Responsive image
博碩士論文 etd-0716116-205405 詳細資訊
Title page for etd-0716116-205405
論文名稱
Title
雙倍質數長度之完美序列
Construction of Perfect Sequence with Length 2p
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
65
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
2016-07-29
繳交日期
Date of Submission
2016-08-16
關鍵字
Keywords
高斯整數、完美序列、週期性自相關函數、有限場域、分圓場域
Finite field, Cyclotomic field, Periodic auto-correlation function, Perfect sequence, Gaussian integer
統計
Statistics
本論文已被瀏覽 5646 次,被下載 148
The thesis/dissertation has been browsed 5646 times, has been downloaded 148 times.
中文摘要
一個序列具備理想的週期性自相關函數(Periodic Auto-Correlation Function, PACF)稱之為完美序列(Perfect Sequence)。此外,序列階度(degree)是根據一個序列週期中,存在非零且不同的元素個數所定義。本篇論文基於分圓場域(cyclotomic field) 與有限場域理論(finite field theory)對兩倍質數長度之完美序列提出有系統性之建構方法。首先假設N為兩倍質數長度並將集合ZN={1,2,...,N-1}分割成三個彼此互斥之子集合C0,C1,C2 。子集合C0內的元素皆與p互質,其餘子集合C1,C2 則皆基於子集合C0所建立。由於子集合C0滿足乘法群組與群環群組的性質且子集合C1為基於子集合C0所建立,因此我們能將子集合C0,C1分割成 K個元素個數為M之子集合,其中子集合C0,C1元素個數皆為p-1=KM。根據此分割結果,我們能分別從時域及頻域上建構出四階或(2K+2)階度之完美序列,其中時域之完美序列須滿足理想的週期性自相關函數,頻域之完美序列則需要滿足等振幅之條件。
Abstract
A sequence is defined as perfect if and only if the out-of-phase value of the periodic autocorrelation function (PACF) is equal to zero. Furthermore, the degree of a sequence is defined as distinct nonzero elements within one period of the sequence. This paper proposes method based on cyclotomic field and finite field theory for systematically constructing perfect sequences with composite length which can be factored into N=2p, where p is an odd prime. The study start by partitioning a set ZN={1,2,...,N-1} into three exclusive subset C0,C1,C2, where one of subset C0 whose elements are coprime with N and the reminder subset are based on the subset C0 to construct. Due to the subset C0 have property of multiplication group and cyclic group, and subset C1 is established by the subset C0, we can partition cyclic group C0,C1, into K coset of M cardinality , where p-1=KM. According to this partition, the four-degree and (2K+2)-degree perfect sequences are constructed by using two different approaches, where these approach are designed to satisfy the time-domain ideal PACF property and the frequency-domain flat magnitude spectrum requirement, respectively.
目次 Table of Contents
論文審定書 i
誌謝 ii
中文摘要 iii
ABSTRACT iv
目錄 v
表目錄 viii
Chapter 1 導論 1
1.1 研究動機 2
1.2 論文架構 2
Chapter 2 基本定義與性質 3
2.1 序列之週期性自相關函數特性 3
2.2 群組(Group) 4
2.3 合集(Coset) 5
2.4 群組總類 8
2.4.1 加法群組(Additive Group) 8
2.4.2 乘法群組(Multiplication Group) 10
2.4.3 循環群組(Cyclic Group) 11
Chapter 3 建構兩倍質數長度之低階度完美序列 12
3.1 集合Z2p 之分割與性質 12
3.2 子集合C0,C1,C2 運算性質 14
3.3 四階度完美序列之建構 17
3.3.1 時域建構 17
3.3.2 頻域建構 22
3.4 三階度完美序列之建構 29
Chapter 4 建構高階度完美序列 32
4.1 集合C0與C1之分割性質 32
4.2 高階度完美序列之建構 35
Chapter 5 完美序列建構實例 42
5.1 四階度完美序列之實例 42
5.2 三階度完美序列之實例 45
5.3 高階度完美序列之實例 48
Chapter 6 結論 53
參考文獻 54
中英對照表.56
參考文獻 References
[1] N. Suehiro and M. Hatori, “Modulatable orghogonal sequences and their applicaiton to SSMA systems,” IEEE Trans. Inf. Theory, vol. 34, no. 1, pp. 93–100, Jan. 1988.
