Constructions of Gaussian Integer Periodic Complementary Sequences Based on Difference Families
-
摘要:
该文给出了基于差族的高斯整数互补序列构造方法。利用差族与互补序列之间的联系，首先推导出高斯整数互补序列存在的充分条件，进而直接构造了阶数为2的高斯整数互补序列。为进一步增加高斯整数互补序列数目，又利用映射方法构造了阶数为4的高斯整数互补序列。同传统的2元互补序列相比，高斯整数互补序列的存在数目很多，因此该文方法可以为通信系统提供大量的互补序列。
Abstract:Constructions of Gaussian integer periodic complementary sequences are presented in this paper. Based on the relationship between periodic complementary sequences and difference families, the sufficient condition of the existence of Gaussian integer periodic complementary sequences is proposed at first, then Gaussian integer periodic complementary sequences with degree 2 are constructed directly. To extend the number of Gaussian integer complementary sequences, Gaussian integer complementary sequences with degree 4 are constructed based on mappings. Compared with binary complementary sequences, there are more Gaussian integer complementary sequences, as a result, the presented methods will propose an abundance of complementary sequences for communication systems.
-
表 1 满足式(6)的高斯整数
${\alpha _0}$ ${\alpha _1}$ ${\beta _0}$ ${\beta _1}$ –2 –1 1 0 –2 –1 1 2 –2 1 1 –2 –2 1 1 0 –1 –2 0 1 –1 –2 2 1 –1 2 0 –1 –1 2 2 –1 1 –2 –2 1 1 –2 0 1 1 2 –2 –1 1 2 0 –1 2 –1 –1 0 2 –1 –1 2 2 1 –1 –2 
下载: 导出CSV
-
WANG Senhung and LI Chihpeng. Novel comb spectrum CDMA system using perfect Gaussian integer sequences[C]. 2015 IEEE Global Communications Conference (GLOBECOM), San Diego, CA, USA, 2015: 1–6. CHANG Ho Hsuan, LIN Shieh Chiang and LEE Chongdao. A CDMA scheme based on perfect Gaussian integer sequences[J]. International Journal of Electronics and Communications, 2017, 75(2017): 70–81. doi: 10.1016/j.aeue.2017.03.008 WANG Senhung, LI Chihpeng, and CHANG Hohsuan, et al. A systematic method for constructing sparse Gaussian integer sequences with ideal periodic autocorrelation functions[J]. IEEE Transactions on Communications, 2016, 64(1): 365–376. doi: 10.1109/TCOMM.2015.2498185 LI Chihpeng, WANG Senhung, and WANG Chinliang. Novel low complexity SLM schemes for PAPR reduction in OFDM systems[J]. IEEE Transactions on Signal Processing, 2010, 58(5): 2916–2921. doi: 10.1109/TSP.2010.2043142 HU Weiwen, WANG Senhung, and LI Chihpeng. Gaussian integer sequences with ideal periodic autocorrelation functions[J]. IEEE Transactions on Signal Processing, 2012, 60(11): 6074–6079. doi: 10.1109/TSP.2012.2210550 YANG Yang, TANG Xiaohu, and ZHOU Zhengchun. Perfect Gaussian integer sequences of odd prime length[J]. IEEE Signal Processing Letters, 2012, 19(10): 615–618. doi: 10.1109/LSP.2012.2209642 MA Xiu Wen, WEN Qiao Yan, ZHANG Jie, et al. New perfect Gaussian integer sequences of periodic pq[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2013, E96-A(11): 2290–2293. doi: 10.1587/transfun.E96.A.2290 PEI Soochang 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 CHANG Hohsuan, LI Chihpeng, LEE Chongdao, et al. Perfect Gaussian integer sequences of arbitrary composite length[J]. IEEE Transactions on Information Theory, 2015, 61(7): 4107–4115. doi: 10.1109/TIT.2015.2438828 CHEN Xinjiao, LI Chunlei, and RONG Chunming. Perfect Gaussian integer sequences from cyclic difference sets[C]. 2016 IEEE International Symposium on Information Theory (ISIT), 2016: 115–119. LEE Chongdao, HUANG Yupei, CHANG Yaostu, et al. Perfect Gaussian integer sequences of odd period 2m-1[J]. IEEE Signal Processing Letters, 2015, 22(7): 881–885. doi: 10.1109/LSP.2014.2375313 Lee Chongdao, LI Chihpeng, and CHANG Hohsuan, et al. Further results on degree-2 perfect Gaussian integer sequences[J]. IET Communications, 2016, 10(12): 1542–1552. doi: 10.1049/iet-com.2015.1144 陈晓玉, 许成谦, 李玉博. 新的完备高斯整数序列的构造方法[J]. 电子与信息学报, 2014, 36(9): 2081–2085. doi: 10.3724/SP.J.1146.2013.01697CHEN Xiaoyu, XU Chengqian, and LI Yubo. New Constructions of perfect Gaussian integer sequences[J]. Journal of Electronics &Information Technology, 2014, 36(9): 2081–2085. doi: 10.3724/SP.J.1146.2013.01697 LI Yubo, TIAN Liying, and LIU Tao. Nearly perfect Gaussian integer sequences with arbitrary degree[J]. IET Communications, 2018, 12(9): 1123–1127. doi: 10.1049/iet-com.2017.1274 LI Chihpeng, CHANG Kuojen, CHANG Hohsuan, et al. Perfect sequences of odd prime length[J]. IEEE Signal Processing Letters, 2018, 25(7): 966–969. doi: 10.1109/LSP.2018.2832719 柯品惠, 胡电芬, 常祖领. 周期为p2的完备高斯整数序列的新构造[J]. 工程数学学报, 2018, 35(3): 319–328. doi: 10.3969/j.issn.1005-3085.2018.03.007KE Pinhui, HU Dianfen, and CHANG Zuling. New construction of perfect Gaussian integer sequence with period p2[J]. Chinese Journal of Engineering Mathematics, 2018, 35(3): 319–328. doi: 10.3969/j.issn.1005-3085.2018.03.007 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/JEIT160276LIU 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 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.0372-2112.2018.03.034LIU Kai and CHEN Panpan. Constructions of optimal of almost optimal Gaussian integer ZCZ sequence sets[J]. Acta Electronica Sinica, 2018, 46(3): 755–760. doi: 10.3969/j.issn.0372-2112.2018.03.034 BOMER Leopold and ANTWEILER Markus. Periodic complementary binary sequences[J]. IEEE Transactions on Information Theory, 1990, 36(6): 1487–1494. doi: 10.1109/18.59954 TSENG Chin-Chong. Complementary sets of sequences[J]. IEEE Transactions on Information Theory, 1972, 18(5): 644–652. doi: 10.1109/TIT.1972.1054860 LI Xudong, LIU Zilong, GUAN Yongliang, et al. Two valued periodic complementary sequences[J]. IEEE Signal Processing Letters, 2017, 24(9): 1270–1274. doi: 10.1109/LSP.2017.2722423 DING Cunsheng. Two Constructions of (v, (v-1)/2, (v-3)/2) difference families[J]. Journal of Combinatorial Designs, 2008, 16: 164–171. doi: 10.1002/jcd.20159 -
表(1)
计量
- 文章访问数: 1676
- HTML全文浏览量: 651
- PDF下载量: 55
- 被引次数: 0
下载:
