序列偶相关性与三元信号偶理论研究
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摘要
最佳离散信号及其设计在现代通信、雷达、声纳、制导以及电子对抗等系统中,起着越来越重要的作用。经过几十年的努力,人们在最佳离散信号的研究上已取得了大量的重要成果。但是,目前最佳离散信号的选取范围还是比较窄,序列的数量还不是很充足。本论文主要研究了序列偶的相关特性,并对近些年国内由两个单个序列组成偶的最佳离散信号设计方式与三元信号进行了综合,在前人研究的基础上对最佳离散信号作了进一步的研究。主要工作如下:
(1)介绍了序列偶的基本概念和序列偶相关函数的性质,以及序列偶在信号处理和通信系统中的应用。
(2)根据q相序列偶的周期和非周期相关函数的概念,定义了相应的序列偶的相关函数量值,利用Levenshtein方法推导形成了序列偶的这些相关函数量值界的理论估计,并使之延伸至一般序列的相关理论界上。
(3)提出了一种新的具有良好循环相关特性的离散信号——伪随机三元阵列偶。首先给出了伪随机三元阵列偶的相关定义;然后研究了伪随机三元阵列偶的变换性质和频谱特性;而且,为了减小搜索范围,提高搜索效率,给出了伪随机三元阵列偶存在的必要条件;证明了伪随机三元阵列偶的唯一性,并给出了一种伪随机三元阵列偶的构造方法。
(4)定义了一种新的最佳相关信号——奇周期最佳三元序列偶,研究了其变换性质,给出了一些组合允许条件,利用计算机搜索出了一些奇周期最佳三元序列偶,并给出了序列偶长度为奇数时,奇周期最佳三元序列偶和周期最佳三元序列偶的关系,以及利用奇周期最佳三元序列偶构造周期最佳三元序列偶的方法。
The perfect discrete signal and its design play an important part in the area of modernistic communication, radar, sonar, navigation and electronically antagonism systems. An abundance of research results were published through several decades. But at present, the range of selecting perfect discrete signal is relatively narrow and the number of the perfect signals is not sufficient. The correlation properties of the sequence pair are the main research object in this paper. The paper integrates the perfect discrete signal design mode of the sequence pair with the ternary signals, and makes further study for the perfect discrete signals on the basis of the predecessor’s research. The main work is as following;
(1)The basic concepts of sequence pair, the correlation properties of the sequence pair and the applications of the sequence pair in the signal process and communication system are introduced.
(2)The concepts of the periodic and aperiodic correlation function of q phase sequence pairs are presented. Based on these concepts, some corresponding quantities are defined. Using Levenshtein method, we deduce the theoretical evaluation of the bounds of correlation quantities of the sequence pairs and expand the bounds to the general sequence sets.
(3)A new periodic correlation signal, pseudorandom ternary array pairs, is proposed. At first, some basic definitions are presented. Then the transformation and spectrum properties are studied. To reduce searching range and improve the efficiency, some admissibility conditions are given out. At last its uniqueness is proved. And a construction method is proposed.
(4) A new kind of perfect correlate signal is presented in this paper, that is, odd-periodic perfect ternary sequence pairs. The transformation features are studied and the limited conditions are discussed. Based on this, we search out many odd-periodic perfect ternary sequence pairs with small length. The relationship between the odd-periodic perfect and periodic perfect ternary sequence pairs when the length of the sequence pairs is odd is also given. A construction method for periodic perfect ternary sequence pairs by using the odd-periodic perfect ternary sequence pairs is proposed, too.
