為了實現低成本光纖傳輸系統，強度調變直接偵測 (Intensity Modulation/ Direct Detection, IM/DD)系統在短距離傳輸中是一個很好的選擇。本篇論文描述，在基於直接調變DFB雷射 (Direct Modulated DFB Lasers, DMLs)的正交分頻多工傳輸系統中，由於色散 (Dispersion)和絕熱啁啾 (Adiabatic Chirp)的交互作用而產生的非線性影響。在實驗中，我們藉由改變不同的光纖傳輸長度 (0-200公里)，來改變不同的色散程度。以及藉由改變雷射的驅動電流 (60-120毫安培)，來產生不同的絕熱啁啾大小。由於絕熱啁啾可以用來調節因為色散引起的功率衰減，甚至可以提供功率增益，因此當透過非線性補償減輕非線性失真時，特定量的絕熱啁啾是有益於傳輸性能的。
本論文使用伏爾泰拉濾波器與神經網路來補償，在基於直接調變DFB雷射的正交分頻多工傳輸系統中產生的非線性失真。論文中探討消除受功率衰減之子載波，能有效提升非線性補償能力。而使用高低通濾波器混合模型之神經網路模型，可以解決因經過神經網路補償後，訊號低頻處訊雜比降低的問題。最後，藉由使用伏爾泰拉濾波器與神經網路能夠消除非線性的影響，使得最大容量提升量分別可達15 Gbps與20 Gbps。

In order to achieve cost-effective transmission, intensity modulation (IM) and direct detection (DD) are preferable for short-range systems. This dissertation provides detailed descriptions of the interplay between dispersion and chirp (specifically adiabatic chirp), in an optical orthogonal frequency-division multiplexing (OFDM) transmission system based on a directly modulated DFB laser (DML). We experimentally investigated various amounts of dispersion and adiabatic chirp by, respectively, varying the length of the fiber (0–200 km) and the bias current (60-120mA) of the laser. Since adiabatic chirp was shown to mediate dispersion-induced power fading and even provide a power gain. This is an indication that a specific amount of adiabatic chirp may be beneficial to transmission performance, particularly when the nonlinear distortion is mitigated by nonlinear compensation.
The Volterra filters and neural networks are used in this dissertation to compensate for nonlinear distortion in DML-based OFDM transmission systems. By disabling the sub-carriers that suffer from significant power fading, we can effectively improve the ability of nonlinear compensation. Moreover, integrating the high/low-pass filters into neural networks can mitigate the degradation in signal-to-noise ratio at low frequency caused by neural networks. Finally, using Volterra filters and neural networks to eliminate nonlinearity can increase the data rate by up to 15 Gbps and 20 Gbps, respectively.

論文審定書 i
致謝 ii
中文摘要 iii
Abstract iv
目錄 v
圖目錄 vii
第1章 緒論 1
1-1 前言 1
1-2 研究動機 2
第2章 直接調變強度偵測系統 4
2-1 正交分頻多工 4
2-1-1 正交分頻多工之簡介 4
2-1-2 正交分頻多工之原理 4
2-1-3 正交分頻多工之優缺點 5
2-2 強度調變直接偵測 9
2-2-1 強度調變直接偵測簡介 9
2-2-2 直接調變DFB雷射 10
2-2-3 光二極體 11
2-3 光纖傳輸系統 13
2-3-1 光纖傳輸簡介 13
2-3-2 色散 13
2-3-3 啁啾 14
2-3-4 功率衰減 14
第3章 非線性補償系統 16
3-1 伏爾泰拉濾波器 16
3-1-1 伏爾泰拉濾波器簡介 16
3-2 神經網路 18
3-2-1 神經網路簡介 18
3-2-2 激發函數 21
3-2-3 誤差反向傳播演算法與梯度下降法 24
3-2-4 基於神經網路之波形迴歸非線性補償 28
第4章 實驗結果與討論 29
4-1 實驗架構 29
4-1-1 實驗設備 29
4-1-2 實驗流程 30
4-2 實驗結果與討論 34
4-2-1 消除受功率衰減之子載波對補償結果之影響 34
4-2-2 神經網路應用不同激發函數探討 36
4-2-3 神經網路超參數調整對補償結果之影響 38
4-2-4 使用高低通濾波器增強神經網路對低頻之補償能力 39
4-2-5 神經網路與伏爾泰拉濾波器補償結果比較 44
結論 50

