfer function and the estimated parameters, the SSII can be calculated by Eqs. (6)–(8), in which

*x*is replaced by

_{m}*x*are different in their magnitude. Accordingly, the SSII weighting shown in Fig. 5 is required to provide proper weighting factors to the calculated SSII to reach the best SSII mitigation. Similar to the data equalization, the SSII weighting factors are found by training symbols at the receiver, and in this work, these factors equal to the regression coefficients of the linear least squares fitting between the calculated SSII and the received distortion of training symbols. Notably, although the weighting factors are irrelevant to frequency in principle, the factor for each frequency component is actually found individually to make the SSII mitigation more tolerant to the possible errors of the simplified model and the estimated parameters.

_{m}^{−3}) is about 16.5 dB [24], which is plotted by the black dashed lines in Fig. 6 as a reference. After 20-km SSMF transmission, more than one third subcarriers cannot reach the FEC limit without the iterative equalization, as shown in Fig. 6(a). In this case, the proposed equalization can apparently improve the SINR, and the 1st equalization can perform as well as the ideal equalization. Since decision errors indeed happen in the simulation, the overlap of two SINR curves indicates the decision errors affect the SSII calculation little. A few subcarriers around 5.5 GHz, however, still cannot reach the FEC limit after the SSII mitigation, because they suffer from fading to become less tolerant to the noises, as shown in Fig. 4(a). When the transmission distance is increased to 100 km, the received subcarrier power is increased due to the chirp-induced gain shown in Fig. 4(a), but the even larger increment of the SSII power leads to the much worse demodulated SINR, as shown in Fig. 6(b). Nonetheless, compared with Fig. 6(a), the benefit of the chirp-induced gain would be noted after the iterative equalization, and all the subcarriers can achieve the FEC limit with the ideal equalization. In addition, owing to the increment of decision errors, the practical equalization cannot perform as well as the ideal one until the 2nd iteration.

*m*

^{th}subcarrier is given as

*ρ*, its BER is approximated as

_{m}^{−3}in Fig. 7(a), but it can be achieved after applying the proposed equalization. Similarly, the BER curves of the signals with the 1st and ideal equalization are almost the same. Compared with the case at BtB, the power penalty at the FEC limit after equalization is about 3 dB mainly contributed by power fading. After 100-km transmission, the demodulated signal suffers from much more serious SSII to show the BER floor of ~0.03 in Fig. 7(b). Furthermore, as the received power is 0 dBm, applying the iterative equalization cannot make the SINR and the BER better than those at BtB owing to the presence of residual distortion, as shown in Figs. 6(b) and 7(b), respectively. Nevertheless, if electrical noises dominate the BER performance at lower received power, the signal with the iterative equalization could outperform the signal at BtB due to the chirp-induced gain. Hence, compared with the case at BtB, the signal after 100-km transmission can behave about 0.9-dB sensitivity improvement, after applying the iterative equalization.

^{−3}, as shown in Figs. 8(a)-8(c). The reason is that power fading shown in Fig. 4(a) will decrease the received signal-to-noise ratios (SNRs). As to the case with 40-mA bias current, not only the subcarriers suffer from the power fading of less than 1 dB, but also about one fourth subcarriers are provided the chirp-induced gain, so that the FEC limit can be achieved after 20-km transmission. Similarly, the lower adiabatic chirp caused by the lower bias current would generate worse fading, and therefore, decrease the maximum transmission distances. The maximum transmission distances without the proposed equalization in Figs. 8(a)-8(d) are about 7, 8, 10 and 23 km, respectively. On the other hand, applying the proposed iterative equalization to mitigate the SSII could improve the transmission performance, but the improvement depends on the bias current and the distance. Within a short distance of ~10 km, the main issue is bad SNRs caused by power fading, and the SSII mitigation does not help much. However, larger adiabatic chirp and even more dispersion might ease power fading, as shown in Fig. 4(a). Consequently, it is possible to improve the performance significantly after longer transmission and SSII mitigation. Unfortunately, SSII mitigation only slightly improves the sensitivity and transmission distance in Fig. 8(a), because not only power fading but also the nonlinear DML response dominates. In Fig. 8(b), similar situation can be observed within 10 km, but it can achieve the FEC limit after the transmission distance between 80 and 115 km owing to more chirp-induced gain and less nonlinear DML response. In Figs. 8(c) and 8(d), because the nonlinear DML response affects the signal little, the proposed iterative equalization could extend the transmission distance beyond 90 km. Meanwhile, since a large portion of distortion can be modeled as SSII and be eliminated by the iterative equalization well, the performance is mainly determined by the SNRs, or equivalently, by power fading. Hence, negative sensitivity penalties are observed after transmission, and the case with the 40-mA bias current can outperform the case with the 30-mA bias current after the transmission of less than 80 km. Nonetheless, because the distortion cannot be completely removed by the 2nd-order SSII mitigation, residual distortion would eventually limit the maximum transmission distance. Hence, the maximum transmission distances in Figs. 8(b)-8(d) decrease with the larger adiabatic chirp, or equivalently, with more deviation from the SSM. On the other hand, corresponding to Fig. 8(c), Figs. 8(e) and 8(f) plot the sensitivities of the signals with the same bias current of 30 mA, but the different peak-to-peak drive currents of 20 and 45 mA, respectively. This indicates the OFDM signals of Figs. 8(e), 8(c) and 8(f) have the same Ω of 94.8 GHz, but they have different