[2] S. H. Choi, J. S. Baek, J. S. Han, and J. S. Seo, “Channel estimations using orthogonal codes for AF multiple-relay networks over frequency-selective fading channels,” IEEE Trans. Veh, Technol., vol. 63, no. 1, pp. 417–423, Jan. 2014.
[3] C.-P. Li, S.-H. Wang, and C.-L. Wang, “Novel low-complexity SLM schemes for PAPR reduction in OFDM systems,” IEEE Trans. Signal Process., vol. 58, no. 5, pp. 2916–2921, May 2010.
[4] K. S. Kim, S. W. Kim, Y. S. Cho, and J. Y. Ahn, “Synchronization and cell-search technique using preamble for OFDM cellular systems,” IEEE Trans. Veh. Technol., vol. 56, no. 6, pp. 3469–3485, Nov. 2007.
[5] H. D. Luke, H. D. Schotten, and H. Hadinejad-Mahram, “Binary and quadriphase sequences with optimal autocorrelation properties: A survey,” IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 3271–3282, Dec. 2003.
[6] R. L. Frank and S. A. Zadoff, “Phase shift pulse codes with good periodic correlation properties,” IEEE Trans. Inf. Theory, vol. 8, no. 6, pp. 381–382, Oct. 1962.
[7] W.-W. Hu, S.-H. Wang, and C.-P. Li, “Gaussian integer sequences with ideal periodic autocorrelation functions,” IEEE Trans. Signal Process., vol. 60, no. 11, pp. 6074–6079, Nov. 2012
[8] W.-W. Hu, S.-H. Wang, and C.-P. Li, “Gaussian integer sequences with ideal periodic autocorrelation functions,” in IEEE Int. Conf. Communications, Kyoto, Japan, Jun. 5–9, 2011.
[9] Y. Yang, X. Tang, and Z. Zhou, “Perfect Gaussian integer sequences of odd prime length,” IEEE Signal Process. Lett.., vol. 19, no. 10, pp. 615–618, Oct. 2012.
[10] X. Ma, Q. Wen, J. Zhang, and H. Zuo, “New perfect Gaussian integer sequences of period pq,” IEICE Trans. Fundam., vol. E96-A, no. 11, pp. 2290–2293, Nov. 2013.
[11] H.-H. Chang, C.-P. Li, C.-D. Lee, S.-H. Wang, and T.-C. Wu, “Perfect Gaussian Integer Sequence of Arbitrary Composite Length,” IEEE Trans. Inf. Theory, vol. 61, no. 7, pp. 4107–4115, July 2015.
[12] C.-P. Li, S.-H. Wang, and C.-L. Wang, “Novel low-complexity SLM schemes for PAPR reduction in OFDM systems,” IEEE Trans. Signal Process., vol. 58, no. 5, pp. 2916–2921, May 2010.
[13] C.-P. Li and W.-C. Huang, “A constructive representation for the Fourier dual of the Zadoff-Chu sequences,” IEEE Trans. Inf. Theory, vol. 53, no. 11, pp. 4221–4224, Nov. 2007.
[14] S.-C. Pei, K.-W. Chang, “Perfect Gaussian integer sequences of arbitrary length,” IEEE Signal Process. Lett., vol. 22, no. 8, pp. 1040–1044, Aug. 2015.
[15] C.-D. Lee, Y.-P. Huang, Y, Chang, and H.-H. Chang, “Perfect Gaussian integer sequences of odd period 2m − 1,” IEEE Signal Process. Lett., vol. 22, no. 7, pp.881–885, July 2015.
[16] J. M. Howie, Fields and Galois Theory. London: Springer, 2006.
[17] Shu Lin, Daniel J. Costello, Error Control Coding. Upper Saddle River, N.J. : Pearson-Prentice Hall, 2004.
電子全文 Fulltext
本電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。
論文使用權限 Thesis access permission:自定論文開放時間 user define
開放時間 Available:
校內 Campus: 已公開 available
校外 Off-campus: 已公開 available


紙本論文 Printed copies
紙本論文的公開資訊在102學年度以後相對較為完整。如果需要查詢101學年度以前的紙本論文公開資訊,請聯繫圖資處紙本論文服務櫃台。如有不便之處敬請見諒。
開放時間 available 已公開 available

QR Code