(1)介绍了序列偶的基本概念和序列偶相关函数的性质,以及序列偶在信号处理和通信系统中的应用。
(2)根据q相序列偶的周期和非周期相关函数的概念,定义了相应的序列偶的相关函数量值,利用Levenshtein方法推导形成了序列偶的这些相关函数量值界的理论估计,并使之延伸至一般序列的相关理论界上。
(3)提出了一种新的具有良好循环相关特性的离散信号——伪随机三元阵列偶。首先给出了伪随机三元阵列偶的相关定义;然后研究了伪随机三元阵列偶的变换性质和频谱特性;而且,为了减小搜索范围,提高搜索效率,给出了伪随机三元阵列偶存在的必要条件;证明了伪随机三元阵列偶的唯一性,并给出了一种伪随机三元阵列偶的构造方法。
(4)定义了一种新的最佳相关信号——奇周期最佳三元序列偶,研究了其变换性质,给出了一些组合允许条件,利用计算机搜索出了一些奇周期最佳三元序列偶,并给出了序列偶长度为奇数时,奇周期最佳三元序列偶和周期最佳三元序列偶的关系,以及利用奇周期最佳三元序列偶构造周期最佳三元序列偶的方法。
The perfect discrete signal and its design play an important part in the area of modernistic communication, radar, sonar, navigation and electronically antagonism systems. An abundance of research results were published through several decades. But at present, the range of selecting perfect discrete signal is relatively narrow and the number of the perfect signals is not sufficient. The correlation properties of the sequence pair are the main research object in this paper. The paper integrates the perfect discrete signal design mode of the sequence pair with the ternary signals, and makes further study for the perfect discrete signals on the basis of the predecessor’s research. The main work is as following;
(1)The basic concepts of sequence pair, the correlation properties of the sequence pair and the applications of the sequence pair in the signal process and communication system are introduced.
(2)The concepts of the periodic and aperiodic correlation function of q phase sequence pairs are presented. Based on these concepts, some corresponding quantities are defined. Using Levenshtein method, we deduce the theoretical evaluation of the bounds of correlation quantities of the sequence pairs and expand the bounds to the general sequence sets.
(3)A new periodic correlation signal, pseudorandom ternary array pairs, is proposed. At first, some basic definitions are presented. Then the transformation and spectrum properties are studied. To reduce searching range and improve the efficiency, some admissibility conditions are given out. At last its uniqueness is proved. And a construction method is proposed.
(4) A new kind of perfect correlate signal is presented in this paper, that is, odd-periodic perfect ternary sequence pairs. The transformation features are studied and the limited conditions are discussed. Based on this, we search out many odd-periodic perfect ternary sequence pairs with small length. The relationship between the odd-periodic perfect and periodic perfect ternary sequence pairs when the length of the sequence pairs is odd is also given. A construction method for periodic perfect ternary sequence pairs by using the odd-periodic perfect ternary sequence pairs is proposed, too.
引文
1李振玉,卢玉民.扩频选址通信.北京:国防工业出版社,1988:74-87
2朱近康.扩展频谱通信及其应用.合肥:中国科学技术大学出版社,1993:16-27
3孙立新,邢宁霞.CDMA(码分多址)移动通信技术.北京:人民邮电出版社,1996:4-12
4竺南直,肖辉,刘景波.码分多址(CDMA)移动通信技术.北京:电子工业出版社,1999:3-10
