完美序列(Perfect Sequence)是一種擁有完美的循環自相關函數的序列，也有學者將其稱作理想序列(Ideal Sequence)。在通訊系統中，同步、通到估測與多重存取……等演算法之效能，都須仰賴自相關特性優良的序列。在許多學者的研究中，提出了許多種方法來結構此種完美序列。其中碼片大多為浮點數，因此在實際上應用時，在量化後即失去了原來完美循環自相關函數的特性。為了解決完美序列在量化後失真的缺點，在此提出了新的僅由高斯整數為碼片之高斯整數完美序列(Gaussian Integer Perfect Sequence, GIPS)。首先討論結構GIPS之方法、參數選擇與基本性質。由於許多應用中，考慮到放大器的效率，對碼的動態範圍有所要求。因此，針對動態範圍的調整進行討論，並提出了產生最低動態範圍之GIPS的方法。

Many researchers had developed polyphase sequences, so called “perfect sequence” or “ideal sequence”, with ideal periodic auto-correlation function. There are lots of applications of communication system depends on the sequences with good auto-correlation property, i.e., synchronization, channel estimation and multiple access. These sequences cannot maintain the ideal property in implementation, because of the error of quantization in digital signal processing of transmitter. On the contrary, we develop a novel set of perfect sequences, Gaussian Integer Perfect Sequence (GIPS), which only contains Gaussian integers. In this paper, we construct them by linear combination and cyclic shift of the eight base sequences. We present the design and basic properties of the sequences. Furthermore, the design method of sequences with the smallest dynamic range is presented.

第 1 章 導論................................................................1
1.1 研究動機............................................................2
1.2 論文架構............................................................3
第 2 章 高斯整數完美序列(GIPS)之結構................4
2.1 完美序列之發展................................................4
2.2 結構高斯整數完美序列(GIPS)........................6
2.3 GIPS的基本性質............................................12
2.4 GIPS的循環交互相關函數............................15
第 3 章 高斯整數完美序列之動態範圍..................20
3.1 高斯整數完美序列之動態範圍分析..............21
3.2 選取位移參數對PAPR之影響...................... 23
3.3 碼長為4(4M+0)之動態範圍與參數選擇......31
3.4 碼長為4(4M+1)之動態範圍與參數選擇......34
3.5 碼長為4(4M+2)之動態範圍與參數選擇......36
3.6 碼長為4(4M+3)之動態範圍與參數選擇......37
第 4 章 結論.............................................................38
第 5 章 附錄.............................................................39
中英對照表..............................................................43
縮寫對照表..............................................................45
參考文獻..................................................................47

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