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 格雷互補序列具有成對序列非週期性自相關函數和為脈衝的特性，在通訊領域中有許多應用。相互正交的序列因彼此不會互相干擾，也常用在通訊系統中。本研究主要探討QPSK正交格雷互補序列的建構，依序列的長度分為二的冪次方及非二的冪次方來分別討論。 當QPSK格雷互補序列長度為二的冪次方時，可採用Huang提出的方法，組合一組Hadamard序列與一個格雷序列，產生出正交QPSK格雷互補序列。本文指出這個做法必須使用標準格雷互補序列，才可成功。 當QPSK格雷互補序列長度為非二的冪次方時，可採用Huang,Li提出的幾乎正交QPSK格雷互補序列的建構法，將短長度的QPSK格雷互補序列經由Iteration Variation及Sign Variation做出特定長度的幾乎正交QPSK格雷互補序列。在Huang,Li的研究中，並未詳細分析Iteration Variation及Sign Variation這兩種建構正交序列的方法，也未詳細分析少數不正交的QPSK格雷互補序列的成因。本文提出詳盡的分析，並且歸納出不正交QPSK序列的出現規則。
 Golay complementary sequences have the property that the sum of the aperiodic autocorrelation functions for pairing sequences is an impulse function, and have been widely used in various communications systems. Mutually orthogonal sequences do not interfere with each other, and have also been useful for many communication applications. This research aims to study the structure of mutually orthogonal QPSK Golay complementary sequences. When the sequence lengths are powers of two, Huang’s method can be used to combine a collection of Hadamard sequences with one QPSK Golay sequence to generate a collection of mutually orthogonal QPSK Golay sequences. We point out that the one QPSK Golay sequence used to combine with the Hadamard sequences must be a standard Golay complementary sequence. When the lengths of QPSK Golay complementary sequences are not powers of two, we analyze the construction of near orthogonal QPSK Golay complementary sequences proposed by Huang and Li. The construction uses short QPSK Golay complementary sequence pairs as initial pairs and extends to long sequence pairs by recursive construction with iteration variation and sign variation. In Huang and Li’s paper, the iteration variation and sign variation are not analyzed in detail. The existence of a few non-orthogonal QPSK Golay complementary sequences is not explicitly analyzed, either. We provide detailed analysis and explain why non-orthogonal QPSK sequences appear in the construction.
 中文摘要..................................................Ⅰ英文摘要..................................................Ⅱ誌謝......................................................Ⅲ目錄......................................................Ⅳ表目錄....................................................Ѵ圖目錄....................................................Ⅵ第一章 序論................................................11.1 研究背景與目的.........................................11.2 研究成果...............................................21.3 各章節提要.............................................4第二章 格雷互補序列與正交序列背景介紹......................52.1 格雷序列...............................................52.1.1 AACF................................................52.1.2 格雷互補序列的定義及特性............................62.1.3 標準格雷互補序列及非標準格雷互補序列................72.1.4 Two Pair遞迴建構法.................................112.2 正交序列..............................................132.2.1 Hadamard 序列.......................................142.2.2 DFT序列.............................................16第三章 正交格雷互補序列建構方法..........................183.1 二的冪次方長度之QPSK正交格雷序列—Golay Hadamard 序列193.2 非二的冪次方長度之QPSK正交互補格雷序列建構...........263.2.1 格雷互補序列與Hadamard序列之組合失效...............263.2.2 Near Orthogonal QPSK 格雷序列建構法分析............293.2.2.1 Iteration Variation..............................303.2.2.2 Sign Variation..................................393.2.2.3 實驗數據分析與歸納正交規則.......................42第四章 結論...............................................48參考文獻..................................................50
 [DJ99] J. A. Davis and J. Jedwab, ”Peak-to-mean power control in OFDM,Golay complementary sequences and Reed-Muller codes,” IEEE Trans. Inf. Theory, vol. 45, no. 7, pp. 2397-2417, 1999.[FJP08] F. Fiedler, J. Jedwab and M. G. Parker, ”A multi-dimensional approach to the construction and enumeration of Golay complementary sequences,” J. Comb. Theory Ser. A, vol. 115, no. 5, pp. 753-776, 2008.[Gol61]M.J.E. Golay ,“Complementary Series”,IRE Trans. Inform. Theory , Vol. IT-7 , Issue 2, pp. 82-87 , Apr. 1961.[HK94]W.H.Holzmann and H.Kharaghani , Department of Mathematics & Computer Science University of Lethbridge ,“A computer search for complex Golay sequences”, Apr . 1994.[Hua06]X.J.Huang ,“Complementary Properties of Hadamard Matrices,” in Proc. IEEE Int. Conf. Communications , Circuits and Systems , pp.588-592.25-28 June.2006.[HuK06]黃國倫 ,”格雷互補序列遞迴建構探討,” , 元智大學碩士論文 , 2006[HL10]Yen-Wen Huang , Ying Li , ”802.16 Uplink Sounding via QPSK Golay Sequences,” IEEE Communications Letters,pp.593-595 July 2010.[HuY11]Yen-Wen Huang , “New Construction of General Complex Golay Complementary Sequences,”元智大學博士論文 , 2011.[Kao05]高翊展 ,”格雷序列結構之探討,”元智大學碩士論文 , 2005.[LC05]儲文彬 , ”以格雷序列與非格雷序列降低OFDM訊號之峰均比,”元智大學碩士論文 , 2005.[LH08]Ying Li , Yen-Wen Huang , ”Extension of Golay’s Two Pair Construction for General Complex Complementary Sequences,” International Symposium on Information Theory and Its Applications, 2008 (ISITA 2008), Dec. 2008.[Li08]Y. Li, ”Comments on ”A New Construction of 16-QAM Golay Complementary Sequences” and Extension for 64-QAM Golay Sequences,”IEEE Trans. Inf. Theory, vol. 54, no. 7, pp. 3246-3251, 2008.[SWW02]J. Seberry, B. J. Wysocki, and T. A. Wysocki. "Golay Sequences for DS CDMA Applications," Faculty of Informatics - Papers.Jan. 2002.[War06]Warren D.Smith ,“Circulant constructions of skew-Hadamard matrices for n= 4 , 8, 12, 20, 24, 32, 44, 48, 60,68,72,80,84”,Aug.2006 ,http://rangevoting.org/SkewHad.html.
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 1 8-QAM格雷互補序列之建構 2 以格雷序列與非格雷序列降低OFDM訊號之峰均比 3 格雷互補序列遞迴建構探討 4 格雷序列結構之探討 5 二維格雷互補陣列建構及字集探討

 1 翁萃芳。(2002a)。台灣地區警察人員休閒活動參與及相關因素之分析。中央警察大學警學叢刊，第33 卷第3 期。25-60 頁。 2 黃中皓、呂佳霙(2006)：職業運動品牌延伸之成功法則。大專體育，84，頁98-105。 3 陳思倫（民82）休閒遊憩參與阻礙區隔之研究。戶外遊憩研究，第六卷，第3期，頁25-52。

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