高斯整数零相关区序列集构造方法的研究
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摘要
该文提出两类高斯整数零相关区(ZCZ)序列集的构造方法。方法1以ZCZ序列集为基础,利用插零滤波法构造高斯整数ZCZ序列集,并给出了所构造的高斯整数ZCZ序列集度的计算方法。方法2提出了两种高斯整数正交矩阵的构造方法,进而基于正交矩阵构造最优高斯整数ZCZ序列集。该文所构造的高斯整数ZCZ序列集可以应用于准同步码多分址(QS-CDMA)、正交频分复用(OFDM)和多输入多输出(MIMO)等多种通信系统中,在抑制干扰的同时,提高系统的频谱效率。
Two constructions of Gaussian integer Zero Correlation Zone(ZCZ) sequence set are researched. In Construction I, the method of zero padding is implemented on the ZCZ sequence set, and then the Gaussian integer ZCZ can be obtained by the filtering operation. Furthermore, the degree of the Gaussian integer ZCZ sequence set is calculated in this paper. In Construction II, two constructions of Gaussian integer orthogonal matrix are proposed. In addition, the optimal Gaussian integer ZCZ sequence sets are constructed based on the orthogonal matrix. The two classes of Gaussian integer ZCZ sequence sets presented in this paper can be applied to many communication systems such as Quasi-Synchronous Code Division Multiple Access(QSCDMA), Orthogonal Frequency Division Multiplexing(OFDM) and Mutiple-Input Multiple-Output(MIMO)system to suppress the interference and improve the spectrum efficiency.
Two constructions of Gaussian integer Zero Correlation Zone(ZCZ) sequence set are researched. In Construction I, the method of zero padding is implemented on the ZCZ sequence set, and then the Gaussian integer ZCZ can be obtained by the filtering operation. Furthermore, the degree of the Gaussian integer ZCZ sequence set is calculated in this paper. In Construction II, two constructions of Gaussian integer orthogonal matrix are proposed. In addition, the optimal Gaussian integer ZCZ sequence sets are constructed based on the orthogonal matrix. The two classes of Gaussian integer ZCZ sequence sets presented in this paper can be applied to many communication systems such as Quasi-Synchronous Code Division Multiple Access(QSCDMA), Orthogonal Frequency Division Multiplexing(OFDM) and Mutiple-Input Multiple-Output(MIMO)system to suppress the interference and improve the spectrum efficiency.
引文
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[5]李玉博,陈邈.几乎完备高斯整数序列构造法[J].电子与信息学报,2018,40(7):1752-1758.doi:10.11999/JEIT170844.LI Yubo and CHEN Miao.Construction of nearly perfect Gaussian integer sequences[J].Journal of Electronics&Information Technology,2018,40(7):1752-1758.doi:10.11999/JEIT170844.
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[9]刘涛,许成谦,李玉博.基于差集构造零相关区高斯整数序列集[J].电子与信息学报,2017,39(9):2277-2281.doi:10.11999/JEIT161177.LIU Tao,XU Chengqian,and LI Yubo.Construction of zero correlation zone Gaussian integer sequence sets based on difference sets[J].Journal of Electronics&Information Technology,2017,39(9):2277-2281.doi:10.11999/JEIT161177.
[10]李玉博,孙嘉安,荆楠.零相关区高斯整数序列集构造法[J].通信学报,2017,38(9):25-30.doi:10.11959/j.issn.1000-436x.2017179.LI Yubo,SUN Jiaan,and JING Nan.Construction of zero correlation zone Gaussian integer sequence set[J].Journal on Communications,2017,38(9):25-30.doi:10.11959/j.issn.1000-436x.2017179.