*w*of 9.5 × 10

^{−6}, 2.1 × 10

^{−5}and 4.8 × 10

^{−5}, respectively. The same Ω represents the OFDM signals would suffer from similar power fading, and the larger

*w*implies larger CSPR and better SNR at the same received power. Accordingly, when the electrical noises dominate the SINR, whether the distortion is inherently small or mitigated mostly by the proposed equalization, the signal with larger

*w*could perform better. For instance, applying the proposed equalization, the OFDM signal of Fig. 8(f) can outperform those of Figs. 8(e) and 8(c) after the transmission of < 50 km. However, the larger

*w*also implies larger distortion, including 2nd-order and higher-order SSIIs, such that there would be more residual distortion after the iterative equalization. As a result, the maximum transmission distance decreases with larger

*w*, as shown in Figs. 8(e), 8(c) and 8(f). In addition, for the many cases of Fig. 8, the 1st equalization can generate apparent improvement, even compared with the ideal equalization, and therefore, the iterative process might be neglected to lower computational complexity. Such good performance of the 1st equalization is because the SSII is contributed by a lot of subcarriers, and a few decision errors may not affect the calculated SSII much around the BER of interest. Even if the iterative process is applied, the 2nd equalization could perform as well as the ideal one, and triple or more iteration might not provide further improvement for the most cases.

*α*and Ω are required to calculate the SSII, they need to be estimated at the receiver. Although the estimation errors of these parameters in Figs. 6-8 are less than ± 5%, it seems necessary to study how the estimation errors affect the equalization performance. Actually, the proposed equalization is quite insensitive to the estimation errors. To show this, the sensitivity penalties caused by the estimation errors of

*α*and Ω are exhibited in Fig. 9 , where the twice iterative equalization is applied after 100-km SSMF and the other operation conditions are identical to those in Fig. 8(c). Because the residual dispersion, i.e.

*L*and/or

*β*

_{2}, may also be measured inaccurately, the effect of inaccurate estimation of residual dispersion is also investigated by providing the dispersion errors of –20%, –10%, 0, + 10% and + 20% to Figs. 9(a)-9(e), respectively. Moreover, the green and red boxes in Fig. 9 indicate the boundaries of ± 10% and ± 20% estimation errors of the chirp parameters, respectively. According to Figs. 9(b)-9(d), if the estimation errors of these three parameters are all within ± 10%, the corresponding penalty would be approximately less than 0.1 dB. Even if the estimation errors are up to ± 20%, the penalty will never exceed 0.5 dB, actually, mostly below 0.3 dB, as shown in Fig. 9. The tolerance to the estimation errors is mainly because the SSII weighting in Fig. 5 would statistically adjust the calculated SSII with the deviated parameters to meet the real distortion.

