- 學位論文
正交格雷互補序列之結構探討
Structure of Orthogonal Golay Complementary Sequences
摘要
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。
關鍵字
正交:格雷互補序列並列摘要
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.