[11]刘凯,陈盼盼.最佳及几乎最佳高斯整数ZCZ序列集的构造[J].电子学报,2018,46(3):755-760.doi:10.3969/j.issn.0372-2112.2018.03.034.LIU Kai and CHEN Panpan.Construction of optimal and almost optimal Gaussian integer sequence sets with zero correlation zone[J].Acta Electronica Sinica,2018,46(3):755-760.doi:10.3969/j.issn.0372-2112.2018.03.034.
[12]LI Yubo,LIU Kai,and XU Chengqian.A construction of optimal 16-QAM+sequence sets with zero correlation zone[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2016,E99-A(4):819-825.doi:10.1587/transfun.E99.A.819.
[13]CHEN Xiaoyu,KONG Deming,XU Chengqian,et al.Constructions of Gaussian integer sequences with zero correlation zone[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2016,E99-A(6):1260-1263.doi:10.1587/transfun.E99.A.1260.
[14]刘凯,姜昆.交织法构造高斯整数零相关区序列集[J].电子与信息学报,2017,39(2):328-334.doi:10.11999/JEIT160276.LIU Kai and JIANG Kun.Construction of Gaussian integer sequence sets with zero correlation zone based on interleaving technique[J].Journal of Electronics&Information Technology,2017,39(2):328-334.doi:10.11999/JEIT160276.
[15]TANG X H,FAN P Z,and MATSUFUJI S.Lower bounds on correlation of spreading sequence set with low or zero correlation zone[J].Electronics Letters,2000,36(6):551-552.doi:10.1049/el:20000462.
[16]LIU Y C,CHEN C W,and SU Y T.New constructions of zero-correlation zone sequences[J].IEEE Transactions on Information Theory,2013,59(8):4994-5007.doi:10.1109/TIT.2013.2253831.
[17]CHUNG J H and YANG K.New design of quaternary lowcorrelation zone sequence sets and quaternary Hadamard matrices[J].IEEE Transactions on Information Theory,2008,54(8):3733-3737.doi:10.1109/TIT.2008.926406.
[18]KONG Deming,CHEN Xiaoyu,and LI Yubo.Constructions of Gaussian integer periodic complementary sequences with ZCZ[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2017,E100-A(9):2056-2060.doi:10.1587/transfun.E100.A.2056.
[19]LI Yubo and XU Chengqian.A new construction of zero correlation zone Gaussian integer sequence sets[J].IEEECommunications Letters,2016,20(12):2418-2421.doi:10.1109/LCOMM.2016.2609383.
[2]LEE C D and HONG Shaohua.Generation of long perfect Gaussian integer sequences[J].IEEE Signal Processing Letters,2017,24(4):515-519.doi:10.1109/LSP.2017.2674972.
[3]刘元慧,许成谦,赵冰.p-1级高斯整数序列的构造[J].北京邮电大学学报,2017,40(1):53-56.doi:10.13190/j.jbupt.2017.01.009.LIU Yuanhui,XU Chengqian,and ZHAO Bing.Constructions of Gaussian integer sequences of degree-(p-1)[J].Journal of Beijing University of Posts and Telecommunications,2017,40(1):53-56.doi:10.13190/j.jbupt.2017.01.009.
[4]CHANG K J and CHANG H H.Perfect Gaussian integer sequences of period pk with degrees equal to or less than k+1[J].IEEE Transactions on Communications,2017,65(9):3723-3733.doi:10.1109/TCOMM.2017.2714702.
[5]李玉博,陈邈.几乎完备高斯整数序列构造法[J].电子与信息学报,2018,40(7):1752-1758.doi:10.11999/JEIT170844.LI Yubo and CHEN Miao.Construction of nearly perfect Gaussian integer sequences[J].Journal of Electronics&Information Technology,2018,40(7):1752-1758.doi:10.11999/JEIT170844.
[6]PEI S C and CHANG Kuowei.Perfect Gaussian integer sequences of arbitrary length[J].IEEE Signal Processing Letters,2015,22(8):1040-1044.doi:10.1109/LSP.2014.2381642.