[1] Cisco®, "Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update, 2016–2021 White Paper," 28 March 2017. [Online]. Available: https://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/mobile-white-paper-c11-520862.html.
[2] K. T., "Fiber to the home/fiber to the premises: what, where, and when?," IEEE, pp. 911-934, 2006.
[3] C. C. Wei, "Small-signal analysis of OOFDM signal transmission with directly modulated laser and direct detection," Optics letters, pp. 36(2), 151-153., 2011.
[4] T. Koch and J. Bowers, "Nature of wavelength chirping in directly modulated semiconductor lasers," Electron. Lett., pp. vol. 20, no. 25,pp. 1038–1040, 12 1984.
[5] K. Sato, S. Kuwahara and Y. Miyamoto, "Chirp characteristics of 40-Gb/s directly modulated distributed-feedback laser diodes," J. Lightw. Technol., pp. vol. 23, no. 11, pp. 3790–3797, 11 2005.
[6] C. C. Wei, "Analysis and iterative equalization of transient and adiabatic chirp effects in DML-based OFDM transmission systems," Optics express, pp. 20 (23), 25774-25789., 2012.
[7] W. Yan, "100 Gb/s optical IM-DD transmission with 10G-class devices enabled by 65 GSamples/s CMOS DAC core," in Proc. Opt. Fiber Commun. Conf., 2013.
[8] T. Takahara, "Discrete multi-tone for 100 Gb/s optical access networks," in Proc. Opt. Fiber Commun. Conf., 2014.
[9] B. Wedding, "Analysis of fibre transfer function and determination of receiver frequency response for dispersion supported transmission," Electron. Lett., pp. vol. 30, no. 1, pp. 58–59, 1 1994.
[10] D. Hsu, "SSII cancellation in an EAM-based OFDM-IMDD transmission system employing a novel dynamic chirp model," Opt. Exp., pp. vol. 21, no. 1, pp. 533–543, 1 2013.
[11] Wei.C.C., "Analysis of nonlinear distortion and SSII cancellation in EAM-Based IMDD OFDM transmission," J. Lightw. Technol., pp. vol. 33, no. 14, pp. 3069–3082, 7 2015.
[12] H.L.Cheng, Y.H.Wang, C.C.Wei. and Chen.J., "30-Gbps 100-km OFDM transmission using 10-GHz DML and adiabatic-chirp-involved SSII cancellation," in Proc. Opt. Fiber Commun. Conf., 2016.
[13] W.Yan, B. Liu, L. Li, Z. Tao, T. Takahara and J. C. Rasmussen, "Nonlinear distortion and DSP-based compensation in metro and access networks using discrete multi-tone," in Proc. Eur. Conf. Opt. Commun., 2012.
[14] C. J. Pan and C.H., "Nonlinear electrical compensation for the coherent opticalOFDMsystem," J. Lightw. Technol., pp. vol. 29, no. 2, pp. 215–221, 1 2011.
[15] H.Y.Chen, C.C.Wei, C.Y.Lin, L.W.Chen, I.C.Lu and J.Chen, "Frequency- and time-domain nonlinear distortion compensation in high-speed OFDM-IMDD LR-PON with high loss budget," Opt. Exp., pp. vol. 25,no. 5, pp. 5044–5056, 3 2017.
[16] Y. Bao, Z. Li, J. Li, X. Feng, B. Guan and G. Li, "Nonlinearity mitigation for high-speed optical OFDM transmitters using digital pre-distortion," Opt. Exp., pp. vol. 21, no. 6, pp. 7354–7361, 3 2013.
[17] C.-Y. Chuang, C.-C. Wei, T.-C. Lin, K.-L. Chi, L.-C. Liu, J.-W. Shi, Y.-K. Chen and J. Chen, "Employing Deep Neural Network for High Speed 4-PAM Optical Interconnect," in European Conference on Optical Communication, 2017.
[18] W. R., "Synthesis of Band‐Limited Orthogonal Signals for Multichannel Data Transmission," Bell System Technical Journal, pp. 45(10), 1775-1796., 1966.
[19] K. Alex, S. Ilya and G. E. Hinton, "ImageNet Classification with Deep Convolutional Neural Networks," in NIPS'12 Proceedings of the 25th International Conference on Neural Information Processing Systems, Lake Tahoe, Nevada, 2012.
[20] D. Attwell and S. B. Laughlin, "An Energy Budget for Signaling in the Grey Matter of the Brain," Journal of Cerebral Blood Flow and Metabolism, pp. 1133-1145, 1 10 2001.
[21] X. Glorot, A. Bordes and Y. Bengio, "Deep Sparse Rectifier Neural Networks," in 14th International Conference on Artificial Intelligence and Statistics, 2010.
[22] dustinstansbury, "The Clever Machine Topics in Computational Neuroscience and Machine Learning," [Online]. Available: https://theclevermachine.wordpress.com/2012/02/13/cutting-your-losses-loss-functions-predominance-of-sum-of-squares/.
[23] B. M. Christopher, Pattern Recognition and Machine Learning, Springer, 2006.
[24] N. A. Michael, Neural Networks and Deep Learning, 2015.
[25] H. Schneider, Master Machine Learning Algorithms, 2016.
[26] T. N. Duong, N. Genay, M. Ouzzif, J. L. Masson, B. Charbonnier, P. Chanclou and J. C. Simon, "Adaptive loading algorithm implemented in AMOOFDM for NG-PON system integrating cost-effective and low-bandwidth optical devices," IEEE Photonics Technol, 2009.