## 5. Conclusions

## Appendix

_{∑m=−2M2Mymejmωt}, and its frequency component can be obtained by discrete convolution,To derive

*X*, Eqs. (10) and (11a) can be derived. On the other hand,

*S*

_{2}without dispersion is the linear combination of

*S*

_{2}with dispersion is represented as

## Acknowledgment

## References and links

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

2. | M. C. Yuang, P.-L. Tien, D.-Z. Hsu, S.-Y. Chen, C.-C. Wei, J.-L. Shih, and J. Chen, “A high-performance OFDMA PON system architecture and medium access control,” J. Lightwave Technol. |

3. | D. F. Hewitt, “Orthogonal frequency division multiplexing using baseband optical single sideband for simpler adaptive dispersion compensation,” in |

4. | W.-R. Peng, B. Zhang, K.-M. Feng, X. Wu, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission incorporating a tunable frequency gap and an iterative detection techniques,” J. Lightwave Technol. |

5. | D.-Z. Hsu, C.-C. Wei, H.-Y. Chen, J. Chen, M. C. Yuang, S.-H. Lin, and W.-Y. Li, “21 Gb/s after 100 km OFDM long-reach PON transmission using a cost-effective electro-absorption modulator,” Opt. Express |

6. | A. Gharba, P. Chanclou, M. Ouzzif, J. L. Masson, L. A. Neto, R. Xia, N. Genay, B. Charbonnier, M. Hélard, E. Grard, and V. Rodrigues, “Optical transmission performance for DML considering laser chirp and fiber dispersion using AMOOFDM,” in |

7. | 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 |

8. | C.-C. Wei, “Small-signal analysis of OOFDM signal transmission with directly modulated laser and direct detection,” Opt. Lett. |

9. | F. Devaux, Y. Sorel, and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol. |

10. | J. Binder and U. Kohn, “10 Gbit/s-dispersion optimized transmission at 1.55 μm wavelength on standard single mode fiber,” IEEE Photon. Technol. Lett. |

11. | B. Wedding, “Analysis of fibre transfer function and determination of receiver frequency response for dispersion supported transmission,” Electron. Lett. |

12. | I. Papagiannakis, C. Xia, D. Klonidis, W. Rosenkranz, A. N. Birbas, and I. Tomkos, “Electronic distortion equalisation by using decision-feedback/feed-forward equaliser for transient and adiabatic chirped directly modulated lasers at 2.5 and 10 Gb/s,” IET Optoelectron. |

13. | L. A. Coldren and S. W. Corzine, |

14. | L. Bjerkan, A. Røyset, L. Hafskjær, and D. Myhre, “Measurement of laser parameters for simulation of high-speed fiberoptic systems,” J. Lightwave Technol. |

15. | K. Sato, S. Kuwahara, and Y. Miyamoto, “Chirp characteristics of 40-Gb/s directly modulated distributed- feedback laser diodes,” J. Lightwave Technol. |

16. | T. L. Koch and R. A. Linke, “Effect of nonlinear gain reduction on semiconductor laser wavelength chirping,” Appl. Phys. Lett. |

17. | J. A. P. Morgado and A. V. T. Cartzxo, “Improved model to discriminate adiabatic and transient chirps in directly modulated semiconductor lasers,” J. Mod. Opt. |

18. | U. Gliese, S. Nørskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimieter-wave links,” IEEE Trans. Microw. Theory Tech. |

19. | 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. |

20. | K. Yuksel, V. Moeyaert, M. Wuilpart, and P. Mégret, “Optical layer monitoring in passive optical networks (PONs): a review,” in |

21. | E. O. Brigham, |

22. | G. P. Agrawal, |

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

24. | L. Hanzo, W. Webb, and T. Keller, |

**OCIS Codes**

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

(060.3510) Fiber optics and optical communications : Lasers, fiber

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: September 12, 2012

Manuscript Accepted: September 16, 2012

Published: October 30, 2012

**Citation**

Chia-Chien Wei, "Analysis and iterative equalization of transient and adiabatic chirp effects in DML-based OFDM transmission systems," Opt. Express **20**, 25774-25789 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-23-25774

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### References

- J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol.27(3), 189–204 (2009). [CrossRef]
- M. C. Yuang, P.-L. Tien, D.-Z. Hsu, S.-Y. Chen, C.-C. Wei, J.-L. Shih, and J. Chen, “A high-performance OFDMA PON system architecture and medium access control,” J. Lightwave Technol.30(11), 1685–1693 (2012). [CrossRef]
- D. F. Hewitt, “Orthogonal frequency division multiplexing using baseband optical single sideband for simpler adaptive dispersion compensation,” in Optical Fiber Communication Conference (2007), Paper OME7.
- W.-R. Peng, B. Zhang, K.-M. Feng, X. Wu, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission incorporating a tunable frequency gap and an iterative detection techniques,” J. Lightwave Technol.27(24), 5723–5735 (2009). [CrossRef]
- D.-Z. Hsu, C.-C. Wei, H.-Y. Chen, J. Chen, M. C. Yuang, S.-H. Lin, and W.-Y. Li, “21 Gb/s after 100 km OFDM long-reach PON transmission using a cost-effective electro-absorption modulator,” Opt. Express18(26), 27758–27763 (2010). [CrossRef] [PubMed]
- A. Gharba, P. Chanclou, M. Ouzzif, J. L. Masson, L. A. Neto, R. Xia, N. Genay, B. Charbonnier, M. Hélard, E. Grard, and V. Rodrigues, “Optical transmission performance for DML considering laser chirp and fiber dispersion using AMOOFDM,” in 2010 International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (2010), pp. 1022–1026.
- 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. Express19(18), 17546–17556 (2011). [CrossRef] [PubMed]
- C.-C. Wei, “Small-signal analysis of OOFDM signal transmission with directly modulated laser and direct detection,” Opt. Lett.36(2), 151–153 (2011). [CrossRef] [PubMed]
- F. Devaux, Y. Sorel, and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol.11(12), 1937–1940 (1993). [CrossRef]
- J. Binder and U. Kohn, “10 Gbit/s-dispersion optimized transmission at 1.55 μm wavelength on standard single mode fiber,” IEEE Photon. Technol. Lett.6(4), 558–560 (1994). [CrossRef]
- B. Wedding, “Analysis of fibre transfer function and determination of receiver frequency response for dispersion supported transmission,” Electron. Lett.30(1), 58–59 (1994). [CrossRef]
- I. Papagiannakis, C. Xia, D. Klonidis, W. Rosenkranz, A. N. Birbas, and I. Tomkos, “Electronic distortion equalisation by using decision-feedback/feed-forward equaliser for transient and adiabatic chirped directly modulated lasers at 2.5 and 10 Gb/s,” IET Optoelectron.3(1), 18–29 (2009). [CrossRef]
- L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).
- L. Bjerkan, A. Røyset, L. Hafskjær, and D. Myhre, “Measurement of laser parameters for simulation of high-speed fiberoptic systems,” J. Lightwave Technol.14(5), 839–850 (1996). [CrossRef]
- K. Sato, S. Kuwahara, and Y. Miyamoto, “Chirp characteristics of 40-Gb/s directly modulated distributed- feedback laser diodes,” J. Lightwave Technol.23(11), 3790–3797 (2005). [CrossRef]
- T. L. Koch and R. A. Linke, “Effect of nonlinear gain reduction on semiconductor laser wavelength chirping,” Appl. Phys. Lett.48(10), 613–615 (1986). [CrossRef]
- J. A. P. Morgado and A. V. T. Cartzxo, “Improved model to discriminate adiabatic and transient chirps in directly modulated semiconductor lasers,” J. Mod. Opt.56(21), 2309–2317 (2009). [CrossRef]
- U. Gliese, S. Nørskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimieter-wave links,” IEEE Trans. Microw. Theory Tech.44(10), 1716–1724 (1996). [CrossRef]
- 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]
- K. Yuksel, V. Moeyaert, M. Wuilpart, and P. Mégret, “Optical layer monitoring in passive optical networks (PONs): a review,” in International Conference on Transparent Optical Networks (2008), Paper Tu.B1.1.
- E. O. Brigham, Fast Fourier Transform and Its Applications, 1st ed. (New York: Wiley, 1997).
- G. P. Agrawal, Fibre-Optic Communication Systems, 2nd ed. (Prentice Hall, 1988).
- W.-R. Peng, “Analysis of laser phase noise effect in direct-detection optical OFDM transmission,” J. Lightwave Technol.28(17), 2526–2536 (2010). [CrossRef]
- L. Hanzo, W. Webb, and T. Keller, Single- and Multi-Carrier Quadrature Amplitude Modulation, 2nd ed. (Wiley, 2000).

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