[7]CHANG H S,LI C P,LEE C D,et al.Perfect Gaussian integer sequences of arbitrary composite length[J].IEEETransactions on Information Theory,2015,61(7):4107-4115.doi:10.1109/TIT.2015.2438828.
[8]CHEN Haibin,ZHANG Rongqing,ZHAI Wenjun,et al.Interference-free pilot design and channel estimation using ZCZ sequences for MIMO-OFDM-Based C-V2Xcommunications[J].China Communications,2018,15(7):47-54.doi:10.1109/CC.2018.8424582.
[9]刘涛,许成谦,李玉博.基于差集构造零相关区高斯整数序列集[J].电子与信息学报,2017,39(9):2277-2281.doi:10.11999/JEIT161177.LIU Tao,XU Chengqian,and LI Yubo.Construction of zero correlation zone Gaussian integer sequence sets based on difference sets[J].Journal of Electronics&Information Technology,2017,39(9):2277-2281.doi:10.11999/JEIT161177.
[10]李玉博,孙嘉安,荆楠.零相关区高斯整数序列集构造法[J].通信学报,2017,38(9):25-30.doi:10.11959/j.issn.1000-436x.2017179.LI Yubo,SUN Jiaan,and JING Nan.Construction of zero correlation zone Gaussian integer sequence set[J].Journal on Communications,2017,38(9):25-30.doi:10.11959/j.issn.1000-436x.2017179.
[11]刘凯,陈盼盼.最佳及几乎最佳高斯整数ZCZ序列集的构造[J].电子学报,2018,46(3):755-760.doi:10.3969/j.issn.0372-2112.2018.03.034.LIU Kai and CHEN Panpan.Construction of optimal and almost optimal Gaussian integer sequence sets with zero correlation zone[J].Acta Electronica Sinica,2018,46(3):755-760.doi:10.3969/j.issn.0372-2112.2018.03.034.
[12]LI Yubo,LIU Kai,and XU Chengqian.A construction of optimal 16-QAM+sequence sets with zero correlation zone[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2016,E99-A(4):819-825.doi:10.1587/transfun.E99.A.819.
[13]CHEN Xiaoyu,KONG Deming,XU Chengqian,et al.Constructions of Gaussian integer sequences with zero correlation zone[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2016,E99-A(6):1260-1263.doi:10.1587/transfun.E99.A.1260.
[14]刘凯,姜昆.交织法构造高斯整数零相关区序列集[J].电子与信息学报,2017,39(2):328-334.doi:10.11999/JEIT160276.LIU Kai and JIANG Kun.Construction of Gaussian integer sequence sets with zero correlation zone based on interleaving technique[J].Journal of Electronics&Information Technology,2017,39(2):328-334.doi:10.11999/JEIT160276.
[15]TANG X H,FAN P Z,and MATSUFUJI S.Lower bounds on correlation of spreading sequence set with low or zero correlation zone[J].Electronics Letters,2000,36(6):551-552.doi:10.1049/el:20000462.
[16]LIU Y C,CHEN C W,and SU Y T.New constructions of zero-correlation zone sequences[J].IEEE Transactions on Information Theory,2013,59(8):4994-5007.doi:10.1109/TIT.2013.2253831.
[17]CHUNG J H and YANG K.New design of quaternary lowcorrelation zone sequence sets and quaternary Hadamard matrices[J].IEEE Transactions on Information Theory,2008,54(8):3733-3737.doi:10.1109/TIT.2008.926406.
[18]KONG Deming,CHEN Xiaoyu,and LI Yubo.Constructions of Gaussian integer periodic complementary sequences with ZCZ[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2017,E100-A(9):2056-2060.doi:10.1587/transfun.E100.A.2056.
[19]LI Yubo and XU Chengqian.A new construction of zero correlation zone Gaussian integer sequence sets[J].IEEECommunications Letters,2016,20(12):2418-2421.doi:10.1109/LCOMM.2016.2609383.