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博碩士論文 etd-0302113-002925 詳細資訊
Title page for etd-0302113-002925
論文名稱
Title
具有理想循環自相關函數之高斯整數序列
Gaussian Integer Sequences with Ideal Periodic Autocorrelation Functions
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
79
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2013-02-27
繳交日期
Date of Submission
2013-03-02
關鍵字
Keywords
基底序列、序列能量、理想序列、交相關函數、高斯整數、完美序列、自相關函數
Gaussian integer, perfect sequence, periodic auto-correlation function, periodic cross-correlation function, ideal sequence, energy efficiency, base sequences
統計
Statistics
本論文已被瀏覽 5701 次,被下載 161
The thesis/dissertation has been browsed 5701 times, has been downloaded 161 times.
中文摘要
完美序列或理想序列具有完美的週期性自相關函數(periodic auto-correlation function, PACF),一般可用於通訊系統中做為通道估測、時間或頻率同步、基地台尋找(cell search)和PAPR降低等。目前完美序列任意長度的建構方式主要以浮點數為主,本論文提出一以高斯整數為碼片的高斯整數完美序列(Gaussian integer perfect sequences, GIPSs),該序列長度為偶數且由兩個基本序列(base sequences)的群組透過線性組合的方式建構而成,所有的基本序列非零元素皆為正負1和正負j 。此外,本論文亦推導出該序列的週期性交相關函數(periodic cross-correlation function, PCCF)和其本身序列的建構式一致並探討該序列具有最大能量效率(energy efficiency)和最小的最大交相關函數的值分別所對應的基本序列係數
Abstract
A Gaussian integer is a complex number whose real and imaginary parts are both integers. Meanwhile, a sequence is defined as perfect if and only if the out-of-phase value of the periodic autocorrelation function is equal to zero. This study presents two novel classes of perfect sequences constructed using two groups of base sequences. The nonzero elements of these base sequences belong to the set . A perfect sequence can be obtained by linearly combining these base sequences or their cyclic shift equivalents with arbitrary nonzero complex coefficients of equal magnitudes. In general, the elements of the constructed sequences are not Gaussian integers. However, if the complex coefficients are Gaussian integers, then the resulting perfect sequences will be Gaussian integer perfect sequences (GIPSs). In addition, a periodic cross-correlation function is derived, which has the same mathematical expression as the investigated sequences. Finally, the maximal energy efficiency and minimax absolute values of PCCF of the proposed GIPSs is investigated.
目次 Table of Contents
誌謝 i
中文摘要 ii
Abstract iii
Contents iv
List of Tables vi
Chapter 1 Introduction 1
Chapter 2 Construction of the Gaussian Integer Sequences of length N=2p 4
2.1 Basic Definitions 4
2.2 Constructing the GIPSs of length N=2p with ideal PACFs 6
2.3 Periodic Cross-Correlation Functions of the GIPSs 17
2.3.1 Periodic Cross-Correlation Functions of Sequences with Length of N=2p, p is odd 17
2.3.4 Periodic Cross-Correlation Functions of Sequences with Length of N=2p, p is even 24
Chapter 3 Energy Efficiency and Mini-max Values of PCCF 30
3.1 Energy Efficiency 30
3.2 Mini-max values of PCCF 35
Chapter 4 Construction of the Gaussian Integer Sequences of length N=4p 41
4.1 Constructing the GIPSs of length N=4p with ideal PACFs 41
4.2 Periodic Cross-Correlation Functions of the GIPSs 48
4.2.1 Periodic Cross-Correlation Functions of Sequences with Length of N=16p, p is positive integer 49
4.2.2 Periodic Cross-Correlation Functions of Sequences with Length of N=16p+4, p is positive integer 50
4.2.3 Periodic Cross-Correlation Functions of Sequences with Length of N=16p+8, p is positive integer 52
4.2.4 Periodic Cross-Correlation Functions of Sequences with Length of N=16p+12, p is positive integer 54
Chapter 5 Conclusions 57
References 58
Abbreviation 65
Publication List 67

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