正交分頻多工(Orthogonal Frequency Division Multiplexing,OFDM)訊號可藉由採用特定頻域訊號序列改善訊號高功率峰均比(Peak-to-Average Power Ratio，PAPR)的問題。其中較為廣為人知的有格雷互補序列與格雷互補集合的序列。雖然這些序列結構佳且PAPR低，但是隨著序列長度增加，這些序列在低PAPR序列中的比率迅速降低。若要提高編碼碼率，必需了解其他低PAPR的序列。
本論文由PAPR低的非互補序列開始，探討OFDM序列與PAPR有關之整體特質。使用各種觀點了解序列結構，包含碼字的雙差分序列(double difference sequence)與布林函數。格雷互補序列常可以利用布林函數精簡描述，但其他非互補序列只能使用列表呈述。我們將低PAPR序列以特徵雙差分序列(Characteristic double difference sequence)依PAPR高低列表，並列出布林函數。此種方法容許我們把總數65536個QPSK OFDM 序列用1072個特徵雙差分序列精簡列出。本文也討論雙差分序列與非週期自相關函數(Aperiodic Auto-correlation Function)性質，並將PAPR低但非互補序列分解再合成，以了解其遞迴生成的可能性。亦列出布林函數係數與碼字序列轉換的關係式。

The high PAPR of OFDM signals can be reduced by using specific frequency domain signal sequences. The better known such sequences include Golay complementary sequences and sequences in Golay complementary sets. These sequences have nice structure and low PAPR. However, as the sequence length increase, the percentage of these sequences reduces rapidly. To increase the code rate of PAPR reduction code, structure of other low PAPR sequences must be understood.

We first examine non-complementary sequences with PAPR not exceeding 2, then proceed to investigate overall properties of OFDM sequence and PAPR sequences are characterized in various ways, including dd-sequences and Boolean functions. Golay complementary sequences represented by Boolean functions concisely. Other low PAPR sequences can only be listed in tables. Using characteristic double difference sequences, the table size for all length 8 QPSK-OFDM sequences can be reduced from 65536 to 1072. Futhermore, we discuss the relation between dd-sequences and Aperiodic Autocorrelation function, and study the recursive contruction of low PAPR non-complementary sequences.

目錄
頁次
中文摘要…………………………………………………………… i
英文摘要……………………………………………………………ii
目錄…………………………………………………………………iii
表目錄………………………………………………………………v
圖目錄……………………………………………………………… vii
符號表……………………………………………………………… viii

第一章 序論………………………………………………………… 1
1.1研究動機與目的………………………………………… 1
1.2研究成果…………………………………………………1
1.3各章節提要………………………………………………2

第二章 研究背景…………………………………………………… 3
2.1 OFDM序列以及功率峰均比(PAPR)性質……………… 3
2.1.1 OFDM訊號與PAPR特性介紹……………………3
2.2 OFDM 序列表示法……………………………………… 4
2.2.1 訊號序列/複數序列…………………………… 5
2.2.2 相位序列/碼字序列…………………………… 5
2.2.3 布林函數(Boolean function)，
Algebraic normal form…………………… 5
2.2.4 布林函數係數序列…………………………… 7
2.3 OFDM序列，非週期自相關函數(AACF)，PAPR……… 8
2.3.1 OFDM序列非週期自相關函數(AACF)與PAPR關係
………………………………………………… 9
2.4 Low PAPR序列………………………………………… 10
2.4.1 格雷互補序列………………………………… 11
2.4.2 以雙差分序列(dd)簡化其他PAPR不超過二的
序列…………………………………………… 13
2.4.3 互補序列集合………………………………… 16
第三章 OFDM序列描述與探討………………………………… 19
3.1序列表示法之轉換與性質…………………………… 20
3.1.1碼字與布林函數之轉換……………………… 20
3.2 碼字特徵dd的種類、數目與AACF性質…………… 28
3.2.1以翻轉與互補區分特徵dd種類與數量……… 29
3.2.2自相關函數與特徵dd………………………… 35
3.3 PAPR 性質整體觀 ………………………………… 43
3.3.1長度八OFDM所有QPSK序列依PAPR排列總
表……………………………………………… 43
3.4 長度8 QPSK-OFDM非互補但PAPR不超過二序列探討
……………………………………………………… 58
3.4.1 Schmidt法合成延長………………………… 58

第四章 結論…………………………………………………………65

參考文獻…………………………………………………………… 67
附錄A ……………………………………………………………… 69
附錄B ……………………………………………………………… 109

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