近年來正交分頻多工(OFDM)系統因為它提升光纖通訊的效能方面的益處使其越來越獲得重視，不僅在長距離傳輸有更好的表現並且有高的比特率(bit-rate)，這些都是正交分頻多工(OFDM)系統令人感興趣的地方。正交分頻多工(OFDM)系統已經在無線通訊上有許多的應用，例如:非同步數位用戶專線(ADSL)、ETSI數字式廣播(DAB)、數字式錄影廣播(DVB)、高清晰度電視(HDTV)、無線寬頻區域網路(WLAN)等等。

正交分頻多工(OFDM)系統已經被廣泛的應用在寬頻架線以及無線通信系統並且有效的解決了碼元間干擾(ISI)。事實上正交分頻多工(OFDM)是多載頻調制技術的一種，並不是一個全新的技術，它的歷史可以追朔到1966年貝爾實驗室的Chang首先介紹了正交分頻多工(OFDM)的概念。

在此篇論文裡，我會首先簡介光纖通訊系統，接著我將解釋我的實驗動機以及實驗架構。

其次是理論研究，在模擬的部分我探討正交分頻多工(OFDM)系統性能與副載波數目及中繼器輸出功率之間的關係。所得的結果為較小數目的載子數會有較佳的傳輸效能。在我的研究條件下，中繼器輸出功率為0時得到最佳的結果。

接著是實驗研究，在實驗研究中正交分頻多工(OFDM)所需的信號波形為離線計算再由任意波形產生器(AWG)來產生。

Recent years, Orthogonal Frequency Division Multiplexing (OFDM) system gets more and more attentions for its great benefit to the optical fiber communication system for improving the transmission performance. Not only better performance in long distance transmission but also high bit-rate is attractive feature of the OFDM system. The OFDM technology has been developed for the wireless communication system, and is now used in Asymmetric Digital Subscriber Line (ADSL), ETSI Digital Audio Broadcasting (DAB), Digital Video Broadcasting (DVB), High Definition Television (HDTV), Wireless Local Area Network (WLAN) and so on.

The OFDM is extensively used in broadband wired and wireless communication systems, and it solves the problem of intersymbol interference (ISI) effectively. Actually, the OFDM is a kind of Multi-Carrier Modulation (MCM), and it is not a brand-new technology. The history of the OFDM can be traced back to 1966 when Chang of Bell Labs introduced the concept of the OFDM.

In this thesis, I will briefly introduce the background of optical fiber communication system, then, explain my motivation and the structure of this thesis.

Next, theoretical study has been conducted. For the simulation, I discuss the performance of the OFDM system related to the number of subcarriers and the erbium-doped fiber amplifier (EDFA) repeater output power. It revealed that small number of subcarriers had better transmission performance. In my study case, repeater output power of 0dBm was the optimum condition.

In addition, experimental study has been conducted. For the experiment, the waveform required for the OFDM signal generation was calculated offline, and it was realized by the Arbitrary Waveform Generator (AWG).

Finally, this thesis is concluded.

致謝 I
中文摘要 III
Abstract IV
Contents V

1　Introduction 1
1.1　Background of Optical Fiber Communication System . . . . .. . . . . . 1
1.2　Motivation of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3　Structure of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2　Theoretical Study of OFDM Transmission 7
2.1　Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2　Simulation method and model . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1　Mathematical formulation of an OFDM signal. . . . . . . . . . . 11
2.2.2　Coherent system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.3　Heterodyne detection . . . . . . . . . . . . . . . . . . . . 15
2.2.4　Cyclic prefix for OFDM . . . . . . . . . . . . . . . . . . . . . . . .. . 17
2.2.5　Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.6　Transmission line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.7　Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3　Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4　Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3　Experimental Study of OFDM 24
3.1　Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2　Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1　Transmitter.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.2　Receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3　Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4　Conclusion 32