5 C. E. Shannon. A Mathematical Theory of Communication. The Bell System Technical Journal,1948,27:379-423 625-656
6李承恕,赵荣黎.扩展频谱通信.北京:人民邮电出版社,1993:18-61
7梅文华,杨义先.跳频通信地址编码理论.北京:国防工业出版社,1996:1-14
8尤肖虎,曹淑敏,李建东.第三代移动通信系统发展现状与展望.电子学报,1999,24 (11):3-9
9 M. Zeng, A. Annamalai, V. K. Bhargava. Recent Advances in Cellular Wireless Communications. IEEE Communications Magazine,1999,36(9):128-138
10朱旭红,卢学军,单天真.宽带CDMA:第三代移动通信技术.北京:人民邮电出版社,2000:2-16
11张敬堂,李红波,赵泽兵.现代通信技术.北京:国防工业出版社,2002:104-110
12 E. H. Dinan, B. Jabbari. Spreading Codes for Direct CDMA and Wideband CDMA Celluar Networks. IEEE Communications Magazine,1998,36(9):48-54
13李进良.移动通信100年.移动通信,2000,24(1):9-17
14 M. B. Pursley, D. V. Sarwate. Performance Evaluation for Phase-Coded Spread- Spectrum Multiple-access Communication. IEEE Trans. on Communications,1977,25 (8):795-803
15 S. W Golomb. Shift Register Sequences. Agean Park Press,1982,25(3):25-133
16 N. Zierler. Several Binary Sequence Generators. Technical report 95, MFT Lincoln Lab,1955:38-63
17 V I. Levenshtein. Lower Bounds on Cross-Correlation of Codes. IEEE 4thInternational Symposium on Spread Spectrum Techniques and Applications Proceedings,1996,2:657-661
18 V. I. Levenshtein. New Lower Bounds on Aperiodic Crosscorrelation of Binary Codes. IEEE Trans. on Inform. Theory,1999,45(1):284-288
19 J. L. Massey. On Welch's Bounds for The Correlation of Sequence Set. Proceedings of ISIT-1990,1990:385
20 P. V Kumar, C. M. Liu. On Lower Bounds to The Maximum Correlation of Complex Roots-of-Unity Sequences. IEEE Trans. on Inform. Theory,1990,36(3):633-640
21 D. V Sarwate. Bounds on Crosscorrelation and Autocorrelation of Sequences. IEEE Trans. on Inform.. Theory,1979,25(6):720-724
22 L. R. Welch. Lower Bomds on The Maximum Cross-Correlation of Signals. IEEE Trans. on Inform. Theory,1974,20:397-399
23钟义信.伪噪声编码通信.北京:人民邮电出版社,1979:155-188
24阮永红,祁玉生.DS-CDMA移动通信系统地址码的正交性.南京邮电学院学报,1997,17(2):21-26
25 F. Adachi, M. Sawahashi, K. Okawa. Tree-Structured Generation of Orthogonal Spreading Codes with Different Length for Forward Link of DS-CDMA Mobile Radio. IEE Electronics Letters,1997,33(1):27-28
26 F. Adachi, M. Sawahashi, H. Suda. Wideband DS-CDMA for Next-Generation Mobile Communications Systems. IEEE Communications Magazine,1998,36(9):56-59
27肖国镇,梁传甲,王育民.伪随机序列及其应用.北京:国防工业出版社,1985:178-183
28杨义先.最佳信号理论与设计.北京:人民邮电出版社,1996:57-62 268-275
29 G. Gong. On Q-ary Cascaded GMW Sequences. IEEE Trans. on Inform. Theory, 1996, 42(1):263-267
30 S. Matsufuji, K. Imamura. On P-Ary Bent Sequences. IEICE Trans. Fundamentals, 1995,78(9):1257-1260
31 J. D. Olsen, R. A. Scholtz, L. R. Welch. Bent-Function Sequences. IEEE Trans. on Inform. Theory,1982,28(6):858-864
32杨义先,林须端.编码密码学.北京:人民邮电出版社,1992:20-214
33 J. Wolfmann. Almost-Perfect Autocorrelation Sequences. IEEE Trans. on Inform. Theory,1992,38(4):1412-1418
34 S. Boztas, R. Hammons, P. V. Kumar. 4-Phase Sequences with Near Optimum Correlation Properties. IEEE Trans. on Inform. Theory,1992,38(3):1101-1113
