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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