Acronyms VII

[1]Cisco Inc, Approaching the zettabyte era, Information available at http://www.cisco.com/en/US/solutions/collateral/ns341/ns525/ns537/ns705/ns827/white_paper_c11-481374_ns827_Networking_Solutions_White_Paper.html
[2]T. H. Maiman, "Stimulated Optical Radiation in Ruby," Nature, Vol. 187, No. 4736, pp. 493-494, 1960.
[3]Kazovsky L., "Multichannel coherent optical communications systems," J Lightwave Technol, Vol. 5, pp. 1095-1102, 1987.
[4]Okoshi T., "Heterodyne and coherent optical fiber communications: Recent progress," IEEE Trans Microwave Techniques, Vol. 82, pp. 1138-1149, 1982.
[5]Gnauck AH, Tkach RW, Chraplyvy AR, Li T, "High-capacity optical transmission systems, " J Lightwave Technol, Vol. 26, pp. 1032-1045, 2008.
[6]B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, " Experimental demonstrations of 20 Gbit/s direct-detection optical OFDM and 12 Gbit/s with a colorless transmitter," Proc. Opt. Fiber Commun. Conf., Anaheim, CA, Paper PDP 18, 2007.
[7]S. C. J. Lee, F. Breyer, S. Randel, M. Schuster, J. Zeng, F. Huijskens, H. P. A. van den Boom, A. M. J. Koonen, and N. Hanik,” 24-Gb/s transmission over 730 m of multimode fiber by direct modulation of an 850-nm VCSEL using discrete multi-tone modulation," in Proc. Opt. Fiber Commun. Conf., Anaheim, CA, Paper PDP 6, 2007.
[8]W. Shieh, X. Yi, and Y. Tang, "Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fibre," Electron. Lett., Vol. 43, No. 3, pp. 183-184, 2007.
[9]Sander L. Jansen, Itsuro Morita, Tim C. W. Schenk, Noriyuki Takeda, and Hideaki Tanaka, "Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF," Journal of Lightwave Technology, Vol. 26, pp. 6-15, 2008.
[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. ", Vol. 26, Issue 1, pp. 6-15, 2008.
[11]H. Masuda, E. Yamazaki, A. Sano, T. Yoshimatsu, T. Kobayashi, E. Yoshida, Y. Miyamoto, S. Matsuoka, Y.Takatori, M. Mizoguchi, K. Okada, K. Hagimoto, T. Yamada, and S. Kamei, "13.5-Tb/s (135 x 111-Gb/s/ch) noguard-interval coherent OFDM transmission over 6,248 km using SNR maximized second-order DRA in the extended L-band", in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America,2009) ,paper PDPB5.
[12]R. W. Chang, "Orthogonal Frequency Multiplex Data Transmission System, " USA U.S. Patent 3,488,445, 1966.
[13]N.E. Jolley, H. kee, R. Rickard and J. Tang, "Generation and propagation of a 1550 nm 10 Gbit/s Optical Orthogonal Frequency Division Multiplexed signal over 1000m of Multimode fibre using a directly modulated DFB", OFC/NFOEC, Anaheim California USA, March 11, 2005, paper OFP3
[14]William Shieh, Ivan Djordjevic, "OFDM for Optical Communications", 2010, Elsevier Inc.
[15]Hidenori Taga, "A theoretical study of OFDM system performance with respect to subcarrier numbers, "Optics Express 17(21), 18638-18642 (2009).
[16]S.L. Jansen, I. Morita, T.C.W. Schenk, D. van den Borne, H. Tanaka., "Optical OFDM - A Candidate for Future Long-Haul Optical Transmission Systems, "Optical Society of America, paper OMU3, 2008.
[17]Sander L. Jansen, Itsuro Morita and Hideaki Tanaka, "16x52.5-Gb/s, 50-GHz spaced, POLMUX-CO-OFDM transmission over 4,160 km of SSMF enabled by MIMO processing,” KDDI R&D Laboratories, Saitama, Japan, 2007.
[18]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. ", Vol. 26, Issue 1, pp. 6-15, 2008.
[19]Jan Tubbax, Boris C6me, Liesbet Van der Perre, Luc Deneire, Stephane Donnay, Marc Engels, "OFDM versus Single Carrier with Cyclic Prefix: a svstem-based comparison", IEEE, Vol. 2, pp. 1115-1119, 2001.
[20]W. Owen Brimijoin, 25 Jun 2010 (Updated 14 Jul 2010) http://www.mathworks.com/matlabcentral/fileexchange/28015