35 Xiaohu H. Tang, Parampalli Udaya. Note on the Optimal Quadriphase Sequences Families. IEEE Transaction on Information Theory,2007,53(1):433-436
36 D. C. Chu. Polyphase Codes with Good Periodic Correlation Properties. IEEE Trans. on Inform. Theory,1972,18:531-532
37 H. D. Luke, H. D. Schotten. Odd-Perfect Almost Binary Correlation Sequences. IEEE Trans on Aerospace and Electronic Systems,1995,31(1):495-498
38 F. Hu, P. Z. Fan, M. Darnell. Binary Sequences with Good Aperiodic Autocorrelation Functions Obtained by Neural Network Search. IEE Electronics Letters,1997,33(8): 688-689
39 P. Z. Fan, M. Darnell. Sequence Design for Communications Applications. John wiley,1996:1-396
40 J. S. No, P V Kumar. A New Family of Binary Pseudorandom Sequences Having Optimal Periodic Correlation Properties and Large Linear Span. IEEE Trans. on Inform. Theory,1989,35(2):371-379
41 G. Gong. Theory and Applications of Q-Ary Interleaved Sequences. IEEE Trans. on Inform. Theory,1995,41(2):400-411
42 Q. Xiang. On Balanced Binary Sequences with Two-Level Autocorrelation Functions. IEEE Trans. on Inform.. Theory,1998,44(7):3153-3156
43梅文华.基于m-序列构造最佳跳频序列族.通信学报,1991,12(1):70-73
44 Feng K, Shiue P J, Xiang Q. On Aperiodic and Periodic Complementary Binary Sequences. IEEE Trans. on Information Theory,1999,45(1):296-303
45赵晓群,何文才,王仲文.最佳二进阵列偶理论研究.电子学报,1999,27(1):34-37
46赵晓群,贾世楼,王仲文.序列偶及其应用.遥测遥控,1998,5:31-35
47许成谦,靳慧龙.几乎最佳自相关序列偶.遥测遥控,2003,24(5):16-20
48 C. Ding, T. Helleseth, H. M. Martinsen. New Families of Binary Sequences with Optimal Three-Level Autocorrelation. IEEE Trans. on Inform. Theory,2001,47(1):428- 433
49 V.M.Sidelnikov. On Mutual Correlation of Sequences. Soviet Mach Doklady,1971, (12):197-201
50 J.S. NO. Generalization of GMW Sequences and No Sequences. IEEE Trans. on Inform. Theory,1996,35:260.262
51蒋挺,毛飞,赵成林.几乎最佳二进阵列偶理论研究.电子学报,2005,33(10):1817- 1821
52毛飞,蒋挺,赵成林.伪随机二进序列偶研究.通信学报,2005,26(8):94-98
53张立东,万超,李琦.伪随机二进阵列偶理论的研究.2007通信理论与信号处理学术年会论文集.北京,2007:467-473
54贾彦国,郭继山.最佳三进阵列偶的研究.第十一届全国青年通信学术会议论文集.中国绵阳,2006:268-275
55贾彦国,郭继山.最佳三进阵列偶构造方法研究.电子与信息学报,2008,30(4):814- 816
56贾彦国,崔莉.几乎最佳三元阵列偶的研究.北京地区研究生学术交流会——通信与信息技术论文集.北京,2006:256-259
57崔珊珊,许成谦.伪随机三元序列偶的研究.电子技术,2007,34(11):177-180
58李刚,许成谦.序列偶的唯一性问题研究.电子与信息学报,2008,30(1):111-113
59赵晓群.阵列偶的完全采样与折叠分析.燕山大学学报,1998,22(2):65-67
60 Hoholdt, T.Justesen. Ternary Sequences with Perfect Periodic Auto-Correlation. Trans. on Inform. Theory,1983,29:597-600
61 Lee C E. Q-ary Sequences from Multiplicative Characters Over GF(p). Electronics Letter,1992,28(9):833-835
62 Luke. H. D, Schotten, H. D. Odd-Perfect Almost Binary Correlation Sequences.IEEE Trans.Aero.and Elec.Syst,1995,31(1):495-498
63 Sarwate D V, Pursley M B. Crosscorrelation Properties of Pseudorandom and Related Sequences. Proceedings of the IEEE,1980,68(5):593-619
64 Fan P Z, Suehiro N, Kuroyanagi N. Class of Binary Sequences with Zero Zone. Electronics Letters,1999,35(10):777-779
