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研究生:羅謙翰 
研究生(外文):Lo Chain-Han
論文名稱:哈達瑪正交分頻多工轉換系統中格雷互補序列之研究
論文名稱(外文):Investigation of Golay Complementary sequences in WHT-OFDM system
指導教授:陳後守
指導教授(外文):Chen Hou-Shou
學位類別:碩士
校院名稱:國立中興大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
中文關鍵詞:峰均值比正交分頻多工系統哈達瑪正交分頻多工轉換系統格雷互補序列里得-米勒碼
外文關鍵詞:PAPROFDMWHT-OFDMGolay complementary sequencesReed-Muller Codes
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本篇論文主要研究哈達瑪正交分頻多工轉換系統中之格雷序列。在傳統正交分頻多工系統能夠利用由里得-米勒碼產生之格雷序列使得其峰均值比保持最大到達2。因此,我們參考傳統的正交分頻多工系統產生格雷序列的方法應用到哈達瑪正交分頻多工轉換系統後,發現當使用BPSK調變時,輸入一階里得-米勒碼R(1,m)或其某些R(1,m)之平移,但其平移仍屬於二階里得-米勒碼R(2,m)時,這些序列能夠使其最大峰均值比之值保持在$2$以下。進一步分析哈達瑪正交分頻多工轉換系統中峰均值比小於2之陪集的形式時,我們發現由這些陪集所產生之哈達瑪正交分頻多工系統之格雷序列與正交分頻多工系統中格雷序列所出現的陪集有相似之處。而且哈達瑪正交分頻多工轉換系統 中格雷序列的數目多於正交分頻多工系統內的格雷序列。最後,我們以圖形的方法來描述其格雷序列所出現的陪集型式。

The use of block coding method, i.e., the Golay Complementary Sequences and Reed-Muller codes, is guaranteed to reduce the peak-to-average power ratio (PAPR) below two in Orthogonal Frequency-Division Multiplexing (OFDM) systems. In this thesis, we investigate the Golay Complementary Sequences in
Walsh-Hadamard transformed OFDM (WHT-OFDM) systems. By computer
search, we find that the Golay Complementary Sequences also exist in WHT-OFDM systems and the number of Golay Complementary
Sequences in WHT-OFDM systems seems to be larger than those in
OFDM systems.
In OFDM systems, these Golay Sequences are the cosets of the first Reed-Muller codes within the second order Reed-Muller codes. This motivates us to study the connection between the Golay Sequences and the cosets of first order Reed-Muller codes in WHT-OFDM systems. We observe that the form of Golay Complementary Sequences in WHT-OFDM systems are like those in OFDM systems and we will use the graphic form to show some constructions of Golay sequences in WHT-OFDM.

第一章 緒論
第二章 理論基礎
2.1 正交分頻多工系統
2.2 相關函數與迴旋總合
2.3 里得-米勒碼
2.4 格雷序列
第三章 兩段式正交轉換
3.1 兩段式正交轉換
3.2 哈達瑪正交分頻多工轉換系統之架構
3.3 哈達瑪正交分頻多工轉換系統的高峰均值比問題
第四章 哈達瑪正交分頻多工轉換系統之格雷序列
4.1 哈達瑪正交分頻多工轉換系統瞬間功率之分析
4.2 哈達瑪正交分頻多工轉換系統之格雷互補序列
第五章 結論

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[2] J. A. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes,” IEEE Trans. Inform. Theory, vol. 45, no. 7, pp. 2397 — 2417, Nov. 1999.
[3] J. A. Davis and J. Jedwab, “Peak-to-mean mower control and error correction for OFDM transmission using Golay sequences and Reed-Muller Codes,” Electron. Lett., vol. 33, no. 4, pp. 267-268, Feb. 1997.
[4] S. Hara and R. Prasad, “Overview of Multicarrier CDMA,” IEEE Commun. Mag., vol. 35, no.12, pp. 126 — 133, Dec. 1997.
[5] K. Kang, K. Choi, and S. K. Shin, ”Reduced Search for Optimum Code Sets to Reduce PAPR in MC-CDMA System,” in 5th Int. Symp. Wireless Personal Multimedia communications, Oct. 2002. vol.1, pp.27-30.
[6] B. Tarokh and H. R. Sadjadpour, “Construction of OFDM M-QAM Sequences With Low Peak-to-Average Power Ratio,” IEEE Trans. Commun., vol. 51, no. 1, pp. 25-28, Jan. 2003.
[7] C. RoBing, “Golay Complementary Sequences for OFDM with 16-QAM,” in Proc. IEEE Int. Symp. Inform. Theory, June 2000, pp. 25-30.
[8] V. Tarokh and H. Jafarkhani, “On the Computation and Reduction of the Peak-to-Average Power Ratio in Multicarrier Communications,” IEEE Trans. Commun., vol. 48, no. 1, pp. 37-44, Jan. 2004.
[9] Y. Wu and C. K. Ho and S. Sun, “On Some Properties of Walsh-Hadamard Transformed OFDM,” in Proc. VTC 2002-Fall IEEE 56th Vehicular Technology Conf., Sept. 2002, vol. 4, pp. 24-28.
[10] N. Ohkubo and T. Ohtsuki, “A Peak to Average Power Ratio Reduction of Multicarrier CDMA Using Selected Mapping,” in Proc. VTC 2002-Fall IEEE 56th Vehicular Technology Conf., Sept. 2002, vol. 4, pp. 24-28
[11] M. Park and H. Jun and J. Cho and N. Cho and D. Hong and C. Kang, “PAPR Reduction in OFDM Transmission using Hadamard Transform,” IEEE Conf. Commun., vol. 1, pp. 430-433, June 2000.
[12] R. V. Nee and R. Prasad, OFDM Wireless Multimedia Communication, Artech House, Boston, 2000.
[13] S. Roman, Coding and Information Theory, Springer-Verlag, New York 1992.
[14] J. Adamek, FUNDATIONS OF CODING: Theory and Applications of Error -correcting Codes, with an Introduction to Cryptography and Information Theory , John Wiley & Sons, Inc., Chichester, 1991.
[15] F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes Amsterdam, The Netherlands: North-Holland, 1986.
[16] K. Yang, “Peak-to-Average Power Control in OFDM Using Standard Arrays of Linear Block Codes,” IEEE Commun. Lett., vol. 7, no. 4, pp. 174-176, April 2003.
[17] K. G. Paterson, “On Codes with Low Peak-to-Average Power Ratio for Multi-Code CDMA,” IEEE Trans. Inform. Theory, vol. 50, no. 3, pp. 550-559, March 2004.

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