| Citation: | Tao LIU, Chengqian XU, Yubo LI. Constructions of Gaussian Integer Periodic Complementary Sequences Based on Difference Families[J]. Journal of Electronics & Information Technology, 2019, 41(5): 1167-1172. doi: 10.11999/JEIT180646
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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.
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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.1146.2013.01697
CHEN 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.1005-3085.2018.03.007
KE 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/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
|
|
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. 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
|
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