65 Cha J S, Kameda S, Yokoyama M. New Binary Sequences with Zero-Correlation During for Approximately Synchronized CDMA. Electronics Letters,2000,36(11):991- 993
66 Alexis R. Search for Sequences with Autocorrelation. Proc. Int.Coll. Coding Theory Appl,Paris,France,1986:159-172
67 Luke H D. Binary Alexis Sequences with Perfect Correlation.IEEE Trans. on Commun, 2001,49(6):966-968
68 Jiang Ting, Zhao Xiaoqun, Hou Lantian. Perfect Punctured Binary Sequence Pair. Journal of Electronics.2003,20(4):285-288
69李兆斌,蒋挺.几乎最佳屏蔽二进序列偶的研究.北京邮电大学学报,2007,2(30):28- 31
70蒋挺,赵晓群.奇周期最佳屏蔽二进序列偶.系统工程与电子技术,2003,25(4):513- 516
71毛飞,蒋挺.奇周期最佳几乎二进序列偶理论研究.北京邮电大学学报,2006,29(6): 77-80
2朱近康.扩展频谱通信及其应用.合肥:中国科学技术大学出版社,1993:16-27
3孙立新,邢宁霞.CDMA(码分多址)移动通信技术.北京:人民邮电出版社,1996:4-12
4竺南直,肖辉,刘景波.码分多址(CDMA)移动通信技术.北京:电子工业出版社,1999:3-10
5 C. E. Shannon. A Mathematical Theory of Communication. The Bell System Technical Journal,1948,27:379-423 625-656
6李承恕,赵荣黎.扩展频谱通信.北京:人民邮电出版社,1993:18-61
7梅文华,杨义先.跳频通信地址编码理论.北京:国防工业出版社,1996:1-14
8尤肖虎,曹淑敏,李建东.第三代移动通信系统发展现状与展望.电子学报,1999,24 (11):3-9
9 M. Zeng, A. Annamalai, V. K. Bhargava. Recent Advances in Cellular Wireless Communications. IEEE Communications Magazine,1999,36(9):128-138
10朱旭红,卢学军,单天真.宽带CDMA:第三代移动通信技术.北京:人民邮电出版社,2000:2-16
11张敬堂,李红波,赵泽兵.现代通信技术.北京:国防工业出版社,2002:104-110
12 E. H. Dinan, B. Jabbari. Spreading Codes for Direct CDMA and Wideband CDMA Celluar Networks. IEEE Communications Magazine,1998,36(9):48-54
13李进良.移动通信100年.移动通信,2000,24(1):9-17
14 M. B. Pursley, D. V. Sarwate. Performance Evaluation for Phase-Coded Spread- Spectrum Multiple-access Communication. IEEE Trans. on Communications,1977,25 (8):795-803
15 S. W Golomb. Shift Register Sequences. Agean Park Press,1982,25(3):25-133
16 N. Zierler. Several Binary Sequence Generators. Technical report 95, MFT Lincoln Lab,1955:38-63
17 V I. Levenshtein. Lower Bounds on Cross-Correlation of Codes. IEEE 4thInternational Symposium on Spread Spectrum Techniques and Applications Proceedings,1996,2:657-661
18 V. I. Levenshtein. New Lower Bounds on Aperiodic Crosscorrelation of Binary Codes. IEEE Trans. on Inform. Theory,1999,45(1):284-288
19 J. L. Massey. On Welch's Bounds for The Correlation of Sequence Set. Proceedings of ISIT-1990,1990:385
20 P. V Kumar, C. M. Liu. On Lower Bounds to The Maximum Correlation of Complex Roots-of-Unity Sequences. IEEE Trans. on Inform. Theory,1990,36(3):633-640
21 D. V Sarwate. Bounds on Crosscorrelation and Autocorrelation of Sequences. IEEE Trans. on Inform.. Theory,1979,25(6):720-724
22 L. R. Welch. Lower Bomds on The Maximum Cross-Correlation of Signals. IEEE Trans. on Inform. Theory,1974,20:397-399
23钟义信.伪噪声编码通信.北京:人民邮电出版社,1979:155-188
24阮永红,祁玉生.DS-CDMA移动通信系统地址码的正交性.南京邮电学院学报,1997,17(2):21-26
25 F. Adachi, M. Sawahashi, K. Okawa. Tree-Structured Generation of Orthogonal Spreading Codes with Different Length for Forward Link of DS-CDMA Mobile Radio. IEE Electronics Letters,1997,33(1):27-28
26 F. Adachi, M. Sawahashi, H. Suda. Wideband DS-CDMA for Next-Generation Mobile Communications Systems. IEEE Communications Magazine,1998,36(9):56-59
27肖国镇,梁传甲,王育民.伪随机序列及其应用.北京:国防工业出版社,1985:178-183
28杨义先.最佳信号理论与设计.北京:人民邮电出版社,1996:57-62 268-275
29 G. Gong. On Q-ary Cascaded GMW Sequences. IEEE Trans. on Inform. Theory, 1996, 42(1):263-267
30 S. Matsufuji, K. Imamura. On P-Ary Bent Sequences. IEICE Trans. Fundamentals, 1995,78(9):1257-1260
31 J. D. Olsen, R. A. Scholtz, L. R. Welch. Bent-Function Sequences. IEEE Trans. on Inform. Theory,1982,28(6):858-864
32杨义先,林须端.编码密码学.北京:人民邮电出版社,1992:20-214
33 J. Wolfmann. Almost-Perfect Autocorrelation Sequences. IEEE Trans. on Inform. Theory,1992,38(4):1412-1418
34 S. Boztas, R. Hammons, P. V. Kumar. 4-Phase Sequences with Near Optimum Correlation Properties. IEEE Trans. on Inform. Theory,1992,38(3):1101-1113
35 Xiaohu H. Tang, Parampalli Udaya. Note on the Optimal Quadriphase Sequences Families. IEEE Transaction on Information Theory,2007,53(1):433-436
36 D. C. Chu. Polyphase Codes with Good Periodic Correlation Properties. IEEE Trans. on Inform. Theory,1972,18:531-532
37 H. D. Luke, H. D. Schotten. Odd-Perfect Almost Binary Correlation Sequences. IEEE Trans on Aerospace and Electronic Systems,1995,31(1):495-498
38 F. Hu, P. Z. Fan, M. Darnell. Binary Sequences with Good Aperiodic Autocorrelation Functions Obtained by Neural Network Search. IEE Electronics Letters,1997,33(8): 688-689
39 P. Z. Fan, M. Darnell. Sequence Design for Communications Applications. John wiley,1996:1-396
40 J. S. No, P V Kumar. A New Family of Binary Pseudorandom Sequences Having Optimal Periodic Correlation Properties and Large Linear Span. IEEE Trans. on Inform. Theory,1989,35(2):371-379
41 G. Gong. Theory and Applications of Q-Ary Interleaved Sequences. IEEE Trans. on Inform. Theory,1995,41(2):400-411
42 Q. Xiang. On Balanced Binary Sequences with Two-Level Autocorrelation Functions. IEEE Trans. on Inform.. Theory,1998,44(7):3153-3156
43梅文华.基于m-序列构造最佳跳频序列族.通信学报,1991,12(1):70-73
44 Feng K, Shiue P J, Xiang Q. On Aperiodic and Periodic Complementary Binary Sequences. IEEE Trans. on Information Theory,1999,45(1):296-303
45赵晓群,何文才,王仲文.最佳二进阵列偶理论研究.电子学报,1999,27(1):34-37
46赵晓群,贾世楼,王仲文.序列偶及其应用.遥测遥控,1998,5:31-35
47许成谦,靳慧龙.几乎最佳自相关序列偶.遥测遥控,2003,24(5):16-20
48 C. Ding, T. Helleseth, H. M. Martinsen. New Families of Binary Sequences with Optimal Three-Level Autocorrelation. IEEE Trans. on Inform. Theory,2001,47(1):428- 433
49 V.M.Sidelnikov. On Mutual Correlation of Sequences. Soviet Mach Doklady,1971, (12):197-201
50 J.S. NO. Generalization of GMW Sequences and No Sequences. IEEE Trans. on Inform. Theory,1996,35:260.262
51蒋挺,毛飞,赵成林.几乎最佳二进阵列偶理论研究.电子学报,2005,33(10):1817- 1821
52毛飞,蒋挺,赵成林.伪随机二进序列偶研究.通信学报,2005,26(8):94-98
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